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XIV International Conference on Phonon Scattering in Condensed Matter

July 8-12, 2012 Ann Arbor, MI USA

www.phonons2012.com

SCHEDULE AND ABSTRACTS

SPONSORS:

College of Engineering College of Literature, Science, and the Arts Department of Physics Department of Mechanical Engineering Office of the Vice President for Research

http://www.phonons2012.com/

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SUNDAY JULY 8th

3:00 – 6:00 Concourse Registration and informal welcome reception

MONDAY JULY 9th

7:00 – 8:00 Concourse Registration

7:00 – 8:00 Ballroom Continental breakfast

8:00 – 8:15 Mendel Opening

8:15 – 9:15 Mendel TUTORIAL: Phonons in nanoelectronics Ken Goodson (Stanford Univ.)

9:20 – 10:35 Mendel GRAPHENE I (Session chair: Zlatan Aksamija) Phonons and thermal transport in graphene (invited)

Alexander A. Balandin (UC Riverside)

Ballistic to diffusive crossover of phonon flow in graphene ribbons Zuanyi Li, Myung-Ho Bae, Pierre Martin, and Eric Pop (UIUC)

Grain-boundary limited thermal transport in graphene Andrey Serov and Eric Pop (UIUC)

Tuning thermal and mechanical properties of graphene Maxim Zalalutdinov, Jeremy Robinson, Douglas Photiadis, Eric Snow, and Brian Houston (Naval Research Laboratory)

Hussey DEVICES (Session chair: Ivana Savic)

Hot-phonon energy conversion to electric energy Seungha Shin, Corey Melnick, and Massoud Kaviany (U. Michigan)

Sub-terahertz phonon control of electronic charge in a resonant tunneling device Eric Sze Kit Young, Andrey Akimov, Mohamed Henini, Laurence Eaves, and Anthony Kent (U. Nottingham)

Photoconductive switches for study of picosecond thermal dynamics in electronic devices Bjorn Vermeersch,1,2 Gilles Pernot,2 Hong Lu,3 Je-Hyeong Bahk,2 Ali Shakouri,1,2 and Art Gossard3 (1Purdue Univ., 2UC Santa Cruz, 3UC Santa Barbara)

Ultrafast piezospectroscopy in optoelectronic devices (invited) Andrey V. Akimov (U. Nottingham)

10:35 – 11:00 Ballroom Coffee break

11:00 – 12:00 Mendel GRAPHENE II (Session chair: Alexander Balandin)

Electron-phonon non-equilibrium in single-layer graphene using Boltzmann transport equation Ajit K. Vallabhaneni,1 Xiulin L. Ruan,1 and Jayathi Murthy1,2 (1Purdue Univ., 2UT Austin)

Phonon transport in silicon and graphene nanostructures (invited) Irena Knezevic and Zlatan Aksamija (U. Wisconsin)

Phonon interactions between graphene and Cu substrate Liang Chen and Satish Kumar (Georgia Tech)

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Hussey ULTRASONICS / COHERENT ACOUSTICS I (Session chair: Emmanuel Péronne)

Hypersound damping in silica measured by ultrafast acoustics at low temperature Arnaud Devos,1 Marie Foret,2 Sabrina Sadtler,1 Benoit Rufflé,2 E. Courtens,2 and René Vacher2 (1IEMN/CNRS, 2LCC/CNRS)

Vibrations of composite nanoobjects: bimetallic and metal-dielectric core-shell nanoparticles D. Mongin,1 M. F. Cardinal,2 V. Juvé,1 A. Crut,1 P. Maioli,1 A. Sánchez-Iglesias,2 I. Pastoriza-Santos,2 B. Rodríguez-González,2 J. Pérez-Juste,2 L. M. Liz-Marzán,2 N. Del Fatti,1 and F. Vallée1 (1LASIM/CNRS, 2Universidade de Vigo)

Confined acoustic vibrations in piezoelectric GaN nanorods Pierre-Adrien Mante,1 Hung-Pin Chen,1 Yueh-Chun Wu,1 Cheng-Ying Ho,2 Li-Wei Tu,2 Jinn-Kong Sheu,3 and Chi-Kuang Sun1,4 (1National Taiwan Univ., 2National Sun Yat-Sen Univ., 3National Cheng Kung Univ., 4Academia Sinica)

Coherent acoustic phonon propagation through ultrathin organic interface layers Mike Hettich,1 Karl Jacob,1 Oliver Ristow,1 Jan Mayer,1 Chuan He,1 Axel Bruchhausen,1 Martin Schubert,1 Vitalyi Gusev,2 and Thomas Dekorsy1 (1U. Konstanz, 2IMMM/CNRS)

12:00 – 1:30 Lunch

1:30 – 2:15 Mendel PLENARY I: Phonon mean free paths studies with picosecond acoustic pulses and monochromatic terahertz bursts

Bernard Perrin (INSP/CNRS)

2:20 – 3:35 Mendel ULTRASONICS / COHERENT ACOUSTICS II (Session chair: Pascal Ruello)

Picosecond ultrasonics study of laterally patterned nanostructures using water as a coupling medium

Thomas Grimsley,1 Shan Che,1 Li Wei Liu,1 Humphrey Maris,1 Arto Nurmikko,1 Andy Antonelli,2 (1Brown Univ., 2Novellus Systems)

Probing interfacial water molecules by using sub-nanometre ultrasonic pulses (invited) Chi-Kuang Sun,1,2 Chien-Cheng Chen,1 Yu-Chieh Wen,1,2 Pierre-Adrien Mante,1 Vitalyi Gusev,3 and Jinn-Kong Sheu4 (1National Taiwan Univ., 2Academia Sinica, 3Université du Maine, 4National Cheng Kung Univ.)

Optical tomographic imaging of picosecond pulses with 150 nm spatial resolution Motonobu Tomoda,1 Hiroyuki Matsuo,1 Osamu Matsuda,1 Oliver Wright,1 Roberto Li Voti,2 (1Hokkaido Univ., 2Sapienza Università di Roma)

Two colors pump probe experiments for an optimized coherent phonon generation and detection Romain Legrand,1 Agnès Huynh,1 Bernard Perrin,1 Eric Charron,1 Serge Vincent,1 Norberto D. Lanzillotti-Kimura,2 and Aristide Lamaître3 (1INSP/CNRS, 2Centro Atómico Bariloche, 3LPN/CNRS)

Hussey HEAT TRANSFER: NANOSTRUCTURES I (Session chair: Qing Hao)

Influence of grain boundary scattering on thermal transport in nuclear fuel Marat Khafizov,1 In-Wook Park,2 Alex Chernatynskiy,3 Bowen Deng,3 Jianliang Lin,2 John J. Moore,2 Simon Phillpot,3 and David H. Hurley1 (1Idaho National Laboratory, 2Colorado School of Mines, 3Univ. of Florida)

Helicity induced thermal conductivity reduction in superlattice nanowires Vikas Varshney,1,2 Ajit K. Roy,1 Douglas Dudis,1 Jonghoon Lee,1,2 and Barry L. Farmer1 (1AFRL, 2Universal Technology Corp.)

Heat capacity on free standing membranes included native oxide E. Chávez,1,2 F. Alzina,1 and C.M. Sotomayor-Torres1,2,3 (1Universitat Àutonoma de Barcelona, 2ICN, 3ICREA)

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Size-dependent thermal diffusivity in free-standing silicon membranes John Cuffe,1 Jeffrey K. Eliason,2 Jeremy A. Johnson,2 Emigdio Chavez,2 Alex A. Maznev,2 Andrey Shchepetov,3 Mika Prunnila,3 Jouni Ahopelto,3 Clivia M. Sotomayor-Torres,1,4,5 and Keith A. Nelson2 (1ICN, 2MIT, 3VTT Technical Research Centre of Finland, 4ICREA, 5Universitat Àutonoma de Barcelona)


4:00 – 5:45 Mendel ULTRASONICS / COHERENT ACOUSTICS III (Session chair: Brian Daly)

Direct measurement of sub-THz coherent-phonon pulse shapes in thin metal films Osamu Matsuda, Shun Koiwa, Ryan Beardsley, Motonobu Tomoda, and Oliver B. Wright (Hokkaido Univ.)

Pulse propagation through a large-grained polycrystalline film: broadening effects of elastic anisotropy Arthur Every1 and Alex Maznev2 (1University of the Wiwatersrand, 2MIT)

THz-bandwidth coherent phonon emission by supported monolayer graphene in the out-of-plane direction

I-Ju Chen,1 Pierre-Adrien Mante,1 Cheng-Kai Chang,1 Chun-Chiang Kuo,1 Kuei-Hsien Chen,1,2 Vitalyi Gusev,3 and Chi-Kuang Sun1,2 (1National Taiwan University, 2Academia Sinica, 3Université du Maine)

Acoustic solitons are seriously testing non-linear ultrafast acoustic models and experiments Emmanuel Peronne, Bernard Perrin, and Nicolas Chuecos (INSP/CNRS)

Theory of the propagation of acoustic phonon solitons Humphrey Maris,1 Shin-Ichiro Tamura,2 and Li Wei Liu1 (1Brown Univ., 2Hokkaido Univ.)

GHz coherent acoustic phonons generated by photoinduced Dember field Pascal Ruello, Gwenanelle Vaudel, Thomas Pezeril, and Vitalyi Gusev (IMMM Université du Maine)

Silicon monolithic acousto-optic modulator Siddharth Tallur and Sunil A. Bhave (Cornell)

Hussey HEAT TRANSFER: NANOSTRUCTURES II (Session chair: Austin Minnich)

Nanoscale heat transport from self-organized germanium hut and dome clusters into silicon substrates

Tim Frigge, Anja Hanisch-Blicharski, Annika Kalus, Martin Kammler and Michael Horn-von Hoegen (Univ. of Duisburg-Essen)

Large scale Monte Carlo approach to the Boltzmann treatment of thermal transport in Si/Ge nanostructures

Ivana Savic,1 Davide Donadio,2 Eamonn D. Murray,1 Francois Gygi,1 and Giulia Galli1 (1UC Davis, 2Max Planck Inst. for Polymer Research)

Frequency-dependent Monte Carlo simulations of phonon transport in SiGe nanocomposites Qing Hao (Univ. of Arizona)

Deviational formulations for efficient Monte Carlo simulations of multidimensional, multiscale phonon transport

Jean-Philippe Peraud and Nicolas Hadjiconstantinou (MIT)

Thermal conductivity of diamond nanowires from first principles Wu Li,1 Lucas Lindsay,2 David Broido,3 Derek Stewart,4 Nebil Katcho,1 and Natalio Mingo1 (1CEA-Grenoble, 2NRL, 3Boston College, 4Cornell)

The new limit of heat transfer under extreme strain Victor Lee,1 Renkun Chen,2 and Chih-Wei Chang1 (1National Taiwan Univ., 2UC San Diego)

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TUESDAY JULY 10th



8:30 – 9:15 Mendel PLENARY II: Testing models for heat conduction using high pressures: crystals, glasses, and interfaces

David Cahill (UIUC)

9:20 – 10:35 Mendel HEAT TRANSFER: NANOWIRES (Session chair: Richard Robinson)

Thermal phonon transport in corrugated silicon nanowires Christophe Blanc and Olivier Bourgeois (Institut Néel / CNRS)

Effect of morphology and roughness on thermal conductivity of silicon nanowires Kedar Hippalgaonkar,1 Jongwoo Lim,1 Peter Ercius,2 Peidong Yang,1,2 and Arun Majumdar1,2,3 (1UC Berkeley, 2LBNL, 3DOE)

Phonon transport in single-walled carbon nanotube aerogels Kejia Zhang,1 Abhishek Yadav,1 Lei Shao,1 Kyu Hun Kim,2 Youngseok Oh,2 Mohammad Islam,2 Ctirad Uher,1 and Kevin Pipe1 (1Univ. Michigan, 2Carnegie Mellon Univ.)

Ballistic phonon transport in nanowires at ambient temperature L. Jalabert,1 T. Sato,2 T. Ishida,2 H. Fujita,2 Y. Chalopin,3,4 and S. Volz1,3,4 (1LIMMS-CNRS/IIS-Univ. Tokyo, 2CIRMM/IIS-Univ. Tokyo, 3LEMMC/CNRS, 4Ecole Centrale Paris)

Kapitza resistance of diameter modulated SiC nanowires: a molecular dynamics study Konstantinos Termentzidis, Heloise Huedro, Anne-Laure Delaye, Yuxiang Ni, Yann Chalopin, and Sebastian Volz (EM2C/Ecole Centrale Paris)

ELECTON-PHONON INTERACTIONS (Session chair: Roberto Merlin)

Electron-phonon coupling in nanoscale Pt/Au bilayers Wei Wang and David Cahill (UIUC)

Electron-phonon scattering from first principles: times and rates for transport calculations Jelena Sjakste,1 Nathalie Vast,1 Paola Gava,1 and Valeriy Tyuterev2 (1CEA-DSM-DRECAM/CNRS, 2Tomsk State Pedagogical Univ.)

Electron-phonon interactions in graphene (invited) Aron Pinczuk (Columbia Univ.)

Phonons and electrons in chalcopyrite semiconductors Manuel Cardona,1 R. K. Kremer,1 R. Lauck,1 Aldo H. Romero,2 and Alfonso Muñoz3 (1MPI for Solid State Research, 2CINVESTAV / Unidad Querétaro, 3Universidad de La Laguna)


11:00 – 12:00 Mendel HEAT TRANSFER: COMPUTATIONAL METHODS (Session chair: Yann Chalopin)

Computational studies of thermal phonon transport in nanostructured materials (invited) Pawel Keblinski (RPI)

Heat flow in nanostructures in the Casimir regime Humphrey Maris,1 Shin-Ichiro Tamura,2 and Li Wei Liu1 (1Brown Univ., 2Hokkaido Univ.)

Phonon interference and anharmonicity effects in nanoconstrictions

Kimmo Sääskilahti, Jani Oksanen, Riku Linna, and Jukka Tulkki (Aalto Univ.)

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Hussey NONLINEAR PHONONICS (Session chair: David Reis)

Coherent second-sound generation in quantum paraelectric Akitoshi Koreeda,1,2 Seishiro Saikan,1 Masaki Takesada,3 and Toshirou Yagi3 (1Tohoku University, 2Japan Sci. and Technol. Agency, 3Hokkaido Univ.)

Reciprocity in reflection and transmission: what is a “phonon diode”? A. A. Maznev,1 A. G. Every,2 and O. B. Wright3 (1MIT, 2Univ. of the Witwatersrand, 3Hokkaido Univ.)

Control of ultrafast lattice dynamics and phase transitions in complex oxides through nonlinear phononics (invited)

Michael Först (Center for Free-Electron Laser Science)

12:00 – 1:30 Lunch

1:30 – 3:30 Mendel HEAT TRANSFER: EXPERIMENTAL METHODS AND BALLISTIC TRANSPORT (Session chair: Sebastian Volz)

Room temperature picowatt resolution calorimetry Seid Sadat, Yi Jie Chua, Woochul Lee, Yashar Ganjeh, Katsuo Kurabayashi, Edgar Meyhofer, and Pramod Sangi Reddy (Univ. of Michigan)

Ultra high vacuum scanning thermal microscopy for nanometer resolution quantitative thermometry

Kyeongtae Kim, Wonho Jeong, Woochul Lee, and Pramod Sangi Reddy (Univ. of Michigan)

Heterodyne and homodyne pump-probe techniques to study thin films thermal properties Gilles Pernot,1,2 Jean-Michel Rampnoux,2 Stefan Dilhaire,2 and Ali Shakouri1,3 (1UC Santa Cruz, 2LOMA/Université de Bordeaux 1, 3Purdue Univ.)

Phonon mean free path spectroscopy of silicon Jonathan Malen, Keith Regner, Shubhaditya Majumdar, and Zonghui Su (Carnegie Mellon Univ.)

Non-diffusive thermal conductivity in GaAs at room temperature Jeffrey K. Eliason, Alexei A. Maznev, Jeremy A. Johnson, Keith A. Nelson, Keivan Esfarjani, Tengfei Luo, Jivtesh Garg, and Gang Chen (MIT)

Analysis of quasiballistic heat transfer in thermal conductivity spectroscopy using variance-reduced Monte Carlo simulations

Austin Minnich (Caltech)

Observation of ballistic thermal phonon transport across 2D nanoscale interfaces Kathleen Hoogeboom-Pot,1 Damiano Nardi,1 Qing Li,1 Xiaobo Li,2 Ronggui Yang,2 Erik H. Anderson,2 Margaret M. Murnane,1 and Henry C. Kapteyn1 (1Univ. of Colorado Boulder, 2LBNL)

Influence of ballistic heat transport in the extraction of thermal interface resistance through TDTR analysis

Bjorn Vermeersch,1,2 Gilles Pernot,2 and Ali Shakouri1,2 (1Purdue Univ., 2UC Santa Cruz)

Hussey RAMAN SCATTERING (Session chair: Mariano Trigo)

Selective Brillouin resonances between extended folded acoustic phonons and non dispersive polaritons modes in multi-quantum wells

B. Jusserand,1 A. Fainstein,2 and A. Lemaitre3 (1INSP/UPMC-CNRS, 2CAB/CNEA, 3LPN/CNRS)

Surface-enhanced Raman spectroscopy study of single stranded DNA sequences on silver nanorod array

Kimber L. Brenneman,1 Xenia Meshik,1 Ke Xu,1 Justin Abell,2 Yiping Zhao,2 Mitra Dutta,1 and Michael A. Stroscio1 (1Univ. of Illinois at Chicago, 2Univ. of Georgia)

Raman phonons in the FeSe-based superconductor AxFe2-ySe2 (invited) Qingming Zhang (Renmin Univ.)

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Monitoring polymer network formation by probing optical and acoustic phonons concurrently Michael Aldridge and John Kieffer (Univ. of Michigan)

Phonons and excitons in pentacene monolayers (invited) Rui He (Univ. of Northern Iowa)

Micro-Raman study of GaAs nanowires Peng Wang,1 Fauzia Jabeen,2 Jean Christophe Harmand,2 and Bernard Jusserand1 (1INSP/UPMC-CNRS, 2LPN/CNRS)


4:00 – 5:00 Mendel HEAT TRANSFER: THERMOELECTRIC MATERIALS (Session chair: Gilles Pernot)

Significant thermal conductivity reduction of defective bismuth telluride Konstantinos Termentzidis, Alex Pokropivny, Yuri Chumakov, Yann Chalopin, and Sebastian Volz (EM2C/Ecole Centrale Paris)

Phonon anharmonicity in thermoelectric materials (invited) Olivier Delaire (Oak Ridge Natl. Lab.)

Reduced thermal conductivity in SiGe alloy-based superlattices for thermoelectric applications Zlatan Aksamija and Irena Knezevic (Univ. of Wisconsin)

Hussey BRILLOUIN SCATTERING (Session chair: John Kieffer)

Huge nonlinear elastic properties at the volume phase transition of aqueous poly(N-isopropylacrylamide) solutions as revealed by Brillouin spectroscopy

Jan-Kristian Krüger,1 Ulrich Müller,1 Martine Philipp,2 and Peter Müller-Buschbaum2 (1Univ. of Luxembourg, 2TU München)

Volume phase transition, demixing and sedimentation in an aqueous solution of poly(N-isopropylacrylamide) as evidenced by scanning Brillouin microscopy

Ulrich Müller,1 Jan-Kristian Krüger,1 Martine Philipp,2 and Peter Müller-Buschbaum2 (1Univ. of Luxembourg, 2TU München)

The effect of intra-molecular relaxations on the damping of longitudinal and transcerse phonons in glass forming liquids

G. Meier,1 H. Kriegs,1 A. Patkowski,2 J. Gapinski2 (1Inst. of Complex Systems 3, 2A. Mickiewicz Univ.)

Dynamical origin of anomalous temperature hardening of elastic modulus in vitreous silica M. Foret,1 B. Rufflé,1 R. Vacher,1 S. Ayrinhac,1,2 and A. Polian2 (1LCC/CNRS, 2LPMC/CNRS)

7:00 – 9:30 Ballroom Poster session

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WEDNESDAY JULY 11th



8:30 – 9:15 Mendel PLENARY III: Phonon amplification and oscillator (SASER) devices: the acoustic equivalents of lasers Anthony Kent (Univ. of Nottingham)

9:20 – 10:35 Mendel PHONONIC CRYSTALS I (Session chair: Daniel Lanzillotti Kimura)

Lifetime of zone-center, sub-THz coherent phonons in GaAs-AlAs superlattices Felix Hofmann, Alexei A. Maznev, Kara J. Manke, and Keith A. Nelson, Adam Jandl, Mayank T. Bulsara, and Eugene A. Fitzgerald (MIT)

Negative refraction and subwavelength imaging with surface acoustic waves István A. Veres,1 Thomas Berer,1,2 and Peter Burgholzer1,2 (1Research Center for Non-Destructive Testing, 2Christian Doppler Lab. for Photoacoustic Imaging and Laser Ultrasonics)

k-space representation of surface phonon propagation in phononic crystal waveguides Paul H. Otsuka,1 Keisuke Nanri,1 Motonobu Tomoda,1 Oliver B. Wright,1 Osamu Matsuda,1 Dieter M. Profunser,1 István A. Veres,2 Sorasak Danworaphong,3 Abdelkrim Khelif,4 Vincent Laude,4 and Sarah Benchabane4 (1Hokkaido Univ., 2Research Center for Non Destructive Testing, 3Walailak Univ., 4FEMTO-ST)

Probing thermomechanics at the nanoscale: impulsively excited pseudosurface acoustic waves in hypersonic phononic crystals

Damiano Nardi,1,2 Marco Travagliati,2,3 Mark E. Siemens,4 Qing Li,1 Margaret M. Murnane,1 Henry C. Kapteyn,1 Gabriele Ferrini,2 Fulvio Parmigiani,5 and Francesco Banfi2 (1Univ. of Colorado Boulder, 2Universià Cattolica, 3NEST-IIT, 4Univ. of Denver, 5Università di Trieste and Sincrotrone Trieste)

Acoustic resonators for far field control of sound on a subwavelength scale Fabrice Lemoult,1,2 Mathias Fink,1 and Geoffroy Lerosey1 (1Institut Langevin / ESPCI Paris, 2Univ. of Manitoba)

Hussey HEAT TRANSFER: INTERFACES I (Session chair: Jonathan Malen)

Phonon transport across epitaxial SrRuO3 / SrTiO3 interfaces R. B. Wilson, B. Apgar, E. Breckenfeld, L. W. Martin, and David G. Cahill (UIUC)

Pressure dependent inelastic phonon transmission at Si / carbon nanotube interface Y. Chalopin,1,2 N. Mingo,3 and S. Volz1,2 (1LEMMC/CNRS, 2Ecole Centrale Paris, 3CEA-LITENLCRE/DTMN/LITEN)

Heat transfer of supported Au nanorods in various organic fluids Jonglo Park, Jingyu Huang, Wei Wang, Catherine J. Murphy, and David G. Cahill (UIUC)

Interfacial phonon transport in Si-Ge heterostructures from equilibrium molecular dynamics simulations

Yann Chalopin,1 Sebastian Volz,1 Keivan Esfarjani,3 Asegun Henry,2 and Gang Chen3 (1EM2C/Ecole Centrale Paris, 2Georgia Tech, 3MIT)

Anomalous phonon/thermal transport in low dimensional nanostructures Baowen Li (Natl. Univ. of Singapore and Tongji Univ.)


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11:00 – 12:00 Mendel PHONONIC CRYSTALS II (Session chair: Mahmoud Hussein)

Optical detection of collective acoustic modes in artificial crystals S. Sadtler, A. Devos, and P.A. Mante (IEMN/CNRS)

Soft phononic structures (invited) Dirk Schneider,1 Tim Still,2 Periklis Papadopoulos,1 and George Fytas1,3 (1MPI for Polymer Research, 2Univ. of Pennsylvania, 3University of Crete and FORTH)

Optical generation and detection of hypersound in opal-based ferromagnetic hypersonic crystals Michael Bombeck,1 Alexey S. Salasyuk,1,2 Jasmin Jäger,1 Dmitri R. Yakovlev,1,2 Ekaterina Yu. Trofimova,2 Dmitry A. Kurdyukov,2 Valery G. Golubev,2 and Manfred Bayer1,2 (1TU Dortmund, 2Ioffe Inst.)

Hussey HEAT TRANSFER: INTERFACES II (Session chair: Pramod Reddy) Phonon transport across organic-metal interfaces

Yansha Jin, Chen Shao, Kevin Pipe, John Kieffer, and Max Shtein (Univ. of Michigan)

Molecular dynamics study of thermal transport across CuPc-metal interfaces Chen Shao, Yansha Jin, Max Shtein, Kevin Pipe, and John Kieffer (Univ. of Michigan)

Molecular dynamics studies of thermal boundary resistance in carbon-metal interfaces Sergei V. Shenogin,1,2 Jamie J. Gengler,1,3 Ajit K. Roy,1 Andrey A. Voevodin,1 and Christopher M. Muratore1 (1AFRL, 2UES Inc., 3Spectral Energies LLC)

Temperature dependence of the thermal boundary resistivity of glass-embedded metal nanoparticles

F. Banfi,1,2 V. Juvé,2 D. Nardi,1 S. Dal Conte,3 C. Giannetti,1 G. Ferrini,1 N. Del Fatti,2 and F. Vallée2 (1Università Cattolica, 2LASIM/CNRS, 3Universita` di Pavia)

12:00 – 1:30 Lunch

1:30 – 3:00 Mendel PHONONIC CRYSTALS III (Session chair: Olivier Bourgeois)

Controlling low-temperature thermal conductance using phononic crystals Nobuyuki Zen, Tuomas Puurtinen, Tero Isotalo, and Ilari J. Maasilta (Univ. of Jyväskylä)

Control of phonon transport via nanophononic crystals Bruce L. Davis and Mahmoud I. Hussein (Univ. of Colorado Boulder)

Brillouin study of a chessboard-structured Bi-component phononic crystal Meng Hau Kuok, Vanessa Li Zhang, Huihui Pan, Chen Guang Hou, Hock Siah Lim, Ser Choon Ng, Mahdi Jamali, and Hyunsoo Yang (Natl. Univ. of Singapore)

2D phononic crystal with anomalous behavior due to overlapping Bragg and hybridization gaps Eric J.S. Lee, Charles Croënne, and John H. Page (Univ. of Manitoba)

Engineering the band diagram of one-dimensional hypersonic phononic crystals Dirk Schneider,1 Faroha Liaqat,2 El Houssaine El Boudouti,3 Youssef El Hassouani,4 Wolfgang Tremel,2 Hans-Jürgen Butt,1 Bahram Djafari-Rouhani,5 George Fytas6 (1MPI for Polymer Research, 2Johannes Gutenberg Univ., 3Université Mohamed I, 4Université Moulay Ismaïl, 5IEMN/CNRS, 6University of Crete and FORTH)

Dynamics of a SASER oscillator Wan Maryam Wan Ahmad Kamil, Andrey Akimov, Richard Campion, and Anthony Kent (Univ. of Nottingham)

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Hussey MEMBRANES (Session chair: Oliver Wright)

Lifetime of high-order acoustic thickness resonances in thin silicon membranes A.A. Maznev,1 John Cuffe,2 Jeffrey K. Eliason,1 Timothy Kehoe,2 Clivia M. Sotomayor Torres,2,3 and Keith A. Nelson1 (1MIT, 2Catalan Inst. of Nanotechnology, 3ICREA)

Mode shape and dispersion relation of bending waves in thin silicon membranes Reimar Waitz, Stephan Nößner, Michael Hertkorn, Olivier Schecker, and Elke Scheer (Univ. of Konstanz)

Confined coherent acoustic phonons in membranes (invited) Thomas Dekorsy (Univ. of Konstanz)

Confined coherent acoustic modes in aluminum/CuPc thin films excited by femtosecond laser pulses

Huarui Sun, Vladimir Stoica, Max Shtein, Roy Clarke, and Kevin Pipe (Univ. of Michigan)


3:25 – 5:25 Mendel RESONATORS AND OPTOMECHANICS (Session chair: Sunil Bhave)

Mechanical resonators in the quantum regime (invited) Andrew Cleland (UC Santa Barbara)

Optomechanics in a GaAs vertical cavity for sub-THz phonons and visible light A. Fainstein,1 N. D. Lanzillotti-Kimura,1 B. Jusserand,2 and B. Perrin2 (1Centro Atómico Bariloche, 2INSP/CNRS)

Optomechanical crystals in piezoelectric media (invited) Matt Eichenfield (Sandia Natl. Labs.)

Surface optomechanics: calculating surface acoustic wave generation on microsphere via photon-phonon interaction

John Zehnpfennig,1 Gaurav Bahl,2 Matthew Tomes,2 and Tal Carmon2 (1U.S. Military Academy, 2Univ. of Michigan)

Observation of spontaneous Brillouin cooling (invited) Gaurav Bahl,1 Matthew Tomes,1 Florian Marquardt,2,3 Tal Carmon,1 (1Univ. of Michigan, 2Universitat Erlangen-Nurnberg, 3MPI for the Science of Light)

Hussey X-RAY SCATTERING (Session chair: Arthur Every)

Anharmonic phonon decay as a parametric squeezing process Stephen Fahy,1,3 Eamonn D. Murray,2 and David A. Reis,3,4 (1University College, Cork, 2UC Davis, 3SLAC/Stanford Univ., 4Stanford Univ.)

Ultrafast x-ray diffraction from coherent and incoherent phonons Roman Shayduk,1 Daniel Schick,2 Peter Gaal,1 Hengameh Navirian,2 Mark Herzog,2 Wolfram Leitenberger,2 Yevgeniy Goldstein,1 and Matias Bargheer,1,2 (1Helmholtz Center for Material and Energy, 2Potsdam Univ. for Physics and Astronomy)

Picosecond x-ray scattering (invited) David Reis (SLAC/Stanford Univ.)

Anharmonic phonons seen by ultrafast x-ray diffuse scattering Mariano Trigo and David A. Reis (SLAC/Stanford. Univ.)

Vibrational dynamics and thermodynamics of nanocrystalline materials S. Stankov,1 M. Miglierini,2,3 A. I. Chumakov,4 I. Sergueev,4 Y. Z. Yue,5,6 B. Sepiol,7 P. Svec,8 L. Hu,5,6 and R. Rüffer4 (1Karlsruhe Inst. of Technol., 2Slovak Univ. of Technol., 3Palacky Univ., 4European Synchrotron Radiation Facility, 5Aalborg Univ., 6Shandong Univ., 7Univ. of Vienna, 8Slovak Acad. of Sci.)

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Probing zone boundary phonons at the nanoscale Gokul Gopalakrishnan,1 Martin Holt,2 Kyle McElhinny,1 J. W. Spalenka,1 David Czaplewski,2 Tobias Schülli,3 and Paul Evans1 (1Univ. of Wisconsin, 2Argonne Natl. Lab., 3European Synchrotron Radiation Facility)

5:25 – 5:30 Load onto buses

5:30 – 10:00 Banquet / strolling dinner at Henry Ford Museum

THURSDAY JULY 12th



8:30 – 9:15 Mendel PLENARY IV: Phonons in mesoscopic glasses and crystals: from super-resolution focusing in phononic crystals to Anderson localization in mesoglasses

John Page (Univ. of Manitoba)

9:20 – 10:35 Mendel AMORPHOUS/DISORDERED MATERIALS (Session chair: Marie Foret)

Anderson universality in a model of disordered phonons Sebastian D. Pinski,1 Walter Schirmacher,2 and Rudolf A. Roemer1 (1Univ. of Warwick, 2Universität Mainz)

Decay of spontanous polarisation echoes in glasses M. Bazrafshan, M. Schwarze, P. Fassl, A. Halfar, A. Fleischmann, and C. Enss (Heidelberg Univ.)

Ordered and disordered contributions to lattice thermal conductivity Jason M. Larkin and Alan J. H. McGaughey (Carnegie Mellon Univ.)

Ultrafast optical measurements of acoustic phonon attenuation in amorphous and nanocrystalline silicon

Brian C. Daly,1 Theodore B. Norris,2 B. Yan,3 J. Yang,3 and S. Guha3 (1Vassar College, 2Univ. Of Michigan, 3Uni-Solar Ovonic LLC)

Heat transport by long mean free path vibrations in amorphous silicon-nitride near room temperature

A. D. Avery, D. Bassett, S. Mason, and B. L. Zink (Univ. of Denver)

Hussey SURFACE ACOUSTIC WAVES (Session chair: Bernard Jusserand)

Ultra-high-frequency surface acoustic waves observed by ultrafast pump-probe spectroscopy Elaine C. S. Barretto,1 Martin Grossmann,1 Oliver Ristow,1 Mike Hettich,1 Martin Schubert,1 Vitalyi Gusev,2 Elke Scheer,1 and Thomas Dekorsy1 (1Univ. of Konstanz, 2IMMM/CNRS)

Surface acoustic waves in MnAs thin films J.-Y. Prieur,1 J.-Y. Duquesne,1 J. Agudo Canalejo,1 V. H. Etgens,1,2 M.Eddrief,1 A. L. Ferreira,1,3 and M. Marangolo1 (1INSP/CNRS, 2Fédération Lavoisier Franklin, 3UFPR/Centro Politécnico)

Acoustic control of carriers and spins in semiconductor wires (invited) Hernández-Mínguez,1 M. Möller,2 S. Lazic,1 S. Breuer,1 C. Pfüller,1 C. Somashini,1 O. Brandt,1 M. M. de Lima, Jr.,2 A. Cantarero,2 L. Geelhaar,1 H. Riechert,1 and P. V. Santos1 (1Paul-Drude-Institut für Festkörperelektronik, 2Universitat de València)

Acoustic nanometrology of ultrathin films using coherent extreme ultraviolet beams Kathleen Hoogeboom-Pot,1 Damiano Nardi,1 Qing Li,1 Chris Deeb,2 Sean King,2 Marie Tripp,2 Erik H. Anderson,3 Margaret M. Murnane,1 and Henry C. Kapteyn1 (1Univ. of Colorado, 2Intel Corp., 3LBNL)


13

11:00 – 12:15 Mendel MAGNETIC AND PLASMONIC COUPLING (Session chair: Jaap Dijkhuis)

High-frequency magneto-acoustics in ferromagnetic semiconductors (invited) Alexey V. Scherbakov (Ioffe Inst.)

Polarization-controlled generation of coherent phonons in plasmonic nanostructures N. D. Lanzillotti-Kimura, K. P. O’Brien, J. S. Rho, H. Suchowski, and X. Zhang (UC Berkeley)

Observation of near-field interaction between surface plasmon polaritons and nanoacoustic pulses Szu-Chi Yang,1 Hui-Hsin Hsiao,1 Hung-Ping Chen,1 Hung-Chun Chang,1 Pei-Kuen Wei,2 and Chi-Kuang Sun1,2 (1National Taiwan Univ., 2Academia Sinica)

Subterahertz near-surface coherent phonons in a plasmonic grating structure C. Brüggemann,1 V. Belotelov,2 B. Glavin,3 I. A. Akimov,1 J. Jäger,1 S. Kasture,4 A. V. Gopal,4 A. S. Vengurlekar,4 D. R. Yakovlev,1 and M. Bayer1 (1TU Dortmund, 2Lomonosov Moscow State University, 3V E Lashkaryov Inst. of Semiconductor Physics, 4Tata Inst. of Fundamental Research)

Hussey PHONON SPECTROMETER AND VACUUM TUNNELING (Session chair: Barry Zink)

Operation of a non-equilibrium phonon source for probing nanoscale phonon transport Jared B. Hertzberg, Obafemi Otelaja, Mahmut Askit, and Richard D. Robinson (Cornell Univ.)

Probing phonon surface scattering in nanostructures using a microfabricated phonon spectrometer Jared B. Hertzberg, Obafemi Otelaja, Mahmut Askit, Derek A. Stewart, and Richard D. Robinson (Cornell Univ.)

Simulating low temperature phonon transport and scattering through Si nanosheets Mahmut Aksit, Jared Hertzberg, Obafemi Otelaja, Derek Stewart, and Richard Robinson (Cornell Univ.)

Vacuum phonon tunneling from STM tip Igor Altfeder and Andrey Voevodin (AFRL)

12:20 – 12:50 Mendel Closing ceremony

14

POSTERS

1. Power‐law time decay of the quantum dot photoluminescence intensity: K. Kral and M. Mensik (Acad. Sci. Czech Repub.) 2. Raman and surface-enhanced Raman scattering studies of DNA: Analysis of shifts in vibrational frequencies: T.-C. Wu, M.

Dutta and M. Stroscio (University of Illinois at Chicago) 3. Localization phenomenon of surface acoustic waves into phononic crystal defect: O. Boyko, R. Marchal, J. Zhao, M. Rénier,

and B. Bonello (INSP) 4. Phonon-assisted near-field activation of electron transfer between a solution and an electrode: T. Yatsui, K. Iijima, K.

Kitamura, and M. Ohtsu (Univ. of Tokyo) 5. Visible-light-induced water splitting by phonon-assisted optical near fields in ZnO nanorods: T. Mochizuki, K. Kitamura, T.

Yatsui, and M. Ohtsu (Univ. of Tokyo) 6. Polarized optical properties of forsterite from room temperature up to the melting point: M. Eckes,1 B. Gibert,2 D. De

Sousa Meneses,1,3 M. Malki,1,3 and P. Echegut1 (1CNRS, 2Université Montpellier, 3U. d’Orléans) 7. Phonons versus short and medium range order in silicate glasses: D. De Sousa Meneses,1,2 M. Eckes,1 C. N. Santos,1 and P.

Echegut1 (1CNRS, 2Univ. d’Orléans) 8. Ultrafast optical measurements of thermal and mechanical properties of amorphous silicon carbide films: B. Daly,1 S. King,2

and J. Bielefeld2 (1Vassar College, 2Intel Corp.) 9. Surface-enhanced Raman spectroscopy as a tool for characterizing nanostructures containing molecular component: Ke

Xu,1 Justin Abell,2 Yiping Zhao,2 Jun Qian,1 Kimber Brenneman,1 Xenia Meshik,1 Mitra Dutta,1 and Michael Stroscio1 (1Univ. of Illinois at Chicago, 2Univ. of Georgia)

10. Fabrication methods for a phonon spectrometer designed to spectrally resolve hypersonic phonon transport through nanostructures: O. Otelaja, J. Hertzberg, M. Aksit, and R. Robinson (Cornell)

11. Probing interparticle vibration by phonon-plasmon coupling in a gold nanoparticles supracrystal: P.-A. Mante,1 M.-H. Lin,2 H.-Y. Chen,2 S. Gwo,2 and C.-K. Sun1,3 (1Natl. Taiwan Univ., 2Natl. Tsing-Hua Univ., 3Acad. Sinica)

12. Finite difference modeling of laser generation of ultrasound in layered media in the coupled thermoelasticity: I. A. Veres,1 T. Berer,1,2 and P. Burgholzer1,2: 1RECENDT Research Center for Non-Destructive Testing, 2Christian Doppler Lab.)

13. Raman scattering investigations of CdS thin films grown by thermal evaporation: S. Farid, M. Stroscio, and M. Dutta (UIC) 14. Surface-enhanced Raman spectroscopy signatures of an RNA molecule: an aptamer that binds to the αVβ3 integrin: X.

Meshik,1 K. Brenneman,1 K. Xu,1 J. Abell,2 Y. Zhao,2 M. Dutta,1 and M. Stroscio1 (1UIC, 2Univ. of Georgia) 15. Surface enhanced Raman spectroscopy of DNA aptamer for immunoglobulin E: S. Ranginwala,1 K. Brenneman,1 X. Meshik,1

J. Abell,2 Y. Zhao,2 M. Stroscio,1 and M. Dutta1 (1Univ. of Illinois at Chicago, 2Univ. of Georgia) 16. Control of intervalley electron scattering and giant piezoresistance of SiGe near the -L crossover: F. Murphy-Armando

and S. Fahy (Univ. College Cork) 17. Time-resolved imaging of surface phonons reflected at microscale circular grooves on silicon surfaces: M. Tomoda,1 O. B.

Wright,1 P. Otsuka,1 O. Matsuda,1 Y. Nishijima,1 K. Ueno,1 J. Saulius,1 H. Misawa,1 and I. A. Veres2 (1Hokkaido Univ., 2RECENDT Research Center for Non-Destructive Testing)

18. Influence of growth temperature on cross-plane thermal conductivity of ZrN, ScN and (Zr,Sc)N thin films measured by Time-Domain Thermoreflectance: G. Pernot,1 P. Burmistrova,2 Y.R. Koh,1 T. Sands2 and A. Shakouri1,2 (1UCSC, 2Purdue)

19. Characteristics of a coherent longitudinal optical phonon in a GaAs buffer layer optically covered with a GaSb top epitaxial layer investigated with use of terahertz spectroscopy: H. Takeuchi,1 S. Tsuruta,2 and M. Nakayama2 (1U. Shiga Prefecture, 2Osaka City Univ.)

20. Longitudinal and transverse acoustic phonon excitations in gold nanowires under uniaxial strain: T. Francisquez,1 C. Sabater,1 G. Saenz-Arce,2 and C. Untiedt1 (1Univ. of Alicante, 2Universidad Nacional, Heredia, Costa Rica)

21. Time resolved vibrational properties of single Si3N4 nanostructures: O. Ristow,1 M. Hettich,1 M. Grossmann,1 M. Schubert,1 E. Barretto,1 J. Grebing,2 A. Bruchhausen,1 D. Mounier,3 A. Erbe,2 E. Scheer,1 V. Gusev,3 and T. Dekorsy1 (1Univ. of Konstanz, 2HZDR, 3Univ. du Maine)

22. Acousto-optic coupling under the conditions of plasmonic resonance in lateral grating structures: V. Belotelov1 and B. Glavin2 (1Lomonosov Moscow State Univ., 2Lashkaryov Inst. of Semicond. Phys.)

23. Brillouin study of the bandgap structure of laterally-patterned phononic crystals: H. H. Pan, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye (Natl. Univ. of Singapore)

24. Multifractal analysis of instantaneous normal modes at mobility edges: T.‐M. Wu and B. J. Huang (Natl. Chiao‐Tung Univ.) 25. Phonon interference and anharmonicity effects in nanoconstrictions: K. Sääskilahti, J. Oksanen, R. Linna, and J. Tulkki

(Aalto Univ.) 26. Nanoscale thermal transport measurements: Bridging ultrafast and steady-state: B. G. Green, B. L. Zink, and M. E. Siemens

(Univ. of Denver) 27. Inelastic phonon tunneling via a quantum point contact: D. Photiadis (Naval Research Laboratory) 28. Study of local heating and thermoelectric effects in quantum point contacts and molecular junctions: W. Lee, K. Kim, W.

Jeong and P. Reddy (Univ. of Michigan) 29. Guided phonon transmission through nanoribbon constrictions: D. Cheney and J. Lukes (Univ. of Pennsylvania)

15

30. High-frequency acousto-electric response of Schottky diodes: D. M. Moss,1 A.V. Akimov,1 B.A. Glavin,2 M. Henini,1 and A.J. Kent1 (1Univ. of Nottingham, 2Lashkaryov Inst. of Semiconductor Phys.)

31. Do zone-center acoustic modes of a superlattice always avoid boundaries?: A. Maznev (MIT) 32. Single mode phonon scattering at CNT-graphene junction in pillared graphene structure: J. Lee,1,2 V. Varshney,1,2 J. Brown,3

A. K. Roy,1 and B. L. Farmer1 (1AFRL, 2Universal Technology Corp., 3Louisiana Tech. Univ.) 33. Acoustic phonon temperature of nanoscale molecular devices during electromigration: W. Jeong, K. Kim, W. Lee, and P.

Reddy (Univ. of Michigan) 34. Detection of shorter-than-skin-depth acoustic pulses in a metal film via transient reflectivity: K. Manke,1 A. Maznev,1 C.

Klieber,1 V. Temnov, S.-H. Baek,2 C.-B. Eom,2 and K. Nelson,1 (1MIT, 2Univ. of Wisconsin) 35. Phonon density of states and phonon dispersion simulation for Si, (4H)SiC, and GaN materials: S. Bose and S. K. Mazumder

(Univ. of Illinois at Chicago) 36. Graphene applications in thermal interface materials: K. M. F. Shahil,1,2 V. Goyal,1,3 R. Gulotty1 and A. A. Balandin1 (1UC

Riverside, 2Intel, 3TI) 37. Non‐contact specific heat measurements of glasses at low temperatures utilizing dielectric polarization echoes: A. Halfar,

M. Bazrafshan, A. Fleischmann, and C. Enss (Heidelberg Univ.) 38. Phononic diode structures produced in a FIB microscope: J. J. Hu,1,2 J. B. Ferguson,2 Chris Muratore,2 and Andrey A.

Voevodin2 (1UDRI, 2AFRL) 39. Piezoelectricity in polar semiconductor nanowires: B. Sen, M. Stroscio, and M. Dutta (Univ. of Illinois at Chicago) 40. Pressure effects on Kapitza conductance at the silicon-superfluid helium interface: A. Ramiere,1 J. Amrit,1 and S. Volz,2

(1LIMSI, 2Ecole Centrale Paris) 41. Two-dimensional phononic thermal conductance in thin membranes in the Casimir limit: I. J. Maasilta (Univ. of Jyväskylä) 42. Observation of optically excited mechanical vibrations in a fluid containing microresonator: K. H. Kim,1 G. Bahl,1 W. Lee,1,2

J. Liu,2 M. Tomes,1 X. Fan,2 and T. Carmon (Univ. of Michigan) 43. Finite element calculation of real and complex band structures for surface acoustic waves: I. A. Veres1 and P. Burgholzer1,2

(1RECENDT Research Center for Non-Destructive Testing, 2Christian Doppler Lab.) 44. Electronic and vibrational properties of multilayer graphene: H. R. Soni, S. K. Gupta, and P. K. Jha (Bhavnagar Univ.) 45. Polarized and depolarized scattering from free-standing metal nanoparticle: Probing confined acoustic phonon: V.

Mankad,1 P. K. Jha,1 and T. R. Ravindran2 (1Bhavnagar Univ., 2Indira Gandhi Center for Atomic Research) 46. First principles study of structural, electronic and dynamical properties of lanthanum nitrides: S. D. Gupta,1 P. K. Jha,1 and

S. P. Sanyal2 (1Bhavnagar Univ., 2Barkatullah Univ.) 47. Probing zone boundary phonons at the nanoscale: G. Gopalakrishnan,1 M. Holt,2 K. McElhinny,1 J. W. Spalenka,1 D.

Czaplewski,2 T. Schülli,3 and P. Evans1 (1Univ. of Wisconsin, 2ANL, 3European Synchrotron Radiation Facility) 48. Interfacial thermal conductance between singlewalled-carbon nanotubes and between multiwalled-carbon nanotubes by

molecular dynamics: M. Shen, W. Evans, and P. Keblinski (RPI) 49. Phonon trapping in ultrathin Bi films studied by ultrafast electron diffraction: T. Frigge, B. Krenzer, A. Kalus, A. Hanisch-

Blicharski, and M. Horn-von Hoegen (Univ. of Duisburg-Essen) 50. Interactions of AlGaN/GaN high electron mobility transistors with surface acoustic waves: L. Shao, M. Zhang, A. Banerjee,

P. Bhattacharya, and K. Pipe (Univ. of Michigan) 51. Thermal conductance at the interface between Lennard-Jones crystals by molecular dynamics: S. Merabia1 and K.

Termentzidis2 (1LPMCN, 2Ecole Centrale Paris) 52. Directed matrix seeding of embedded semiconductor nanocomposites for high efficiency thermoelectrics: M. V. Warren,

G. Wang, V. A. Stoica, R. Clarke, C. Uher, and R. S. Goldman (Univ. of Michigan)

16

MONDAY

Phonons in Nanoelectronics

Kenneth E. Goodson

Mechanical Engineering Department, Stanford University

nanoheat.stanford.edu

Nanoelectronic devices - and their constituent materials and interfaces - present some of the most promising and challenging opportunities for the study of phonon transport. Examples include scaled and nanopillar FETs1,2, phase change memory cells3,4, photonic sources and mirrors5, and composite substrates for power amplifiers6. Furthermore, phonon transport and scattering plays a critical role in some of the most exciting, exploratory nanoelectronic technologies including brain-inspired computing and nanowire/nanotube transistors. The temperature distributions in these structures, especially those near interfaces, consume a significant (and increasing) fraction of the available “thermal budget” for electronic and optoelectronic systems. A subcontinuum phonon-based analysis is not always essential for the accurate simulation of these structures. However, this situation is changing with continued dimensional scaling, heterogeneous integration, and structures with 2D/3D band manipulation. This tutorial provides an overview of thermal transport phenomena in nanoelectronic devices and materials with a focus on phonons, experimental methodologies, and industrial impact. Particular attention is given to interfaces, whose thermal properties are influenced by multicarrier transport, electron-phonon nonequilibrium, and near-interfacial disorder. Interface transport is complicated by materials (including chalcogenides relevant for phase change memory) in which electrons and phonons contribute comparably to heat conduction. The varying conductivity contributions of electrons and phonons, and their dependence on lengthscale, feature prominently in several examples including metal-semiconductor multilayers and metal interconnects with dimensions down to 7 nm.

1Pop, Sinha, Goodson, "Heat Generation and Transport in Nanometer Scale Transistors," Proceedings of the IEEE 94, 1587-1601 (2006). 2Rowlette, Goodson, "Fully-Coupled, Nonequilibrium, Electron-Phonon Transport in Nanometer-Scale Silicon FETs," IEEE Transactions on Electronic Devices 55, 220-232 (2008). 3Wong, Raoux, Kim, Liang, Reifenberg, Rajendran, Asheghi, Goodson, "Phase Change Memory," Proceedings of the IEEE 98, 2201-2227 (2010). 4Lee, Asheghi, Goodson, "Impact of Thermoelectric Phenomena on Phase-Change Memory Performance Metrics and Scaling," Nanotechnology 23, 205201 (2012). 5Li, Tan, Bozorg-Grayeli, Kodama, Asheghi, Goodson, et al., "Phonon Dominated Heat Conduction Normal to Mo/Si Multilayers with Period below 10 nm," Nano Letters (2012, accepted and in press). 6Cho, Bozorg-Grayeli, Altman, Asheghi, Goodson, "Low Thermal Resistances at GaN-SiC Interfaces for HEMT Technology," IEEE Electron Device Letters 33, 378-380 (2012).

17

MONDAY

Phonons and Thermal Transport in Graphene

Alexander A. Balandin

Department of Electrical Engineering and Materials Science and Engineering Program, Bourns College of Engineering, University of California, Riverside, CA 92521 USA

Properties of phonons in graphene have recently attracted strong interest of the physics and

engineering communities. Acoustic phonons are the main heat carriers in graphene near room

temperature1 while optical phonons are used for counting the number of atomic planes in

Raman experiments with the few-layer graphene. The Raman G peak in graphene – comprised

of the zone center optical phonons – is highly sensitive to temperature2 and shifts to smaller

wave numbers despite the negative coefficient of thermal expansion3. The G peak sensitivity to

temperature allowed us to perform the first measurements of the thermal conductivity of

graphene1,3 and became instrumental for further studies of phonon transport in suspended

graphene and related materials4-5 (Fig. 1). It was shown both theoretically and experimentally

that the properties of phonons, e.g. energy dispersion and scattering rates, are substantially

different in 2-D graphene as compared to 3-D graphite3,6-7. In this talk I will focus on several

unresolved issues in the theory of phonon transport in graphene including the “problem of the

low-energy phonons in graphene”, divergence of the intrinsic thermal conductivity in 2-D

systems, as well as relative contributions of the in-plane (LA, TA) and out-of-plane (ZA) phonon

modes to heat transport in graphene. I will also discuss recent results on the effect of the

strain, defects and isotopes on phonon spectra and transport in graphene.

1A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao and C.N. Lau, "Superior thermal conductivity of single-layer graphene," Nano Lett., 8, 902 (2008).

2I. Calizo, A.A. Balandin, W. Bao, F. Miao and C.N. Lau, "Temperature dependence of the Raman spectra of graphene and graphene multi-layers," Nano Lett., 7, 2645 (2007).

3A.A. Balandin, "Thermal properties of graphene and nanostructured carbon materials," Nature Mat., 10, 569 (2011).

4S. Ghosh, W. Bao, D.L. Nika, S. Subrina, E.P. Pokatilov, C.N. Lau and A.A. Balandin, "Dimensional crossover of thermal transport in few-layer graphene," Nature Mat., 9, 555 (2010).

5S. Chen, Q. Wu, C. Mishra, J. Kang, H. Zhang, K. Cho, W. Cai, A.A. Balandin and R.S. Ruoff, "Thermal conductivity of isotopically modified graphene," Nature Mat. , 11, 203 (2012).

6D.L. Nika, S. Ghosh, E.P. Pokatilov and A.A. Balandin, "Lattice thermal conductivity of graphene

flakes: Comparison with bulk graphite," Appl. Phys. Lett., 94, 203103 (2009).

7D.L. Nika, E.P. Pokatilov, A.S. Askerov and A.A. Balandin, "Phonon thermal conduction in

graphene: Role of Umklapp and edge roughness scattering," Phys. Rev. B, 79, 155413 (2009).

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MONDAY

FIGURE 1: (a) Schematic of the thermal conductivity measurement showing suspended FLG flakes and excitation laser light. (b) Optical microscopy images of FLG attached to metal heat sinks. (c) Colored scanning electron microscopy image of the suspended graphene flake to clarify typical structure geometry. (d) Experimental data for Raman G-peak position as a function of laser power, which determines the local temperature rise in response to the dissipated power. (e) Finite-element simulation of temperature distribution in the flake with the given geometry used to extract the thermal conductivity. Figure is after S. Ghosh, W. Bao, D.L. Nika, S. Subrina, E.P. Pokatilov, C.N. Lau and A.A. Balandin, "Dimensional crossover of thermal transport in few-layer graphene," Nature Mat., 9, 555 (2010).

19

MONDAY

Ballistic to diffusive crossover of phonon flow in graphene ribbons

Zuanyi Li,1,2 Myung-Ho Bae,1 Pierre Martin,3 and Eric Pop1,3,4 1Micro & Nanotechnology Lab, University of Illinois, Urbana-Champaign, IL 61801, USA

2Dept. of Physics, University of Illinois, Urbana-Champaign, IL 61801, USA 3Dept. of Electrical & Computer Eng., University of Illinois, Urbana-Champaign, IL 61801, USA

4Beckman Institute, University of Illinois, Urbana-Champaign, IL 61801, USA

Nanoscale thermal transport has attracted much interest in materials research, particularly for energy-efficient and energy-conversion devices. Among two-dimensional materials, monolayer graphene is considered to have thermal conductivity greater than diamond when freely suspended,1 but significantly reduced when in contact with a substrate.2 However, little is known about heat flow in graphene samples and nanoribbons (GNRs) with sub-micron dimensions, of the order of the phonon mean free path (mfp).

In this work, we measure and model thermal transport in “short” (~260 nm) graphene samples and GNRs (45-130 nm wide) on a SiO2/Si substrate. We use a supported thermometry platform (Fig. 1) for measurements and a 3D simulation model (Fig. 2) to extract thermal conductivity. We find that the effective thermal conductivity of the short graphene is ~300 W/m/K at room temperature, a factor of two lower than that previously found in “long” samples2 (Fig. 3). However, the thermal conductance of the short sample reaches ~35% of the ballistic limit for graphene3 up to room temperature (Fig. 4). Thus, the apparent reduction in thermal conductivity is due to the size effect which occurs when the short sample length becomes comparable to the phonon mfp and heat flow enters a quasi-ballistic regime (Fig. 5).

We next pattern graphene into GNRs, and find their thermal conductivity is a strong function of their width (Figs. 3 and 6), e.g., from ~230 W/m/K for 130 nm to ~80 W/m/K for 45 nm wide GNRs at room temperature. Heat flow in the narrow (albeit short) GNRs appears to be fully diffusive (Fig. 4) unlike in wide samples. Comparison with extensive Boltzmann transport simulations reveals that transport in such GNRs is limited by both the SiO2 substrate and by edge scattering. The simulations also indicate that the intrinsic phonon mfp in graphene on SiO2 is ~110 nm, consistent with both our new data and that from the previous study.2 Our results indicate that heat flow in graphene can be controlled by changing sample dimensions and edges, and could provide new pathways to manipulate thermal management in nanoelectronics.

1A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior Thermal Conductivity of Single-Layer Graphene”, Nano Lett. 8, 902-907 (2008). 2J. H. Seol et al., “Two-Dimensional Phonon Transport in Supported Graphene”, Science 328, 213-216 (2010). 3N. Mingo, and D. A. Broido, “Carbon Nanotube Ballistic Thermal Conductance and Its Limits”, Phys. Rev. Lett. 95, 096105 (2005).

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MONDAY

FIGURE 1. Colored SEM image of sample showing array of ~65 nm wide GNRs spanning a heater and thermometer. Scale bar 2 μm. Inset: AFM image of GNRs. Scale bar 200 nm.

FIGURE 2. Temperature distribution obtained from finite element (FE) model to simulate heat flow in the test sample and to extract thermal conductivity.

FIGURE 4. Replot of the data in Fig. 3 as thermal conductance per unit area, G/A=k/L, to compare with purely ballistic conduction of graphene (Ref. 3).

FIGURE 3. Measured thermal conductivity, k as a function of temperature for GNRs with different widths as well as a short graphene sample. Long graphene data is from Ref. 2.

FIGURE 5. Theoretical prediction vs. experimental data of 2D graphene thermal conductivity as a function of sample length at several temperatures.

FIGURE 6. Measured thermal conductivity as a function of graphene width, W, at several temperatures. Solid curves are best fit with a simple model. Here sample length = 260 nm.

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21

MONDAY

Grain-Boundary Limited Thermal Transport in Graphene

Andrey Yu. Serov, 1,2 and Eric Pop1,2,3* 1 Dept. of Electrical and Computer Eng., Univ. of Illinois, Urbana-Champaign, IL 61801, USA

2 Micro & Nanotechnology Lab., Univ. of Illinois, Urbana-Champaign, IL 61801, USA 3Beckman Institute, Univ. of Illinois, Urbana-Champaign, IL 61801, USA.

Contact: [email protected]

Graphene is a promising candidate for nanoscale electronics and thermal materials due to its outstanding electrical and thermal properties. However, graphene grown by chemical vapor deposition (CVD) is polycrystalline, and phonon scattering at its grain boundaries (GBs)1 can degrade thermal conductivity. In this context2,3, little is known about the effect of GBs on thermal transport in graphene spanning length scales from atomistic to macroscopic. Here we theoretically investigate heat flow through individual GBs using Non-Equilibrium Green’s functions (NEGF) for all phonon modes, then use these findings to predict the thermal conductivity of polycrystalline graphene spanning a wide range of grain dimensions.

As shown in Fig. 1, we construct nanoribbons with line defects and with several types of GBs3 using the optimized Tersoff potential4 and energy minimization in the molecular dynamics (MD) simulator LAMMPS. We use periodic boundary conditions in the width direction, and we define a spring matrix based on the same optimized Tersoff potential. Then we perform NEGF simulations to find the transmission function across the GB or line defect, as shown in Fig. 2. We then calculate and plot the thermal conductance through the considered defects in Fig. 3. We observed that although the number of octagons and pentagons per unit width in grain-10 GBs is higher than in grain-4 and grain-7 GBs (Fig. 1), the transmission properties of grain-10 are worse, which we attribute to higher lattice strain propagating deeper from the defect line.

We calculate the ratio TGB(ω)/T0(ω) between transmission along a ribbon with a defect and transmission through a pristine ribbon to understand the defect contribution, as shown in Fig. 4. Then we use this transmission ratio in the relaxation time formalism akin to Mayadas model5 to calculate the thermal conductivity of polycrystalline graphene. We use Mathiessen’s rule to calculate the relaxation time taking into account Umklapp scattering, substrate scattering and GB scattering. We calibrate Umklapp and substrate scattering relaxation times to match the experimental data6 for monocrystalline exfoliated graphene on SiO2, as shown in Fig. 5. The thermal conductivity of polycrystalline graphene at 300 K is then plotted in Fig. 6 as a function of grain size, using the calculated transmission function through our four different defect types. The thermal conductivity of graphene with line defects is the most suppressed, and in general the effect of GB scattering becomes non-negligible for GB dimensions < ~0.5 μm. 1P. Y. Huang, et al., Nature 469, 389 (2011) 2W. Cai, et al., Nano Letters 10, 1645 (2010)

3A. Bagri, S.-P. Kim, R. S. Ruoff, and V. B. Shenoy, Nano Letters 11, 3917 (2011). 4L. Lindsay and D. A. Broido, Phys. Rev. B 81, 205441 (2010) 5A. F. Mayadas, M. Shatzkes, and J. F. Janak, Applied Physics Letters 14, 345 (1969)

6J. H. Seol, I. Jo, A. L. Moore et al., Science, 328, 213 (2010)

mailto:[email protected]

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MONDAY

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no defect

grain-4

grain-7

grain-10

line defect

FIGURE 1. Atomic structures of simulated grain

boundaries (GBs) and line defect. FIGURE 2. Phonon transmission through the

GBs and line defects shown in Fig. 1.

FIGURE 3. Calculated thermal conductance

through individual GBs and line defect. The line

defect shows the strongest thermal resistance.

FIGURE 5. Thermal conductivity of monocrystalline

supported graphene fitted with relaxation time

approximation (no GBs) to experiment6.

FIGURE 6. Prediction of thermal conductivity

along SiO2-supported graphene as a function

of GB size.

0 50 100 150 2000

0.2

0.4

0.6

0.8

1

phonon energy (meV)

transm

issio

n r

atio

grain-4

grain-7

grain-10

line defect

FIGURE 4. Ratio of the transmission through GB

or line defect to the ballistic transmission of

pristine graphene, TGB(ω)/T0(ω).

101

102

103

104

0

100

200

300

400

500

600

average grain size (nm)

(

Wm

-1K

-1)

grain-4

grain-7

grain-10

line defect

60 80 100 200 300 40010

1

102

103

T (K)

(

Wm

-1K

-1)

ZA

LA

TA

exp [6]

our model

ta model

la model

za model

23

MONDAY

Tuning thermal and mechanical properties of graphene

Maxim K. Zalalutdinov†, Jeremy T. Robinson†, Douglas M. Photiadis,

Eric S. Snow, Brian H. Houston

Naval Research Laboratory, Washington DC, USA

† These authors contributed equally

Drastic transformation of the mechanical properties and thermal conductivity has been

demonstrated in multilayer graphene-based films through chemical modification and high

temperature laser anneal. The observed metamorphosis from a “paper-mache-like” stack of

graphene platelets1 into a high strength, high stiffness ultra-thin (10-40 nm) film is attributed to

inter-platelet crosslinks created through defect formation and re-crystallization. The level of

disorder in chemically modified graphene (CMG) at different stages of transformation was

monitored by Raman spectroscopy. Mechanical properties (Young’s modulus, stress and

strength) were calculated from the dynamic response of drum and cantilever-type

nanomechanical resonators microfabricated in CMG film (Fig. 1). Thermal conductivity was

extracted from the known temperature dependence of graphene’s thermal expansion coefficient

(TEC) and the frequency shift of the drums’ fundamental frequency induced by optical heating

(Fig. 2). The Young's modulus of the suspended film exposed to 1mW laser beam (wavelength

513 nm, beam diameter 1 m, estimated temperature under the laser beam T ~1300 K) shows

over an order of magnitude enhancement in stiffness, E ~ 800 GPa, compared to E0 ~ 60 GPa of

CMG film before the laser treatment. The quenching of the platelets’ slippage by the crosslinks

leads to high yield stress ~ 1GPa (a low-bound estimate, provided by the level of tensile stress

sustainable in drum resonators at room temperature). An observed increase in thermal

conductivity up to 40 W/mK is also attributed to out-of-plane coupling between platelets.

A potential impact that tunability of graphene’s properties might have in the field of

nanomechanics is illustrated by the record-high performance (quality factor Q~ 31,000) of radio

frequency CDMG drum resonators.

This work was supported by the Office of Naval Research.

1 Robinson, J. T. et al. “Wafer-scale Reduced Graphene Oxide Films for Nanomechanical

Devices” Nano Letters 8, 3441-3445 (2008).

24

MONDAY

FIGURE 1. (A) Scanning electron microscope image of a nanomechanical cantilever resonator

cut out of a laser-annealed drum (Plaser ~ 1.7 mW, film thickness h=20 nm) using focused ion

beam (Ga+, 30 keV); (B) The slope of the f

2 vs. h

2/L

4 plot for CMG cantilevers of different

geometries (f is the fundamental frequency, L is cantilever length) provides the estimate for the

CMG Young's modulus E~ 800 GPa.

FIGURE 2. Plot of normalized resonance frequency (f/fo) versus optical heating power for two

CMG drum resonators and one graphite resonator. The peak in resonant frequency f(T) is

attributed to non-monotonous TEC temperature dependence (T). The position of the cusp

(defined by the inflection point (T)=0) provides the estimate for the in-plane thermal

conductivity of suspended CMG film. Before measurement, the CMG resonators were laser

annealed at 1.7 mW and 5.5 mW as labeled, and the graphite resonator was annealed at 12 mW.

The estimated is labeled by each curve.

25

MONDAY

Hot-Phonon Energy Conversion to Electric Energy

Seungha Shin, Corey Melnick, and Massoud Kaviany Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

Nonequilibrium (i.e., hot) optical phonons, which are populated over their equilibrium distribution, are generated in various energy conversions, and they are finally thermalized tuning their energy into heat and increasing the system entropy. These energetic phonons with small entropy are promising for the conversion to versatile electrical energy.

Electric barrier structure effectively converts electron kinetic energy gained from the phonon absorption to potential energy, and this can be realized by band gap engineering in semiconductors. In this work, GaAs is employed as an example, and the barrier is designed through varying Al concentration. We show the conditions for electrons to absorb these hot phonons for electrical barrier potential gain, based on statistical thermodynamics and kinetics of nonequilibria phonon and electron systems in semiconductors1,2 [Figure 1(a)]. Using the Fermi golden rule, we show simultaneous absorption of more than one phonon is improbable, so multiple barriers are preferred. The evolution of electron and phonon populations during hot-phonon relaxation including phonon up/downconversion demonstrates that barrier transition should take place at the optimal point for high efficiency [Figure 1(b)]. Based on this result as well as the transport properties of energy carriers, we propose and analyze the barrier structure for electrical harvesting of hot phonons.

We also investigate the source of hot phonons. Chemisorbed product molecules such as CO initially contain resonant frustrated vibration energies which can be converted to substrate hot phonons and in turn into electric potential [Figure 2(a)]. Starting with the role of this frustrated vibration we examine the relaxation channels leading to multiple optical phonon emissions.3 Another possible application is the solar photovoltaic cell, which creates hot phonons during the relaxation of hot electrons excited by photon irradiation [Figure 2(b)]. Our study suggests an effective way to harvest the energy in nonequilibrium state, which is wasted as heat, and through this it is expected to enhance the efficiency in many energy conversion applications.

1 M. Lundstrom, Fundamentals of Carrier Transport, (Cambridge University Press, Cambridge, 2000).

2 M. Kaviany, Heat Transfer Physics (Cambridge University Press, Cambridge, 2008).

3 S. Sakong, P. Kratzer, X. Han, K. Laß, O. Weingart, and E. Hasselbrink, “Density-functional theory study of vibrational relaxation of CO stretching excitation on Si(100)”, J. Chem. Phys. 129, 174702 (2008).

26

MONDAY

(a) (b) FIGURE 1. (a) Electron (Te) and polar optical phonon (Tp,LO) temperatures for favorable phonon

absorption (b) Electron (e, blue) and phonon (p, red) distributions at 1 ps since hot phonon relaxation begins. [Initial e (cyan) and p (magenta) distributions are also presented. Initial Te

and Tp = 300 K, and Tp,LO = 600 K].

(a)

(b)

FIGURE 2. (a) Chemisorbed vibration energy relaxation, and (b) irradiated photon relaxation for hot phonon assisted electric barrier transition.

27

MONDAY

Sub-Terahertz Phonon Control of Electronic Charge in a Resonant Tunneling Device

E. S. K. Young, A. V. Akimov, M. Henini, L. Eaves, and A. J. Kent

School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, U.K.

In this work we demonstrate that coherent phonon pulses can be used to control the transfer of bursts of electronic charge through a double-barrier resonant tunnelling diode (DBRTD) on a sub-nanosecond timescale.

An n-i-n DBRTD1, grown on a semi-insulating GaAs substrate, had an active intrinsic region comprised of a 5 nm GaAs quantum well (QW) between two 5.5 nm undoped Al0.4Ga0.6As barriers. Emitter and collector regions consisting of 2.5 nm undoped GaAs separated the barriers from the n+ contact layers. Samples were processed into 100 μm cylindrical mesas with InGeAu ohmic contacts.

The band structure of the DBRTD under bias near threshold and resonance are shown in Fig. 1 (a) and (b) respectively, and the I-V characteristic of the device is shown in Fig.1(c). Coherent phonon wavepackets in the form of picosecond strain pulses were generated in a 100 nm Al film directly opposite the device [inset in Fig.1 (d)] by optical pump pulses of wavelength 400 nm and 60 fs duration from an amplified titanium-sapphire laser having 5 kHz repetition rate. The experiments were performed in an optical cryostat at temperatures in the range 5 – 100 K.

The coherent phonon wavepacket modulates the energy separation between the quantized levels in the emitter and QW via the deformation potential. This results in the modulation of charge accumulated in the QW and, correspondingly, the current though the device. The work exploits the non-linear electrical properties of the device when the DBRTD is biased near the threshold and near the resonance peak, with the most pronounced effects at these extremes. In both regimes, small shifts of induced by coherent phonons, as shown in Fig. 1(d), result in a significant change, ΔI(t) in the current for various bias voltages, as seen in Fig.2. The detected signals have high amplitudes due to the strongly asymmetric response of the device to the compressive and tensile parts of the picosecond strain pulse, which form the acoustic wavepacket of sub-THz coherent phonons. Thus ΔI(t) displays a rectifying response to the coherent phonons, analogous to the operation of a mechanical pump.

We call this experimental observation the “coherent phonon charge pumping effect”, and it demonstrates the possibility of current control in tunnelling devices in the sub-THz range. The sensitivity of the system is not restrained by its relatively limited temporal resolution, as the induced current is detected over a period longer that the duration of the coherent acoustic wavepacket. Thus this coherent phonon charge pumping effect may be used to control charge and current in tunnelling devices, with potential applications in integrated sub-THz and THz acousto-electronic devices.

1F. F. Ouali, N. N. Zinov'ev, L. J. Challis, F. W. Sheard, M. Henini, D. P. Steenson and K. R. Strickland, “Nonequilibrium Acoustic Phonon-Assisted Tunneling in GaAs/(AlGa)As Double Barrier Devices”, Phys. Rev. Lett. 75, 308-311 (1995).

28

MONDAY

FIGURE 1. Band diagrams of the DBRTD biased near (a) threshold and (b) resonance; (c) The current-voltage characteristics of the DBRTD for increasing and decreasing bias; (d) Picosecond strain pulse temporal shape in the centre of the emitter barrier, and the induced shift between

emitter and quantum well electron levels; Experimental setup (insert in (d)).

FIGURE 2. Signals, ( ), detected for different applied biases (left) through the resonant bias region of the current-voltage (I0-Vb) characteristics of the DBRTD (right).

Δ≈ EFE

EFE

EFW ≈0

Δ≈ 0

EFW

we

wc

0.0 0.5 1.0 1.50

10

20

30

Cu

rre

nt

(mA

)

Voltage on the device (V)

Resonant peak T

hre

shold

0.0 0.1 0.2

-5

0

5

10

15

20

25

30

Shift

(t

)-

0 (m

eV)

Time (ns)

Strain

-5

-4

-3

-2

-1

0

1

2

Str

ain,

103(c) (d)

RTD

Laser

(b) (a)

20 10 00.0

0.5

1.0

1.5

2.0

2.5

3.0

Bia

s V

olta

ge

, V

b (

V)

I0 (mA)

58 59 60 61

Cu

rre

nt C

ha

ng

es,

I(t)

Time (ns)

0.1 mA

29

MONDAY

Photoconductive Switches for Study of Picosecond Thermal Dynamics in Electronic Devices

Bjorn Vermeersch1,2*, Gilles Pernot2, Hong Lu3, Je-Hyeong Bahk2, Ali Shakouri1,2* and Art Gossard3

1 Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA 2 Baskin School of Engineering, University of California, Santa Cruz, CA, USA

3 Materials Department, University of California, Santa Barbara, CA, USA * Email: [email protected] , [email protected]

A photoconductive switch (PCS) is an integrated optoelectronic device that temporarily becomes conductive when stimulated by light. In essence, it consists of an electrode with embedded gap over which a DC bias is set, on top of a non-conducting substrate. Photons with energy exceeding the bandgap will induce electric carriers, allowing current to flow through the gap (Fig. 1a). Embedding impurities with energies inside the bandgap provokes quick recapture of the induced carriers, at rates well beyond that of the interband recombination. With this technique, picosecond electrical pulses have been generated in the last 20 years. This offers interesting potential for the study of ultrafast phonon dynamics and thermal transients in electronic devices using a modified TDTR approach (Fig. 1b). The ‘pump’ beam operates the switch, creating picosecond pulses which are sent to the device under test (DUT). The electrically induced thermal response of the latter is then monitored by the ‘probe’ beam. In this paper, we will present the design and characterisation of PCS devices based on a ErAs:GaAs superlattice as active medium on semi-insulating GaAs. The isolated ErAs islands self-assemble by surface chemistry during MBE growth and act as efficient carrier traps. Appropriate choice of the superlattice period allows to achieve sub-ps lifetimes. The gold metalisation is laid out as a coplanar waveguide (CPW) as this ground-signal-ground structure combines the ability to maintain impedance matching via tapering sections with convenient full connection access on the top surface (Fig. 1c). Optimisations of the switch gap in the central electrode, including interdigitation to collect more carriers and rounded edges to avoid electric field enhancement, further improve the performance. The electrical pulses scale linearly with DC bias and sublinearly with incident laser power, in accordance with earlier observations. A

first batch of test chips provided pulses of roughly 45ps (FWHM), 10mA into a 50 load. Deposition of an aluminium transducer on top of the central CPW electrode enabled TDTR characterisation of the PCS device itself, with the pump beam activating the switch and the probe beam monitoring the reflectance variations of the electrode. Our measurements reveal picosecond Joule heating in the metal: ultrafast signal transitions, scaling quadraticly with bias voltage, are observed (Fig 2). In addition, probing different sections on the electrode allows to track the propagation of the electrical pulse and heating along the transmission line. The authors wish to acknowledge DOE/EFRC and AFOSR/MURI for supporting this work.



30

MONDAY

FIGURE 1. Photoconductive switch: (a) schematic principle, (b) application for ultrafast thermal characterisation of electronic devices, (c) typical device on fabricated test chip.

FIGURE 2. TDTR measurement of picosecond Joule heating in the electrode metal (central CPW line inside the photoconductive switch) under different bias levels.

31

MONDAY

Ultrafast Piezospectroscopy in Optoelectronic Devices

Andrey V. Akimov

School of Physics and Astronomy, University of Nottingham, UK

Uniaxial stress applied to a crystal results in the energy shift and splitting of electron states and, correspondingly, leads to changes in the optical spectra. This phenomenon in objects with a sharp optical resonance is called the piezospectroscopic effect and has been studied in optical spectroscopy for 50 years. In nanostructures, like semiconductor quantum wells (QWs) and quantum dots (QDs), the piezospectroscopic effects have been used during last decade for the detection of picosecond acoustic wavepackets [1].

In this talk a review of ultrafast piezospectroscopic experiments with sub-Terahertz coherent acoustic phonons in several optoelectronic devices will be presented. Some recent experiments with QW embedded into p-i-n tunneling device [2] and the picosecond acoustic control of emission in QD laser [3] will be described in more detail.

In the experiments with p-i-n device, the picosecond time evolution of the coherent phonon wavepackets with frequencies up to 1 THz is monitored by probing the photoconductivity of the device with optical femtosecond pulses. The photon energy of the probe pulse is chosen to be close to the energy of the exciton resonance in the QW. Coherent phonons modulate the energy of the exciton resonance and respectively the photocurrent changes. The technique shows extremely high sensitivity to coherent phonons and possesses a temporal resolution of about 1 ps.

In the second type of experiments, the coherent phonons are injected into a laser device which includes the layer of QDs embedded into an optical microcavity. The exciton QD spectrum has a broad energy distribution and only the QDs with exciton energy in resonance with the optical microcavity mode give laser emission perpendicular to the plane of the device. Out of resonance QDs emit only incoherent luminescence in the plane of the device. Coherent phonons modulate the energy of the QD excitons and the intensity of the laser output changes. Under certain conditions the increase of the lasing output by more than 100 times is observed on a picosecond timescale. The method shows the potential for ultrafast control of laser emission by coherent phonons.

1 A. V. Akimov, et al. "Ultrafast band-gap shift induced by a strain pulse in semiconductor heterostructures", Phys. Rev. Lett. 97, 037401 (2006).

2D. Moss, et al. "Picosecond strain pulses probed by the photocurrent in semiconductor devices with quantum wells", Phys. Rev. B 83, 245303 (2011).

3C. Brüggemann, et. al. “Laser mode feeding by shaking quantum dots in a planar microcavity”, Nature Photonics, 6, 30 (2012).

32

MONDAY

Electron-Phonon Non-Equilibrium in Single-Layer Graphene Using Boltzmann Transport Equation

Ajit K. Vallabhaneni,1 Xiulin L. Ruan, 1,2 and Jayathi Murthy2,3 1 Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

2 BIRCK Nanotechnology Center, Purdue University, West Lafayette, IN, USA 3 Department of Mechanical Engineering, University of Texas of Austin, Austin, TX, USA

Since its discovery in 2004, graphene has attracted extensive attention due to its exceptional thermal and electronic properties like high thermal conductivity (2,000-6,000 W/mK) and very large intrinsic carrier mobility (105 cm2V-1s-1). The gapless semi-metallic nature of graphene leads to significant electron-phonon (e-p) interactions near the Dirac point at room temperature. E-p scattering limits the performance of graphene-based electronic devices due to the difference in the timescales of relaxation between various charge carriers which leads to various bottleneck effects, as demonstrated in the recent experimental studies.1 Furthermore, recently-published thermal conductivity measurements on graphene are sensitive to the laser spot size.2 All these studies warrant the need to study the spatially-resolved non-equilibrium between various charge carriers in graphene. In this work, we demonstrate non-equilibrium in the e-p interactions in graphene by solving the linearized electron and phonon Boltzmann transport equations (BTE) iteratively. The electron and phonon BTEs are coupled because the e-p scattering rate depends on the phonon population while the rate of phonon generation depends on the e-p scattering rate. Poisson’s equation is used to obtain the electric field which serves as in input for the electron BTE. To determine the e-p coupling rate, the electronic structure and the self consistent calculations of single layer graphene are performed within the local-density approximation (LDA) using the Quantum-espresso package.3 A plane-wave basis with a kinetic energy cutoff of 75 Ry is used to model the wave functions of valence electrons and a norm-conserving pseudo-potential is used to model the core-electrons. A Monk-Horst packed grid of size 48x48x1 is used to discretize the Brillouin zone (BZ). A vacuum space of 10 Å is provided in the super cell to avoid any interactions between the periodic images in the out of plane (Z) direction. The phonon frequencies and the e-p coupling matrix elements are calculated using density-functional perturbation theory (DFPT). Fermi’s golden rule is then used to obtain relaxation times which serve as an input for solving the BTE. Our results on the e-p coupling matrix element (g) averaged over the two degenerate bands near the Dirac point agree well with the experimental values. 1D. H. Chae, B. Krauss, K. V. Klitzing and J. H. Smet, “Hot phonons in an electrically biased graphene constriction”, Nano letters 10, 466-471 (2010). 2 D. Singh, Ph.D Thesis, Purdue University (2011). 3P.Giannozzi, S. Baroni et al., “QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials”, Journal of Physics: Condensed matter 21,399502 (2009).

33

MONDAY

Phonon transport in silicon and graphene nanostructures

Irena Knezevic 1 Department of Electrical and Computer Engineering, Physics, University of Wisconsin –

Madison, Madison, WI, USA

In nanostructures, the interplay between boundary scattering and internal scattering

mechanisms governs lattice transport. As a result of the interplay, signature features of

nanoscale thermal transport emerge as we vary the structure’s size, surface or boundary

roughness, or temperature. I will present my group’s recent work on solving the phonon

Boltzmann transport equation (PBTE) in low-dimensional semiconductor nanostructures --

specifically silicon nanomembranes [1] and nanowires [2], as well as both suspended [3] and

supported graphene nanoribbons [4]. The PBTE employs full phonon dispersions and either the

relaxation-time approximation [1,3] or phonon ensemble Monte Carlo [2]. We will discuss the

merits of treating edge or boundary roughness via a specularity parameter versus real space

roughness, the anisotropy of the thermal conductivity tensor that stems from phonon focusing

and boundary scattering, and the relative importance of intrinsic mechanisms (umklapp three-

phonon scattering, mass-difference scattering, and substrate scattering where applicable) with

respect to boundary scattering in these structures.

1. Z. Aksamija and I. Knezevic, “Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes,” Physical Review B 82, 045319 (2010).

2. E. B. Ramayya and I. Knezevic, “Thermoelectric properties of ultrathin silicon nanowires,” Physical Review B, submitted.

3. Z. Aksamija and I. Knezevic, "Lattice thermal conductivity of graphene nanoribbons: anisotropy and edge roughness scattering," Appl. Phys. Lett. 98, 141919, 2011.

4. Z. Aksamija and I. Knezevic, “Thermal Transport in Supported Graphene Nanoribbons,” submitted, 2012.

34

MONDAY

Phonon Interactions between Graphene and Cu Substrate

Liang Chen, and Satish Kumar

G. W. Woodruff School of Mechanical Engineering,

Georgia Institute of Technology, Atlanta, GA, USA

Graphene has been identified as a promising nano-material for future electronics due to its exceptional electronic, thermal and mechanical properties. The investigation of heat transport at the interface of graphene and its nano-contacts in the electronic devices is critical for the efficient thermal management of graphene based nanoelectronics. Thermal transport at graphene-metal contact becomes particularly important in short channel field effect transistors1 and the graphene-Cu hybrid-interconnects2 where the metal contact can turn into a crucial heat removal pathway. Therefore, a good understanding of the thermal transport at the graphene-metal interface is essential for the development of the graphene based nanoelectronics.

In this study, we investigate the effect of Cu substrate on the phonon dispersion relation of graphene and the interfacial thermal conductance at graphene-Cu interface using molecular dynamics (MD) simulations. We consider a single layer graphene supported on (1 1 1) surface of the Cu substrate to explore the thermal interactions at the interface (Fig. 1). The Lennard-Jones (L-J) interatomic potential has been considered for the interfacial interaction between graphene and Cu. An additional parameter is added in the formulation of L-J potential to change the strength of the interaction3 between

graphene and Cu. The phonon dispersion relations4 of isolated and Cu-supported graphene are obtained by plotting the contour of spectral energy density at different wave vectors and frequencies (Fig. 2). The interactions with substrate significantly affect the acoustic phonons modes with lower frequencies and low wave vectors (see Fig 2b), which will have a strong effect on the thermal conductivity of graphene as these modes are major contributors of the graphene thermal conductivity.

In order to analyze the phonon thermal conductance at graphene-Cu interface, system shown in Fig. 1 is first equilibrated at 300 K and then the temperature of graphene is raised to 500 K followed by relaxation of the system till the temperature of both graphene and metal reached to a same temperature. The interfacial thermal conductance is obtained by fitting the transient decay of temperature difference ( T ) between graphene and metal in the following form,

( ) (0) exp( / )T t T t and estimating thermal conductance as g=C/ , where C is heat capacitance

(Fig. 3). The interfacial thermal conductance is observed to be highly dependent on the interaction strength ( ) between C and Cu atom in the L-J potential model. Changing from 1 to 16 increases the

interfacial thermal conductance, g, from 11.4 to 38.4 MW/m2K-1 (Fig. 3).

1A. D. Liao, J. Z. Wu, X. R. Wang, K. Tahy, D. Jena, H. J. Dai, and E. Pop, "Thermally Limited Current Carrying Ability of Graphene Nanoribbons", Phys Rev Lett 106, 256801 (2011). 2T. H. Yu, C. W. Liang, C. Kim, E. S. Song, and B. Yu, "Three-Dimensional Stacked Multilayer Graphene Interconnects", Ieee Electr Device L 32, 1110 (2011). 3Z. Y. Ong and E. Pop, "Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and SiO(2)", Phys Rev B 81, 155408 (2010). 4J. A. Thomas, J. E. Turney, R. M. Iutzi, C. H. Amon, and A. J. H. McGaughey, "Predicting phonon dispersion relations and lifetimes from the spectral energy density", Phys Rev B 81, 081411 (2010).

35

MONDAY

FIGURE 1. Schematic diagram of the single layer graphene supported on Cu (1 1 1) substrate. (a) 3D view; and (b) Top view.

FIGURE 2. Phonon dispersion relations for (a) isolated single layer graphene (SLG) and (b) SLG supported on Cu (111).

FIGURE 3. (a) Transient decay of temperature difference ( T ) between graphene and Cu as a function of time obtained from molecular dynamics simulations; and (b) Interfacial thermal

conductance at graphene-Cu interface as a function of interaction strength parameter (χ) in L-J potential.

(a) (b)

(a) (b)

36

MONDAY

Hypersound damping in silica measured by ultrafast acoustics at low temperature

A. Devos,1 M. Foret,2 S. Sadtler,1 B. Rufflé,2 E. Courtens,2 and R. Vacher2 1 Institut d’Electronique, de Microélectronique et de Nanotechnologie, UMR CNRS 8250 BP 69,

Avenue Poincaré, F-59652 Villeneuve d’Ascq Cedex, France 2 Laboratoire Charles Coulomb, UMR 5221 CNRS and Université Montpellier 2, F- 34095

Montpellier Cedex 5, France

Recently we proposed an alternative way of measuring hypersound attenuation in silica thin films using ultrafast acoustics [1-2]. This way, the attenuation of longitudinal acoustic phonons up to 300 GHz has been measured in vitreous silica [3].

Our method is based on the emission of a short acoustic pulse from the absorption of an ultrashort optical pulse in a thin metallic layer deposited on top of the sample. The high frequency content of the pulse is detected in the substrate after propagation in silica using another laser pulse. By comparing the signal obtained for various film thicknesses, we can extract sound attenuation in silica in the sub-terahertz range. Multiple interference effects in the multilayer are analyzed and fully taken into account[3]. Our accurate acoustic attenuation results are found to follow rather well a model combining thermally activated relaxations (TAR) and anharmonicity.

In the present work, we first show how to reach higher and higher frequencies. For that it is needed to improve both acoustic emission and detection. Concerning emission, it is governed by the thin metallic layer deposited on top which converts the ultrashort optical pulse in an acoustic pulse. Usually Al is preferred due to its efficiency in light-sound conversion.

We will also report the results obtained using the same experimental scheme but at low temperatures. On cooling, the TAR contribution is expected to first increase, and this should be rather easily observable. As shown, an important difficulty to overcome is the thermal heating induced with the laser technique. We will present different experimental evidences which attest that the sample is at the expected low tempetature and then some hypersound attenuation measurements.

1. P. Emery et A. Devos, “Acoustic Attenuation Measurements in Transparent Materials in the Hypersonic Range by Picosecond Ultrasonics», Applied Physics Letters, 89, 191904 (2006).

2. A. Devos, M. Foret, S. Ayrinhac, P. Emery, et B. Ruffle, « Hypersound damping in vitreous silica measured by picosecond acoustics”, Phys. Rev. B 77, 100201(R) (2008).

3. S. Ayrinhac, M. Foret, A. Devos, B. Ruffle, E. Courtens et R. Vacher, « Subterahertz hypersound attenuation in silica glass studied via picosecond acoustics », Phys. Rev. B. 83, 014204 (2011).

37

MONDAY

Vibrations of composite nanoobjects: bimetallic and metal-dielectric core-shell nanoparticles

D. Mongin1, M. F. Cardinal2, V. Juvé1, A. Crut1, P. Maioli1, A. Sánchez-Iglesias2, I. Pastoriza-Santos2, B. Rodríguez-González2, J. Pérez-Juste2, L. M. Liz-Marzán2, N. Del Fatti1 and F. Vallée1

1 FemtoNanoOptics Group, LASIM, Université Lyon 1-CNRS, Villeurbanne, France 2 Departamento de Quimica Fisica, Universidade de Vigo, Vigo, Spain

Nanoobjects exhibit discrete low-frequency vibrations whose properties reflect their morphology and environment. These vibrations have been extensively investigated in single-material nanoparticles, and the excellent degree of description reached now permits to use them for nanoobject characterization. In contrast, only few experimental and theoretical studies were performed on composite nanoobjects, which are particularly interesting as playing with their composition and the interaction of their components opens new degrees of freedom for designing novel properties. As the acoustic modes of nanoobjects are very sensitive to these parameters, their investigation offer unique possibilities for nanoobject analysis. This potential has not yet been exploited, and we present here time-resolved optical investigations and theoretical modelling of the acoustic vibrations of nanoobjects made of materials of same (metal) or different (metal - dielectric) natures.

The vibrations of bimetallic nanoparticles were investigated in the case of chemically synthesized gold nanorods coated with palladium. Similarly to bare gold nanorods, both their extensional and breathing vibrational modes were coherently excited and detected. Their periods were found to decrease and increase with the amount of deposited Pd, respectively (Fig. 1).1 These a priori surprising opposite behaviors reflect changes of both the nanoparticle size and mechanical properties. They were found in excellent agreement with numerical simulations, this comparison permitting determination of the amount and spatial repartition of the deposited material for very low quantities, difficult to estimate by other means.

The acoustic vibrations of composite nanoparticles formed by materials of different nature is more complex, as illustrated in the case of metal core-dielectric shell Ag@SiO2 nanospheres (Fig. 2). Depending on the relative size of the core (radius R1) and shell sizes (full particle radius R2), the measured periods are found to be either larger or smaller than that predicted for the breathing mode of the bare metal core (Fig. 1).2 These results are in excellent agreement with the predictions of a model based on continuum thermoelasticity assuming good mechanical contact between the metal core and the dielectric shell (the core breathing mode period being recovered for poor contact).3 These results demonstrate the potential of acoustic vibrations to characterize the composition and mechanical contact of materials in composite nanoobjects.

1M. F. Cardinal et al., J. Phys. Chem. Lett. 3, 613 (2012). 2D. Mongin et al., Nano Lett. 11, 3016 (2011). 3A. Crut et al., Phys. Rev. B 83, 205430 (2011).

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FIGURE 1. Left: time-dependent transmission T/T changes (black lines) and fits (red lines) of a solution of Au@Pd nanorods, highlighting their extensional (main plot) and breathing vibrations. Right: experimental periods of the extensional (a) and breathing (b) modes (black squares) of Au@Pd nanorods as a function of Pd volume (34 nm length – 10 nm diameter gold nanorods). The blue, green and red lines are computed assuming palladium deposited along the side of nanorods, at their tips, and uniformly, respectively.

FIGURE 2. Reduced periods (i.e., normalized to the breathing period of the core) measured using time-resolved spectroscopy in different composite nanospheres (Ag@SiO2) of full radius R2, formed by a silver sphere of radius R1 coated with a silica shell, as a function of R2/R1 (black squares). The reduced periods computed for the fundamental radial mode (n=0) of an Ag@SiO2 core-shell nanoparticle and for its four first harmonics (n = 1-4) are shown by the plain lines assuming perfect metal-SiO2 contact. The reduced period of the mode with the computed largest amplitude in a time-resolved experiment is shown by the blue dots. A constant reduced period of 1 (dashed line) is expected for full core-shell decoupling.

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Confined acoustic vibrations in piezoelectric GaN nanorods

Pierre-Adrien Mante,1 Hung-Pin Chen,1 Yueh-Chun Wu1, Cheng-Ying Ho,2 Li-Wei Tu,2 Jinn-Kong Sheu3 and Chi-Kuang Sun1, 4, 5

1 Department of Electrical Engineering and Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan

2 Department of Physics, National Sun Yat-Sen University, Kaohsiung, Taiwan 3 Institute of Electro-Optical Science and Engineering, National Cheng Kung University, Tainan,

Taiwan 4 Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan

5 Molecular Imaging Center and Graduate Institute of Biomedical Electronics and Bioinformatics, National Taiwan University, Taipei, Taiwan

GaN nanorods have revealed themselves as promising building blocks for a great number of applications, especially because of their piezoelectric properties and the possibility to use them for the generation of electricity.1 A better understanding of the elastic properties of nanorods is necessary for future energy applications, especially the size-dependent effect. Femtosecond pump-probe spectroscopy allows the generation of confined acoustic vibrations and their time-resolved detection. Through the observation of various confined acoustic vibrations, one can investigate the size dependent elastic properties. Here, we present results on the excitation and time-resolved measurements on various confined acoustic vibrations of GaN nanorods. In order to be able to study one specific type of confined vibration, the geometrical characteristics influencing this vibrational mode have to exhibit a low variation. We adopted different sample growth processes to control our study on different vibrational characteristics. We used a top down fabrication process to generate GaN nanorods with a narrow dispersion in diameter for the study of the radial breathing modes. Through samples with various diameters, we observed the diameter dependent elastic properties and were able to extract size-dependent mechanical coefficients, for example, Young’s modulus. Concerning the extensional modes, the length of the nanorods has to be well defined. We thus opted for a bottom up fabrication in which nanorods exhibit a large dispersion in diameter but are with a similar rod length. Thanks to inhomogeneous excitation by the laser pulse, we show that it is possible to resolve high order extensional modes. Finite element method simulations confirm the nature of these vibrations. We then developed and demonstrated a model, based on the Fabry-Pérot cavity formed by the GaN nanorods array, to explain the detection mechanism. 1 W. S. Su, Y. F. Chen, C. L. Hsiao and L. W. Tu, “Generation of electricity in GaN nanorods

induced by piezoelectric effect”, Appl. Phys. Lett. 90, 063110 (2007).

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Coherent acoustic phonon propagation through ultrathin organic interface layers

Mike Hettich,1 Karl Jacob,1 Oliver Ristow,1 Jan Mayer,1 Chuan He,1 Axel Bruchhausen,1 Martin Schubert,1 Vitalyi Gusev,2 and Thomas Dekorsy1

1 Department of Physics, University of Konstanz, Germany. 2 IMMM, UMR CNRS 6283, Université du Maine, 72085 Le Mans, France.

We investigate the influence on the propagation of coherent longitudinal acoustic phonons of self-assembled molecular (SAMs) layers introduced at the interface of gold films and silicon substrates. The sample layer structure is shown schematically in the inset of Figure1(b). The gold films are impulsively excited by femtosecond laser pulses and the ultrafast vibrational dynamics in the films are monitored using asynchronous optical sampling (ASOPS) pump-probe spectroscopy.1 The gold films vibrate in their lowest thickness mode whose damping time is modified by the SAMs at the gold-silicon interface. We study two types of molecules: Aminopropyltriethoxysilane (APTES) and Octadecyltrichlorosilane (OTS). Figure 1(a) shows the extracted damping times for both kinds of molecules over a frequency range of 100GHz. The frequency is tuned by varying the thickness of the gold films. The frequency dependence can be modelled in good qualitative agreement with the acoustic mismatch model assuming differing acoustic impedances of the SAMs.2 In order to investigate the influence of the APTES-SAM thickness, samples with various gold and APTES thicknesses were prepared. Figure 1(b) shows the obtained results, where a strong dependence of damping times on the SAM thickness is observed, ranging from 40ps for a monolayer to 110ps for SAMs with 12nm thickness at 50GHz. The solid grey lines indicate the calculated results from the acoustic mismatch model for a bare gold-silicon interface (lower curve) and the fit to our previously obtained data (upper curve).2

We also utilize the increase in damping time for SAM interfaces for subsurface imaging of patterned molecular layers. A focused ion beam is used to remove the molecules in a 10x10µm square area from a thick (~6nm) APTES layer. Subsequently a gold film is evaporated onto this structure. A part of the square is mapped with ASOPS using a stepsize of 1.7µm. The color-coded damping times are shown in Fig.2. The patterned area is represented by the dark blue region while the red areas correspond to regions where the molecules are present. We also show that not only the damping times can be utilized to gain an image contrast but also the phase information between the gold film vibration and the Brillouin signal originated in the silicon substrate. 1A.Bartels, R.Cerna, C.Kistner, A.Thoma, F. Hudert, C.Janke and T.Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling”, Rev. Sci. Instrum. 78, 035107 (2007)

2M.Hettich, A.Bruchhausen, S.Riedel, T.Geldhauser, S.Verleger, D.Issenmann, O.Ristow, R. Chauhan, J. Dual, A. Erbe, E. Scheer, P. Leiderer, and T. Dekorsy, “Modification of vibrational damping times in thin gold films by self-assembled molecular layers”, Appl. Phys. Lett. 98, 261908 (2011)

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FIGURE 1. (a) Comparison between damping times obtained for APTES and OTS-interfaces in the range from 40 to 150GHz including the damping times for the Au/Si reference system. (b) Damping times for various APTES thicknesses, the upper grey line is an acoustic mismatch

model fit to the data in (a) the lower grey line shows the expected behaviour for a bare Au/Si interface. The inset shows the layer structure of the samples.

FIGURE 2. Color-coded damping times obtained from an area scan over a patterned APTES molecule layer. Blue regions indicate the area where the molecules are removed.

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Phonon mean free paths studies with picosecond acoustic pulses and monochromatic terahertz bursts

Bernard Perrin

Institut des NanoSciences de Paris, UMR 7588 CNRS/Université Pierre & Marie Curie, 4 place Jussieu 75005 Paris, France

Accurate measurements of the mean free paths for phonons with well-defined wave vector, energy and polarization can be obtained for very low frequency acoustic phonons (in the GHz range) where ultrasonic methods can still be used. In the subterahertz range, resolution of inelastic neutron or X-ray scattering techniques is still too low to allow good measurements for acoustical phonons lifetimes. Then, the main source of information for this quantity came, for years, from comparisons of thermal conductivity measurements with theoretical expressions1 which involve averaging over a broad energy range for phonons with different polarizations.

This situation drastically changed with the advent of picosecond acoustics.2 At this time, generation, propagation and detection of very short acoustic pulses, with a broad band spectrum going up to a few hundred GHz, became available. This technique has been rapidly applied to the measurement of the attenuation of longitudinal acoustic waves with a well-defined wave vector in thin amorphous silica films,3,4 quasi-crystalline plates5 or crystalline silicon wafers.6

Today, coherent generation of terahertz acoustic phonons using semiconductor superlattices gives a unique opportunity to perform accurate measurements of phonon mean free paths in the terahertz frequency range.7 Phonon detection with the same devices can also be performed8 and propagation experiments, over large distances, of coherent monochromatic acoustic waves at 1 THz, has already been achieved.9

After a review on the different ways propagation of picosecond acoustic pulses has been used for phonon mean free paths measurements, a special emphasis will be given to recent experiments performed with bursts of monochromatic phonons in the subterahertz and terahertz ranges. Results for the phonon mean free paths will be discussed in terms of phonon-phonon interactions such as Herring’s processes.10

1J. Callaway, Phys. Rev. 113, 1046 (1959). 2C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986). 3T. C. Zhu, H. J. Maris, and J. Tauc, Phys. Rev. B 44, 4281 (1991). 4A. Devos, M. Foret, S. Ayrinhac, P. Emery, and B. Rufflé, Phys. Rev. B 77, 100201 (2008). 5J.-Y. Duquesne, B. Perrin, Phys. Rev. B 68, 134205 (2003). 6B. C. Daly, K. Kang, Y. Wang, and David G. Cahill, Phys. Rev. B 80, 174112 (2009). 7A. J. Kent, N. M. Stanton, L. J. Challis, and M. Henini, Appl. Phys. Lett. 81, 3497 (2002). 8M. F. Pascual Winter, A. Fainstein, B. Jusserand, B. Perrin, A. Lemaître, Appl. Phys. Lett. 94, 103103 (2009) 9A. Huynh, B. Perrin, B. Jusserand, A. Lemaître, Appl. Phys. Lett. 99, 191908 (2011). 10C. Herring, Phys. Rev. 95, 954 (1954).

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Picosecond Ultrasonics Study of Laterally Patterned Nanostructures Using Water as a Coupling Medium

T.J. Grimsley1, S. Che1, L.-W. Liu1, H.J. Maris1 and A.V. Nurmikko2

1 Department of Physics, Brown University, Providence, Rhode Island 02912, USA

2Division of Engineering, Brown University, Providence, Rhode Island 02912, USA

We have constructed an apparatus in which we use the picosecond ultrasonic

technique to generate sound pulses in water and detect this sound after it has

been reflected from the surface of a laterally-patterned nanostructure. The

apparatus includes a high precision stage which makes it possible to control the

position of the sound source above the sample surface with nanometer accuracy.

The stage is also able to adjust the orientation to make the source and the sample

surface accurately parallel. The returning sound is detected through the use of a

time-delayed probe light pulse. The sensitivity of the optoacoustic detection

process is improved through the use of a resonant optical cavity for the probe

light.

In the present work we have studied nanostructures consisting of a series of

equally-spaced lines with trenches between the lines. We detect echoes reflected

from the top of the each line and echoes from sound which has penetrated down

to the bottom of the trenches before reflection. We present a comparison of the

returning acoustic echo patterns with the results of computer simulations. These

simulations include correctly the effects of both shear and bulk viscosity on the

sound propagation in the water.

This work was supported in part by the Department of Energy through grant DE-

SC0001988.

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Probing Interfacial Water Molecules by Using Sub-Nanometre Ultrasonic Pulses

Chi-Kuang Sun 1,2,3, Chien-Cheng Chen1, Yu-Chieh Wen1,2, Pierre-Adrien Mante1, Vitalyi Gusev4, and Jinn-Kong Sheu5

1 Department of Electrical Engineering and Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei 10617, Taiwan

2 Institute of Physics, Academia Sinica, Taipei 115, Taiwan 3Molecular Imaging Center, National Taiwan University, Taipei 10617, Taiwan

4 Laboratory of the Condensed Matter Physics, Universit’e du Maine, LeMans 72085, France

5Institute of Electro-Optical Science and Engineering and Advanced Optoelectronic Technology Center, National Cheng Kung University, Tainan 70101, Taiwan

Water molecules in the vicinity of solid have attracted much interest because they play a crucial role in many physical, chemical, and biological phenomena. Several experimental techniques have been utilized to investigate the molecular structure1, mass densities2, and mechanical properties3. However, ultrasonic investigation on interfacial water molecules is still absent. To be sensitive to molecule structure, the wavelength of the ultrasound should be in the order of molecular distance, corresponding to frequencies on the order of THz. It is impossible to generate such a high frequency ultrasound by traditional electrically-driven transducer. In the past decade, the so-called nano-ultrasonic technique4 has been well developed. In this work, we show the result of probing interfacial water molecules by sub-nanometer acoustic pulse generated by optically excitation of an ultra-thin piezoelectric film. The ultrafast acoustic impulse response of the interfacial water, unlike that of the solid/ice interface which can be well explained by mechanical properties of bulk ice, quantitatively indicates that the liquid water next to our studied specific solid surface can be 3 times denser, 4 times more rigid, and 50% less viscous than the bulk liquid water. The presented result is the first ever noninvasive measurement of simultaneous mass density and visco-elastic property of interfacial water at an ambient solid surface. Besides, the observed anomalous phonon transport is the first observation of Kapitza anomaly5 at solid/liquid water interface. Moreover, our result provides a direct experimental evidence to explain the high thermal conductance of hydrophilic surface6.

1. J. A. McGuire and Y. R. Shen, "Ultrafast Vibrational Dynamics at Water Interfaces," Science 313, 1945

(2006).

2. M. F. Toney et al., "Voltage-dependent ordering of water molecules at an electrode–electrolyte interface,"

Nature 368, 444 (1994).

3. K. Voїtchovsky et al., "Direct mapping of the solid–liquid adhesion energy with subnanometre resolution,"

Nature Nanotechnology 5, 401 (2010).

4. K. H. Lin et al., “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nature

Nanotechnology 2, 401 (2010).

5. E. T. Swartz and R. O. Pohl, “Thermal-Boundary Resistance,” Reviews of Modern Physics 61, 605 (1989).

6. Z. Ge, D. G. Cahill, and P. V. Braun, "Thermal Conductance of Hydrophilic and Hydrophobic Interfaces,"

Phys. Rev. Lett. 96, 186101 (2006).

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Optical tomographic imaging of picosecond pulses

with 150 nm spatial resolution

Motonobu Tomoda,1 Hiroyuki Matsuo,1 Osamu Matsuda,1 Oliver B. Wright,1

and Roberto Li Voti2 1 Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan

2 Dipartimento di Energetica, Sapienza Università di Roma, Roma, Italy

Time-resolved imaging of the propagation of ultrasonic waves in the interior of materials is useful for the study of their physical properties. Photoelastic methods for solid materials and Schlieren methods for liquid and gas materials can image the ultrasonic field through changes in refractive index. These methods are often combined with high speed video camera detection. But GHz frequency and submicron wavelength ultrasonic waves cannot be investigated with these types of detection. Picosecond laser ultrasonics, which makes use of ultrasonic waves in the frequency range 10-1000 GHz, provides new opportunities to investigate internal structures or physical properties of thin films or micro-/nanomaterials.1 In the conventional setup, ultrashort pump light pulses generate longitudinal ultrasonic pulses in opaque thin films, and delayed probe light pulses detect ultrasonic pulses which are reflected at some internal inhomogeneity and return to the surface. However, until recently, no existing experimental method could image picosecond ultrasonic pulses continuously during propagation.

We have developed an optical visualizing technique that allows picosecond ultrasonic pulse shapes to be measured during propagation in a homogenous and isotropic transparent medium.2 This method is based on the Brillouin scattering of light by ultrasonic waves. When monochromatic light is reflected from an ultrasonic pulse, the amplitude of the reflected light is proportional to the amplitude of the ultrasonic wave component at a particular ultrasonic wavelength, corresponding to the Bragg scattering condition. The reflected probe light from an ultrasonic pulse interferes with the reflected light from an interface in the sample. We measure the optical reflectivity changes at different incident angles and then reconstruct the ultrasonic pulse shapes by use of an inverse method called the singular value decomposition method.

Here we have extended this technique to the use of a shorter optical wavelength for the probe beam, 415 nm, allowing a ~150 nm resolution of the ultrasonic pulse shape in a glass substrate. We make use of an automatic measurement system involving a pair of θ-2θ rotation stages for the sample and detector (Fig. 1). We use a hemi-spherical sample of BK7 glass of diameter 10 mm coated with an Al film of thickness 400 nm. We detect relative reflectivity changes as a function of angle (10-75°) and pump-probe delay time (−20-650 ps) (Fig. 2(a)). We then compute the reconstructed ultrasonic pulse shapes for each delay time (Fig. 2. (b)).

1C. Thomsen, H. T. Grahn, . J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses”, Phys. Rev. B 34, 4129 (1986).

2M. Tomoda, O. Matsuda, O. B. Wright, and R. Li Voti, “Tomographic reconstruction of picosecond acoustic strain propagation”, Appl. Phys. Lett. 90, 041114 (2007).

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FIGURE 1. Optical system of the experiment. The sample is an Al-coated BK7 glass hemisphere.

The sample and photodetector are set on θ-2θ rotational stages. SHG: second harmonic

generation crystal, AOM: acousto-optical modulator.

FIGURE 2. (a) Measured relative reflectivity changes. (The vertical dark line is an artifact.) The angle step is 0.2 ps and the time step is 5 ps. (b) Reconstructed strain images computed from a data of (a). The two parallel oblique straight lines indicate ultrasonic pulses propagating at the

longitudinal sound velocity (5900 m/s) in BK7 glass.

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Two colors pump probe experiments for an optimized coherent phonon generation and detection

Romain Legrand,1 Agnès Huynh,1 Bernard Perrin,1 Eric Charron,1 Serge Vincent,1 Norberto D. Lanzillotti-Kimura,2 and Aristide Lamaître3

1 INSP, CNRS-UMR 7588-Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France 1 Instituto Balseiro and Centro atomico Bariloche, 8400 S. C. de Bariloche Argentina

2 LPN, CNRS-UPR 20, Route de Nozay, 91460 Marcoussis, France

Experiments with picosecond strain pulses generated thanks to femtosecond laser have shown the way to extend traditional acoustics to the terahertz frequency range. Terahertz acoustics phonons with wavelength in the nanometer range would be very useful to probe the electronic structure of low dimensional semiconductors, for application in areas as phonon spectroscopy, acoustic imaging and study of sound attenuation at high frequencies. The realization of compact and high frequency emitters and detectors is then very important. Monochromatic THz transduction recently became possible based on the epitaxial growth of semiconductors heterostructures.1-3 Using semiconductor superlattices (SLs), coherent phonon generation at a frequency c/dSL have been demonstrated, with c the sound velocity and dSL the SL period, that corresponds to a wave vector q=0 in the SL.2-3 Quasi monochromatic waves at a frequency of 1 THz could be produced with a 5nm periodic GaAs/AlAs SL and could propagate in the underlying substrate. Moreover, SLs are very sensitive phonon detectors. Indeed, index modifications induced by a strain pulse impinging on the SL can be measured by the change of reflectivity of a probe light. The detection process involves a conservation rule on the wave vectors. Only the phonons modes which satisfy q = 2 k (k is the electromagnetic wave vector) will be detected. Thus generation and detection have different spectral responses, implying that a single SL cannot be used both as generator and detector for the same phonons. We design a sample allowing these two possibilities, by embedding a SL in an optical microcavity.4 In this work we present experimental results performed at low temperature to study the generation of 0.3 and 0.6 THz phonons, and their detection by the same device after one round trip in the substrate. We demonstrate that this device works as expected, and in particular we study the influence of the spectral position of the laser probe and pump relatively to the cavity mode. We could independently change the probe or pump wavelengths thanks to an asynchronous optical sampling technique using two femtosecond lasers. The optimal spectral positions for the pump and probe wavelengths have been obtained and a gain is obtained for the 0.3 THz amplitude signal compared to a traditional homodyne pump-probe technique.

1A. huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne and A. Lemaître, Phys. Rev. Lett. 97, 115502 (2006).

2A. Huynh, B. Perrin, B. Jusserand, and A. Lemaître, Appl. Phys. Lett. 99, 191908 (2011).

3A. Huynh, B. Perrin, N. D. Lanzillotti-Kimura, B. Jusserand, A. Fainstein and A. Lemaître, Phys. Rev. B 84, 191908 (2011).

4N. D. Lanzillotti-Kimura, A. Fainstein, B. Perrin, B. Jusserand, Phys. Rev. B 84, 064307 (2011).

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Influence of grain boundary scattering on thermal transport in nuclear fuel Marat Khafizov1, In-Wook Park2, Alex Chernatynskiy3, Bowen Deng3, Jianliang Lin2, John J. Moore2, Simon

Phillpot3, David H. Hurley1 1

Department of Materials Science and Engineering, Idaho National Laboratory, Idaho Falls, ID, USA 2 Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO, USA

3Department of Materials Science and Engineering, University of Florida, Gainesville, FL, USA

Phonon mediated thermal conductivity of oxide nuclear fuel is influenced by fission products, stoichiometry variations, extended defects, dislocation loops and grain boundaries. Many previous studies have considered the combined influence of all of these microstructure features. Recently, an emphasis has been placed on the development of a fundamental understanding of thermal transport in nuclear fuel that necessitates separate effect studies. Along these lines, our current work focuses on the influence of grain boundaries on thermal transport. Grain boundaries are especially important in oxide nuclear fuel at high burnup. Towards the end of life UO2 develops a rim structure composed of subgrains having nanometer size grain diameters.

We utilized a modulated thermoreflectance approach to generate and image thermal waves in surrogate fuel samples. This technique is well suited for studies of lateral thermal transport. The work presented here involves measuring thermal transport across a bicrystal interface and across multiple grain boundaries in a nanocrystalline sample. The bicrystal interface, which is perpendicular to the sample surface, is composed of a 4-nm-thick SiO2 layer sandwiched between two Si crystals. Thermal conductance of the interface was measured to be 0.11 GW/m2K. Molecular dynamics simulation was performed across the same interface with atomic structure informed by high resolution microscopy. We find a good agreement between theory and experiment.

We also studied thermal transport in a nanocrystalline ceria thin film fabricated by pulsed

unbalanced magnetron sputtering. We found that the thermal conductivity of the film is

significantly reduced as compared to a large grained polycrystalline ceria pellet. Compositional

analysis reveals a large amount of oxygen vacancies (point defects). However, using a

Boltzmann transport model (BTE) we observed that the decreased thermal conductivity can’t

be explained solely by scattering from point defects. Instead a good agreement with the

experiment is obtained when considerable grain boundary scattering is introduced. The

anomalously large boundary conductance obtained by fitting model and experimental data

suggests that there is significant segregation of vacancies at the grain boundary. In order to

confirm this explanation we also perform non-equilibrium molecular dynamics (MD)

simulations of individual grain boundaries. Different types of grain boundaries are considered

as well as stoichiometry variations across grain boundaries. Results of the MD simulations are

compared to the Boltzmann transport model and to experimental data.

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FIGURE 1. (left) Microstructure characterization of SiO2 layer sandwiched between two Si crystals. (right) Background subtracted thermal wave phase profile. The influence of interface is clearly identified

by an offset.

FIGURE 2. Comparison of thermal conductivity in nanocrystalline thin film and polycrystalline pellet in ceria. Effect of grain boundary scattering is evident from reduced conductivity across wide temperature range.

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Helicity Induced Thermal Conductivity Reduction in Superlattice Nanowires

Vikas Varshney,1,2 Ajit K. Roy,1 Douglas Dudis, 1 Jonghoon Lee, 1,2 and Barry L. Farmer3

1 Thermal Sciences and Materials Branch, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Dayton, OH, USA

2 Universal Technology Corporation, Dayton, OH, USA 3Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Dayton, OH, USA

One of the essential contributors towards the development of high ZT thermoelectric systems is low thermal conductivity of the system of interest. Over past decade, significant efforts have been put forward towards reducing thermal transport by developing novel nanostructures such as tubular nanowires, introducing surface roughness, formulating multi-component alloy-like systems and superlattice structures. All these nano-modifications in design space promote phonon scattering at boundaries and/or interfaces, thus lowering the thermal conductivity.

Along the same lines, we propose a novel helical nano-configuration towards the designing of high ZT thermoelectric devices (Figure 1). By employing non-equilibrium MD (NEMD) simulations and using an example of bi-component nanowires, we demonstrate that significant reduction in thermal transport properties –similar to that of flat superlattice nanostructures– can be achieved using a helical geometric configuration (Figure 2). The reduction is attributed to a plethora of phonon scattering events which result from the continuous rotation of the helical interface. For phonon vibrations that propagate within the same atomic type, this rotation continuously changes their direction, leading to multiple reflective phonon scattering events at the inner interface and outer boundaries. Similarly, the thermal energy that propagates through the interface between the two atomic types, also encounter a continuous interface (hence resistance to heat flow) along the nanowire length resulting in transmittive phonon scattering. Both of these processes help in lowering the heat flux, hence the thermal transport. We also demonstrate that increasing the relative mass ratio of the two components lowers the phonon energy transmission at the interface (differences in vibrational frequency spectrum), thereby relatively ‘easing’ the phonon energy propagation along the helical pathway.

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FIGURE1. (a) Schematic of the starting Si nanowire. (b) Representation of the nanowire sectioning. The empty space in between is purely shown for the sake of visualization purposes and clarity. (c) Helical partitioning of the nanowire by a rotating discussed line into two atomic types (shown as blue and red). Top (bottom) shows the orthographic (perspective) view of the same bi-component helical nanowire. (d) The schematic of final bi-component helical nanowire.

FIGURE 2. Ratio of predicted thermal conductivity values (Helix/SL) as a function of the helical angle. The calculation of helical angle is schematically shown in the inset as well. Here, p = helix pitch; r = nanowire radius; SL = superlattice.

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Heat capacity on free standing membranes included native oxide

E. Chávez1, 2, F. Alzina1, and C.M. Sotomayor-Torres1, 2, 3 1 Dept. of Physics, Universitat Àutonoma de Barcelona, Campus de la UAB, 08193 Bellaterra

(Barcelona), Spain. 2 Catalan Institute of Nanotechnology CIN2(ICN-CSIC), Campus de la UAB 08193 Bellaterra

(Barcelona), Spain. 3 Catalan Institute for Research and Advanced Studies (ICREA) 08010 Barcelona, Spain.

One of particular structures that have attracted a lot of attention is the free standing membranes, this due to continuous decrease in size in microelectronics device and circuits. These structures are: solids plates (slabs) or rods (bars) connected to solid substrate by of the smallest cross-section. The major feature of these structures is that its dimensions can be as small as few interatomics distances. This characteristic is special interest in experimental and theoretical point of view. Between its several possible applications, the free-standing structures may find as very sensitive sensors of forces and displacements, low voltage field emitters, light emitting devices, and mirror for optical resonators1.

The reduced dimension of the structure leads to the confinement of acoustics modes and the discretization of the acoustic spectrum, which, in turn, results in changes in the phonon density of states, group velocity, and phonon-phonon interaction.

Our approach to investigate the acoustic phonon dispersion in single and three-layered ultra thin free-standing silicon membranes is based on the elastic continuum model and naturally allows us compute the associated heat capacity.

We find that the temperature dependence of the heat capacity in low-temperature regime departs from 3D to 2D behaviour for shear and dilatational polarizations, while flexural polarization shifts from 3D to 1D behaviour1. This dependence reflects the different relation of dispersion of the three fundamental phonon branches for small wavevector, i.e., directly proportional for shear and dilatational waves, and quadratic for flexural waves2.

1 M.J. Huang, T.M. Chang, C.K. Liu and C.K. Yu, Int. J. Heat Mass Tran., 51(2008),4470.

2 T. Kühn, D.V. Anghel, Y.M. Galperin, and M. Manninen, Phys. Rev. B, 76(2007), 165425

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Size-dependent Thermal Diffusivity in Free-standing Silicon Membranes

John Cuffe1, Jeffrey K. Eliason2, Jeremy A. Johnson2†, Emigdio Chavez1,4, Alex A. Maznev2, Andrey Shchepetov3, Mika Prunnila3, Jouni Ahopelto3, Clivia M.

Sotomayor Torres1,4,5, Keith A. Nelson2

1 Catalan Institute of Nanotechnology, Campus UAB, 08193 Bellaterra (Barcelona), Spain 2

Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 3VTT Technical Research Centre of Finland, PO Box 1000, 02044 VTT, Espoo, Finland

4Department of Physics, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spain. 5Catalan Institute for Research and Advanced Studies ICREA, 08010 Barcelona, Spain.

†Current address: Paul Scherrer Institut, Villigen, Switzerland

The thermal properties of nanoscale materials are important for many developing fields, such as nanoelectronics and advanced thermoelectric materials. Here we present measurements of the thermal diffusivities in free-standing silicon membranes with thickness values ranging from 15 to 400 nm. These suspended single-crystalline silicon membranes are model systems to investigate fundamental aspects and consequences of reduced dimensions on phonon propagation, due to their two-dimensional geometry and precisely controlled physical properties.

The measurements were performed with a transient thermal grating (TTG) technique. In this method, two crossed laser pulses interfere to form a thermal grating. A probe beam is diffracted from this transient grating, and the thermal transport properties can be determined from the signal decay. The thermal length-scale may be varied by controlling the crossing angle of the pump pulses. At long periods, the transport is observed to be diffusive; however, the thermal conductivity is reduced from the intrinsic bulk value due to the boundaries. For a 15 nm membrane, the thermal conductivity was found to be just 13% of that of bulk silicon. The results are compared with a theory accounting for both boundary scattering and phonon-phonon scattering in the membrane.

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FIGURE 1. Schematic of Transient Thermal Grating apparatus. The angle between the pump beams is controlled by splitting the beams with a phase mask with a well-defined pitch. The

pump beams are later blocked, while the signal from the probe beam that is diffracted from the thermal diffraction grating is recorded. This signal is mixed with an attenuated reference beam

for heterodyne detection.

FIGURE 2. Thermal conductivity as a function of membrane thickness for free-standing silicon

membranes with thickness values ranging from 15 to 400 nm. The thermal conductivity is

calculated from the thermal diffusivity and the volumetric heat capacity.

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Direct Measurement of sub-THz Coherent-Phonon Pulse Shapes in Thin Metal Films

Osamu Matsuda, Shun Koiwa, Ryan Beardsley, Motonobu Tomoda, and

Oliver B. Wright Division of Applied of Physics, Faculty of Engineering, Hokkaido University,

Sapporo 060-8628, Japan

The propagation of coherent phonon pulses in solids excited by ultrashort light pulses can be monitored by delayed probe light pulses that pick up transient changes in optical reflectance.[1] The phonon pulse generation is affected by the ultrafast relaxation of the electron and phonon systems through electron-electron scattering, electron-phonon scattering or electronic and thermal diffusion.[2, 3] In the case of opaque thin film samples with a free surface, the acoustic strain pulse shape can be obtained from the time derivative of the surface displacement.[2] The surface displacement causes a phase modulation in the reflected probe light, but it is not straightforward to retrieve this displacement experimentally even when using an interferometer because the photoelastic effect also contributes to the phase modulation.

To overcome this problem we have previously proposed a method which allows the direct measurement of the surface displacement in opaque samples while at the same time fully suppressing the photoelastic contribution.[4, 5] Here we demonstrate this experimentally using sub-THz phonon pulse generation in tungsten and chromium films formed on glass substrates. The coherent phonon pulses are excited by light pulses at wavelength 830 nm and with pulse duration 200 fs. The induced surface displacement is monitored using delayed probe light pulses at wavelength 415 nm. The obtained acoustic pulse temporal width for the chromium film is about 5 ps which is much shorter than that obtained for the tungsten film (20 ps). We use two-temperature model to evaluate the strength of electron-phonon interaction from these results.

This interferometric technique should prove useful in general for studying the dynamics of coherent phonon generation in metals and semiconductors as well as in quantum heterostructures.

[1] C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).

[2] O. B. Wright, B. Perrin, O. Matsuda, and V. E. Gusev, Phys. Rev. B 64, R081202 (2001).

[3] T. Saito, O. Matsuda, and O. B. Wright, Phys. Rev. B 67, 205421 (2003).

[4] O. Matsuda and O. B. Wright, Rev. Sci. Inst. 74, 895 (2003).

[5] O. Matsuda, K. Aoki, T. Tachizaki, and O. B. Wright, J. Phys. IV, France 125, 361 (2005).

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Pulse Propagation through a Large-Grained Polycrystalline Film: Pulse Shaping Effects of Elastic Anisotropy

A. G. Every1 and A.A. Maznev2,

1School of Physics, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa 2Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts

02139, USA

The field of picosecond acoustics relies heavily on thin metal films for generation and detection of ultra-short acoustic pulses. These films typically have a polycrystalline structure, with grain size and orientation distribution varying widely, depending on the deposition conditions. A common observation is that in polycrystalline films of highly anisotropic metals such as copper, gold or silver, there is considerable broadening of sharp features of picosecond laser-generated acoustic waveforms compared to model calculations.1 For the mean field approach to acoustic behaviour of polycrystalline materials to be valid requires that the grain size be much smaller than both the sample dimensions and the acoustic wavelength, which is often not the case in picosecond acoustics. In this paper, we consider the opposite case where lateral grain size is much larger than the film thickness. This situation is frequently encountered in the application of laser ultrasonics to metrology of copper interconnects in microelectronics.2 As-deposited electroplated Cu films typically have small grain size and a strong <111> texture.3 However, subsequent secondary grain growth either at room temperature (“self-anneal”) or during intentional annealing in a furnace typically results in large grains extending right through the film and having a more random orientation distribution.3 A picosecond acoustic pulse launched into a large-grained film at a normal direction to the film boundary will propagate within each grain as if it were a single crystal layer. With the laser spot size much larger than the grain size, as is typically the case, the measured acoustic waveform will reveal dispersion resulting from the dependence of the acoustic velocity on the orientations of the grains. In this paper we present a theoretical analysis of this effect for the case of random grain orientation. We show that the random grain structure will not just broaden the acoustic pulse but will result in characteristic features, discontinuities and logarithmic and power law singularities, related to stationary values of the directionally dependent acoustic slowness of the medium. Our model assumes pancake shaped grains extending right through the layer and taking on all possible crystallographic orientations with equal probability. A short duration acoustic pulse, enters the film simultaneously at all points on the upper surface over an area encompassing a sufficiently large number of grains that statistical averaging over grain orientations is permitted. The excitation pulse could be transmitted from an incident longitudinally polarized pulse in an adjacent isotropic and homogeneous medium or it could be generated by laser ablative or thermo-elastic excitation at the surface itself. Our model is quite general, requiring only that in each grain it is the longitudinal mode that is predominantly excited. Pulse broadening effects in three different metal films are shown in Fig. 1.

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(a)

(b)

(c)

FIGURE 1. The modified pulse shape 0

LU t of an initially t function pulse on transmission

through a (a) 200 nm Cu film, (b) 200 nm Al film, and (c) 400 nm hexagonal Co film. P t shows

the effect of convoluting this pulse shape with a 1 ps Gaussian input pulse.

1 O. B. Wright and V. E. Gusev, "Ultrafast Generation of Acoustic Waves in Copper", IEEE Trans. UFFC 42, 331 (1995). 2A. C. Diebold and R. Stoner, "Metal Interconnect Process Control using Picosecond Ultrasonics", in Handbook of Silicon Semiconductor Metrology, edited by A. C. Diebold (Marcel Dekker, New York, 2001), p. 197. 3C. Lingk, M. E. Gross, and W. L. Brown, "Texture Development of Blanket Electroplated Copper Films", J. Appl. Phys. 87, 2232 (2000).

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THz-Bandwidth Coherent Phonon Emission by Supported Monolayer Graphene in the Out-of-Plane Direction

I-Ju Chen,1 Pierre-Adrien Mante,1 Cheng-Kai Chang,2 Chun-Chiang Kuo,3 Kuei-Hsien Chen,3,4 Vitalyi Gusev,5 and Chi-Kuang Sun1,6,7

1Department of Electrical Engineering and Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan

2Institute of polymer science and engineering, National Taiwan University, Taipei, Taiwan 3Center for Condensed Matter Sciences, National Taiwan University, Taipei, Taiwan

4Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan 5IMMM, UMR CNRS 6283, Université du Maine, Av. O. Messiaen, 72085 Le Mans, France

6Molecular Imaging Center, National Taiwan University, Taipei, Taiwan 7Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan

The superior heat conducting ability of graphene, in addition to its high electronic mobility and mechanical strength, has made it a promising candidate for future ultrafast electronic and photonics devices. Inspired by graphene’s ultrathin (one-atom-thick~0.3nm) characteristic and its extraordinary out-of-plane thermal expansion coefficient in spite of its two-dimensional nature1, in this paper we explore graphene’s potential to realize ultrafast acoustic device. In this presentation, we report our investigation and observation of supported graphene’s emission of THz-bandwidth phonon in the out-of-plane direction. Our observation also indicates that THz-bandwidth phonons can be emitted and then transmitted into the substrate by graphene, thus revealing a new channel for ultrafast energy dissipation in supported graphene.

Experiments were performed on CVD grown graphene deposited on epitaxially grown GaN with an embedded 3nm InGaN quantum well (QW) as shown in Fig. 1. The use of QW allows a broadband coherent longitudinal acoustic phonon detection up to 2.6THz. In the experiment, the femtosecond pump wavelength was tuned to 800nm to selectively excite the graphene. The propagating acoustic waveform of the emitted longitudinal coherent phonon pulses through the piezoelectric QW will then be monitored by a delayed 400 nm femtosecond probe pulse.2

In this study, we have observed a strong coherent phonon pulse of a bipolar waveform emitted from a supported monolayer graphene with a full duration less than 4ps and a THz bandwidth. Theoretical calculation considering different forces has been carried out to analyze the generation mechanism of the THz-bandwidth coherent phonon, indicating the dominant role of thermal expansion and deformation potential forces. Femtosecond transient spectroscopy on the carrier and phonon dynamics of the studied graphene was simultaneously performed to confirm the proposed mechanism. More details will be presented in the conference including the effect of multilayer graphene and nonlinear power dependency of the phonon excitation.

1M. Pozzo, D. Alfe, P. Lacovig, P. Hofmann, S. Lizzit, and A. Baraldi, “Thermal Expansion of Supported and Freestanding Graphene: Lattice Constant versus Interatomic Distance”, Phys. Rev. Lett. 106, 135501 (2011). 2G.-W. Chern, K.-H. Lin, and C.-K. Sun, “Transmission of light through quantum heterostructures modulated by coherent acoustic phonons”, J. Appl. Phys. 95, 1114 (2004).

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FIGURE 1. Graphene is layered on epitaxially grown GaN with InGaN quantum well buried

inside.

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Acoustic Solitons are seriously testing non-linear ultrafast acoustic models and experiments

Emmanuel Péronne,1 Nicolas Chuecos,1 and Bernard Perrin1 1 Institut des NanoSciences de Paris, CNRS UMR 7588, Université Pierre et Marie Curie 5 Place

Jussieu, Paris, France

Ultrafast laser ultrasonic is now a mature and well spread technique especially suited to study various nano-systems such as quantum wells, quantum dots, multi-layers, p-n junction, etc… Its success is mainly based on its sub-picosecond time resolution which allows THz acoustics wave generation and detection. Non-linear laser ultrasonic is very useful in this regards: THz acoustics frequencies are reached with simple metallic thin layer as transducer.

Non-linear acoustic experiments are modeled in three steps: acoustic pulse generation by a metallic layer (transduction model), pulse propagation through a “thick” substrate (propagation model) and detection of the pulse reflecting at the surface of the sample (detection model). The standard transduction model is based on the so-called Two Temperature Model (TTM). However, due to the increase in the power of the laser used nowadays, non-linear effects in the generation mechanism should become important as well, a regime where the TTM model has not been fairly tested. The propagation model has been introduced “heuristically” by adding successively the different terms which were required, looking like a Komdomtsev-Piatshvilli equation (KPE). How the different approximations are involved when considered together in the framework of laser ultrasonics? The detection model is usually based on the well-known photo-elastic detection model (PEM) where the photo-elastic coefficient is by definition evaluated at zero frequency (stationary regime). Does this definition still hold at THz frequencies? Because of the shortness of the acoustic pulses and their high amplitudes, non-linear acoustic waves are testing the limits of the models commonly used in laser ultrasonics.

The aim of this report is to test experimentally and numerically the limits of the three previous models (TTM, KPE and PEM) in the framework of non-linear laser ultrasonics. To that end, this works makes use of the acoustic solitons which are wave solution of a simplified KPE (the KdV equation). After a concise derivation of the KPE, emphasizing its limits of validity, the very interesting properties of solitons are detailed. Since the shape of solitons is completely defined by a single parameter (which relates the amplitude, the speed and the width of the soliton) the PEM can be tested for different metallic layers. Since the time distribution of the solitons is related to the pulse profile produced by the metallic transducer (see figure 1), the non-linear behavior of the TTM is also tested depending on the optical pump fluences (see figure 2).

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FIGURE 1. Soliton time distribution as a function of the shape of the initial pulse.

FIGURE 2. Several solitons are measured after propagation through 350µm-thick GaAs wafer. While signal are very similar at low pump fluence (see insert), the number of solitons and their distributions are different at high power. This is the signature of different non-linear behaviors

of Aluminium and Titane transducer.

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Theory of the Propagation of Acoustic Phonon Solitons

Humphrey J. Maris1 and Shin-ichiro Tamura2 1 Department of Physics, Brown University, Providence, Rhode Island 02912, USA

2 Hokkaido University, Sapporo 060-8628, Japan

We consider the theory of the propagation of acoustic phonon solitons in non-metallic crystals.

For a soliton with a high strain amplitude the width is small and so the soliton will contain

Fourier components of high frequency. These components will be attenuated but will be

replaced as a result of the elastic non-linearity. The attenuation mechanisms result in a steady

decrease in the amplitude and velocity of a soliton. Important attenuation mechanisms are

spontaneous anharmonic decay processes, scattering from thermal phonons, the Akhiezer

process, and in some crystals the scattering due to the variation in mass of the different

isotopes. We present numerical results for the magnitude of these processes in several crystals

of experimental interest, and then calculate how these processes affect the soliton

propagation.

This work was supported in part by the Air Force Office of Scientific Research under Contract

No. FA9550-08-1-0340.

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GHz coherent acoustic phonons generated by photoinduced Dember field

P. Ruello, G. Vaudel, T. Pezeril, V. Gusev.

Institut des Molécules et Matériaux du Mans, UMR 6283 CNRS-Université du Maine, FRANCE.

Ultrafast acoustics allows the investigation of physical mechanisms of opto-acoustic transformation such as deformation potential and inverse piezoelectric effect. Recently acoustic phonons generation by laser-induced inverse piezoelectric effect has been reported experimentally [1-4]. In particular, we demonstrated that the transient electric fields, necessary for the piezoelectric optoacoustic transformation, can be induced by the separation of the photo-generated electrons and holes in pre-existing residual electric fields [1-4]. In this communication, we present new experimental results where we show that the photoinduced Dember field can directly drive the inverse piezoelectric effect. We have studied the amplitude changes of Brillouin oscillations versus the increase of photocarriers concentration for both A[111] and B[-1-1-1] faces. A non-linear trend in the amplitude evolution with the pump fluence is observed. This non-linear behavior is the signature of the inverse piezoelectic effect which is the dominating mechanism at low pump fluence. Furthermore, while for face B, the contributions of the deformation potential and Dember inverse piezoelectric mechanisms add, we show that they compete for face A. For this face A, we report that the Brillouin signal can nearly vanish for a given pump fluence. This singularity precisely determines the transition from the photoinduced Dember piezoelectric effect to the electron-hole deformation potential mechanism becoming the most efficient mechanism at high pump fluence.

[1] O. Matsuda, O. B. Wright, D. H. Hurley, V. E. Gusev, K. Shimizu, Phys. Rev. Lett. 93, 095501 (2004). [2] K.-H. Lin, C.-T.Yu, Y.-C. Wen and C.-K. Sun, Appl. Phys. Lett. 86, 093110 (2005). [3] P. Babilotte, P. Ruello, G. Vaudel, T. Pezeril, D. Mounier, J.-M. Breteau, V. Gusev, Appl. Phys. Lett. 97, 174103 (2010). [4] P. Babilotte, P. Ruello, T. Pezeril, G. Vaudel, D. Mounier, J-M. Breteau, V. Gusev, J. Appl. Phys. 109, 064909 (2011).

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Silicon Monolithic Acousto-Optic Modulator

Siddharth Tallur and Sunil A. Bhave

Department of Physics, OxideMEMS Lab, Cornell Univesity, Ithaca, NY, USA

Frequency modulation of a continuous wave laser source enables generation of photons at multiple frequencies from a single pump laser. Such multiple closely spaced laser lines are important for high data rate QAM in dense-WDM networks. In this paper we present a 1.09 GHz acousto-optic modulator in silicon with resolved motional sidebands generated via electrostatic transduction of a coupled-optomechanical resonator. We demonstrate frequency modulation of a 1564nm wavelength pump laser, resulting in generation of sideband laser lines spaced by 0.009nm.

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Nanoscale Heat Transport from Self-organized Germanium Hut and Dome Clusters into Silicon Substrates

T. Frigge, A. Hanisch-Blicharski, A. Kalus, M. Kammler* and M. Horn-von Hoegen Faculty of Physics and Center for Nanointegration Duisburg-Essen (CeNIDE), University of

Duisburg-Essen, 47057 Duisburg, Germany

* Present address: University of Applied Sciences, 93049 Regensburg, Germany

The impact of vertical and lateral confinement of nanoscale structures on their thermal properties and heat conductivity is of fundamental importance for many applications. To study these effects, we use the self-organized formation of well-defined Ge hut and dome clusters on Si(001) as a robust model system.

Due to a lattice mismatch of 4.2%, Ge grows on Si(001) in a Stranski-Krastanov mode. First, a strained wetting layer is formed, followed by the kinetically self-limited epitaxial growth of so-called hut and dome clusters.1 These islands have a very narrow size distribution, typically with

dimensions smaller than the mean free path phonon > 100 nm of phonons in Ge at 80 K: the huts are 2 nm high and 20 nm wide, while the domes are 6 nm high and 50 nm in diameter. Within very robust growth parameters of 400°C < Tgrowth < 600°C both cluster types are mono-

crystalline, free of defects or dislocations. Below Tgrowth 550°C there is no interdiffusion with the substrate.

The thermal transport properties from the in-situ grown clusters to the substrate were determined by the dynamics of the cooling process upon heating by femtosecond laser pulses at a base temperature of 20 K. The transient temperature rise was measured by the Debye-Waller effect through ultrafast high energy electron diffraction at 20 keV in a pump-probe setup under ultra high vacuum conditions2,3 (Fig. 1). Grazing incidence at 3° ensures surface sensitivity. The diffraction pattern after deposition of 8 ML Ge/Si(001) is shown in Fig. 2 a). Regularly ordered spots reflect diffraction in transmission geometry through hut and dome clusters.

The Ge clusters were excited by 50 fs laser pulses at a wavelength of 800 nm and a fluence of 8 mJ/cm2. Diffraction patterns were taken as a function of the time delay, and the measured transient spot intensity is shown in Fig. 2 b). Due to the very different mean size of hut and dome clusters we expect a large difference for their cooling time constants, i.e., a bi-exponential cooling behaviour. From the drop in the intensity and the bi-exponential recovery of the

intensity, we obtain an initial temperature jump T = 100 K and the two cooling time constants

of hut = 50 ps and dome = 250 ps. With the bulk values for the Ge heat capacity, we estimate a

thermal boundary conductance of TBC = 1500 Wcm-2K-1. This thermal boundary conductance of the Ge clusters is a factor of two to three smaller than predictions from acoustic mismatch model and diffuse mismatch model for a homogeneous Ge heterofilm of an equivalent thickness. Such a strong reduction in heat conductivity clearly shows that size effects are significant for the thermal properties of nanoscale heterosystems.

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1 Y.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally ,"Kinetic pathway in Stranski-Krastanov

growth of Ge on Si(001)", Phys. Rev. Lett. 65, 1020–1023 (1990)

2 B. Krenzer, A. Janzen, P. Zhou, D. von der Linde, M. Horn-von Hoegen,"Thermal Boundary Conductance in

Heterostructures Studied by Ultrafast Electron Diffraction", New J. Phys. 8 (2006) p. 190

3 A. Janzen, B. Krenzer, O. Heinz, P. Zhou, D. Thien, A. Hanisch, F.-J., Meyer zu Heringdorf, D. von der Linde,

M. Horn-von Hoegen, "A pulsed electron gun for ultrafast electron diffraction at surfaces", Rev. Sci. Inst. 78

(2007) p. 13906

FIGURE 1. Schematic setup of the time resolved RHEED experiment and an illustration of the TED through the hut and dome clusters.

FIGURE 2. a) Diffraction pattern of 8 ML Ge/Si(001), grown at 550°C, at an electron energy of 20 keV and an angle of incidence of 3.5°. The sample temperature was 25 K. b) Transient spot

intensity of the marked spot in Fig. 2a).

http://publish.aps.org/search/field/author/Mo_Y_W

http://publish.aps.org/search/field/author/Savage_D_E

http://publish.aps.org/search/field/author/Swartzentruber_B_S

http://publish.aps.org/search/field/author/Lagally_M_G

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Large scale Monte Carlo approach to the Boltzmann treatment of thermal transport in Si/Ge nanostructures

Ivana Savic,1 Davide Donadio,2 Eamonn D. Murray,1 Francois Gygi,3 and

Giulia Galli1 1 Department of Chemistry, University of California at Davis, Davis, CA, USA

2 Max Planck Institute for Polymer Research, Mainz, Germany 3 Department of Applied Science, University of California at Davis, Davis, CA, USA

Decreasing the thermal conductivity of bulk materials by nanostructuring and reducing their dimensionality, or by introducing some amount of disorder, represents a promising strategy to significantly increase the efficiency of thermoelectric materials.1 In order to describe and predict thermal transport properties of complex nanostructured materials, the development of theoretical and computational approaches that can efficiently scale to large samples are highly desirable. Unlike molecular dynamics approaches,2 methods based on the solution of the Boltzmann transport equation3 are computationally too demanding, at present, to treat large scale systems and thus to investigate realistic materials. On the other hand, the Boltzmann framework provides more intuitive understanding of the physical quantities that determine the thermal conductivity, and can be easily coupled with accurate first principles methods.

In this work, we present our newly developed Monte Carlo method4 to solve the Boltzmann transport equation in the relaxation time approximation,5 that enables computation of the thermal conductivity of nanostructured systems with an effective number of atoms up to two orders of magnitude larger than is feasible with straightforward integration. We demonstrate a very good agreement between the exact and Monte Carlo Boltzmann transport results for small SiGe nanostructures and then use the Monte Carlo method to calculate the thermal conductivity of realistic SiGe nanostructured materials. We show how and why the change in the morphology of Si/Ge superlattices (from regular via nanowire to nanodot superlattices) affects the thermal conductivity. Finally, we demonstrate successful coupling of the Boltzmann transport and first principles (density functional theory) methods and discuss the differences between the thermal conductivities of bulk Si and Ge obtained using first principles and Tersoff empirical interatomic potentials. Work supported by DOE-SciDAC-e, DE-FC02-06ER25777.

1See e.g. A. J. Minnich, M. S. Dresselhaus, Z. F. Ren, and G. Chen, Energy Environ. Sci. 2, 466 (2009).

2See e.g. Y. He, D. Donadio, and G. Galli, Nano Lett. 11, 3608 (2011).

3See, e.g. A. Ward and D. A. Broido, Phys. Rev. B 81, 085205 (2010).

4I. Savic, D. Donadio, F. Gygi, and G. Galli, in preparation.

5See e.g. J. E. Turney, E. S. Landry, A. J. J. McGaughey, and C. H. Amon, Phys. Rev. B, 79, 064301 (2009).

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Frequency-Dependent Monte Carlo Simulations of Phonon Transport in SiGe Nanocomposites

Qing Hao Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, USA

In recent years, nanocomposites used as high-performance thermoelectric (TE) materials have received enormous attentions and triggered active research.1,2 The effectiveness of a TE material is evaluated by its dimensionless figure of merit (ZT), defined as ZT=S2σT/k, where S, σ, k, and T represent Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively. Inside a nanocomposite, nanostructured interfaces would strongly scatter phonons but only slightly affect the charge carrier transport. As a result, a nanocomposite has shown significantly reduced lattice thermal conductivity kL concurrently with maintained or even increased power factor S2σ,1 resulting in ZT enhancement.

Despite many promising experimental results, theoretical studies are still very limited for phonon transport inside a nanocomposite. Earlier studies by either numerically solving the Boltzmann transport equation or phonon Monte Carlo (MC) simulations were always based on the gray-medium approximation, i.e., a frequency-independent phonon mean free path (MFP). For 2D porous Si3 and general polycrystals,4 it has been pointed out that the gray-medium approximation will lead to significant overestimation of kL. However, currently no frequency-dependent phonon transport analysis has been carried out for a “composite” with regions of different materials because of (1) the lack of accurate phonon MFPs for individual material regions and (2) limited understanding of the phonon transport process across the heterogeneous interfaces. Based on the recently reported Si and Ge phonon MFPs from first-principle calculations5 and frequency-dependent phonon transport studies across interfaces in SiGe superlattices,6 frequency-dependent phonon MC simulations will be carried out for 3D SiGe nanocomposites that have been widely studied as high-temperature TE materials. Because dependable phonon MFPs are unavailable for optical branches, the MC simulations will only consider acoustic branches but the optical phonon contribution to kL will be briefly discussed. 1 A. J. Minnich et al., Energy Environ. Sci. 2 (5), 466 (2009). 2 B. Poudel et al., Science 320 (5876), 634 (2008). 3 Q. Hao et al., J. Appl. Phys. 106 (11), 114321/1 (2009). 4 Q. Hao, J. Appl. Phys. 111 (1), 014307 (2012). 5 A. Ward et al., Phys. Rev. B 80 (12), 125203 (2009); A. Ward and D. A. Broido, Phys. Rev. B 81

(8), 085205 (2010). 6 D. Singh et al., J. Heat Transf. 133 (12), 122401 (2011).

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Deviational formulations for efficient Monte Carlo simulations of multidimensional, multiscale phonon transport

Jean-Philippe M. Péraud1, Nicolas G. Hadjiconstantinou1

1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

We present and discuss a class of methods for efficiently simulating phonon transport1 in the diffusive (Fourier), transition and ballistic regimes. The computational efficiency derives from augmenting the standard Monte Carlo approach for solving the Boltzmann equation with a control-variate formulation in which only the deviation from equilibrium is simulated. By describing part of the solution deterministically, the statistical uncertainty is significantly reduced, thus addressing one of the most important limitations associated with Monte Carlo methods whose cost becomes prohibitive in problems featuring small deviations from equilibrium (small temperature differences). Moreover, by distributing particles in the computational domain according to the local deviation from equilibrium, and thus focusing the computational effort to the regions where it is most needed, this formulation results in a very effective multiscale method. Such methods can be used to obtain solutions of the Boltzmann equation for a wide range of multiscale problems of engineering interest, such as calculations of the thermal conductivity of complex periodic nanostructures, or high-dimensional simulations of transient nanoscale heat transfer problems.

We additionally show that for sufficiently small perturbations from equilibrium, deviational methods can be further simplified and accelerated by exploiting the fact that trajectories of deviational particles can be simulated independently. This simplification, which can be rigorously derived from the Boltzmann transport equation, yields a particularly efficient and simple algorithm that does not introduce any numerical approximation in time.

We showcase this algorithm by simulating a transient thermo-reflectance (TTR) experiment (see Figure 1) over several microseconds, thus resolving approximately 7 orders of magnitude in time and 4 orders of magnitude in space; this is possible due to the large speedup (several orders of magnitude) achieved by the proposed multiscale methodology. We also demonstrate the effectiveness of the method for performing steady-state calculations for determining the effective thermal conductivity of complex nanostructures (see Figure 2).

1Jean-Philippe M. Péraud, Nicolas G. Hadjiconstantinou, “Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations”, Phys. Rev. B 84, 205331 (2011).

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FIGURE 1. Simulation of a transient thermo-reflectance experiment. A slab of aluminum over a substrate of silicon is irradiated by a laser at t=0. The variance-reduced method efficiently

simulates small temperature variations (ΔT).

FIGURE 2. Temperature field in a periodic nanostructure, calculated with the variance-reduced Monte-Carlo method.

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Thermal conductivity of diamond nanowires from first principles

Wu Li,1 L. Lindsay,2 D. A. Broido,3 D. A. Stewart,4 N. A. Katcho,1 and Natalio Mingo1

1 LITEN, CEA-Grenoble, Grenoble, France 2 Naval Research Laboratory, Washington, D.C., USA

3 Department of Physics, Boston College, Chestnut Hill, Massachusetts, USA 4 Cornell Nanoscale Facility, Cornell University, Ithaca, New York, USA

The Recent advances in nano fabrication and characterization techniques have made it possible to study the thermal conduction properties of very small systems, notably nanowires (NWs). The synthesis of diamond NWs eluded researchers for a long time, and they were only successfully produced recently.1 Given the exceptional thermal conduction properties of bulk diamond, and the importance of heat dissipation in nanoscale devices, it is crucial to investigate the thermal conductivity of this new system, and to compare it with other NWs of the group IV family, Si.

Using ab initio calculations we have investigated the thermal conductivity () of diamond NWs, unveiling unusual features unique to this system.2 In sharp contrast with Si, (T) of diamond NWs as thick as 400 nm still increase monotonically with temperature up to 300K, and room temperature size effects are stronger than for Si. A marked dependence of on the crystallographic orientation is predicted, which is apparent even at room temperature. [001] growth direction always possesses the largest in diamond NWs. The predicted features point at a potential interest of diamond NWs for the precise control of thermal flow in nanoscale devices.

1C.-H. Hsu, S. G. Cloutier, S. Palefsky, and J. Xu, “Synthesis of diamond nanowires using atmospheric-pressure chemical vapor deposition”, Nano Lett. 10, 3272 (2010). 2W. Li, N. Mingo, L. Lindsay, D. A. Broido, D. A. Stewart, and N. A. Katcho, submitted.

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The new limit of heat transfer under extreme strain

Victor Lee,1,2 Renkun Chen,3 and Chih-Wei Chang1 1 Center for Condensed Matter Sciences, National Taiwan University, Taipei, Taiwan

2Department of Physics, National Taiwan University, Taipei, Taiwan 3 Department of Mechanical Engineering, University of California at San Diego, La Jolla,

California, USA

Ballistic phonons can propagate without dissipating energy to environments and thus the

number of them determines the heat transfer capabilities for a given material. Based on the

particle picture of phonons, it was predicted that the thermal conductivity (κ) of a deformed 1D

system will start to decrease when the radius of curvature (Rc) is comparable the phonon mean

free path (l). However, due to limited mechanical strengths and short phonon mean free paths

of most materials, so far no experimental works are capable of testing this fundamental limit of

heat transfer.1 Here we utilize the superior mechanical strength and high thermal conductivity

of single-wall carbon nanotubes (SWCNTs) to investigate the heat transfer phenomena at a

previously inaccessible condition. As shown in Fig. 1, the thermal conductivities of SWCNTs are

surprisingly robust under cyclic strains. Moreover, the unusual robustness of heat transfer is

found to be independent of defects, dislocations, structural kinks, bent angles, or bent

curvatures. From the measured κ’s, we obtain l’s to be 255nm, 235nm, 382nm, and 223nm for

Samples 1 to 4, respectively. At the extremes of structural deformation shown in the right

column of Fig. 1, l/Rc’s have reached 1.34, 4.19, 8.49 and 10.14 for Samples 1 to 4, respectively.

In contrast to previous theoretical works that suggested a 10% reduction of κ at l/Rc ~ 1,2 the

robustness of κ tested beyond l/Rc > 10 in our experiment clearly refines the limit of heat

transfer under strain. Our results demonstrate that SWCNTs are exceptional 1D thermal

conductors with capabilities of going beyond the established wisdom on the heat transfer

under extreme strain and may inspire certain revisions of the associated theoretical models.

1C. W. Chang, D. Okawa, H. Garcia, A. Majumdar and A. Zettl, “Nanotube phonon waveguide”, Phys. Rev. Lett 99, 045901 (2007).

1Z. Xu and M. J. Buehler, “Strain controlled thermomutability of single-walled carbon nanotubes”, Nanotechnology 20, 185701 (2009).

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FIGURE 1. (Upper images): Representative SEM images of Sample 1 to 4 undergoing cycles of bending. The number of each image denotes the frame number in the lower panel. The reconstructed 3D images at the extremes of deformation are shown at the right column. (Lower panel): the corresponding thermal conductivity (normalized to their initial values) measured during the bending. The last data point of Sample 3 shows thermal conductivity reducing to zero when the sample was cut using an electron beam.

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TUESDAY

Testing models for heat conduction using high pressures:

crystals, glasses, and interfaces

David G. Cahill and Wen-Pin Hsieh Department of Materials Science and Engineering, Materials Research Laboratory, University

of Illinois, Urbana, Illinois 61801

Time-domain thermoreflectance (TDTR) is a modulated pump-probe optical technique based on

an ultrafast model-locked laser as the light source. Over the past decade, we have advanced the

state-of-the-art of TDTR by improving the optical design and introducing quantitative modeling

of heat transport in cylindrical coordinates for an arbitrary multilayer geometry. Because TDTR

is an all-optical method, TDTR is applicable to the study of materials under extreme conditions

of high temperatures and pressures. The high pressure environments provided by diamond anvil

cells enable elegant tests of models for heat transport. The pressure-dependent thermal

conductivity of phase VII of water ice to 20 GPa is in excellent agreement with the scaling

predicted by the Liebfried-Schlomann equation using the equation-of-state as an input. Despite

the complexity of the atomic and molecular vibrations of an amorphous polymer, the pressure

dependence predicted by the model of the minimum thermal conductivity is in excellent

agreement with data for PMMA to 12 GPa. The pressure dependence of clean and graphene-

modified interfaces between Al and SiC reveal the strong dependence of interface thermal

conductance on the stiffness of interfacial bonds.

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Thermal phonon transport in corrugated silicon nanowires Christophe Blanc

1, and Olivier Bourgeois

1

1 Institut Néel, CNRS-UJF, 25 avenue des Martyrs, 38042 Grenoble Cedex 09, France

Phonon thermal transport in system of reduced dimensions or in nanostructured materials attracts

a strong interest. This is particularly true at low temperature where the characteristic lengths like

the phonon mean free path and the dominant phonon wave length become very large. Here we

focus our interest on the thermal conductance of corrugated nanowires from 0,3K to 6K. The

experimental method is based on the 3ω method1.

It has been shown that the thermal transport on straight nanowire and serpentine ones agree with

the Casimir and the Ziman models2,3

. In the Casimir theory, the mean free path is only limited by

the section of the nanowire, and in the Ziman theory thanks to specular reflection (at very low

temperature) the mean free path can be even larger than the diameter (depending on the phonon

wavelength and the roughness). However, several recent studies are predicting that the mean free

path could be smaller than that of the Casimir theory (the Casimir limit) with a rough

nanowire4,5

. Using e-beam lithography we have introduced a periodic roughness on silicon

nanowire. These corrugated surfaces are made to have an amplitude of 25% the nanowire section

section. Our measurements of the thermal conductance of these corrugated nanowires indicate

that the mean free path of phonon is strongly reduced. It can be largely below the smallest

diameter of the nanowire, meaning a mean free path three times smaller than the Casimir limit

(see figure 1). This will be discussed in view of the recent theoretical models of phonon transport

below the Casimir limit5,6

.

In all our measurements, despite the low temperature regime, the universal quantum of thermal

conductance has not been evidenced. Furthermore the measured thermal conductance is largely

smaller than the universal value (2kB

2T/3h). One possible origin for this reduction of thermal

conductance may arise from the low value of the transmission coefficient of phonon between the

nanowire and the heat bath reservoir. In order to test this issue, we have measured nanowire with

catenoïdal shape at the contact interface (nanowire-heat bath). With such a profiled contact, the

transmission from the wire to the bath should be improved by at least 25%. Three nanowires

with catenoïdal contacts have been measured versus temperature. It is shown that as compared to

straight nanowire, the thermal conductance is absolutely identical (see figure 2). No effect of

transmission coefficient has been evidenced here.

To address the phonon transport in the quantum regime, we are currently developing a new

thermal sensor. This will permit measurements of heat exchange below 100mK, a temperature

range where the universal phonon transport between two heat reservoirs through a phonon wave

guide should be measurable.

1 O. Bourgeois, T. Fournier and J. Chaussy, J. Appl. Phys. 101, 016104 (2007).

2 J.-S. Heron, T. Fournier, N. Mingo and O. Bourgeois, Nanoletters 9, 5 (2009).

3 J.-S. Heron, C. Bera, T. Fournier, N. Mingo and O. Bourgeois, Phys. Rev. B 82, 155458 (2010).

4 A.L. Moore, S.K. Saha, R.S. Prasher, and L. Shi, Appl. Phys. Lett. 93, 083112 (2008).

5 J. Carrete, L.J. Gallego and L.M. Varela, N. Mingo, Phys. Rev. B 84, 075403(2011).

6 I. Duchemin and D. Donadio. Phys. Rev. B 84, 115423 (2011) and unpublished.

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FIGURE 1. Thermal conductance for a straight nanowire and three with artificially created

roughness. The scale bar for a) is 2µm and for b) is 300nm.

FIGURE 2. Thermal conductance for a straight nanowire and three with catenoidal interface.

The scale bar for a) is 2µm and for b) is 2µm.

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Effect of Morphology and Roughness on Thermal Conductivity of Silicon Nanowires

Kedar Hippalgaonkar,1 Jongwoo Lim,2 Peter Ercius,3 Peidong Yang,2,4 Arun Majumdar1,4,5

1 Department of Mechanical Engineering, University of California at Berkeley, CA, USA 2 Department of Chemistry, University of California at Berkeley, CA, USA

3National Center for Electron Microscopy, Lawrence Berkeley National Labs, Berkeley, CA, USA 4Material Sciences Division, Lawrence Berkeley National Labs, Berkeley, CA, USA

5Current Address: US Department of Energy, Washington, DC, USA

Silicon Nanowires with smooth surfaces have been known to diffusively scatter phonons and reduce the mean free path reducing the thermal conductivity1. Since, it has been qualitatively demonstrated that surface roughness can reduce the thermal conductivity of crystalline Si nanowires (SiNWs)2. However, the underlying reasons remain unknown and warrant quantitative studies and analysis. In this work, vapor-liquid-solid (VLS) grown SiNWs were controllably roughened, and then thoroughly characterized with transmission electron microscopy (TEM) to obtain detailed surface profiles3. Once the roughness information (root

mean square (rms), correlation length, L and power spectra, p) was extracted from the surface profile of a specific SiNW, the thermal conductivity of the same SiNW was measured. The thermal conductivity correlated well with the power spectra of surface roughness, which varies as a power law in the 1-100 nm length scale range. Further, rough Electrolessly Etched (EE) Silicon Nanowires were then characterized with the same technique. In order to provide a direct comparison between two separate roughening techniques, the morphology of the EE wires was studied in detail including porosity, single-crystallinity, cross-section and roughness4. The power spectra of the EE wire roughness was similarly studied. Results from both the roughened-VLS and EE wires show dependence of thermal conductivity on the roughness power spectra suggesting a new realm of frequency-dependent phonon scattering from rough interfaces below the Casimir limit. Insights gained from this study can help develop a more concrete theoretical understanding of phonon – surface roughness interactions.

1D. Li, Y. Wu, P. Kim, L. Shi, P. Yang, A. Majumdar, “Thermal Conductivity of Individual Silicon Nanowires”, Applied Physics Letters 83, 2934 (2003).

2A.I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, P. Yang, “Enhanced thermoelectric performance of rough silicon nanowires”, Nature 451, 163 (2008)

3J. Lim, K. Hippalgaonkar, S. C. Andrews, A. Majumdar, P. Yang, “Quantifying surface roughness effects on phonon transport in silicon nanowires”, submitted to Nano Letters (2012)

4K. Hippalgaonkar, J. Lim, P. Ercius, M. Z. Li, R. Chen, P. Yang, A. Majumdar, “Effect of Morphology on thermal conductivity of silicon nanowires”, in preparation for Physical Review Letters (2012)

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Phonon Transport in Single-Walled Carbon Nanotube Aerogels

Kejia Zhang,1 Abhishek Yadav,1 Lei Shao,1 Kyu Hun Kim,2 Youngseok Oh,2 Mohammad F. Islam,2 Ctirad Uher,3 and Kevin P. Pipe1,4

1 Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA 2 Department of Materials Science and Engineering, Carnegie Mellon University,

Pittsburgh, PA, USA 3 Department of Physics, University of Michigan, Ann Arbor, MI, USA

4 Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA

Single-walled carbon nanotubes (SWCNTs) have found numerous applications due to their outstanding thermal, electrical, and mechanical properties.1,2 For many such applications, CNT networks are utilized, with network junctions primarily governed by van der Waals interactions. Prior models3,4 for phonon transport in CNT networks have only considered the CNT junction resistance and have not considered the resistances of the CNTs themselves. In this work, we examine phonon transport in two types of SWCNT aerogels (as-grown samples and samples coated with graphitic layers) through measurements of thermal conductivity from 100K – 300K and phonon transport models.

Because SWCNT aerogels have ultralow density (~10 mg/cm3) and a relatively small number of junctions, we are able to quantify the separate contributions of SWCNTs and SWCNT junctions to the thermal conductivity of a CNT network for the first time. We also measure the suppression factor (which captures phonon interference effects in a CNT network) for the first time. We find that the contribution of nanotube thermal resistance to the total thermal resistance of as-grown SWCNT networks can be significant, particularly at low temperatures. For coated SWCNT networks, thermal transport is dominated by nanotube resistance, mainly due to a dramatically decreased phonon mean free path. The resulting large decrease in thermal conductivity is an important consideration for applications which may coat a SWCNT network in order to improve its mechanical strength. We further observe a plateau in the temperature dependence of thermal conductivity for graphitic coated SWCNT networks, which suggests a frequency-dependent phonon mean free path.

1C. M. Aguirre et al., “Carbon nanotube sheets as electrodes in organic light-emitting diodes”, Appl. Phys. Lett. 88, 183104 (2006).

2N. K. Mahanta, A. R. Abramson, M. L. Lake, D. J. Burton, J. C. Chang, H. K. Mayer, and J. L. Ravine, “Thermal conductivity of carbon nanofiber mats”, Carbon 48, 4457 (2010).

3C. W. Nan, G. Liu, Y. Lin, and M. Li, “Interface effect on thermal conductivity of carbon nanotube composites”, Appl. Phys. Lett. 85, 3549 (2004).

4R. S. Prasher, X. J. Hu, Y. Chalopin, N. Mingo, K. Lofgreen, S. Volz, F. Cleri, and P. Keblinski, “Turning carbon nanotubes from exceptional heat conductors into insulators”, Phys. Rev. Lett. 102, 105901 (2009).

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Ballistic phonon transport

in nanowires at ambient temperature

L. Jalabert1, T. Sato2, T. Ishida2, H. Fujita2, Y. Chalopin3,4, S. Volz1,3,4

1LIMMS-CNRS/IIS-University of Tokyo, UMI CNRS 2820, 4-6-1 Komaba,

Meguro-ku 153-8505 Tokyo, Japan 2CIRMM-IIS University of Tokyo, 4-6-1, Komaba, Meguro-ku, 153-8505 Tokyo, Japan

3CNRS, UPR 288 Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion,

Grande Voie des Vignes, 92295 Chatenay-Malabry 4 Ecole Centrale Paris, Grande Voie des Vignes, 92295, Châtenay-Malabry

Atomic to nano-scale solid-state device technologies have opened application fields involving new classes of physical phenomena. As such, phonon heat conduction is marked by the shift from a diffusive transport regime with predominant interactions between heat carriers to a ballistic one when the system size shrinks below the carrier mean free path. In this latter case, the interaction with surfaces or interfaces governs the energy transport as shown for wires with micron scale diameters at a few kelvins, and nanowires with diameters of 15-20nm at ambient temperature.

In this work, the measurement of the thermal conductance of short nanowires is presented and appears to be at least two orders of magnitude larger than the ones of long nanowires at temperatures ranging from 380K to 460K. The predominance of ballistic phonon transport remains the best hypothesis to retrieve quantitative predictions of this abnormal behaviour.

The measurement is based on a MEMS structure including an electrostatic actuator that allows producing nanojunctions with accuracy based on the resolution of a transmission electron microscope. The thermal conductance is measured by two integrated resistors that are simultaneously heating and measuring the local temperatures at the nearest of the nanojunction.

This unexpected behaviour might constitute a new key element in the design of nanosystems and in the understanding of the damaging of mechanical micro-nanocontacts. This conducting behaviour is also paving the way for the development of nanoscale cooling devices as well as of the recent phononic information technology.

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Kapitza Resistance of Diameter Modulated SiC Nanowires, a Molecular Dynamics Study.

Konstantinos Termentzidis, Heloise Huedro, Anne-Laure Delaye, Yuxiang Ni, Yann Chalopin and Sebastian Volz

EM2C, CNRS UP288, Ecole Centrale Paris, Chatenay-Malabry, France

The Kapitza resistance of diameter modulated SiC nanowires is computed with the non-

equilibrium Molecular Dynamics (NEMD) and the Equilibrium Molecular Dynamics (EMD)

method. The two main polytypes the 3C (zinc-blend) and 2H (wurtzite) of SiC nanowires are

investigated, but also the superlattice SiC nanowires with shape modulation.

SiC nanomaterials of one-dimension (nanowires, nanocables, nanofibers and nanorods) attract

much attention as they feature numerous unique properties as high thermal conductivity and

thermal stability at high temperatures, high mechanical strength and wide band gap1,2. These

properties make SiC a promising material candidate for various applications in nano-electronics,

optics, nanocomposites, photocatalysts, hydrogen storage and superhydrophobic coatings.

Furthermore, nanowires SiC/SiC composites have superior fracture toughness, with a proven

resistance to neutron radiation.

Several properties of nanomaterials can be modulated by varying their sizes or their

morphologies3. Here we investigate the influence of SiC polytypes on the Kapitza resistance. We

study the 2H and 3C polytypes, which both are known to be the most stable among the

plethora of SiC polytypes of nanowires with small cross-section. We compare these results with

nanowires composed of alternating polytypes with diameter modulation (fig1). We will show

that the restrictions between two different cross sections exhibit considerable Kapitza

resistance and we will proceed to the physical explanation with the help of the partial densities

of states of phonons. Preliminarily results show that for low frequencies there is the

appearance of confined modes, while at higher frequencies of the interfacial modes.

1 E. Wong, P. Sheehan and C.Lieber, “Nanobeam Mechanics: Elasticity, Strength and Toughness

of Nanorods and Nanotubes”, Science 277, 1974 (1997). 2 C. Tang, et al, “SiC and its bicrystalline nanowires with uniform BN coatings ”, Appl. Phys. Lett. 80, 4641 (2002). 3 C. Burda, X .B. Chen, R. Nararyanan and M. El-Sayed, “Chemistry and Properties of Nanocrystals of Different Shapes”, Chem. Rev. 105, 1025 (2005).

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FIGURE 1. Superlattice nanowires of SiC with diameter modulation.

FIGURE 2. Density of states versus frequency for a diameter modulated hcp SiC nanowires. “A” signifies atoms from the small section, “B” atoms of the large section, while “A1, A2, B1, B2” are

the bilayers closest to the interface.

83

TUESDAY

Electron-phonon coupling in nanoscale Pt/Au bilayers

Wei Wang and David G. Cahill

Department of Materials Science and Engineering, University of Illinois, Urbana, IL, USA

Electron-phonon coupling plays a critical role in experiments on ultrafast thermal transport

and the emerging field of spin caloritronics because nonequilibrium between electrons and

phonons creates an additional resistance to the diffusion of heat. We use time-domain

thermoreflectance (TDTR) with picosecond time resolutionto measure the effective thermal

conductance of the interface between Au and Pt in the temperature range 50 <T< 300 K.

Bilayer samples (50 nm of Pt followed by 20 nm of Au) are prepared by multi-target sputter

deposition on sapphire substrates. The bilayer is heated from the Pt side by the pump optical

pulse and the subsequent cooling of the Pt layer is measured by changes in the reflectivity of Pt

measured by the probe optical pulse. The thermal conductance at the Au/Pt interface can be

extracted from the data between 10 ps and 100 ps delay time with the use of an analytical

model of thermal transport in the sapphire/Pt/Au structure. We compare our data for the

effective thermal conductance of the interface Geffto a theoretical prediction based on the

series sum of the electronic thermal conductance Gee of the Pt/Au from the diffusive mismatch

model for electrons; and the electron-phonon conductance given by Gep=gh, where h is the Au

thickness and g is the volumetric electron-phonon conductance in Au. The effective interfacial

thermal conductance is then Geff=GeeGep/(Gee+Gep). The data are in good agreement with this

model at low temperatures, T<100 K, but the data for Geffexceed the predicted value at room

temperature by a factor of ≈2.

84

TUESDAY

Electron-Phonon Scattering From First Principles:

Times and Rates for Transport Calculations

Jelena Sjakste,1 Nathalie Vast,1 Paola Gava,1 Valeriy Tyuterev2

1 Laboratoire des Solides Irradiés, CEA-DSM-DRECAM, CNRS, 91128 Palaiseau, France. 2 Tomsk State Pedagogocal University, Tomsk, Russia.

Electron-phonon coupling is well known as a limiting factor of the electrical charge transport. From the theoretical point of view, it is important to be able to predict various transport properties without resorting to adjustable parameters.

Recently, we developed from-first-principles description of phonon-induced scattering of electrons excited in the conduction band of bulk semiconductors.1 Electron-phonon matrix elements turn out to be a crucial ingredient, whose neglect prevents a correct understanding of which phonons are responsible for the electronic scattering and estimation of the electron-phonon contribution to stability of electronic levels. 1,2,3 This is illustrated on Fig. 1 in the case of impurity states in doped silicon, which we considered in Ref. 2. The complex behaviour of the electron-phonon matrix elements determines the fact that the effect of the electron-phonon scattering on the stability of impurity levels is much smaller than what was previously believed for 50 years. Previous calculations, which considered electron-phonon coupling to be a constant, overestimated the effect by several orders of magnitude. 2

Despite great advances in predicting the electronic structure of materials, the ability to compute thermoelectric transport properties from first principles is still unrealized in general, even for simple bulk materials. Recently, in collaboration with a group of N. Mingo (Grenoble, France), we combined our ab initio data for electronic structure and electron-phonon scattering with Boltzmann solver for transport coefficients. 4 As shown on Fig. 2, the silicon mobility obtained with our method is in excellent agreement with experiment. This approach permitted us to reduce the number of ad hoc parameters in calculation of transport coefficients.

1 J. Sjakste, N. Vast, V. Tyuterev, Ab initio method for the electron-phonon scattering time in semiconductors: application to GaAs and GaP, Phys. Rev. Lett. 99 (2007).

2 V. Tyuterev, J. Sjakste, N. Vast, Theoretical intrinsic lifetime limit of shallow donor states in silicon, Phys. Rev. B 81 (2010) 245212.

3 V. G. Tyuterev, S. V. Obukhov, N. Vast, and J. Sjakste, Ab initio calculation of electron-phonon scattering time in germanium, Phys. Rev. B 84 (2011) 035201.

4 Z. Wang, S. Wang, S. Obukhov, N. Vast, J. Sjakste, V. Tyuterev, N. Mingo, Thermoelectric properties of silicon: Toward an ab initio approach, Phys. Rev. B 83 (2011) 205208.

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FIGURE 1. Electronic relaxation due to electron-phonon coupling in doped silicon calculated ab

initio in Ref. 2. Panels (a) and (b): complex behaviour of the electron-phonon matrix elements

in silicon which was completely neglected in earlier calculations and which is responsible for the

very small contribution of the electron-phonon coupling to the total width of impurity levels.

Panel (c): Schematic representation of shallow impurity levels in Si:P.

FIGURE 2. From Ref. 4. Electronic mobility versus the carrier concentration N for n-doped

silicon at 300 K. The symbols stand for experimental data. Crosses indicate previous

calculations. Solid line represents our calculations using ab initio parameters for electron-

phonon scattering. Dashed line represents our results with electron-phonon parameters fitted

on experiment (from literature).

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Electron-Phonon Interactions in Graphene(*,†)

Aron Pinczuk1,2 1 Dept. of Appl. Physics and Appl. Mathematics, Columbia University, New York, NY, USA

2 Dept. of Physics, Columbia University, New York, USA

The quest for ultra-high quality graphene is driven by expectations of discoveries of novel physics and applications linked to massless Dirac fermions. Numerous experimental probes and theoretical frameworks are currently applied to the study of fermions in graphene. We are concerned here with studies of electron-phonon interactions in graphene structures that are probed by Raman scattering measurements of the long wavelength optical phonon (the G-band).

Low-temperature Raman spectra from single layer graphene with carrier density modulated by voltage applied through a gate have revealed that carrier doping by the electric-field-effect (EFE) has marked impacts on the G-band (long wavelength) optical phonons. In these results the EFE Raman spectra display the interactions of lattice vibrations with the unique carriers (Dirac fermions) that are supported by graphene layers. The changes in the G-band frequency and line-width are extremely sensitive to atomic layer properties such as particle-hole symmetry about the charge-neutral Dirac-point and the marked non-uniformity of graphene layers that, for example, occur when the layer is supported by conventional Si/SiO2 substrates.

Magneto-phonon resonances (MPR’s) belong to a class of electron-phonon interaction effects that are crucially dependent on the removal of disorder. The rather weak interaction of electronic excitations of Dirac fermions in a strong magnetic field with quantized optical lattice vibrations represents a coherent coupling of particle-hole transitions of Dirac fermions in Landau levels with G-band optical phonons. The coupling is resonantly tuned when the strength of the external magnetic field is such that transitions between Landau levels are close to the optical phonon energy. While in this MPR the impact of the coupling can be tuned with magnetic fields, the clear resolution of the predicted anti-crossing of coupled electron-phonon modes requires relatively long lifetimes of the fermion excitations. The observation of clear MPR signatures largely requires that the lifetime broadening and inhomogeneous broadening are both below the strength of the weak electron-phonon coupling.

(*) Collaboration with J. Yan, T.D. Rhone, S. Goler, R. He, V. Pellegrini, M. Han, Y. Zhang, P. Kim, E. Henriksen, and T. Villarson.

(†) Supported by ONR (N000140610138 and Graphene Muri); and NSF (CHE-0641523)

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TUESDAY

Phonons and Electrons in Chalcopyrite Semiconductors

Manuel Cardona,1 R. K. Kremer,1 and R. Lauck1

Aldo H. Romero2

Alfonso Muñoz3 1 Max Planck Institute for Solid State Research, Stuttgart, Germany

2 CINVESTAV, Departamento de Materiales, Unidad Querétaro, Querétaro, Mexico 3 MALTA Consolider Team, Departamento de Física Fundamental II, and Instituto de Materiales

y Nanotecnología, Universidad de La Laguna, La Laguna, Tenerife, Spain

In recent years the phonons and the electron phonon interaction of binary tetrahedral semiconductors have been profusely investigated by ab initio techniques and compared with experimental results. Of particular interest have been binary compounds in which the cations contain semi-core d-electrons (CuCl, CuI, AgI)1 which display anomalies related to the semi-core d-states (3dCuCl, 4dAgI). Here we present the corresponding data and anomalies which have been observed in ternary compounds of chalcopyrite structure (e.g. CuGaS2, AgGaTe2)2. Although no inelastic neutron scattering measurements are available for these materials some information has been obtained for the k = 0 phonons from Raman and IR spectroscopy. Similar data for thermodynamic properties such as (low temperature) specific heat and the thermal expansion will also be presented. Anomalies in the temperature dependence of the electronic gaps, which have been found in the binary chalcogenides, are also hinted at by the results for the ternary compounds with chalcopyrite structure. In view of the large number of atomic combinations possible for these materials (AgGaS2, AgGaSe2, CuGaTe2, …) we believe that a detailed investigation of the whole family of chalcopyrites should provide a clear picture of their properties and lattice anomalies.

1 J. Serrano, Ch. Schweitzer, C. T. Lin, K. Reimann, M. Cardona, and D. Fröhlich, Phys. Rev. B 65, 125110 (2002).

2 A. H. Romero, M. Cardona, R. K. Kremer, R. Lauck, G. Siegle, C. Hoch, A. Muñoz, and A. Schindler, Phys. Rev. B 83, 195208 (2011).

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Title: Computational studies of thermal phonon transport in nanostructured materials

Author: Pawel Keblinski, Materials Science and Engineering Dept. RPI

Abstract: When microstructural features, such as grain size in nanocrystalline materials or fiber

diameter in nanocomposites, becomes comparable with the mean free path of the phonon (heat

carrying thermal wave) the thermal transport is determined by thermal resistance of interfaces

rather than by bulk thermal properties. This can lead to surprising behavior such at lack of

significant thermal conductivity enhancement due to the presence of carbon nanotube fibers

dispersed in fluids or polymers or thermally insulating materials made of carbon nanotubes. On

the other hand, this degrading influence of interfaces on thermal transport can be used to design

ultra-low conductivity solids, which is highly desired for thermoelectric applications. Also, from

the fundamental point of view, heat transfer across interfaces can be used as a probe of

interfacial bonding strength thus providing a novel characterization tool. Using examples from

our molecular level modeling work we will illustrate positive and negative consequences of

interfaces on thermal transport and interfacial characterization.

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Heat Flow in Nanostructures in the Casimir Regime

Humphrey J. Maris1 and Shin-ichiro Tamura2 1 Department of Physics, Brown University, Providence, Rhode Island 02912, USA

2 Hokkaido University, Sapporo 060-8628, Japan

In small structures the phonon mean free path due to phonon-phonon interactions and defect scattering may exceed the sample dimensions even at room temperature. The thermal conductivity then becomes dependent on the size and shape of the sample. In this work we have calculated the heat flow in this regime for several different sample geometries. These geometries include cylindrical rods, hollow cylinders, rods, and plates with different ratios of width to thickness. It is assumed that the scattering at the surface of the sample is diffusive. The calculations have been performed using the experimentally-measured dispersion relations for silicon and gallium arsenide, and thus include quantitatively the effects of both phonon dispersion and phonon focusing. For a plate the heat flow exhibits a logarithmic divergence as the width tends to infinity. As a consequence, it may be possible to make a significant change in the thermal conductivity by bending.

Work supported in part by the Air Force Office of Scientific Research under Contract No. FA9550-08-1-0340.

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Phonon interference and anharmonicity effects in nanoconstrictions

Kimmo Sääskilahti, Jani Oksanen, Riku Linna, and Jukka Tulkki Department of Biomedical Engineering and Computational Science, Aalto University, Finland

Mesoscopic phonon transfer phenomena have lately gained much attention due to the advances in fabrication and characterization of nanostructures and their potential in allowing the tailoring of thermal properties of materials.1 To realistically simulate the effects of phonon interference, phonon-phonon scattering and contact resistance in nanoconstrictions connecting bulk reservoirs, it is necessary to be able to simultaneously account for interference and scattering effects.2 To satisfy this requirement, we perform molecular dynamics (MD) simulations of non-equilibrium thermal conduction through nanoconstrictions.

We report local temperature and heat current profiles for different nanoconstriction geometries and anharmonicities in interatomic potentials. In the ballistic phonon transport regime the local temperature and heat current profiles exhibit clear interference patterns and directionality effects (Fig. 1a) that are suppressed as the scattering increases (Fig. 1b). We study the effect of the constriction geometry on the variations in the interference patterns and their dependence on the anharmonicity as well as the other thermal properties of the nanoconstriction and the contact between the bulk and the constriction. We also compare our results with predictions obtained from Landauer-Büttiker formalism.

Our current MD model is based on the Fermi-Pasta-Ulam (FPU) potential to study the effects of anharmonic interactions in a simple manner.3 The FPU model is expected to be sufficiently refined to generate regular diffusive heat transfer in three dimensions, but we will also examine more realistic interatomic potentials allowing more quantitative simulations. We also include the reservoirs in the MD simulations, thereby making it possible to account in detail for the coupling of the phonons in the nanostructure and in the bulk and to access e.g. the local temperature profiles not only in the junction area, but also in the bulk. Our simulations allow one to understand in detail how e.g. temperature, geometry and the bulk phonons affect heat transfer in the nanostructure.

1D. G. Cahill et al., “Nanoscale thermal transport”, J. Appl. Phys. 93, 793 (2003).

2S. K. Saha and Li Shi, “Molecular dynamics simulation of thermal transport at a nanometer scale constriction in silicon”, J. Appl. Phys. 101, 074304 (2007).

3G. P. Berman and F. M. Izrailev, “The Fermi–Pasta–Ulam problem: Fifty years of progress“, Chaos 15, 015104 (2005).

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FIGURE 1. Kinetic temperature profile between two thermal reservoirs at different temperatures in a two-dimensional Fermi-Pasta-Ulam lattice at (a) low temperature and (b)

higher temperature. The atoms thermalized to the temperatures of the thermal reservoirs are located at the far edges of the upper and lower bulk region (not shown).

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Coherent Second-Sound Generation in Quantum Paraelectrics

Akitoshi Koreeda1, 2, Seishiro Saikan,1 Masaki Takesada3, and Toshirou Yagi3 1 Department of Physics, Tohoku University, Sendai, Japan

2 Japan Science and Technology Agency, PRESTO, Kawaguchi, Japan 3Department of Physics, Hokkaido University, Sapporo, Japan

In solids, it is widely believed that heat can only diffuse. However, if a certain condition is satisfied, heat can propagate as a wave, which is known as the “second sound” in solids. Second sound in solids had been verified only in a few exceptional materials, namely, helium, bismuth, and sodium fluoride (NaF)1. Recently, however, second sound in SrTiO3, which is known as a quantum paraelectric (QPE), has been verified by light-scattering experiment and its careful analysis2. Since the frequency of the second sound in QPE is much higher (>GHz range) than in the conventional cases, it would be a useful excitation for the purposes of temperature modulation/control in micro and nano-structures, if one could generate it as a coherent wave, for example, by controlled irradiation of lasers. In order for a wave of temperature to be defined, the so-called “window condition” must be fulfilled:

, where

are resistive (umklapp + impurity) scattering time, normal scattering time, and second-sound frequency, respectively. In this paper, we first show, from Brillouin scattering experiments, that the window condition is indeed fulfilled in a quantum paraelectric KTaO3. Then, we try to generate “coherent second sound” by impulsive stimulated thermal/Brillouin scattering (ISTS/ISBS) with a picosecond laser.

Figure 1 shows the temperature dependence of the Brillouin linewidth, which is proportional to the hypersonic attenuation, of a TA mode in KTaO3. As shown in the figure, the linewidth scales as , and decreases slowly as even in the very low temperature range. These features are clearly characteristics of the Akhieser damping process, which requires very frequent phonon scattering. Since the thermal conductivity data shows that the resistive scattering is not dominant below 30 K, the Akhieser damping must be governed by the normal scattering. Therefore, we can conclude that the window condition is indeed fulfilled in KTaO3.

Figure 2 shows the measurement principle and the experimental results of ISTS. On cooling from 30K, the decay rate becomes faster according to the temperature dependence of the thermal diffusion. However, there are a few anomalous aspects (i) the rising rate appears to become slower on cooling; (ii) the decay rate does not become faster than it is predicted from the known thermal diffusivity. In Fig.2, we also show the responses calculated by assuming second sound excitation (i.e., not diffusion of heat). It appears that the calculated second-sound response reproduces the observed signal, implying that we are about to generate the coherent second sound. We will discuss the response at even lower temperatures, namely, below 1K, where resistive scattering is much less dominant.

1Ashcroft and Mermin, Solid State Physics (Thomson Learning), chap25 (1976), and refs therein

2A. Koreeda, R. Takano, and S. Saikan, “Second sound in SrTiO3”, Phys. Rev. Lett., 99, 265502 (2007); see also, Phys. Rev. B 80, 165104 (2009), Phys. Rev. B 82, 125103 (2010)

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FIGURE 1. Temperature and frequency dependences of the Brillouin linewidth of a TA mode in KTaO3.

FIGURE 2. Measuring principle of ISTS (left), and temperature dependence of the observed (center) and calculated (right) responses. The calculation assumes only a “wave of heat” rather than “diffusion of

heat”, and uses only the known parameters (no adjustable parameters).

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7

2

4

6

810

8

2

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6

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9

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z)

4 5 6 7

102 3 4 5 6 7

1002 3

Temperature (K)

: 40 GHz

: 20 GHz

KTaO3

TA mode

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Reciprocity in Reflection and Transmission:

what is a “Phonon Diode”?

A. A. Maznev,1 A. G. Every,2 and O. B. Wright3 1 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2 School of Physics, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa

3 Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan

In recent years we have witnessed increased interest in acoustic “diodes” or “isolators”.1-3 We didactically discuss this issue in the context of the broader problem of reciprocity in reflection/transmission (R/T) of waves. The first part of the discussion is centered on a theorem well known in optoelectronics4 but underappreciated in acoustics and phonon physics, stating that the matrix of R/T coefficients for properly normalized amplitudes is symmetric for linear systems that conform to power conservation and time reversibility for wave fields. We show how this theorem applies to mode conversion, diffraction gratings, and reflection/transmission in scattering media and at rough surfaces, and conjecture that R/T reciprocity is preserved even in the presence of linear dissipation. In the second part of the discussion we show that some linear structures proposed for “acoustic diodes” in fact do obey R/T reciprocity, and thus should not strictly be called diodes or isolators. We also review examples of non-linear designs violating reciprocity and discuss whether an efficient acoustic isolator has been demonstrated. Finally, we consider the relationship between acoustic isolators and “thermal diodes”.

1R. Krishnan, S. Shirota, Y. Tanaka, and N. Nishiguchi, “High-efficient acoustic wave rectifier”, Solid State Commun. 144, 194 (2007).

2X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode”, Phys. Rev. Lett. 106, 084301 (2011).

3X. Zhu, X. Zou, B. Liang, and J. Cheng, “One-way mode transmission in one-dimensional phononic crystal plates”, J. Appl. Phys. 108, 124909 (2010).

4H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).

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FIGURE 1. Linear reciprocal structure that appears to work like an isolator or “diode” but is not one.

FIGURE 2. Nonreciprocal nonlinear filter that could be called a “diode”, albeit an inefficient one.

Forward: transmission 100%

Backward: transmission close to zero

mirror

lens

nonlinear medium

linear attenuator

Forward: nonlinear + linear attenaution

nonlinear medium

Backward: linear attenaution only

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Control of ultrafast lattice dynamics and phase transitions in complex oxides through nonlinear phononics

Michael Först 1 Max-Planck Research Department for Structural Dynamics,

Center for Free Electron Laser Science, University of Hamburg, Hamburg, Germany

Optical excitation of a crystal lattice in the mid-infrared wavelength range forces oscillatory atomic motions along the eigenvectors of resonantly driven vibrational modes. About 40 years ago, a nonlinear coupling of such large amplitude infrared-active phonons to Raman-active modes has been predicted and cast in the picture of ionic Raman scattering1. The interaction can be described through the Hamilton operator

, where QIR and QRS are the normal coordinates of the respective modes and A the anharmonic constant2.

The solution of the coupled equations for QIR and QRS shows that the pulsed excitation of the infrared mode leads to a constant force on the Raman mode. For frequencies small compared to the resonantly driven mode, this force induces an abrupt displacement of the atoms from their equilibrium and coherent oscillations around the new positions3. In other words, the coherent nonlinear lattice response can be understood as rectification of the vibrational field of the resonantly driven IR-active mode, which has the well-known analogy of optical rectification in nonlinear optics.

In this talk, I will present experimental evidence of this nonlinear lattice effect in a manganite perovskite crystal excited by intense femtosecond mid-infrared laser pulses. Using coherent detection at near infrared wavelengths, enhancement of the amplitude of a Raman mode is observed when the excitation pulses are tuned in resonance with a specific infrared-active vibration. Furthermore, femtosecond hard X-ray diffraction at a free electron laser has recently allowed for quantifying the atomic displacements associated with the Raman mode and thus the lattice anharmonic constant.

Finally, I will show how this effect can help understanding ultrafast vibrationally driven phase transitions in various complex oxides, where important electronic properties are determined by a subtle interplay between charge, orbital, spin and the lattice degrees of freedom.

1R.F. Wallis and A.A. Maradudin, “Ionic Raman effect II. The first-order ionic Raman effect”, Phys. Rev. B 3, 2063 (1971).

2T.P. Martin and L. Genzel, “Ionic Raman scattering and ionic frequency mixing”, phys. stat. sol. (b) 61, 493 (1974).

3M. Först et al., “Nonlinear phononics as an ultrafast route to lattice control”, Nature Physics 7, 854 (2011).

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Room Temperature Picowatt Resolution Calorimetry

Seid Sadat1, *

, Yi Jie Chua 1, *

, Woochul Lee1, Yashar Ganjeh

1, Katsuo Kurabayashi

1, Edgar

Meyhofer1, Pramod Reddy

1, 2, ‡

1Department of Mechanical Engineering, University of Michigan, Ann Arbor, 48109

2Department of Materials Science, University of Michigan, Ann Arbor, 48109

Email: †

[email protected], ‡[email protected]

Abstract

Experimental techniques capable of picowatt resolution are necessary to enable fundamental

studies of nanoscale conductive and radiative heat transport. Here we demonstrate a

microfabricated device capable of <4 pW resolution, which represents more than an order of

magnitude improvement over state-of-the-art room temperature calorimeters. This significant

enhancement is achieved by the incorporation of two important features into the microdevice.

First, the active area of the device is suspended by thin and long beams making it possible to

achieve a thermal conductance (G) as low as ~600 nW/K. Further, a bimaterial cantilever

thermometer is integrated into the device, which when combined with a phase locked loop

measurement scheme enables temperature measurements with a resolution (∆Tres) of ~4 µK and

a noise floor of ~6.4 µK. The small thermal conductance coupled with the excellent temperature

resolution enable measurement of modulated heat currents (q = G ∆Tres) with a resolution

better than 4 pW.



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Figure 1. (a) Schematic diagram of picowatt calorimeter. The thermal deflection response of the

bimaterial cantilever is calibrated via a 4-probe heater/thermometer, which is integrated into the

suspended region of the device. (b) Scanning electron micrograph of the microfabricated

calorimeter. Active area of the device is a 4040 µm2 region suspended by thin (2 µm) and long

(40 µm) beams. The suspended region is 500 nm thick SiNx into which a 200 µm long and 0.5

µm thick bimaterial temperature sensor with a 125 nm thick Au layer is integrated. The 4-probe

heater/thermometer integrated into the suspended region is 0.6µm wide and 30 nm thick and is

used for heating as well as the calibration of the bimaterial thermometer.

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Ultra High Vacuum Scanning Thermal Microscopy for Nanometer Resolution Quantitative Thermometry

Kyeongtae Kim1, Wonho Jeong1, Woochel Lee1, Pramod Reddy1,2 1 Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

2 Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

Nanometer resolution thermometry is critical for probing and understanding energy dissipation in a variety of electronic and photonic devices1. Nanoscale thermometry also plays an important role in fundamental studies of transport in nanoscale devices. The wide applicability and importance of nanoscale thermometry has spurred the development of various experimental techniques that can be used to obtain information regarding temperature fields with nanometer to micrometer spatial resolution. Among these techniques, scanning thermal microscopy (SThM), an atomic force microscope (AFM) based technique, has succeeded in achieving high spatial resolutions (~50 nm) on dielectric and metal surfaces.

Although impressive progress has been achieved in scanning thermal microscopy, obtaining quantitative information regarding thermal fields using SThM has remained elusive. Further, achieving high spatial resolutions of ~10 nm or lower has also not been possible despite the need for such resolution in detailed thermal studies on nanoscale devices. These apparent limitations of SThM arise due to operation in ambient conditions where local measurement of temperature fields is impeded by parasitic heat transfer between the tip and the sample via conduction through both air and the liquid meniscus that exists at the tip-sample interface. Further, the spatial resolution of SThM in the ambient is limited to ~50 nm due to the large tip-sample contact size (~50 nm) that arises from the liquid film existing at the tip-sample interface.2

In this study, we overcome some of the major limitations of traditional SThM and unambiguously demonstrate the feasibility of performing quantitative nanoscale thermometry using UHV-SThM. Specifically, we demonstrate that it is possible to quantitatively measure temperature fields with excellent thermal (~15 mK) and spatial (~10 nm) resolutions. The improvement in spatial resolution is possible due to the absence of the liquid film at the tip-sample interface. Further, quantitative local temperature measurements can be accomplished because heat transfer is completely dominated by the solid-solid contact (diameter of ~10 nm) between the probe and the sample. Given the high spatial resolution and ability to obtain quantitative thermal measurements UHV-SThM it is expected to be broadly applicable to materials science research and nano engineering.

1A. Majumdar, "SCANNING THERMAL MICROSCOPY," Annual Review of Materials Science 29 (1), 505-585 (1999). 2Li Shi and Arunava Majumdar, "Thermal Transport Mechanisms at Nanoscale Point Contacts," Journal of Heat Transfer 124 (2), 329-337 (2002).

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Heterodyne and Homodyne Pump-Probe techniques to study thin films thermal properties

Gilles Pernot,1,2 Jean-Michel Rampnoux,2 Stefan Dilhaire,2 and Ali Shakouri1,3 1 Baskin School of Engineering, University of California, Santa Cruz, CA, USA

2 Laboratoire Ondes et Matières d'Aquitaine, Université de Bordeaux 1, Bordeaux, France 3 Birk Nanotechnology Center, Purdue University, West Lafayette, IN, USA

Time Domain Thermoreflectance (TDTR) is a well-know Pump-Probe technique widely

employed to study materials properties. The key driving force of TDTR is its ability to obtain the

temporal response of a sample with a picosecond time resolution over few nanoseconds after

being heated up. By fitting the experimental data with a 3D heat spreading Fourier model, one

can extract the thermal properties of thin films and separate thermal interface resistance effects

from the properties of the layer of interest.

The Pump-Probe delay can be obtained in two distinct manners. The most common approach

uses a mechanical translation line (TL). In that case, the maximum delay is limited by the length

of the TL (50cm produces a 3.2ns delay) while the acquisition time is mostly limited by its

speed. To improve the signal-to-noise ratio, the pump beam is modulated at the MHz frequency

and the signal is filtered by a lock-in detection. In 2004, Cahill1 proposed to fit the ratio between

the real and imaginary part of the lock-in output signals. This quantity is less sensitive to the

experimental artifacts introduced by the TL. Nevertheless, Koh et Al showed how the modulation

frequency can be changed to emphasize the sensitivity to one parameter depending on the

structure of the sample. More recently, a newest approach of TDTR has been proposed by

Dilhaire2 et Al where two different laser sources are used to generate Pump and Probe beams. In

this heterodyne method, a slight difference in the laser repetition rates creates a Pump-Probe

delay sliding continuously with time. Assuming a beating frequency of 500Hz, a complete scan

of the full delay (~12ns) between 2 consecutive Pump pulses is obtained in 2ms. In addition to

the suppression of the TL, the optical modulation of the Pump and the lock-in detection are no

longer required.

In this paper, we present a theoretical and experimental comparison of the so-called "homodyne"

and "heterodyne" TDTR techniques and their ability to study nanoscale heat transfer. We

demonstrate the analytical expressions of the signals in both cases. We provide a sensitivity

analysis of the set of parameters that are usually sought. Those results are applied to the

experimental study of a GaAs substrate and a 50nm SiO2 thin layer. The identified top interface

resistance and thermal conductivity, and their associated uncertainties, are compared in both

cases. 1D. G. Cahill, “Analysis of heat flow in layered structures for time-domain thermoreflectance”, Rev. Sci. Instrum. 75, 12 (2004).

2S. Dilhaire et Al, “Heterodyne picosecond thermoreflectance applied to nanoscale thermal metrology”, J. Appl. Phys. 110, 114314 (2011).

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0 2 4 6 8 10 12

(b)

Var

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on o

f re

flec

tivit

y

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urf

ace

(a.u

.)

Pump-Probe Delay (ns)

0.1 11

10

Rat

io (

-Vin/V

out)

Pump-Probe Delay (ns)

(a)

FIGURE 1. Example of the thermoreflectance signals obtained for a 50nm SiO2 thin film by (a) homodyne technique, the ratio between real (Vin) and imaginary (Vout) given by the lock-in

detection is plotted versus the Pump-Probe delay and (b) heterodyne technique, the variation of reflectivity is plotted versus the full Pump-probe delay.

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Phonon Mean Free Path Spectroscopy of Silicon

Jonathan A. Malen1, Shubhaditya Majumdar1, Keith Regner1, Zonghui Su1

1 Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA

The phonon mean free path spectrum has been measured in intrinsic silicon over the temperature range 77-300K using a novel CW laser based technique called Broad-Band Frequency Domain Thermoreflectance (BB-FDTR). Conventional frequency domain thermoreflectance (FDTR) techniques use a modulated CW laser (a.k.a. the pump) to periodically heat a sample, and an unmodulated CW laser (a.k.a. the probe) to sense the temperature response based on the sample’s thermoreflectance. The amplitude and phase of the thermal response, relative to the heating, are used to determine the thermal properties of the underlying sample. Periodic modulation at high frequency f (0.1-20 MHz) confines the

thermal penetration depth Lp=(/f)1/2 (where is thermal diffusivity) so that it is possible to probe thin films and interfaces without being overwhelmed by the substrate properties.

Recent time domain thermoreflectance (TDTR) measurements show that setting an experimental length scale shorter than the phonon mean free path leads to observations of reduced thermal conductivity. Koh et al.1 used Lp in alloys while Minnich et al.2 used the spot diameter dspot in Si at cryogenic temperatures. Both asserted that phonons with mean free paths larger than this dimension did not contribute to the measured thermal conductivity. By changing Lp or dspot and measuring thermal conductivity, they probed the phonon mean free path spectrum. Although these initial measurements are promising, TDTR’s limited frequency range (1-10 MHz) has accessed only a small portion of the phonon mean free path spectrum. BB-FDTR was developed to interrogate more of the phonon mean free path spectrum by imposing a broader range of Lp through an expanded frequency range (0.1-200 MHz). Faster electro-optic modulators and noise rejection through heterodyning the pump and probe lasers, enabled low noise measurements up to 200 MHz.

Figure 1 shows our measurements of thermal conductivity vs. Lp for silicon and SiO2 at 300K. For silicon, the thermal conductivity smoothly varies from 140 W/m-K at the largest Lp, to 60 W/m-K at the smallest Lp. For SiO2 the data is roughly constant at 1.4 W/m-K because our Lp range is still too large to probe very short mean free paths in an amorphous solid. Our data for silicon compares favorably with ab-initio and molecular dynamics predictions from Esfarjani et al.3 and Henry et al.4. This is the first experimental confirmation that 30-40% of the thermal

conductivity in silicon at 300K comes from phonons with mean free paths longer than 1 m. Future measurements of the phonon mean free path spectrum will foster understanding of thermal transport and the effect of nanostructuring on phonon transport in solids.

1 Y. K. Koh and D. G. Cahill, Physical Review B 76, 075207 (2007). 2 A. J. Minnich, J. A. Johnson, A. J. Schmidt, K. Esfarjani, M. S. Dresselhaus, K. A. Nelson, and G. Chen,

Physical Review Letters 107 (2011). 3 K. Esfarjani, G. Chen, and H. T. Stokes, Physical Review B 84 (2011). 4 A. S. Henry and G. Chen, Journal of Computational and Theoretical Nanoscience 5, 141-152 (2008).

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FIGURE 1. Measured thermal conductivity of Si (circles) and SiO2 (squares) vs. thermal penetration depth. Phonons having mean free paths larger than the penetration depth do

not contribute to the observed thermal conductivity. Data is compared with thermal conductivity predictions by Esfarjani et al. [3] and Henry et al. [4].

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Non-diffusive thermal conductivity in GaAs at room temperature

Jeffrey K. Eliason,1 Alexei A. Maznev,1 Jeremy A. Johnson,1 Keith A. Nelson,1 Keivan Esfarjani,2 Tengfei Luo,2 Jivtesh Garg,2 and Gang Chen2

1Dept. of Chemistry, MIT, Cambridge, MA 02139, U.S.A.

2 Dept. of Mechanical Engineering, MIT, Cambridge, MA 02139, U.S.A.

Phonon mediated thermal transport is expected to deviate from the Fourier law at length scales comparable to the phonon mean free path (MFP).1 A conventional estimate yields an average MFP of ~30 nm for GaAs at room temperature.2 We show, contrary to the traditional view, that a significant deviation from the Fourier law in GaAs is observed at distances >1 μm. We employ the transient thermal grating technique in which absorption of two crossed laser pulses leads to a sinusoidal temperature profile whose decay is monitored via diffraction of a probe laser beam. The thermal grating period was changed to vary the length scale of the thermal transport

in the range ~1-10 m. The decay rate of the thermal grating was found to deviate from the expected quadratic dependence on the grating period which provides model-independent evidence of non-diffusive transport. The simplicity of the experimental configuration permits a rigorous analytical treatment of non-diffusive transport using the Boltzmann transport equation.3 Our theoretical analysis takes advantage of first-principles calculations of phonon lifetimes in GaAs based on recently developed ab initio techniques.4 The results indicate that low-frequency phonons with long MFPs play a much larger role in room temperature thermal transport than previously thought. 1Cahill et. al. J. Appl. Phy. 93, 793 (2003) 2J.S. Blakemore. Gallium Arsenide (American Institute of Physics, New York 1987) 3Maznev et al, Phys. Rev. B. 84, 195206 (2011). 4Broido et al. Appl. Phys. Lett. 91, 231922 (2007)

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Analysis of quasiballistic heat transfer

in thermal conductivity spectroscopy

Austin J. Minnich1 1 Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena,

CA, USA

The mean free paths (MFPs) of phonons involved in heat conduction, which largely determine a material’s thermal properties, are mostly unknown in many materials. A recently introduced thermal conductivity spectroscopy technique1 is able to measure MFPs using observations of quasiballistic transport, in which some phonon MFPs are comparable to a characteristic thermal penetration length. The measurements are typically interpreted by assuming that phonons with MFP longer than the penetration length do not contribute to thermal conduction. However, the validity of this model and the proper choice of the penetration length are unclear. Here, we use the Boltzmann transport equation to show that the model is valid, and that accurate measurements of MFPs are possible using suitably chosen values of the penetration length. We determine the proper length and confirm that phonons with MFPs exceeding 1 micron conduct a substantial portion of the heat in typical semiconductors.

1 A. J. Minnich, J. A. Johnson, A. J. Schmidt, K. Esfarjani, M. S. Dresselhaus, K. A. Nelson, and G.

Chen. A thermal conductivity spectroscopy technique to measure phonon mean free paths. Physical Review Letters, 107:095901, Aug 2011.

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Observation of Ballistic Thermal Phonon Transport Across 2D Nanoscale Interfaces

Kathleen Hoogeboom-Pot,1 Damiano Nardi,1 Qing Li,1 Xiaobo Li,2 Ronggui Yang,2 Erik H. Anderson,3 Margaret M. Murnane,1 and Henry C. Kapteyn1

1JILA and Department of Physics, University of Colorado and NIST, Boulder, CO, USA

2Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA

3Center for X-Ray Optics, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Thermal transport is generally depicted in the Fourier description as a diffusive process in which the flow of energy is driven by a temperature gradient. However, experiments have demonstrated that this picture fails for length scales smaller than the mean free path of the energy carriers in a material. The breakdown of conventional Fourier heat conduction has been observed in a variety of nanostructured materials such as thin films,1 superlattices,2 and nanowires,3 as well in silicon wafers.4

In a recent work, we observed size-dependent ballistic thermal transport for heat dissipation from a nanoscale line heat source into the bulk, and reported the first systematic observation and quantitative measurements of the transition from diffusive to ballistic regimes.5 These measurements showed a significant decrease in thermal transport away from one-dimensional metallic nano-gratings into a sapphire substrate compared with Fourier law predictions, for lines of width 80 – 300 nm.

In this work, we study thermal transport from two-dimensional nanoscale hot spots. By monitoring the time-resolved diffraction of coherent extreme ultraviolet light (Figure 1), we observe significantly stronger ballistic contributions to the thermal transport dynamics in two-dimensions compared with lines confined only in one-dimension. Quantitative comparison is possible by finding an effective thermal boundary resistance for hot spots of a given lateral size through comparison with finite-element thermo-mechanical simulations (Figure 2). These experimental studies significantly advance the understanding of heat transport at the nanoscale, as well as having direct implications for the thermal management and reliability of nanoelectronics and photovoltaics, as well as applications in nanomedicine. 1Y. S. Ju and K. E. Goodson, “Phonon scattering in silicon films with thicknesses of order 100 nm”, App. Phys. Lett. 74, 3005 (1999). 2W. S. Capinski et al., “Thermal conductivity measurements of GaAs/AlAs superlattices using a picosecond pump-and-probe technique”, Phys. Rev. B 59, 8105 (1999). 3R. Chen et al., “Thermal conductance of thin silicon nanowires”, Phys. Rev. Lett. 101, 105501 (2008). 4A. J. Minnich et al., “Thermal conductivity spectroscopy technique to measure phonon mean free paths”, Phys. Rev. Lett. 107, 095901 (2001). 5M. E. Siemens et al., “Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams”, Nature Mat. 9, 26 (2010).

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FIGURE 1. Samples consist of 2D metallic gratings on a substrate transparent to the pump light from a 30fs, 800nm pump pulse. The dynamics of thermal transport from the metal heat sources are monitored by the time-resolved diffraction of 30nm EUV probe pulses captured on a CCD.

FIGURE 2. By comparing our dynamic diffraction signal (red) with finite-element thermo-mechanical simulations we extract an effective thermal boundary resistivity for nickel square of varying sizes.

L

P

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Influence of Ballistic Heat Transport in the Extraction of Thermal Interface Resistance through TDTR Analysis

Bjorn Vermeersch1,2*, Gilles Pernot2, and Ali Shakouri1,2* 1 Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA 2 Baskin School of Engineering, University of California, Santa Cruz, CA, USA

* Email: [email protected] , [email protected]

Time domain thermoreflectance (TDTR) is a commonly used pump-probe laser thermal characterisation technique. A thin (50-100nm) aluminium transducer is deposited onto the sample under test to carry out the measurements. The pump beam, modulated at frequency fmod, heats up the sample while the probe beam monitors the instantaneous reflectivity. Lock-in detection at fmod provides in-phase (Vin) and out-of-phase (Vout) components of the thermally

induced signal variations. Fitting of the ratio –Vin()/Vout() as function of the pump-probe delay

to a diffusive heat spreading model then finally provides the thermal boundary conductance rc

-1 of the aluminium/sample interface and the desired thermal conductivity k of the material under study. In 2007, Koh and Cahill observed a remarkable frequency dependence k(fmod) in semiconductor alloys. Reductions of 30-50% in apparent conductivity over the 100kHz-10MHz range were found. In these analyses the interface resistance is fitted on the 10MHz data as the sensitivity for this parameter is largest at higher frequencies. The extracted value is then kept constant throughout identification of the conductivity at other frequencies. In this paper, we investigate how ballistic transport can affect extraction of the interface resistance from TDTR data. Recently, we proposed a model incorporating ballistic effects as an internal heat source (exponentially decaying with the phonon mean free path MFP) for the diffusive channel. A weight factor wB controls the ballistically carried fraction of the heat injected at the aluminium interface. Fitting the simulation data using the procedure described above produces frequency dependent conductivities similar to those experimentally observed. Interestingly however, our results show a systematic underestimation of the interface resistance, in some cases down to 1/3 of the actual value. The effect gets stronger as ballistic effects become relatively more important, i.e. in poorer thermal conductors and at larger MFPs (Fig. 1a), and for increasing fraction of energy transported via ballistic channel wB (Fig. 1b). To assess the impact of rc on the thermal identification process, we have repeated the fitting procedure on the same data while forcing the resistance to the value set in the simulation. It is striking that the majority of the frequency dependence in k(fmod) disappears, even for low nominal conductivities typically found in alloys. This suggests that measurement uncertainties and ballistically induced misestimations of the interface resistance can play a significant role in the analysis of experimental data. We will therefore also investigate other methods suitable for accurate determination of this parameter. The authors wish to acknowledge DOE/EFRC and AFOSR/MURI for supporting this work.



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FIGURE 1. TDTR extracted interface resistance based on ballistic-diffusive model simulations for various materials: (a) influence of ballistic mean free path, (b) influence of weight factor of

ballistic channel. Open symbols/dashed lines from 1D model; full symbols/lines from 3D model.

FIGURE 2. Simulated influence of interface resistance on TDTR identification: (a) rc as fitted, (b) rc forced to actual value. All data simulated with MFP = 100nm, wB = 100%, 1D model.

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Selective Brillouin resonances between extended folded acoustic phonons and non dispersive polaritons modes in

multi-quantum wells

B. Jusserand1, A. Fainstein2, and A. Lemaitre3 1 Institut des Nanosciences de Paris, UPMC-CNRS, 4 Place Jussieu 75005 Paris 2 Instituto Balseiro and Centro Atomico Bariloche, CNEA, Bariloche, Argentina

3 Laboratoire de Photonique et de Nanostructures, CNRS, Route de Nozay, 91460 Marcoussis

We report on Raman/Brillouin scattering at resonance with exciton polaritons in a GaAs/AlAs multi quantum well (MQW) in which the electronic coupling between adjacent wells is negligible. We follow the resonance of the Brillouin line and several folded acoustic phonon lines, both in the Stokes and the Anti-Stokes sides, across the energies of the excitons E1HH1, E2HH2 and E3HH3, in which n = 1, 2 or 3 is the confinement number of the electron and heavy hole constituting the exciton. We observe a very strong dependence of the relative intensities of the different Raman lines with the exciton involved in the resonance. Qualitatively, folded phonons with high folded index and high energies are selectively enhanced when the laser is resonant with an exciton with a confinement number comparable to the folding index. We quantitatively explain this difference based on a form factor describing the wavevector dependent overlap between the envelopes of the folded phonons and the excitons in the quantum wells. This observation demonstrates that the standard photoelastic approach based on a homogeneous photoelastic function in each layer completely fails at strong excitonic resonance. This opens the possibility to monitor the spectrum of phonons interacting with light, for instance for the generation and the detection of coherent acoustic phonons in a pump probe experiment.

Focusing on the most intense and narrow E1HH1 resonance, we have been able to observe a clear variation of the Raman shift and linewidth of several folded modes through the whole resonance and discuss them in terms of polariton scattering. Folded acoustic mode energies exhibit well resolved signatures of the incident and scattered polariton energy dispersion thus giving access to the oscillator strength and damping of the MQW polariton, found to equal 0.3 meV. Significant variations of the Raman line widths are observed which confirms this value of the damping, which appears to be significantly smaller than the photoluminescence excitation linewidth for the same exciton, reaching 1 meV. A polariton description of the scattering events provides an excellent quantitative description of the energy and damping dispersions. Such observations have never been reported in the case of MQWs in which the absence of spatial dispersion along the superlattice axis allows a very detailed description of the Raman scattering process. These results open the route to a direct determination of the polariton dispersion and damping in resonant photonic structures, in particular in photonic Bragg superlattices in which the polariton gap and the folded photon gap strongly interfere.

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Surface-Enhanced Raman Spectroscopy Study of Single Stranded DNA Sequences on Silver Nanorod Array

Kimber L. Brenneman,1 Xenia Meshik,1 Ke Xu2, Justin Abell,4 Yiping Zhao,5 Mitra Dutta2,3, and Michael A. Stroscio1,2,3

1 Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA 2 Department of Electrical & Computer Engineering, University of Illinois at Chicago, Chicago, IL, USA

3 Department of Physics, University of Illinois at Chicago, Chicago, IL, USA 4Nanoscale Science and Engineering Center, Department of Biological and Agricultural Engineering, The

University of Georgia, Athens, GA, USA 5 Nanoscale Science and Engineering Center, Department of Physics and Astronomy, The University of

Georgia, Athens, GA, USA

Surface-Enhanced Raman Spectroscopy (SERS) was used to study the spectral signature of single stranded DNA molecules. The SERS substrate is an array of silver nanorods (AgNR) that was fabricated using oblique angle deposition (OAD). These substrates have shown SERS enhancement factors of 108 when compared with regular Raman spectroscopy1. This enhancement is critical for the analysis of DNA Raman signatures otherwise the signals are often too weak.

The first sample was a 15 base sequence known as Thrombin Binding Aptamer (TBA) because of its ability to bind to the protein thrombin. It is also capable of interacting with ions such as potassium, mercury, and lead. The sequence is 5’-GGTTGGTGTGGTTGG-3’. The second sample was a sequence of 15 thymine bases. Both samples were dissolved in Milli-Q water at a

concentration of 10 M. Then 20 L of sample was pipette onto the SERS substrate and allowed to incubate overnight, allowing the DNA to adsorb to the silver surface. Next the samples were rinsed using Milli-Q water and dried with compressed air. The two sequences were analyzed using a Renishaw micro-Raman system with an Ar+ -ion laser (514.5 nm wavelength). The power density for each sample was 13,000 W/cm2 and the acquisition time was 30 seconds.

The spectra contained many prominent lines for both samples. For TBA there are bands associated with ring breathing for thymine at 611, 714, 1007, 1187, 1241, and 1399 cm-1 2. The poly-T spectrum also shows thymine ring breathing modes at 610, 777, 1007, 1184, 1230, and 1399 cm-1. The sharp peak at 805 cm-1 is attributed to the guanine bases in the TBA3 and is not seen in the poly-thymine sample.

1S. B. Chaney, S. Shanmukh, R. A. Dluhy, and Y. P. Zhao, “Aligned silver nanorod arrays produce high sensitivity surface-enhanced Raman spectroscopy substrates”, Appl. Phys. Lett. 87, 031908 (2005).

2Z. Shang, D. N. Ting, Y. T. Wong, Y. C. Tan, B. Ying, and Y. Mo, “A study of DFT and surface enhanced Raman scattering in silver colloids for thymine”, J. Mol. Struct. 826, 64-67 (2007).

3C. Otto, T. J. J. Van Den Tweel, F. F. M. de Mul, and J. Greve, “Surface-enhanced Raman spectroscopy of DNA bases”, J. Raman Spec. 17, 289–298 (1986).

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FIGURE 1. microRaman spectrum of TBA on SERS substrate.

FIGURE 2. microRaman spectrum of Poly-thymine on SERS substrate.

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Raman phonons in the FeSe-based superconductor AxFe2-ySe2

Qingming Zhang

Department of Physics, Renmin University, Beijing 100872, P.R. China

Newly discovered FeSe-based superconductors are unique among iron-based superconducting families because they have no poisonous element and show tremendous potential in raising superconducting transition temperature. In this talk I will discuss Raman phonons and related issues in these superconductors.

In K0.8Fe1.6Se2 crystal (Tc~31 K) we observe over 13 Raman modes, far more than we expect for an ideal BaFe2As2-like structure. Raman spectra obtained by rotating polarization and crystal

allow us to deduce a novel Fe-vacancy-ordered structure, in good agreement with neutron measurements. We further make first-principles calculations and assign the observed modes. More interestingly, it seems that phonons are involved in two-magnon process in this material. Four small but clear features are superposed on the main two-magnon peak, with almost an identical separation. We discuss this in term of spin wave and phonon-assisted magnon excitation.

Furthermore, we observe a new superconducting transition at 44K in AxFe2-ySe2 crystals. By combining Raman scattering with scanning electron microscopy and crystal X-ray diffraction, we identify the new superconducting phase as a nearly-ideal 122 structure but with an unexpected large c-axis.

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Monitoring polymer network formation by probing optical and acoustic phonons concurrently

Michael Aldridge,1 John Kieffer1 1 Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

Polymer network formation affects both molecular vibrations associated with specific bonding configurations, and the ability of the extended structure to sustain the propagation of acoustic phonons. Using concurrent Brillouin (BLS) and Raman light scattering (RLS) we have investigated the structural evolution in different types of thermoset polymers, in-situ, during the curing process. RLS allows us to monitor changes in the chemical structure of the molecular groups as they are incorporated into the greater network structure. Specifically changes in the Raman spectra are used to measure the degree of cure of a system, and to determine to what extent different reactive sites have transitioned in the cure process. BLS allows us to measure the complex mechanical modulus at the molecular scale, as the structure evolves from a monomeric liquid to a continuous three-dimension network, by probing the propagation and attenuation of acoustic phonons. By carrying out these two light scattering measurements concurrently, we can determine the mechanical properties of the network as a function of the chemical degree of cure.

We have applied this approach to study the cure of two types of thermoset systems,

dicyclopentadiene (DCPD) and epoxy. The Grubbs’s catalyzed chain growth polymerization of

DCPD involves two reactive sites, presumed to have different reactivity, which results in an

initial prevalence of chain growth compared to cross-linking. Upon every reaction, the catalyst

relocates to the free end of the newly incorporated monomer, so that the final network

geometry delineates the catalyst progression through space. Both reactive sites have distinct

Raman signatures, allowing us to track linear- and cross-links during polymerization (Figure 1).

For this system, the relationship between elastic modulus and the degree of cure is

independent of catalyst concentration (Figure 2). Conversely, in the step growth polymerization

of an epoxy/amine system both the amine concentration and the temperature at which the

reaction takes place affect the relationship between modulus and degree of cure. The higher

the temperature, the lower the elastic modulus at intermediate degrees of cure, while the

modulus of the fully reacted system remains independent of temperature. Deviations in the

amine concentration below the ideal stoichiometric composition result in a reduction of the

final elastic modulus, while amine concentrations in excess of the stoichiometric ideal have no

significant effect on the final modulus. The concurrent use of RLS and BLS provides a unique

means for relating the mechanical properties of a polymer network to its chemical state.

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FIGURE 1. Concentration of DCPD reactive species during cure. Q0, Q1, and Q2 designate monomers with zero, one, and both of their sites reacted respectively.

FIGURE 2. Longitudinal modulus of DCPD as a function of the degree of cure for different catalyst concentrations.

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Phonons and Excitons in Pentacene Monolayers

Rui He

Physics Department, University of Northern Iowa, Cedar Falls, IA, USA

Organic semiconductors are of great current interest for applications in electronic devices that require large area coverage, low cost, compatibility with flexible substrates, ease of processing, etc. Pentacene is a benchmark material in the large organic semiconductor family because of its high mobility in organic thin film devices. By probing highly uniform pentacene films grown on a compliant polymeric substrate (see Fig. 1) at low temperatures, we demonstrated that optical emission and resonance Raman scattering are powerful venues to characterize organic ultrathin layers with thicknesses reaching the sub-monolayer limit.

The highly uniform pentacene monolayers display a sharp and intense free exciton (FE) luminescence band. The intensity of the FE luminescence band increases with the number of pentacene layers N.1 For N less than 5, the intensity of the FE optical emission band is proportional to N2. This quadratic increase of luminescence intensity is interpreted as evidence that the probabilities for optical absorption and emission processes are each proportional to the number of layers N in the few monolayer limit.

The sharp and intense FE luminescence band offers giant resonance enhancements of Raman scattering intensities by pentacene vibrations, which enables the first observation of low-lying lattice modes (below 100 cm-1) from pentacene single monolayer films.2 Raman spectra of low-lying lattice modes display major changes when the thickness of the film changes from 1 to 2 monolayers, revealing that a phase akin to a thin film phase of pentacene already emerges in films of only 2 monolayers.

The Raman intensities from a totally symmetric intra-molecular vibrational mode display resonance enhancement double peaks when incident or scattered photon energies overlap the FE optical emission. The two resonances are of about equal strength, which suggests that Franck–Condon overlap integrals for the respective vibronic transitions have the same magnitude.3 The interference between scattering amplitudes in the Raman resonance reveals quantum coherence of the symmetry-split states (Davydov doublet) of the lowest intrinsic singlet exciton in pentacene monolayers.

*In collaboration with Nancy G. Tassi (Dupont), Graciela B. Blanchet (Nanoterra, Cambridge, MA), and Aron Pinczuk (Columbia University). Supported by NSF and NYSTAR.

1Rui He, Nancy G. Tassi, Graciela B. Blanchet, and Aron Pinczuk, “Intense photoluminescence from pentacene monolayers,” Appl. Phys. Lett. 96, 263303 (2010).

2Rui He, Nancy G. Tassi, Graciela B. Blanchet, and Aron Pinczuk, “Low-lying lattice modes of highly uniform pentacene monolayers,” Appl. Phys. Lett. 94, 223310 (2009).

3Rui He, Nancy G. Tassi, Graciela B. Blanchet, and Aron Pinczuk, “Franck-Condon processes in pentacene monolayers revealed in resonance Raman scattering,” Phys. Rev. B 83, 115452 (2011).

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FIGURE 1. (a) Schematic drawing of the configuration of a pentacene monolayer on polymeric substrate poly α-methylstyrene (PAMS). The drawing is not to scale. (b) AFM image of a

pentacene submonolayer film grown on PAMS with 70% coverage. (c) and (d) AFM image of pentacene 1ML and 2ML on PAMS, respectively.

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Micro-Raman study of GaAs nanowires

Peng WANG1,*, Fauzia JABEEN2, Jean Christophe HARMAND2, and Bernard JUSSERAND1

1 Institut des Nanosciences de Paris, CNRS/UPMC, 4 Place Jussieu, 75005 Paris, France

2 CNRS-LPN, Route de Nozay, 91460 Marcoussis, France

Semiconductor nanowires (NWs) open a route for the conception and fabrication of electronic

and optoelectronic devices based on the confinement of electrons, photons, and phonons in

nanostructured materials. We have successfully grown GaAs NWs by MBE method with Au or

Ga as catalyst. Compared to zinc blende (ZB) crystalline structures, the wurtzite (WZ) is not

stable in the bulk form and the phonon dispersion and the near band gap electronic structure in

WZ NWs are still not well known. In this work, we compare the results of Raman scattering

studies performed on both ZB and WZ GaAs NWs with similar diameters.

We developed a Micro-Raman system to make it suitable for a systematic Raman spectroscopy

study of single GaAs nanowire. We use a titanium sapphire laser to make the resonant Raman

study as it provides intense signal at low power and gives access to information on the near

band gap electronic structure in GaAs NWs. In our experiment, we observed TO and LO phonon

modes in both WZ and ZB NWs. The LO is forbidden in normal conditions and it can only be

observed around the band gap. We changed incident laser wavelength and found that the

forbidden LO of NWs with ZB structure is resonant at 1.46 eV which is close the ZB band gap.

For WZ GaAs NWs, the forbidden LO mode is resonant at a new energy (1.56 eV). According to

ab initio calculations of the band structure of WZ GaAs (1), this compound should display a very

unusual conduction band configuration. Due to the band folding, additional zone center

transitions are expected to appear, coming from the L point in the ZB dispersion. In this work,

we assign the new resonance observed in the WZ NWs at 1.56 eV to the transition between the

Г7 conduction state and the highest valence state, while the lowest Г8 minimum does not

contribute to the resonant Raman signal. In order to determine the selection rules in NWs and

to get more information about the shape effect and crystal structure of the GaAs NWs, we

carried out a polarization Raman study. We found that the calculated angular variation of the

intensity of TO and LO modes based on ZB or WZ bulk materials is quite different from the

experimental observations. We demonstrate that because of the small diameter (70 nm) of the

NWs studied in our experiment and of the very large aspect ratio (~100), it is necessary to

consider the dielectric anisotropy effect due to the dielectric constant mismatch between the

nanowire and its surroundings. Based on simulations of the electromagnetic distribution in and

around the wire, we could quantitatively describe the angular variation of the intensities.

(1). A. De and C. E. Pryor, Phys. Rev. B 81, 155210 (2011).

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Significant Thermal Conductivity Reduction of Defective Bismuth Telluride

Konstantinos Termentzidis, Alex Pokropivny, Yuri Chumakov, Yann Chalopin and Sebastian Volz

EM2C, CNRS UP288, Ecole Centrale Paris, Chatenay-Malabry, France

The Bi2Te3 and its alloys are of the best thermoelectric materials in the temperature range of 200-400K1, while nanostrucured Bi2Te3 thin films or superlattices with Sb or Ti doping have even better figure of merits than the bulk material. The aim of this study is to decrease the thermal conductivity with the structural engineering of Bismuth Telluride compounds to obtain an enhanced figure of merit due to the charge carrier and phonon confinements2,3. For this we created vacancy defects of the adequate stoichiometry compound (Bi2Te3) and then superlattices having the most interesting stoichiometries with vacancies for further reducing thermal conductivity.

The optimization of materials under investigation are performed with molecular dynamics and first-principle approaches. The prediction of the thermal conductivity is made by NEMD method, using the code LAMMPS. We used the two-body interatomic Morse potential form developed by Qiu and Ruan4 for the correct description of its thermal properties. This potential contains two terms, i.e. a short-range interaction term and a Coulombic term for the description of the long-range electrostatic interactions.

Our results for bulk Bi2Te3 show a very good agreement with the available experimental data. After this first validation state, we created vacancy defects for both Bi atoms and Te atoms as reported in figure-1. The thermal conductivity versus the vacancy defect is plotted in figure-2, where one can see that the thermal conductivity can be reduced by 63,5% for 5% of Bi vacancies or even by 71,1% for 4% of Te vacancies. This important reduction of the lattice thermal transport is a promising way to increase the figure of merit. Finally Bi2Te3/Bi35Te60, Bi2Te3/Bi40Te56 and Bi35Te60/Bi40Te56 superlattices are created. The preliminarily results agree with the expected trend. The first-principle calculations revealed strong dependence of electrical properties function the type of defects. Bismuth antisite and Bi-vacancy compounds became p-type conductors, while Tellurium antisite and Te-vacancy compounds became n-type conductors

1 Y. Tong et al, “Molecular dynamics study on the thermo-mechanical properties of bismuth telluride bulk”, Comp. Mat. Science 48, 343 (2010)

2 M.Dresselhaus et al, “Low dimensional Thermoelectric Materials”, Phys. Solid State 41, 679 (1999) 3 A. Balandin and K.L. Wang, “Effect of phonon confinement on the thermoelectric figure of merit of quantum wells”, J. Appl. Phys. 84, 6149 (1998) 4 B. Qiu and X. Ruan, “Molecular dynamics simulations of lattice thermal conductivity of bismuth telluride using two-body interatomic potentials”, Phys. Rev. B 80, 165203 (2009)

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FIGURE 1. Adequate stoichiometry compound Bi2Te3 (left) and 5% Bi vacancy defect (right).

FIGURE 2. Thermal conductivity of several defected and the adequate stoichiometry compounds of Bismuth Telluride function the vacancy defect.

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Phonon Anharmonicity in Thermoelectric Materials

Olivier Delaire1 1 Materials Science and Technology Division, Oak Ridge National Laboratory, TN, USA

Thermoelectric materials are of broad interest for energy applications, as they can convert waste heat into electricity, and provide solid-state refrigeration. Achieving high thermoelectric

conversion efficiency requires limiting the lattice thermal conductivity, lat, through the disruption of phonon propagation. A detailed understanding of phonon dispersions and mean-free-paths is critical in microscopic theories of thermal conductivity, and suggests avenues to improve thermoelectric performance. Our inelastic neutron scattering experiments map phonon excitations throughout reciprocal space, and reveal broadenings associated with anharmonic effects. Electronic structure calculations, including effects of finite temperatures, are used to analyze the experimental results. We investigated the phonon dispersions and linewidths in thermoelectric materials for both refrigeration (FeSi) and waste heat recovery (PbTe, (Ag,Sb)Te), and identified strong effects of electron-phonon interaction and phonon anharmonicity.

Our investigations of the phonons and electronic structure in FeSi showed that an adiabatic electron-phonon coupling leads to pronounced anomalies in the temperature dependence of both phonons and electron states1. The mechanism is general and could affect a broad class of materials. The electron-phonon coupling also represents an important source of

phonon scattering and carrier doping strongly suppresses lat in this material2. Our measurements of PbTe revealed a strong anharmonicity of the ferroelectric

transverse-optic mode, which couples to acoustic phonons, leading to an anomalously low thermal conductivity for a rocksalt compound3. This strong coupling between the transverse-optic and longitudinal acoustic modes in PbTe was reproduced in first-principles anharmonic lattice dynamics calculations4. We have also performed systematic investigations of phonon dispersions and linewidths in rocksalt (Ag,Sb)Te , which provide insights into the microscopic

scattering mechanisms responsible for the extremely low lat of this material.

1 O. Delaire, K. Marty, M. B. Stone, P. R. C. Kent, M. S. Lucas, D. L. Abernathy, D. Mandrus, and B. C. Sales, Phonon softening and metallization of a narrow-gap semiconductor by thermal disorder, Proc. Nat. Acad. Sci. USA 108, 4725 (2011). 2 B. C. Sales, O. Delaire, M. A. McGuire, and A. F. May, “Thermoelectric properties of FeSi and Related Alloys: Evidence for Strong Electron-Phonon Coupling”, Phys. Rev. B 83, 125209 (2011). 3 O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M.-H. Du, D. J. Singh, A. Podlesnyak, G. Ehlers, M. D. Lumsden, and B. C. Sales, Giant Anharmonic Phonon Scattering in PbTe, Nature Materials 10, 614 (2011). 4 T. Shiga, J. Shiomi, J. Ma, O. Delaire, T. Radzynski, A. Lusakowski, K. Esfarjani, G. Chang, Phys. Rev. B accepted. O.D. acknowledges funding from the US DOE, Office of Basic Energy Sciences as part of the S3TEC Energy Frontier Research Center, DOE DE-SC0001299 and from the Materials Science and Engineering Division,

US DOE.

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Reduced Thermal Conductivity in SiGe Alloy-based Superlattices for Thermoelectric Applications

Zlatan Aksamija and Irena Knezevic

Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI, USA

Silicon-germanium (SiGe)1 and Si/Si1-xGex superlattices2 show promise for application as efficient thermoelectrics because of their low thermal conductivity, below that of bulk Si1-xGex alloys (Fig. 1). Addition of quantum dots at the interface between layers of the SL has also been shown to decrease thermal conductivity3,4. Lattice thermal conductivity in superlattices is dominated by scattering from the rough interfaces between layers, even at room temperature5. Therefore, interface properties, such as roughness, orientation, and composition, are expected to play a significant role in thermal transport and they offer additional degrees of freedom to control the thermal conductivity in semiconductor nanostructures based on superlattices.

We demonstrate the sensitivity of the lattice thermal conductivity in SLs to the interface properties, based on solving the phonon Boltzmann transport equation under the relaxation time approximation. Previous calculations relied on treating the interface scattering with an empirical specularity parameter, which is then adjusted to fit measured data. In this work, in order to accurately treat phonon scattering from a series of rough interfaces with a given rms roughness height (Δ), we employ a momentum-dependent specularity parameter p(q) that is the fraction of specular reflections to the total number of reflections from a rough boundary (0<p(q)<1). p(q) is obtained from the momentum-dependent specularity parameter for a single interface6 p(q)=exp(-4π2Δ2q2cos2θ) by averaging this single-interface specularity parameter over the distribution of many uncorrelated interfaces present between the layers of the superlattice.

Diffuse boundary scattering gives a phonon a lifetime that is proportional to the smallest distance between the boundaries; in the case of superlattices, this is the thickness L of each layer. In the calculation of the total phonon lifetime, surface roughness, Umklapp phonon-phonon, and isotope scattering have been considered. The expressions for τphonon and τisotope were taken from Ref. 6. The full thermal conductivity tensor καβ is computed for each layer of the superlattice as a sum over all phonon momenta and branches. The two alternating layers of the superlattice are combined in series for cross-plane transport through the SL, and in parallel for in-plane transport along the plane of the interfaces. Results for 4 nm SiGe SLs (Fig. 2) show a strong anisotropy of thermal conductivity due to the directional dependence of the phonon velocity and boundary scattering 7. The computed values of κ show excellent agreement with the measurements on Si1-xGex SLs 2 (Fig. 3 and Fig. 4) at both high and low temperatures.

1. Lee, S.-M., Cahill, D. G. & Venkatasubramanian, R. Thermal conductivity of Si–Ge superlattices. Appl. Phys. Lett.

70, 2957-2959 (1997).

2. Huxtable, S. T. et al. Thermal conductivity of Si/SiGe and SiGe/SiGe superlattices. Appl. Phys. Lett. 80, 1737-

1739 (2002).

3. Lee, M. L. & Venkatasubramanian, R. Effect of nanodot areal density and period on thermal conductivity in

SiGe/Si nanodot superlattices. Appl. Phys. Lett. 92, 053112 (2008).

4. Pernot, G. et al. Precise control of thermal conductivity at the nanoscale through individual phonon-scattering

barriers. Nat. Mater. 9, 491–495 (2010).

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5. Chen, G. Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys.

Rev. B 57, 14958–14973 (1998).

6. Aksamija, Z. & Knezevic, I. Anisotropy and boundary scattering in the lattice thermal conductivity of silicon

nanomembranes. Phys. Rev. B 82, 045319 (2010).

7. Liu, W. L., Borca-Tasciuc, T., Chen, G., Liu, J. L. & Wang, K. L. Anisotropic Thermal Conductivity of Ge Quantum-

Dot and Symmetrically Strained Si/Ge Superlattices. Journal of Nanoscience and Nanotechnology 1, 39-42(4)

(2001).

FIGURE 1. Thermal conductivity of bulk SiGe alloys, showing a strong variation of thermal

conductivity with the germanium proportion x.

FIGURE 2. Thermal conductivity of a 9 nm period Si/Ge superlattice in the cross-plane direction (blue diamonds), and a 4 nm period Si/Ge superlattice in both the in-plane (black circles) and cross-plane directions (red squares).

Figure 3. Thermal conductivity of a 3.5 um Si0.9Ge0.1 alloy film (black) and a 15 nm period thickness Si/Si0.4Ge0.6 alloy superlattice (red). Dashed lines indicate lattice thermal conductivity, while solid lines include the electronic contribution.

Figure 4. Cross-plane thermal conductivity of Si1-xGex/Si1-yGey superlattices showing strong decrease due to combined effect of alloying and interface scattering.

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Huge nonlinear elastic properties at the volume phase transition of aqueous poly(N-isopropylacrylamide) solutions

as revealed by Brillouin spectroscopy

Jan-Kristian Krüger,1 Ulrich Müller,1 Martine Philipp2 and Peter Müller-Buschbaum2

1 Physics of condensed matter and advanced Materials, University of Luxembourg, 162a avenue de la Faiencerie, 1511 Luxembourg, Luxembourg

2 Technische Universität München, Physik-Department, Lehrstuhl für Funktionelle Materialien, D-85748 Garching, Germany

The combination of hypersonic and density measurements permits to elucidate the influence of elastic nonlinearities at the volume phase transition of aqueous solutions of the thermo-responsive polymer poly(N-isopropylacrylamide), abbreviated PNIPAM1. This volume phase transition is based on a coil-to-globule transition of the polymer chains leading to phase separation. Although this kind of transition is known for many years, many of its fundamental aspects are still not understood. The strong changes of mass density and elastic properties at the transition bear a certain resemblance to ferroelastic phase transitions where especially the non-linear elastic properties are believed to play a crucial role2. Knowledge about the temperature-dependent behavior of the mass density, obtained by a highly precise densitometer, and of the elastic properties, obtained by high-performance Brillouin spectroscopy, allows for the determination of third-order elastic constants3,4. The isostructural character of the volume phase transition of PNIPAM opens up the possibility to study third-order elastic constants across a ferroelastic-like phase transition for the very first time. As can be seen in figure 1, below and well above the isostructural phase transition the combined third-order elastic constant c111 + 2c112 is dominated by that of water. The onset of the phase transition coincides with the disappearance of elastic nonlinearity followed by a very strong peak-like anomaly. The peak reaches down to -1400 GPa indicating an enormous stress softening.

1 S. Hirotsu, "Static and time-dependent properties of polymer gels around the volume phase transition", Phase Transitions 47, 183 (1994).

2 E. K. H. Salje, Phase transitions in ferroelastic and co-elastic crystals (CUP, Cambridge, 1990).

3 B. A. Auld, Acoustic fields and waves in solids (John Wiley, New York, 1973). 4 Thermphysical properties of polymers; Vol. XVIII, edited by G. Grimvall (North-Holland,

Amsterdam, 1986).

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24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

-1250

-1000

-750

-500

-250

0

c

111 +

2 c

112 [

GP

a]

T [°C]

PNIPAM concentration

0 w%

3 w%

6 w%

FIGURE 1. Combined third-order elastic constant c111 + 2c112 around the volume phase transition of aqueous PNIPAM solutions of different concentrations.

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Volume phase transition, demixing and sedimentation in an aqueous solution of poly(N-isopropylacrylamide) as evidenced

by scanning Brillouin microscopy

Ulrich Müller,1 Jan-Kristian Krüger,1 Martine Philipp2 and Peter Müller-Buschbaum2

1 Physics of condensed matter and advanced Materials, University of Luxembourg, 162a avenue de la Faiencerie, 1511 Luxembourg, Luxembourg

2 Technische Universität München, Physik-Department, Lehrstuhl für Funktionelle Materialien, D-85748 Garching, Germany

The volume phase transition of aqueous poly(N-isopropylacrylamide) (PNIPAM) solutions and gels has been studied for many years1. It is a coil-to-globule transition of the lower critical solution temperature (LCST) type. The microscopic mechanism responsible for the transition is related to intermolecular and intramolecular interactions, especially hydrogen bonds2,3. Above the transition temperature Tc the globules tend to aggregate leading to strong light scattering and sedimentation, at least for higher concentrations of PNIPAM. Scanning Brillouin microscopy4 was employed to study the actual phase transition, the demixing and the sedimentation process. Figure 1 shows the frequencies of the measured longitudinal acoustic phonons around the volume phase transition and compares them with those of pure water. At Tc=29.6 °C the phonon frequency shows a comparably strong decrease and eventually merges with that of water. At T=33.8 °C a second longitudinally polarized phonon appears in the Brillouin spectra at much higher frequency representing the demixed polymer-rich aggregates. Because their size easily exceeds one micrometer, they are also subjected to gravity and therefore sediment. The sedimentation can be visualized by cooling the sample down again below Tc where the one remaining longitudinal phonon shows a frequency evolution which is indicative for the temporally varying spatial distribution of PNIPAM. Figure 2 nicely demonstrates the re-equilibration of the PNIPAM concentration throughout the sample with time.

1 S. Hirotsu,"STATIC AND TIME-DEPENDENT PROPERTIES OF POLYMER GELS AROUND THE VOLUME PHASE-TRANSITION", Phase Transitions 47, 183-240 (1994).

2 H. J. Lai and P. Y. Wu,"A infrared spectroscopic study on the mechanism of temperature-induced phase transition of concentrated aqueous solutions of poly(N-isopropylacrylamide) and N-isopropylpropionamide", Polymer 51, 1404-1412 (2010).

3 B. J. Sun, Y. N. Lin, P. Y. Wu, and H. W. Siesler,"A FTIR and 2D-IR spectroscopic study on the microdynamics phase separation mechanism of the poly(N-isopropylacrylamide) aqueous solution", Macromolecules 41, 1512-1520 (2008).

4 J.-K. Krüger, U. Müller, R. Bactavatchalou, D. Liebschner, M. Sander, W. Possart, C. Wehlack, J. Baller, and D. Rouxel,"Mechanical Interphases in Epoxies as seen by Nondestructive High-Performance Brillouin Microscopy ", in Adhesion: Current Research and Applications, edited by W. Possart ( Wiley-VCH, Weinheim, 2005), p. 125-142.

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24 26 28 30 32 34 36 38 40 42 44 46 48 507.8

8.0

8.2

8.4

8.6

8.8

9.0

13.5

14.0

14.5

20 w%

H2O

ph

on

on

fre

qu

en

cy

(G

Hz)

temperature (°C)

FIGURE 1. Phonon frequencies measured around the volume phase transition of PNIPAM.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 158.4

8.6

8.8

9.0

9.2

9.4

9.6

9.8

ca. 12 w%

20 w%, 25°C

4.5h

31h

100h

ph

on

on

fre

qu

nc

y [

GH

z]

position [mm]

ca. 30 w%

bottom top

FIGURE 2. Phonon frequency as a function of position and time after cooling the phase-separated state down below Tc.

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TUESDAY

The effect of intra-molecular relaxations on the damping of longitudinal and transverse phonons in glass forming systems

G. Meier1, H. Kriegs1, A. Patkowski2, J. Gapinski2 1 Forschungszentrum Jülich, Institute of Complex Systems 3, 52425 Jülich, Germany

2 Faculty of Physics, A. Mickiewicz University, 61-614 Poznan, Poland

Theories describing the propagation and damping of longitudinal and transverse phonons in terms of the structural relaxation, i.e. translational motion of the molecules and translational-rotational coupling, have been developed, improved and tested experimentally [1]. Usually they did not take into account the coupling of intra-molecular relaxations to the structural relaxation. For liquids which consist of molecules having internal relaxation, a theoretical model was developed in the limit of weak coupling of intra-molecular relaxations to the translational degrees of freedom [2].To estimate the contribution of internal relaxations to the damping of the Brillouin lines it is necessary to separate this contribution from that of structural relaxation.

This can be achieved by studying the pressure dependence of the Brillouin width B [3], since

the pressure dependence of the structural relaxation times dlogs/dP5x10-3 bar-1 [4] is much

stronger than that of the internal relaxation time dlogint/dP2-5x10-4 bar-1 [5]. Usually, B is decreasing with increasing pressure, reaching a high pressure plateau value. In order to obtain

this value 0, the data was analyzed using the formula:

00

expp

B

D PP T A T

P P

where 0(T) is the residual width at Tg, due to internal relaxations, A(T) is the amplitude, DP is a fit parameter identical for all temperatures and P0 is the parameter characterizing the pressure

dependence of the structural (-) relaxation. In the temperature dependent studies on both polymers and simple glass formers at ambient pressure, systems with strong internal relaxations exhibited much larger residual broadening at Tg than systems with weaker internal processes. It is also shown that the pressure dependent measurements allow for the separation of the contributions due to intra-molecular and structural relaxations to the polarized Brillouin line widths and the damping of the longitudinal phonons likewise unexpectedly for the transverse phonons. 1A. Aouadi, C. Dreyfus, M. Massot, R.M. Pick, T. Berger, W. Steffen, A. Patkowski, C. Alba-Simonescu, J. Chem. Phys. 112, 9860 (2000)

2R. Zwanzig, J. Chem. Phys. 43, 714 (1965)

3A. Patkowski, J. Gapinski, G. Meier, H. Kriegs, J. Chem. Phys. 126, 014508 (2007)

4H. Kriegs, J. Gapinski, G. Meier, M. Paluch, S. Pwalus, A. Patkowski, J. Chem. Phys. 124,104901 (2006)

5G. Fytas, G. Meier, A. Patkowski, Th. Dorfmüller, Coll. Polym. Sci. 260, 949 (1982)

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TUESDAY

Dynamical origin of anomalous temperature hardening of elastic modulus in vitreous silica

M. Foret1, B. Rufflé1, R. Vacher1, S. Ayrinhac1,2, A. Polian2 1 Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095 Montpellier, France

2 Université Pierre et Marie Curie - Paris 6, Institut de Minéralogie et de Physique des Milieux Condensés CNRS UMR 7590,4 place Jussieu, F-75252 Paris Cedex 05, France

We report on high-resolution Brillouin scattering experiments performed under hydrostatic pressures ranging from 0 to 10 GPa in vitreous silica. The hypersound-attenuation coefficient exhibits a sharp maximum located at 2 GPa, which appears to coincide with the well-known minimum in sound velocity. Two main processes contribute to sound damping: the thermal relaxation of local defects and the anharmonic interactions with thermal vibrations. By analyzing the temperature dependence of the velocity and subtracting the changes produced by the above mechanisms, the unrelaxed velocity is found. It is constant at low temperatures and increases anomalously above a temperature onset. We show that the onset strongly depends on pressure, which is in agreement with a dynamical origin of the structural changes that produce the hardening.1

1S. Ayrinhac, B. Rufflé, M. Foret, H. Tran, S. Clément, R. Vialla, R. Vacher, J. C. Chervin, P. Munsch, and A. Polian, “Dynamical origin of anomalous temperature hardening of elastic modulus in vitreous silica”, Phys. Rev. B 84, 024201 (2011).

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Phonon Amplification and Oscillator (SASER) Devices: The Acoustic Equivalents of Lasers

A J Kent

School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD UK.

The quest to realize practical acoustic amplifier and oscillator devices based on the principle of sound amplification by the stimulated emission of radiation (saser) started over 50 years ago, at around the time of the invention of the maser and laser. The motivating factors have been largely fundamental scientific interest and also the potential for such devices to transform the field of acoustics in a similar way to how lasers have transformed optics during the last half century. In recent years considerable progress has been made, with the demonstration of electrically and optically pumped devices working at frequencies in the range of a few MHz to a few hundred GHz1-5.

In this talk, I will begin with a brief review some of the key steps in the history of saser research. After that, I will consider in more detail some of our recent work on epitaxially-grown semiconductor superlattice-based saser devices. These have been shown to work in the sub-terahertz frequency range, which is probably the most important with regard to potential saser applications in science and technology. I will discuss the electron-phonon interaction processes that give rise to phonon amplification in a superlattice under electrical or optical pumping, and the realization of vertical-cavity saser devices using superlattices also as Bragg mirrors.

I will review the experimental measurements of saser devices made using non equilibrium phonon techniques such as: bolometer detection; phonon imaging; and optical pump-probe measurements of coherent phonons. The results show the following key signatures of saser action as the threshold for oscillation is reached, which are the exact equivalents to the signatures of optical oscillation in lasers6:

a sudden large rise in the power output in the oscillating mode;

a sudden spectral narrowing;

a sudden spatial narrowing of the output beam;

clamping of the upper state population and hence the edge emission. I plan to end the talk with a brief discussion of some potential applications for terahertz and sub-terahertz sasers.

1 L G Tilstra et al., Phys. Rev. B 68, 144302 (2003)

2 A J Kent et al., Phys. Rev. Lett. 96, 215504 (2006)

3 P M Walker et al., Phys. Rev. B 79, 245313 (2009)

4 I S Grudinin et al., Phys. Rev. Lett. 104, 083901 (2010)

5 R P Beardsley et al., Phys. Rev. Lett. 104, 085501 (2010)

6 A E Siegman, Lasers, (Oxford: Oxford University Press, 1986)

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Lifetime of zone-center, sub-THz coherent phonons in GaAs-AlAs superlattices

Felix Hofmann,1 Alexei A. Maznev,1 Kara J. Manke,1 and Keith A. Nelson,1 Adam Jandl,2 Mayank T. Bulsara,2 and Eugene A. Fitzgerald2

1 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2 Department of Materials Science and Engineering, Massachusetts Institute of Technology,

Cambridge, MA 02139, USA

Characterizing the role of phonons in non-diffusive, nano-scale thermal transport is essential for thermal management in micro-electronic devices1. Semiconductor superlattices (SLs) provide excellent model systems for the study of thermal and coherent phonons in nanostructured materials.2-4. Whilst the relationship between phonon dispersion and SL structure is well understood, phonon lifetimes in SLs are largely unexplored even for the most studied GaAs-AlAs system5.

We have measured the decay of longitudinal, zone-center phonons excited and probed by femtosecond laser pulses in 8nmGaAs/8nmAlAs and 14nmGaAs/2nmAlAs SLs. By considering the variation of phonon lifetime with both temperature and acoustic frequency we clarify the roles played by different relaxation mechanisms. In particular we establish that the transition from intrinsic (phonon-phonon scattering) to extrinsic (scattering at interfaces, surface roughness, etc.) relaxation mechanisms occurs at approximately 0.5 THz. Comparison with lower frequency experimental observations6 and theoretical calculations for bulk GaAs7 indicates that our room temperature measurements of 320-340GHz phonons fall into the transition region between Landau-Rumer (three-phonon scattering) and Akhiezer relaxation models.8 At 80K we found a lifetime of ~1.5ns for 320-340Ghz phonons, which is a significant increase over measurements at 296K. Assuming that the lifetime at liquid nitrogen temperatures is dominated by extrinsic relaxation mechanisms, we can assess the quality of the CVD-grown SL structures. 1 A. A. Maznev, J. A. Johnson, K. A. Nelson, “Onset of nondiffusive phonon transport in transient thermal grating decay”, Phys. Rev. B 84, 195206 (2011) 2 D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, S. R. Phillpot, “Nanoscale thermal transport”, J. Appl. Phys. 93, 793 (2003). 3 S. Tamura, D.C. Hurley and J.P. Wolfe, “Acoustic phonon propagation in superlattices”, Phys. Rev. B 38, 1427

(1988). 4 A. Bartels, T. Dekorsy, and H. Kurz, “Coherent Zone-Folded Longitudinal Acoustic Phonons in Semiconductor Superlattices: Excitation and Detection”, Phys. Rev. Lett. 82, 1047 (1999). 5 M. F. Pascual-Winter, A. Fainstein, B. Jusserand, B. Perrin, and A. Lemaître, “Photocarrier-induced reduction of the lifetime of acoustic phonons in semiconductor superlattices” Chinese J. Phys. 49, 250 (2011). 6 W. Chen, H. J. Maris, Z. R. Wasilewski, S.-I. Tamura, “Attenuation and velocity of 56 GHz longitudinal phonons in gallium arsenide from 50 to 300 K”, Phil. Mag. B 70 (1994), 3, pp. 687-698 7 Keivan Esfarjani, personal communication, 11/22/2011

8 H. J. Maris, in Physical Acoustics, edited by W. P. Mason and R. N. Thurston (Academic, New York, 1971), Vol. 8, p.

279.

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Negative refraction and subwavelength imaging with surface acoustic waves

István A. Veres,1 Thomas Berer,1,2 and Peter Burgholzer1,2 1 Research Center for Non-Destructive Testing GmbH, Altenberger Str. 69, 4040 Linz, Austria

2 Christian Doppler Laboratory for Photoacoustic Imaging and Laser Ultrasonics, 4040 Linz, Austria

Phononic crystals with drilled holes are probably the simplest approach of a meta-material with properties, otherwise not found in nature. Besides stop bands and Bloch harmonics, negative refraction is one of their most important property1 allowing the construction of flat acoustic lenses with subwavelength imaging.2 Negative refraction occurs if the Poynting vector and the wave vector are antiparallel, hence, in the presence of folded modes or in the case of concave equifrequency contours. This phenomenon has attracted great attention in bulk or slab phononic crystals, but reports are rare for surface acoustic waves (SAWs) as pursued in the presented work in a solid-air phononic crystal with triangular lattice.

We investigate negative refraction of SAWs in a flat lens formed by a seven-layer solid-air surface phononic crystal capable of focusing the waves. We show that the equifrequency contours of the leaky-Rayleigh wave become locally concave (Fig.1) in the first band of the crystal. This concaveness is the result of the anisotropy of the crystal and allows negative refraction of the SAWs in the absence of modes with negative slope or directional stop band. The main advantage of this approach is, that such concave frequency contours do not require the presence of Bragg scattering and therefore, negative refraction occurs with well-defined single-beam propagation. Successful focusing of SAWs will be presented experimentally and by numerical simulations. Due to the sixfold symmetry of the equifrequency contour the essential criterion of all-angle negative refraction (AANR3) for subwavelength imaging is not satisfied. The lens performance is, however, improved by embedding the aluminum lens into a fast material (diamond). This combination, investigated only numerically, not only fulfills the AANR condition thus showing subwavelength imaging, but also enables the focusing of the acoustic waves into a single spot (Fig.2).

The presented work investigates negative refraction and acoustic lensing in surface phononic crystals utilizing anisotropic effects. Successful focusing is presented experimentally and by numerical simulations. The lens performance is enhanced by the application of an inhomogeneous lens which facilitates subwavelength imaging.

1V. G. Veselago and E. E. Narimanov, “The left hand of brightness: past, present and future of negative index materials”, Nat. Mater. 5, 759-762 (2006).

2A. Sukhovich et.al, “Experimental and Theoretical Evidence for Subwavelength Imaging in Phononic Crystals”, Phys. Rev. Lett. 15, 154301 (2009).

3C. Luo et.al, “Subwavelength imaging in photonic crystals”, Phys. Rev. B 68, 045115 (2003).

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FIGURE 1. a) Dispersion relation of the surface phononic crystal in kx-ky directions from simulation. b)-c) Circular and concave equifrequency contours for the surface and leaky surface

waves, respectively, at 2.2 and 2.3 MHz.

FIGURE 2. Focusing of the SAWs through an aluminum lens embedded in diamond (simulation). The spot diameter is smaller than the wavelength of the surface acoustic waves at 2.4 MHz,

providing numerical evidence for superlensing of surface acoustic waves.

134

WEDNESDAY

k-Space Representation of Surface Phonon Propagation in Phononic Crystal Waveguides

Paul H. Otsuka, 1 Keisuke Nanri, 1 Motonobu Tomoda, 1 Oliver B. Wright, 1 Osamu Matsuda, 1 István A. Veres, 2 Sorasak Danworaphong, 3 Dieter M. Profunser, 1

Abdelkrim Khelif, 4 Vincent Laude, 4 and Sarah Benchabane4 1 Graduate School of Engineering, Hokkaido University, Japan

2 Recendt, Research Center for Non Destructive Testing, Linz 4020, Austria 3 School of Science, Walailak University, Thailand

4 FEMTO-ST, Besancon, France

Waveguide devices for controlling the path of propagation of surface phonons can be created by introducing defects in the periodicity of a phononic crystal. Such waveguides have more complex frequency and k-space behavior than conventional waveguides, and are useful in applications such as signal processing. Ultrafast optical methods have proved very effective for studying phonon propagation in real time in a range of materials1,2. Here we present spatio-temporal Fourier analysis of real-time imaging and simulation of laser-induced surface phonon pulses at frequencies up to ~1 GHz in phononic crystal waveguides. The results reveal time-resolved effects such as diffraction, reflection and waveguiding in both real and k-space. Interaction between the surface phonons and the phononic crystal structure, as well as between different phonon modes, results in a complex transmission spectrum dependent on the band structure of the phononic crystal.

The phononic crystals are made by deep reactive ion etching of circular holes 100 μm deep and arranged in a square array on (100) silicon . The hole spacing is 6.2 μm and the filling fraction is 64%, with waveguides formed by the absence of selected holes. In the experiment a 415 nm pump beam from a mode-locked Ti:sapphire laser excites the phonon modes, and an 830 nm probe beam delayed relative to the pump beam is used for detection with an interferometer. The optical pulse duration is ~200 fs and the repetition rate is 80 MHz. The beams are focused to a spot of about 1 μm in diameter. The probe beam is scanned across the sample to generate images of regions of about 160×160 μm2 in area. By varying the probe delay time, we build up animations of the surface waves propagating through the waveguides. The k-space representation is then calculated by Fourier analysis. An image from a linear waveguide taken at a fixed time is shown in figure 1. The experimental results are shown to be in good agreement with numerical simulations based on the time-domain finite-element method.

1D. M. Profunser, E. Muramoto, O. Matsuda, O. B. Wright, and U. Lang, “Dynamic visualization of surface acoustic waves on a two-dimensional phononic crystal”, Phys. Rev. B 80, 014301 (2009).

2D. M. Profunser, O. B. Wright, and O. Matsuda, “Imaging ripples on phononic crystals reveals acoustic band structure and Bloch harmonics”, Phys. Rev. Lett. 97, 055502 (2006).

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FIGURE 1. Phonons propagating in a linear waveguide. Inset: k-space image. The green line is a horizontal cross section through the center (at ky=0).

136

WEDNESDAY

Probing Thermomechanics at the Nanoscale: Impulsively Excited Pseudosurface Acoustic Waves in Hypersonic

Phononic Crystals

Damiano Nardi1,2, Marco Travagliati2,3, Mark E. Siemens4, Qing Li1, Margaret M. Murnane1, Henry C. Kapteyn1, Gabriele Ferrini2, Fulvio Parmigiani5, and Francesco

Banfi2

1JILA, University of Colorado at Boulder, Boulder, Colorado 80309, United States 2i-LAMP and Dipartimento di Matematica e Fisica, Universià Cattolica, I-25121 Brescia, Italy

3Center for Nanotechnology Innovation @NEST-IIT, I-56127 Pisa, Italy 4Department of Physics and Astronomy, University of Denver, Denver, Colorado 80208, U.S.A

5Dip. di Fisica, Università di Trieste and Sincrotrone Trieste, I-34012 Basovizza, Trieste, Italy

High-frequency surface acoustic waves can be generated by ultrafast laser excitation of nanoscale patterned surfaces1-4. Here we study this phenomenon in the hypersonic frequency limit. By modeling the thermomechanics from first-principles, we calculate the system’s initial heat-driven impulsive response and follow its time evolution. A scheme is introduced to quantitatively access frequencies and lifetimes of the composite system’s excited eigenmodes. A spectral decomposition of the calculated response on the eigemodes of the system5 reveals asymmetric resonances that result from the coupling between surface and bulk acoustic modes. This finding allows evaluation of impulsively excited pseudosurface acoustic wave frequencies and lifetimes and expands our understanding of the scattering of surface waves in mesoscale metamaterials. The model is successfully benchmarked against time-resolved optical diffraction measurements performed on one-dimensional and two-dimensional surface phononic crystals, probed using light at extreme ultraviolet and near- infrared wavelengths6.

1 H.-N Lin, H. J. Maris, L. B. Freund, K. Y. Lee, H. Luhn, D. P. Kern, J. Appl. Phys. 73, 37 (1993). 2 G. A. Antonelli, H. J Maris, S. G. Malhotra, J. M. E. Harper, J. Appl. Phys. 91, 3261. (2002). 3 R. I. Tobey,E. H. Gershgoren, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, T. Feurer, K. A. Nelson, Appl. Phys. Lett. 85, 564 (2004). 4 C. Giannetti, B. Revaz, F. Banfi, M. Montagnese, G. Ferrini, F. Cilento, S. Maccalli, P. Vavassori, G. Oliviero, E. Bontempi, L. E. Depero, V. Metlushko, and F. Parmigiani, Phys. Rev. B 76, 125413 (2007). 5 D. Nardi, F. Banfi, C. Giannetti, B. Revaz, G. Ferrini, and F. Parmigiani, Phys. Rev. B 80, 104119 (2009). 6 D. Nardi, M. Travagliati, M. E. Siemens, Qing Li, M. M. Murnane, H. C. Kapteyn, G. Ferrini, F. Parmigiani, and F. Banfi, Nano Lett. 11, 4126 (2011)

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FIGURE 1. (a) Projection |ci| of the initial thermal expansion displacement on the symmetric eigenmodes of the composite system (red circles) and the Fano-line shape fit (blu line). (b) Normalized relative variation of the diffracted signal measured in the transient NIR diffraction experiment (black line) and the theoretical prediction (red line).

138

WEDNESDAY

Acoustic resonators for far field control of sound on a subwavelength scale

Fabrice Lemoult,1,2 Mathias Fink,1 and Geoffroy Lerosey1 1 Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 10 rue Vauquelin, 75005 Paris, France

2 Currently at the Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

Sound, just as light, is subject to the diffraction limit which sets a critical bound to any imaging or focusing technique. For example, sound focusing in the audible range is limited by diffraction effects and the typical focal spot size in room acoustics is metric. During this talk we will show that broadband audible sound can be manipulated and focused on a subwavelength scale, that is on a scale much smaller than the wavelength in air, by the use of a resonant phononic crystal. This medium consists in a periodic arrangement of subwavelength acoustic resonators. For this purpose, we use a collection of simple everyday life objects: an array of soda cans1.

The concept is based on our theoretical proposal of resonant metalens, which was demonstrated with electromagnetic waves at radio frequencies using metallic wires. We show that the strong coupling between neighboring resonators induces a splitting of the resonant frequency of a single Helmholtz resonator, which can be interpreted as a polariton wave. We demonstrate that monochromatic waves emitted by commercial computer loudspeakers in the farfield of such a medium excite efficiently, in the array of cans, resonant modes with spatial scales much thinner than the wavelength in air. Those subwavelength Bloch modes have different resonant frequencies and radiation patterns depending on their wavevectors.

Harnessing those sub-diffraction wavefields using broadband sounds, we are able to experimentally obtain from the far field subwavelength focusing of sound onto spots as small as 1/25th of a wavelength in air (Figure 1). Finally we establish that subwavelength focusing results in a strong enhancement of the acoustic displacement, and we prove it experimentally through a visual experiment.

1F. Lemoult, M. Fink, and G. Lerosey, “Acoustic resonators for far-field control of sound on a subwavelength scale”, Phys. Rev. Lett., 107, 064301 (2011).

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FIGURE 1. Sub-diffraction Focusing of sound. a) and b), focal spots obtained using time reversal in the laboratory room and without the array of cans, typical diffraction limited spots are

displayed. c) and d), the foci obtained using time reversal onto the same locations with the array of Helmholtz resonators show λ/8 width, 4 times smaller than the diffraction limit. e) and

f), the experiment is realized in the same conditions with an iterative time reversal scheme, demonstrating focal spots as thin as λ/25.

140

WEDNESDAY

Phonon transport across epitaxial SrRuO3 / SrTiO3 interfaces

R. B. Wilson, B. Apgar, E. Breckenfeld, L. W. Martin, and David G. Cahill

Department of Materials Science, University of Illinois Urbana Champaign, IL, USA

Scattering of phonons by crystalline interfaces is important for understanding thermal transport

on nanometer length-scales. We characterized the role of interfacial structure and bonding on

phonon scattering by time-domain thermoreflectance (TDTR) measurements of heat transport

across ordered-epitaxial-SrRuO3/SrTiO3 and disordered-Al/SrTiO3 interfaces from 40 to 300K.

The nearly perfect epitaxial interfaces between SrRuO3 and SrTiO3 enable efficient exchange of

thermal energy across the interface; the observed room temperature thermal interface

conductance of 500 MW/m2K is the second highest phonon mediated interface conductance

ever observed. We find a diffusive description of thermal transport that assumes bulk values for

the heat capacities and thermal conductivity of SrRuO3 and SrTiO3 to be consistent with the

TDTR measurements at nearly all temperatures (Figure 1). This is in stark contrast to the

Al/SrTiO3 system, where modeling based on diffusive heat transfer requires the use of a

thermal conductivity of SrTiO3 more than an order of magnitude lower than previously reported

values for bulk crystals. We hypothesize that the low effective thermal conductivity observed

in the Al/STiO3 system is caused by the disordered Al/SrTiO3 interface that preferentially

scatters high-frequency phonons with short mean-free-paths.

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FIGURE 1. Thermal conductivity of SrTiO3 as determined by TDTR measurements of SrRuO3/ SrTiO3 (circles) and Al/ SrTiO3 (triangles) systems. The blue curve represents previously reported values for bulk crystals.

142

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Pressure dependent inelastic phonon transmission at Si/Carbon Nanotube interface

Y. Chalopin1,2, N. Mingo 3, S. Volz1,2

1CNRS, UPR 288 Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion,

Grande Voie des Vignes, 92295 Chatenay-Malabry 2 Ecole Centrale Paris, Grande Voie des Vignes, 92295, Châtenay-Malabry

3CEA-LITENLCRE/DTMN/LITEN, CEA-Grenoble

17, rue des Martyrs, F-38054 Grenoble Cedex 9, France

Earliest theoretical attempts to provide an analytical description of phonon transport at interface have yielded the acoustic mismatch theory and the diffuse mismatch theory. Both were found to rather poorly reproduce most experimental results on solid-He, semiconductor or metal interfaces. It is in fact very difficult to assess the contribution of anharmonic process on interfacial energy transport as it requires an explicit treatment of the multi-phonon processes, which is a tremendous task. Most of the commonly employed approaches still relies on interatomic elastic properties of solids and (lattice dynamics or the Green's function theory) but quantifying how a phonon splits into two phonons when crossing an interface remains a important open question.

In this work, we introduce a theoretical approach that allows capturing the complete phonon transmission at interfaces by the means of equilibrium Molecular Dynamics (EMD) simulation, which includes inelastic vibrational processes. Our approach relies on the recovery of the atomic time-dependent displacements of atoms forming the interface layers in order to derive the phonon transmission probabilities. We have calculated the transmission spectrum in a Silicon/CNT junction under varying applied pressure and compared these results with the transmissions obtained with those predicted by the Non-Equilibrium Green's (NEGF) function theory. We found a significant difference in the transmission demonstrating that inelastic processes play a key role by reducing significantly the Kapitza resistance. From the comparison with NEGF data, we conclude that increasing pressure opens anharmonic channels, which predominantly carry the thermal energy across the interface.

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Heat transfer of supported Au nanorods in various organic fluids

Jonglo Park,1 Jingyu Huang,2 Wei Wang,1 Catherine J. Murphy,2 and David G. Cahill1

1 Department of Materials Science and Engineering, University of Illinois, Urbana, IL, USA 2Department of Chemistry, University of Illinois, Urbana, IL, USA

Fundamental understanding of heat transport from nanoscale heat source to their surroundings is needed for applications such as thermally-based medical therapies. Au nanorods are of particular interest due to high absorption coefficient, narrow spectral bandwidth, and tunability of optical absorption in the near-infrared by controlling their aspect ratio. We investigate heat transfer of Au nanorods immobilized on a crystalline quartz substrate to surrounding organic fluids. The temperature change of Au nanorods abruptly heated by a sub-picosecond optical pulse is monitored by transient absorption. The thermal decay data of Au nanorods is analyzed using a two-dimensional heat flow model with an additional thermal conductance per unit length to describe heat transfer between the Au nanorod and high thermal conductivity substrate. At short times, t < 300 ps, the cooling-rate of the nanorods is predominately controlled by transport of heat through the nanorod-fluid interface and the diffusion of heat into the surrounding fluid. At longer times, t > 300 ps, heat transfer to the solid-support dominates. For methanol, ethanol, toluene, and hexane, the thermal conductance of the nanorod-fluid interface falls within a narrow range, e.g., 26 ± 3 W m-2 K-1 for methanol, and 20 ± 3 W m-2 K-1 for toluene. The thermal conductance per unit length of the nanorod-substrate interface is nearly constant at, Gs ≈ 0.6 W m-1 K-1.

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FIGURE 1. Transient changes in the optical absorption created by heating of supported Au nanorods by the pump optical pulse; ΔTr is the measured change in optical transmission of the probe beam. Data for the sample measured in air are compared data measured in four fluids. The signal in the air shows a simple exponential decay controlled by the thermal conductance of the nanorods-quartz interface. At short times, t < 300 ps, the temperature decay is faster

when the sample is in contact with fluids.

FIGURE 2. The correlation between Gs and Gf variables for fitting the data with the two-dimensional model for 30 ps to 1500 ps.

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Interfacial Phonon Transport in Si-Ge Heterostructures from Equilibrium Molecular Dynamics Simulations

Yann Chalopin,1 Sebastian Volz,1 Keivan Esfarjani3, Asegun Henry 2 and Gang Chen3

1 Em2c Laboratory, Ecole Centrale Paris, France 2George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology

3 Department of Mechanical Engineering, Massachusets Institute of Technology, Cambridge MA, USA

One of the key issues in microelectronic and thermoelectric science is the extent to which thermal energy can transfer across an interface made of dissimilar materials. The development of models establishing the microscopic interplays between two phonon reservoirs has thus become an intense subject of research. In this context, we propose a microscopic approach based on equilibrium molecular dynamics simulations. It allows to calculate thermal boundary conductance as well as phonon transmission from the recovery of the temperature-dependent displacement fluctuations of atoms forming the interfaces.

We have illustrate our formalism on Si/Ge superlattices by investigating the period thickness dependance of thermal boundary conductance. This unveiled rather different phonon transport regimes we discuss in the light of the phonon transmission spectra. This provides powerful strategies for tuning thermal properties of superlattices at the nanoscale.

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Anomalous Phonon/Thermal Transport in Low Dimensional Nanostructures

Baowen Li1,2

1 Department of Physics and Centre for Computational Science and Engineering,

National University of Singapore, Singapore 117542, Singapore 2 NUS-Tongji Cnter for Phononics and Thermal Energy Science, Department of Physics,

Tongji University, Shanghai 200092, People’s Republic of China [email protected], [email protected]

Abstract The thermal transport in low dimensional nano scale structures is important for both fundamental research and industrial applications. On the one hand, the low dimensional nanostructures such as graphene, nanowires, and nanotubes provide a test bed for the conjectures and hypothesis proposed in the last two decades for heat transport in two dimensional (2D) and one dimensional (1D) systems1. On the other hand, low dimensional nano structured materials have been found to be an ideal candidates

to realize phononic functions such as thermal rectifier2． In this presentation, I will give a brief review about recent years progress on this topic both experimentally and theoretically. In bulk material, heat conduction is governed by Fourier’s law as:

(1) where is the local heat flux and the temperature gradient, is the thermal conductivity which is size independent. This is based on the assumption that phonons transport diffusively. However, for the low dimensional systems, in particular 1D systems, except for a simple harmonic oscillator chains, we don’t have any rigorous mathematical proof if the normal diffusion process can happen. Therefore it is still an open question whether the Fourier law is valid in 1D and 2D systems. Especially the sufficient and necessary condition for Fourier’s law is not clear yet1. In this talk, I will demonstrate that heat transfers in 1D and 2D systems are significantly from bulk material. (1) Both numerically and experimentally show that thermal conductivity in 1D and/or quasi 1D system

such as nanowire and nanotube is not a constant. It depends on the system length as3-4 (Fig 1 for silicon nanowire and Fig 2 for nanotube):

, with 0< <1.

(2) Thermal conductivity in single layer suspended graphene depends on the length logarithmically when the width is fixed5. In the last part, I will present our recent mathematical theory which bridges the anomalous thermal conductivity to anomalous energy diffusion9-10. 1A Dhar, Adv. Phys. 57, 457 (2008). 2N.-B Li, J. Ren, L Wang, G Zhang, P Hanggi, and B Li, Rev. Mod. Phys, in press (2012) 3N. Yang, G. Zhang, and B. Li, Nano Today 5, 85 (2010). 4C W Chang, D Okawa, H Garcia, A Majumdar, and A Zettl, Phys. Rev. Lett. 101, 075903 (2008). 5X-F Xu et al Nature Materials (submitted) 6L Lindsay, D A Broido, and N Mingo, Phys. Rev. B 82, 115427 (2010). 7D L Nika, S Ghosh, E P Pokatilov, and A A Balandin, Appl. Phys. Lett. 94, 203103 (2009)

J T

J T

~ L



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8L Yang, P Grassberger, and B Hu, Phys. Rev. E 74, 062101 (2006). 9B Li and L Wang, Phys. Rev. Lett 91, 044301 (2003). 10S Liu, J Ren, N.-B Li, and B Li, Phys. Rev. Lett (submitted)

Figure 1. The dependence of thermal conductivity of SiNWs on the longitude length Lz. The results by Nose-Hoover method coincide with those by Langevin methods, indicating that the results are independent of the heat bath used. The black solid curves are the power law fitting curves (linear in log-log scale). For more details see Ref [3].

Figure 2. Left: A SEM image of a thermal conductivity test fixture with a nanotube after five sequences of (CH3)3(CH3C5H4)Pt deposition. The numbers denote the nth deposition. The inset shows the SEM image after the first (CH3)3(CH3C5H4)Pt deposition. Right: Normalized thermal resistance vs normalized sample length for CNT (solid black circles), best fit assuming β=0.6 (open blue stars), and best fit assuming Fourier’s law (open red circles). For more details see Ref [4].

Figure 3: Length dependence of κ at room temperature (black solid circles) of single suspended graphene. The black linear line is a guide to the eyes. The black arrow and dashed line indicate the phonon mean free path. The red solid honeycombs and squares are plotted by extracting the data calculated by Lindsay el al.[6] and Nika et al.[7], respectively. Note that this ~ logL is only valid when L >> λ and deviations from ~ logL in the shortest samples is expected [8].

Insert: illustration of logκ ~ logL scaling behavior for 1D, 2D and 3D systems, where thermal conductivity scales as ~L

0.3, ~logL

and constant, respectively.

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Optical detection of collective acoustic modes in artificial crystals

S. Sadtler, A. Devos, and P.A. Mante 1 Institut d'Electronique, de Microélectronique et de Nanotechnologie, UMR CNRS 8250, BP 69,

Avenue Poincaré, F-59652 Villeneuve d'Ascq Cedex, France

In picosecond acoustics, we use ultrashort light pulses to excite and detect very high frequency acoustics waves up to several hundred GHz. Most of the time, the optical detection of such high frequency acoustic waves is governed by the photo-elastic mechanism. The strain affects the optical properties of the sample that is detected by the probe laser.

Recently we reported the observation of individual and collective acoustic modes on 2D artificial crystals made of nanocubes[1,2] We showed the collective modes can only be detected if the probe wavelength is shorter than the lattice parameter [3]. We also demonstrated that detection was not based on the photo-elastic mechanism contrary to the individual vibration of the cubes. Several other mechanisms have been proposed: diffraction, plasmonic coupling but none of them can account for our experimental evidences. The exact nature of the optical detection mechanism of the collective modes is thus still open. Here we report some new experimental results obtained using an interferometric detection. The interferometric technique permits to detect ultrafast changes in the real and imaginary components of the refractive index as well as phase changes that are due to surface displacement. This technique has been used for probing opaque samples such as gold samples [4], and also in multilayers and particles in colloids [5]. Thanks to the interferometric detection, we detect collective modes in arrays of Al nanocubes irrespectively of the lattice parameter. From that we propose an alternative mechanism based on surface displacement.

1. J.F Robillard, A. Devos et I. Roch-Jeune, « Time-resolved Vibrations of two-dimensional Hypersonic

Phononic Crystals», Physical Review B 76, 092301 (2007).

2. J.-F. Robillard, A. Devos, I. Roch-Jeune et P.A. Mante, « Collective Acoustic Modes in various two-

dimensional crystals by ultrafast acoustics : Theory and Experiments », Phys. Rev. B 78, 064302

(2008).

3. S. Ayrinhac, A. Devos, A. Le Louarn, P.-A. Mante et P. Emery, « Ultrafast acoustics in the middle UV

range: coherent phonons at higher frequencies and in smaller objects », Optics Letters Vol. 35, Iss.

20, pp. 3510–3512 (2010).

4. H. Hurley and B.Wright, Optics Letters, 24, 18 (1999)

5. B. Perrin et al, Physica B, 263-264,571-573 (1999)

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FIGURE 1. SEM picture of one studied sample, an artificial crystal made of 200 nm nanocubes arranged along a 400 nm step lattice

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Soft Phononic Structures

Dirk Schneider,1 Tim Still,2Periklis Papadopoulos,1 George Fytas1,3 1 Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, German

2 Department of Physics & Astronomy, University of Pennsylvania, Philadelphia ,PA 19104, USA 3 Department of Materials Science, University of Crete and FORTH, 71110 Heraklion, Greece

Phononic crystals, the acoustic equivalents of the photonic crystals, are controlled by a larger number of

material parameters1,2. The study of hypersonic crystals imposes substantial demand on fabrication and

characterization techniques. Colloid and polymer science offer methods to create novel materials that

possess periodic variations of density and elastic properties at mesoscopic length scales commensurate

with the wave length of hypersonic phonons and hence photons of the visible light. Polymer-and colloid-

based phononics is an emerging new field at the interface of soft materials science and condensed

matter physics with good perspectives ahead. Here, examples from fabricated structures will be

highlighted. The key quantity is the dispersion of high frequency (GHz) acoustic excitations which is

nowadays at best measured by the noninvasive high resolution spontaneous Brillouin light scattering.

Depending on the components of the nanostructured composite materials, the resolved vibration

eigenmodes (their music) of the individual particles sensitively depend on the particle architecture and

their thermo-mechanical properties3,4. In periodic structures (the concert) of polymer based colloids, the

dispersion relation ω(k) between the frequency and the phonon wave vector k has revealed hypersonic

phononic band gaps of different nature2,5,6: Bragg gap for propagation near the edge of the first Brillouin

zone due to destructive interference and hybridization gap due to the interaction of particle eigenmodes

with the effective medium acoustic branch; the latter is therefore robust against structural. Boosting the

strength of the phonon scattering by the individual spheres, e.g., elastically hard SiO2 particles can

activate additional mechanisms6 for tunability of the phononic band structure. The elucidation of all

important parameters towards the general design of optimal phononic structures remains complicated

due to the vector nature of elastic wave propagation. In this regard, 1D phononic crystals (SiO2/PMMA)

multilayer films turns out to be a model system7. Since hypersonic crystals can simultaneously exhibit

phononic and photonic band gaps in the visible spectral region, and phonons are the main heat carriers

in dielectrics, many technological applications are feasible. Elastic wave propagation through

hierarchically nanostructured matter can involve unprecedented mechanisms as observed in the

dispersion diagram of the spider dragline silk.

[1] T. Gorishnyy, L.U. Ullal, M. Maldovan, G. Fytas, E. L. Thomas, Phys. Rev. Lett, 94, 115501 (2005). [2] W. Cheng, M. Retsch, U. Jonas, G. Fytas, N. Stefanou, Nature Mater. 5, 830 (2006). [3] T. Still, R. Sainidou, M. Retsch, U. Jonas, P. Spahn, G. Hellmann, G. Fytas, Nano Lett. 10, 3194 (2008). [4] T. Still, M. Mattarelli, D. Kiefer, G. Fytas, M. Montagna, J. Phys. Chem. Lett. 1, 2440 (2010). [5] T. Still, W. Cheng, M. Retsch, R. Sainidou, U. Jonas, N. Stefanou, G. Fytas, Phys. Rev. Lett. 100, 194301 (2008). [6] T. Still, G. Gatzounis, D.Kiefer, G.Hellmann, R.Sainidou, G. Fytas, N.Stefanou Phys. Rev. Lett. 106, 175505 (2011) [7] N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, G. Fytas, Nano Lett. 10, 980 (2010).

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FIGURE 1. A dry opaque assembly of colloidal particles (left) and the experiment and theoretical eigenmode spectrum of silica mesoscopic spheres4

FIGURE 2. A polystyrene spheres (diameter 300nm) fcc colloidal crystal infiltrated with liqid poly(dimethylsiloxane) (left) displays two hypersonic phononic gap (middle) due to “Bragg” interference and anti-crossing between particle lowest eigenmode (l=2) (right) and effective medium acoustic branch 5,6

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Optical generation and detection of hypersound in opal-based ferromagnetic hypersonic crystals

Michael Bombeck,1 Alexey S. Salasyuk,1,2 Jasmin Jäger,1 Dmitri R. Yakovlev,1,2 Ekaterina Yu. Trofimova,2 Dmitry A. Kurdyukov,2 Valery G. Golubev2 and Manfred

Bayer1,2 1 Experimentelle Physik 2, Technische Universität Dortmund, D-44227 Dortmund, Germany

2 Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St.Petersburg, Russia

We demonstrate the direct optical excitation of GHz coherent elastic vibrations in an opal-based ferromagnetic hypersonic crystal. In time-domain measurements with applied external magnetic field we separate the elastic vibrations of SiO2 mesoporous spheres forming the opal matrix and the magnetization evolution of ferromagnetic nanoparticles embedded into the opal crystal.

Stacking submicrometer sized silica spheres periodically in a FCC-lattice results in the formation of a artificial crystal called synthetic opal. Due to the periodicity of the optical as well as elastic properties they are known to form high quality photonic and phononic crystals with optical and acoustic band gaps [1]. The incorporation of ferromagnetic particles inside the opal leads to hybrid ferromagnetic structure [2] that may realize the possibility of resonant coupling of optical, acoustic and magnetic excitations.

In the experiment we study opal films consisting of a few monolayers of 1um diameter silica spheres deposited on silica substrate. Contrary to the conventional opal-based composites in the studied structure Ni nanorods are embedded directly inside the mesoporous spheres, while the voids of the opal are not infiltrated. The nanorods have a diameter of 3nm and a longer extension along the cylinder axis [3]. Coherent elastic vibrations inside the silica spheres are excited by the absorption of an optical pump pulse (800 nm, 100 fs, 100 kHz repetition rate, up to 3μJ pulse energy) by the Ni nanorods. The evolution of the generated excitations inside the hybrid structure is probed by measuring either intensity modulation or polarization rotation of a frequency doubled probe pulse transmitted through the sample. The time resolution is achieved by the variation of the relative delay between red pump and blue probe pulses. An external magnetic field, B, is applied perpendicular to the opal film.

The time evolution of the transmitted intensity at B=100mT shows high amplitude oscillations with a frequency of 3GHz that decay within 3ns (Figure 1). The detected oscillations are attributed to the eigenmode (Lambmode) of the silica spheres excited by the rapid thermal extension of the Ni nanorods. The long life time of the oscillations shows a high coherency of the eigenmodes originating from homogenous coupling of the silica spheres with the Ni inside the spheres. The time evolution of the Faraday rotation of the linearly polarized probe beam transmitted through the sample shows a pronounced step-like behaviour with transient return to its equilibrium value (Figure 1). The step-like behaviour is attributed to a fast demagnetization of the ferromagnetic Ni nanorods due to heating by the optical pump pulse.

1 A. S. Salasyuk et al., Nano Lett. 10, 1319-1323 (2010)

2 V. V. Pavlov et al., Appl. Phys. Lett. 93, 072502 (2008)

3 E. Yu. Trofimova et al., Glass Phys. Chem. 37, 378-384 (2011)

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FIGURE 1. Time evolution of the optically induced change in intensity (black, solid line) and Faraday rotation (red, dashed line) in the Ni opal sample at an applied magnetic field of 100mT.

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Phonon Transport Across Organic-Metal Interfaces

Yansha Jin1, Chen Shao1, Kevin P. Pipe2, John Kieffer1 and Max Shtein1 1 Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

2 Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

The thermal boundary conductance (TBC) of organic solids (e.g. Copper phthalocyanine - CuPc Sub-phthalocyanine - SubPc) and several metals (Al, Mg, Au, Ag) has been measured using the 3-omega method at room temperature, revealing that TBC values increase with the strength of interfacial bonding between the organic and metal phases. Molecular dynamics (MD) simulation of these systems supports this observation; particularly for highly mismatched and weakly-bonded interfaces (exemplified by the organic-metal system), the TBC is sensitive to the interfacial bonding strength.

Conventional mismatch models (i.e. the acoustic mismatch model, AMM, and the diffuse mismatch model, DMM) fail to predict TBC accurately for the material system under investigation. Gradually strengthening the bonding at organic-metal interface in the MD simulation will increase the calculated TBC value until saturation. The AMM model can be modified by introducing an effective spring constant, capturing the general trend of many experimental and simulation observations, 1 but this approach still fails in predicting TBC values of the metal-organic interface. More sophisticated analysis of MD-generated data shows that interfacial bonding is weak (~2 GPa), amplifying the importance of anharmonic coupling of vibrations across the metal-organic interface. We discover that in some systems (e.g. CuPc / Al), spatially non-uniform (on the sub-molecular length scale) phonon transmission dominates. A clear overestimation by conventional model is observed, which can be corrected by introducing the spatial non-uniformity. (See Figure 1.)

1 R. Prasher Appl. Phys. Lett. 94, 04195 (2009).

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FIGURE 1. (Left) – Plot of TBC versus effective modulus at the interface of CuPc/Al interface. Black: MD simulation values. Blue: Modified AMM and AMM calculated values. (Middle) – Spatial distribution of the average displacement of the 1st layer of CuPc molecules adhering to aluminum. (Right) – TBC map that considers spatially non-uniform spring constants using modified AMM model, normalized to TBC using an effective spring constant at the same bond ratio.

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Molecular Dynamics Study of Thermal Transport across CuPc-Metal Interfaces

Chen Shao1, Yansha Jin1, Max Shtein1, Kevin Pipe2, and John Kieffer1 1 Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA


Organic-inorganic interfaces provide critical functionality for many electronic devices, such as

organic solar cells and organic light-emitting devices, as well as nanocomposites for engineered

heat transfer, such as thermal interface materials and thermal epoxies. For all of these

applications, interfacial heat transfer plays a key role in performance and reliability, yet the

fundamental processes that govern this transfer remain poorly understood.

In this study, we use classical molecular dynamics (MD) simulations to carry out a systematic

study of the nanoscale processes that govern the thermal boundary resistance at copper

phthalocyanine (CuPc)/metal interfaces. Non-equilibrium MD simulations (NEMD) are

performed on metal–CuPc–metal junctions to study thermal energy transport across the

interfaces through the Müller-Plathe method. The interfacial bonding strength is controlled

directly in the MD simulation by scaling the interaction parameters for the materials juxtaposed

at the interface. The thermal boundary resistance is closely related to the interfacial bonding

strength. By comparing the MD calculation results with the experimental measurements, the

work of adhesion between CuPc and metal substrates is estimated to be 0.06 J/m2 for CuPc/Au,

0.04 J/m2 for CuPc/Ag, and 0.4 J/m2 for CuPc/Al interfaces. These findings confirm the

experimental observation of very weak bonding between CuPc and Au or Ag and strong

bonding at the CuPc/Al interface.1 Our study shows that the interfacial bonding strength is a

very important factor in predicting thermal boundary resistance at CuPc/metal interface.

Conversely, the acoustic impedance mismatch between the adjoining materials appears to be

less important. To further investigate the mechanisms of interfacial heat transfer we carry out

a detailed analysis of the momentum exchange across the interface, based on incoherent

space-time correlation functions of the atomic motion and their spectral representations. Our

results suggest that the anharmonic contributions to the phonon spectrum directly correlate

with the thermal boundary resistance at the CuPc-metal interface.

1Y. Jin, A. Yadav, K. Sun, Hong-Bo Sun, K. P. Pipe, Max Shtein, “Thermal boundary resistance of copper phthalocyanine-metal interface”, Applied Physics Letters 98, 3 (Feb, 2011).

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FIGURE 1. Illustration of the NEMD procedure to calculate thermal boundary resistance.

CuPc/Ag

CuPc/Au

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FIGURE 2. Comparison between experimental data and MD simulation results indicating the prevalent influence of interfacial bonding strength on thermal the boundary resistance for

weakly bonded interfaces.

Molecular Dynamics Study of Thermal Transport across CuPc-Metal Interfaces

Chen Shao1, Yansha Jin1, Max Shtein1, Kevin Pipe2, and John Kieffer1 1 Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA


Organic-inorganic interfaces provide critical functionality for many electronic devices, such as

organic solar cells and organic light-emitting devices, as well as nanocomposites for engineered

heat transfer, such as thermal interface materials and thermal epoxies. For all of these

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applications, interfacial heat transfer plays a key role in performance and reliability, yet the

fundamental processes that govern this transfer remain poorly understood.

In this study, we use classical molecular dynamics (MD) simulations to carry out a systematic

study of the nanoscale processes that govern the thermal boundary resistance at copper

phthalocyanine (CuPc)/metal interfaces. Non-equilibrium MD simulations (NEMD) are

performed on metal–CuPc–metal junctions to study thermal energy transport across the

interfaces through the Müller-Plathe method. The interfacial bonding strength is controlled

directly in the MD simulation by scaling the interaction parameters for the materials juxtaposed

at the interface. The thermal boundary resistance is closely related to the interfacial bonding

strength. By comparing the MD calculation results with the experimental measurements, the

work of adhesion between CuPc and metal substrates is estimated to be 0.06 J/m2 for CuPc/Au,

0.04 J/m2 for CuPc/Ag, and 0.4 J/m2 for CuPc/Al interfaces. These findings confirm the

experimental observation of very weak bonding between CuPc and Au or Ag and strong

bonding at the CuPc/Al interface.1 Our study shows that the interfacial bonding strength is a

very important factor in predicting thermal boundary resistance at CuPc/metal interface.

Conversely, the acoustic impedance mismatch between the adjoining materials appears to be

less important. To further investigate the mechanisms of interfacial heat transfer we carry out

a detailed analysis of the momentum exchange across the interface, based on incoherent

space-time correlation functions of the atomic motion and their spectral representations. Our

results suggest that the anharmonic contributions to the phonon spectrum directly correlate

with the thermal boundary resistance at the CuPc-metal interface.

1Y. Jin, A. Yadav, K. Sun, Hong-Bo Sun, K. P. Pipe, Max Shtein, “Thermal boundary resistance of copper phthalocyanine-metal interface”, Applied Physics Letters 98, 3 (Feb, 2011).

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FIGURE 1. Illustration of the NEMD procedure to calculate thermal boundary resistance.

FIGURE 2. Comparison between experimental data and MD simulation results indicating the prevalent influence of interfacial bonding strength on thermal the boundary resistance for

weakly bonded interfaces.

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Molecular Dynamics Studies of Thermal Boundary Resistance in Carbon-Metal Interfaces

Sergei V. Shenogin,1,2 Jamie J. Gengler,1,3 Ajit K. Roy,1 Andrey A. Voevodin,1 and Christopher M. Muratore1

1Thermal Sciences and Materials Branch, Air Force Research Laboratory Wright-Patterson Air Force Base, OH, USA

2UES Inc, Dayton, OH 45432 3 Spectral Energies LLC, Dayton, OH 45431

High thermal conductivity of carbon nanotubes and other graphitic structures, considering their large aspect ratios, makes them attractive materials for a variety of applications where thermal management is important. These applications include heat dissipation in microelectronics devices and polymer based composites with high thermal conductivity. The reduction of interfacial boundary resistance between carbon structures and other materials in these applications is a key factor for improving thermal properties of such materials. Considering metal coatings as a way to improve interfacial conductance, we used molecular dynamics and vibrational modes analysis to study heat transfer through carbon nanotube - metal interfaces in highly nonequilibrium conditions (NEMD). The validity of NEMD for studying thermal transport through the interfaces with large mismatch in vibrational properties is discussed. It is shown that for carbon-metal interfaces, the redistribution of thermal energy between vibrational modes dominates other reasons for thermal boundary resistance. Furthermore, the effective interface conductance is only defined by the interface area and scales linearly with nanotube diameter. This suggests that at low volume fraction, the use of nanotubes with larger diameter is preferred for high conductivity of composites, while at higher volume fraction thin single-wall nanotubes are better. It is shown that using a metal coating, it is easier to establish better thermal coupling between fibers and the matrix than using other methods like chemical functionalization. Multiple intermediate layers of different metals help to match the Debye temperature to every phase separately, while preserving the intrinsically high thermal conductivity of the nanotubes. The simulation results were compared with our recent experimental results on thermal conductance in metal coated highly oriented pyrolitic graphite (HOPG) and multiwall carbon nanotube (MWCNT) structures.

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Temperature dependence of the thermal boundary resistivity of glass- embedded metal nanoparticles

F. Banfi1,2, V. Juvé2, D. Nardi1, S. Dal Conte3, C. Giannetti1, G. Ferrini1, N. Del Fatti2 and F. Vallée2

1i-LAMP and Dipartimento di Matematica e Fisica, Università Cattolica, I-25121 Brescia, Italy 2FemtoNanoOptics Group, LASIM, Universit Lyon 1, CNRS, 69622 Villeurbanne, France

3Dipartimento di Fisica A. Volta, Universita` di Pavia, I-27100 Pavia, Italy

With the ever decreasing size of nanodevices, investigation and modeling of heat exchange at the nanoscale has become of central technological interest. Under a fundamental standpoint, metal nanoparticles (NPs) embedded in a host matrix constitute a model system, as they can be selectively heated-up and their cooling monitored using time-resolved spectroscopy1-3. The electromagnetic energy harvested by the NPs is dissipated as thermal energy in the environment. The corresponding energy flux Jp is ruled by the thermal boundary resistivity rbd, i.e., Kapitza resistivity, and by the temperature mismatch DT between the two media: Jp= DT/ rbd. Investigating rbd is, therefore, crucial to tailor thermal energy delivery from the NP to the matrix or matrix-embedded target and, more generally, to analyze heat transfer at the nanoscale.

Whereas effort has been devoted to understand and model the Kapitza resistivity between two solids, both bulk and thin films4-6, the scenario remains relatively unexplored when one of the two materials downscales to the nanometer range. A lack of extensive experimental evidence2,7,8 spanning the space of parameters affecting rbd, most notably the temperature9,10 , has so far prevented a consistent account of the mechanisms ruling the Kapitza resistivity at the nanoscale.

We here report on the temperature dependence of the thermal boundary resistivity in glass-embedded Ag particles of radius 4.5 nm, in the temperature range from 300 to 70 K, using all-optical time-resolved nanocalorimetry. The present results11 provide a benchmark for theories aiming at explaining the thermal boundary resistivity at the interface between metal nanoparticles and their environment, a topic of great relevance when tailoring thermal energy delivery from nanoparticles as for applications in nanomedicine and thermal management at the nanoscale.

1G. V. Hartland, Chem. Rev. 111, 3858 (2011). 2V. Juve , M. Scardamaglia, P. Maioli, A. Crut, S. Merabia, L. Joly, N. Del Fatti, and F. Valle e, Phys. Rev. B 80, 195406 (2009). 3A. Plech, S. Grésillon, G. von Plessen, K. Scheidt, and G. Naylor, Chem. Phys. 299, 183 (2004). 4E. D. Swartz and R. O. Pohl, Rev. Mod. Phys. 61, 605 (1989). 5R. J. Stoner and H. J. Maris, Phys. Rev. B 48, 16373 (1993). 6G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R.

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Phillpot, J. Appl. Phys. 93, 793 (2003). 7A. Plech, V. Kotaidis, S. Gre sillon, C. Dahmen, and G. von Plessen, Phys.

Rev. B 70, 195423 (2004). 8O. M. Wilson, X. Hu, D. G. Cahill, and P. V. Braun, Phys. Rev. B 66, 224301 (2002). 9E. D. Swartz and R. O. Pohl, Rev. Mod. Phys. 61, 605 (1989). 10R. J. Stoner and H. J. Maris, Phys. Rev. B 48, 16373 (1993). 11F. Banfi, V. Juvé, D. Nardi, S. Dal Conte, C. Giannetti, G. Ferrini, N. Del Fatti and F. Vallée, Appl. Phys. Lett. 100, 011902 (2012).

FIGURE 1. Kapitza resistivity ρbd vs cryostat temperature Tcryo (black circles). The horizontal arrows indicate the temperatures spanned by the nanoparticle during the thermalization process. Inset: normalized transmission change (red curve) and its best fit (black curve) for the case Tcryo=200 K.

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Controlling Low-temperature Thermal Conductance Using Phononic Crystals

Nobuyuki Zen,1 Tuomas Puurtinen,1 Tero Isotalo1 and Ilari J. Maasilta1 1 Nanoscience Center, Department of Physics, University of Jyväskylä, Finland

We have studied both experimentally and theoretically the thermal conductance of thin free-standing silicon nitride membranes at sub-Kelvin temperatures, with the main focus at controlling the conductance using periodic arrays of perforated holes on the membrane. These type of structures are also known as phononic crystals, where the acoustic phonon modes are strongly modified due to the periodic hole structure. The experiments were performed using sensitive normal metal-insulator-superconductor (NIS) tunnel junction thermometers.

Using finite element method based calculations, we have successfully found geometries which have a complete phononic bandgap in the energy range of the dominant thermal phonons at 100 mK. We have also developed an algorithm that successfully sorts the phonon energy surfaces in the 2D reciprocal space in such a way that intersecting energy surfaces are identified, so that correct group velocities can be calculated. Using the algorithm, we have then succeeded in calculating accurately the thermal conductance in the ballistic limit, which is relevant at low temperatures. The resulting thermal conductance is unisotropic due to the phononic crystal structure, and is significantly suppressed in comparison with the uncut membrane at temperatures above 100 mK, due to the significantly lower group velocities. However, at temperatures below 100 mK, the thermal conductance is actually enhanced because of the higher density of states below the gap in the phononic crystals.

Experimental results support the theoretical picture, with clear evidence of the suppression effect at higher temperatures (almost an order of magnitude), and a trend where the phononic crystal and full membrane results approach each other at around 100 mK.

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FIGURE 1. Optical micrograph (left) and a scanning electron micrograph (right) of a phononic crystal sample with a bandgap for thermal phonons at 100 mK.

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Control of phonon tranport via nanophononic crystals

Mahmoud I. Hussein* and Bruce L. Davis

Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, USA *[email protected]

The concept of a phononic crystal can in principle be realized at the nanoscale whenever the conditions for coherent phonon transport exist.1-6 Under such conditions, the dispersion characteristics of both the constitutive material lattice (defined by a primitive cell) and the phononic crystal lattice (defined by a supercell) contribute to the value of the thermal conductivity. It is therefore necessary in this emerging class of phononic materials to treat the lattice dynamics at both periodicity levels. In this work we investigate the thermal transport behavior of three-dimensional nanophononic crystals formed from silicon and cubic voids of vacuum (see Fig. 1). The periodicity of the voids follows a simple cubic arrangement with a lattice constant that is around an order of magnitude larger than that of the bulk crystalline silicon primitive cell. We consider an atomic-scale supercell which incorporates all the details of the silicon atomic locations and the void geometry. For this supercell, we compute the phonon band structure and subsequently predict the thermal conductivity following the Callaway-Holland model.

In our calculations we first perform a convergence analysis on a supercell representing bulk silicon (i.e., without voids). From this analysis we establish that when using the Callaway-Holland model a minimum supercell size is needed for an analysis based on supercell lattice dynamics to be representative of the properties of the underlying lattice model. Furthermore, a minimum wave vector sampling resolution is needed to properly capture the group velocities from the complex band structure that is represented in the nanophononic crystal’s Brillouin zone. The latter condition is independent of the type of thermal conductivity model used.

With these computational parameters established we study the effect of the nanophononic crystal unit cell size and volume fraction on the thermal conductivity. Figure 2 demonstrates the effect of the latter on the dispersion relations. Our findings show that for the relatively small voids and void spacings we consider (where boundary scattering is dominant), dispersion at the phononic crystal unit cell level plays a noticeable role in determining the thermal conductivity (see Fig. 3). Further details on this investigation are available in Ref. 7.

1N. Cleland, D. R. Schmidt, and C. S. Yung, Phys. Rev. B 64, 172301 (2001). 2A. Khitun, A. Balandin, J. L. Liu, and K. L. Wang, Superlattice Microst. 30, 1 (2001). 3A. J. H. McGaughey, M. I. Hussein, E. S. Landry, M. Kaviany and G. M. Hulbert, Phys. Rev. B 74, 104304 (2006). 4J.-N. Gillet, Y. Chalopin, and S. Volz, J. Heat Trans.-T. ASME 131, 043206 (2009). 5J. Yu, S. Mitrovic, D. Tham, J. Varghese and J. Heath, Nat. Nanotechnol. 5, 718 (2010). 6P. E. Hopkins, C. M. Reinke, M. F. Su, R. H. Olsson III, E. A. Shaner, Z. C. Leseman, J. R. Serrano, L. M. Phinney and I. El-Kady, Nano Lett. 11, 107 (2011). 7B. L. Davis and M. I. Hussein, AIP Advances 1, 041701 (2011).

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FIGURE 1. Macroscale versus nanoscale phononic crystal based on silicon: (a) macroscale

continuum model (scalable), (b) atomistic model (discrete, scale fixed by atomic spacing).

FIGURE 2. Dispersion of a supercell (consisting of 5×5×5 conventional cells) for various void

volume fractions vf. The curves for the nominal case (bulk, vf = 0%) are in black and the curves

for the nanophononic crystal (for increasing values of vf) are in red.

FIGURE 3. Supercell-based thermal conductivity calculations for nanophononic crystals without

boundary scattering

(solid black) and with boundary scattering

(dashed black),

both normalized with respect to a supercell-based thermal conductivity calculation for bulk

silicon with no boundary scattering

incorporated. Three supercell sizes, of side length

A = 2.2, 2.7 and 3.2 nm, are analyzed with varying volume fractions.

(a) (b)

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Brillouin Study of a Chessboard-structured

Bi-component Phononic Crystal

M. H. Kuok,1 V. L. Zhang,1 H. H. Pan,1 C. G. Hou, 1 H. S. Lim,1 S. C. Ng,1

M. Jamali,2 and H. Yang2

1Department of Physics, National University of Singapore, Singapore 117542 2Department of Electrical and Computer Engineering, National University of Singapore,

Singapore 117576

While much theoretical work has been done on the phonon dispersion relations of hypersonic phononic crystals, relatively little experimental research has been undertaken on them.1-3 Here we have used Brillouin light scattering to investigate the phonon dispersion relations of a two-dimensional bi-component hypersonic phononic crystal. The sample studied is in the form of a chessboard-structured periodic array of 250nm × 250nm cobalt and Ni80Fe20 squares on a SiO2/Si substrate. The dispersion relations have been measured for phonon wavevectors along the Γ-X and Γ-M directions. Partial phononic bandgaps have been observed. Numerical simulations of the frequency band structure using finite element analysis yield good agreement with experiment.

1T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, “Hypersonic phononic crystals”, Phys. Rev. Lett. 94, 115501 (2005).

2W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals”, Nat. Mater. 5, 830 (2006).

3A. A. Maznev and A. G. Every, “Surface acoustic waves in a periodically patterned layered structure”, J. Appl. Phys. 106, 113531 (2009).

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2D phononic crystal with anomalous behavior due to

overlapping Bragg and hybridization gaps

Eric J.S. Lee, Charles Croënne, and John H. Page

Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada

Many of the interesting properties of phononic crystals are due to the existence of band gaps, which may arise from a number of different mechanisms.1 The most familiar mechanism is Bragg scattering, which causes wave propagation to break down in certain frequency ranges due to the destructive interference of waves from the period structure of the crystals. Band gaps may also be caused by coupling between a scattering resonance and the propagating mode of the embedding medium; such gaps are often called hybridization gaps. Recently, the coexistence of both kinds of gaps in a single system has been shown for both 2D and 3D crystals, leading to remarkably deep and wide gaps in some cases.1-5 Open questions remain, however, about the nature of the interactions between Bragg and hybridization effects when the two overlap in frequency.

In this presentation, we investigate the effects of this coupling between Bragg and hybridization effects on the properties of simple 2D phononic crystals, where the lattice constant has been chosen to ensure that both mechanisms can occur in the same frequency range. The 2D phononic crystals consist of 0.46-mm-diameter nylon rods arranged in a triangular lattice and immersed in water. Nylon rods of this diameter have a strong scattering resonance for ultrasonic waves near 1 MHz; this resonance can be tuned in frequency by varying the temperature, enabling fine control of the overlap between hybridization and Bragg effects. The dispersion relations were measured experimentally from the phase of transmitted ultrasonic pulses and calculated theoretically by finite element simulations (using ATILA code). Typical

results for both the dispersion relations and transmission coefficients along the M direction are shown in Figs. 1 and 2. Good agreement between experiment and simulations is seen, revealing strikingly atypical behavior near the resonant frequency, with different phase characteristics being observed for different crystal thicknesses and temperatures. A quantitative interpretation of these results will be presented, showing that this anomalous behavior is a consequence of the coupling between the resonant states of neighboring rods.

1J. Croënne, E.J.S. Lee, H. Hu, and J.H. Page, “Band gaps in phononic crystals: Generation mechanisms and interaction effects”, AIP Advances 1, 041401 (2011). 2R. Sainidou, N. Stefanou, and M. Modinos, “Formation of absolute frequency gaps in three-

dimensional solid phononic crystals”, Phys. Rev. B 66, 212301 (2002). 3J. H. Page, S. Yang, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Tunneling and Dispersion in

3D Phononic Crystals”, Z. Kristallogr., 220, 859 (2005). 4T. Still, et al., “Simultaneous occurrence of structure-directed and particle-resonance-induced phononic gaps in colloidal films”, Phys. Rev. Lett., 100, 194301 (2008). 5V. Leroy, et al. “Design and characterization of bubble phononic crystals”, Appl. Phys. Lett, 95

171904 (2009).

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2 4 6 8

k' (mm-1)

(c) (d)

-60 -40 -20 0

Transmission (dB)

0.6

0.8

1.0

1.2

1.4

2 4 6 8

(a) (b)

Fre

quency (

MH

z)

k' (mm-1)

-60 -40 -20 0

Transmission (dB)

2 4 6 8

k' (mm-1)

(c) (d)

-60 -40 -20 0

Transmission (dB)

FIGURE 1. Experimental (a) dispersion relation and (b) transmission coefficient, and simulated

(c) dispersion relation and (d) transmission coefficient, obtained for four nylon-water PCs of

different thicknesses at room temperature, from one to seven layers.

FIGURE 2. Experimental (a) dispersion relation and (b) transmission coefficient, and simulated (c) dispersion relation and (d) transmission coefficient, obtained for the seven-layer-thick PC of

nylon rods in water at four different temperatures, corresponding to four different sets of water and nylon shear velocities.

0.6

0.8

1.0

1.2

1.4

2 4 6 8

Fre

quency (

MH

z)

k' (mm-1)

(a) (b)

-60 -40 -20 0

Transmission (dB)

Sim Exp CL Water c

s Nylon

1434.5 m/s 1000 m/s

1459.5 m/s 950 m/s

1505.4 m/s 900 m/s

1518.2 m/s 780 m/s

Brillouin zone boundaries

Sim Exp # of Layers

1

3

5

7

Brillouin zone boundaries

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Engineering the band diagram of one-dimensional hypersonic phononic crystals

Dirk Schneider,1 Faroha Liaqat,2 El Houssaine El Boudouti,3 Youssef El Hassouani,4

Bahram Djafari-Rouhani,5 Wolfgang Tremel,2 Hans-Jürgen Butt,1 George Fytas1,6 1 Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany

2 Johannes Gutenberg University, Duesbergweg 10–14, 55128 Mainz, Germany 3 LDOM, Département de Physique, Université Mohamed I, 60000 Oujda, Morocco

4 Département de Physique, Université Moulay Ismaïl, Boutalamine 52000, Errachidia, Morocco 5 IEMN, UMR-CNRS 8520, UFR de Physique, Université de Lille 1, 59655 Villeneuve d’Ascq, France

6 Department of Materials Science, University of Crete and FORTH, 71110 Heraklion, Greece

Phononic crystals have attracted increasing interdisciplinary interest due to their ability to mold the flow

of elastic energy that involves condensed matter physics and materials science. Various fabrication and

characterization techniques are being utilized to realize phononic structures with different

dimensionality, periodicity (meter-sized to nanoscale), and composing materials. No generalized full

description of phonon propagation in such structures is available as yet, mainly due to the large number

of variables determining their band diagrams. A detailed understanding is therefore necessary in order

to address fundamental concepts such as heat management and strong phonon-photon interactions.

From this perspective, high frequency phononics become important but their realization demands

fabrication at short length scales utilizing the wealth of polymer and colloid science. The phononic

dispersion relation at hypersonic frequencies is directly measured using the powerful non-destructive

technique of high-resolution spontaneous Brillouin light scattering (BLS).[1] Due to the vector nature of

the elastic wave propagation, theoretical phononic band structures can be uniquely verified at low

dimensionality[2] and hence 1D phononic crystals constitute appropriate model systems for fundamental

studies. Such hybrid Bragg stacks, composed of alternating layers of porous silica (p-SiO2) and

poly(methyl methacrylate) (PMMA), respectively, exhibit clear hypersonic phononic band gaps (gap

width up to 30%).[3] Here we report on the fabrication, characterization, and both experimental and

theoretical dispersion diagrams along and normal to the periodicity direction (on-axis) of silica/PMMA.

The width of the gap, the phonon frequencies, and their intensities near the first Brillouin zone are

sensitive probes of the longitudinal moduli and elasto-optic constants of the individual layers and

structural parameters. Mixing with saggital modes of the individual layers under oblique incidence (off-

axis) condition alters the observed dispersion and allows access to the shear moduli of the two layers.

Incorporation of defects holds a wealth of opportunities to engineer the band structure. The choice of

the cap layer, e.g., sensitively determines the width of the Bragg gap. A heteroperiodic Bragg stack, i.e.

two stacks of different lattice spacing joint together, launches new spectral features whose

computational description is on its way.

[1] W. Cheng et al.,“Observation and tuning of hypersonic bandgaps in colloidal crystals” Nat. Mater. 5, 830 (2006). [2] E. H. El Boudouti et al., “Acoustic waves in solid and fluid layered materials” Surf. Sci. Rep. 64, 471 (2009). [3] N. Gomopoulos et al., “One-Dimensional Hypersonic Phononic Crystals.” Nano Lett. 10, 980 (2010).

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FIGURE 1: Two Bragg-stacks and the phononic band gap at a glance; scanning electron

microscopy images (left) and splitting into two phonon branches (1 and 2, middle panel). The right panel maps the eight found frequencies in the normalized dispersion diagram.

FIGURE 2: Oblique phonon propagation and impact on the dispersion relation. a) Scheme of

experimental geometry. Theoretical dispersion relation f(qpara, qperp) around the center of the longitudinal acoustic band is illustrated in a 3D surface. The experimental data are depicted in

red and the theoretical dispersions f(qperp) at different qpara are presented by dotted lines.

FIGURE 3: Example for controlled defects. A joint heteroperiodic Bragg stack launches

additional modes in the BLS spectrum.

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Dynamics of a SASER oscillator

W. Maryam, A. V. Akimov, R. Campion and A. J. Kent

School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7

2RD, UK

We have measured the build-up time of the oscillations in a vertical-cavity superlattice saser device using the bolometric detection technique. The measured time is found to be consistent with numerical estimates based on the cavity lifetime and saser gain coefficient.

The experimental device was an MBE-grown vertical-cavity saser consisting of a 50-period gain superlattice (SL), each period consisting of 5.9 nm of GaAs and 3.9 nm of AlAs uniformly n-doped (with Si) to a density of 1017 cm-3. This structure has previously been shown to exhibit acoustic gain and acoustic spectral line narrowing under hopping electron transport1,2. The gain superlattice was within a 1.6 μm-long cavity defined by two SL Bragg reflectors at its ends. A single period of a mirror SL consisted of 4 nm of GaAs and 4 nm of AlAs. One mirror, the output coupler, had 16 periods and a reflectance of 97% at 325 GHz, and the high reflector had 40 periods and a reflectance of close to 100% at 325 GHz. The gain SL was pumped by electrical pulses of varying duration and amplitude applied via ohmic contacts, and the phonon flux exiting the cavity via the output coupler was detected using a superconducting Al bolometer on the opposite side of the semi-insulating GaAs substrate.

Based on earlier work using μs-duration pulses3, it is expected that when the Stark splitting matches the energy of the phonons confined within the cavity, the threshold for saser oscillation is achieved and there is a resonant peak in the detected phonon flux. Here it was found that for short pulses (<~ 100 ns) no such resonant peak was observed, but for longer pulses it was clearly detectable, Fig. 1. We attribute these observations to the finite build-up time for saser oscillations in the cavity, which we estimate to be of the order 100 ns.

By analogy to calculations of the build-up time in a laser oscillator4, we may use the following

expression to estimate the saser build up time,

(

) where τc is the cavity lifetime, r

is the normalised ratio of the initial unsaturated gain to the loss and (

) is the ratio of steady

state phonon intensity against the initial phonon intensity . Using the following values, τc = 23 ns,

r = 8.62 and (

) , we estimate ≈ 60 ns; in reasonably good agreement with the

measurements.

1 R P Beardsley, R P Campion, B A Glavin and A J Kent, New J. Phys. 13, 073007 2 R. P. Beardsley, A.V. Akimov, M. Henini, and A. J. Kent, Phys. Rev. Lett.104, 085501 (2010). 3 A. J. Kent, R. N. Kini, N. M. Stanton, M. Henini, B. A.Glavin, V. A. Kochelap, and T. L. Linnik, Phys. Rev. Lett.96, 215504 (2006). 4A.E Siegman, “LASERS”, Oxford University Press (1986), chapter 13.

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FIGURE 1. The acoustic signals (normalised to total electrical power) from the bolometer situated directly opposite the centre of the device as a function of the applied pump pulse amplitude at the early stages of build up (t = 45 ns) and after the build up is complete (t = 140 ns). The peak observed at 130 mV shows that a larger fraction of the supplied electrical power is reaching the bolometer opposite the device indicating saser oscillation occurring at this particular voltage.

0

10

20

30

40

0 100 200 300

at 140 ns after arrival of LAat 45ns after arrival of LA

Applied pump pulse (mV)

No

rma

lise

d a

co

ustic s

ign

al (a

rb.

un

its

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WEDNESDAY

Lifetime of High-Order Acoustic Thickness Resonances in Thin Silicon Membranes

A.A. Maznev,1 John Cuffe,2 Jeffrey K. Eliason,1 Timothy Kehoe,2 Clivia M. Sotomayor Torres,2,3 and Keith A. Nelson1

1 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2 Catalan Institute of Nanotechnology, Campus UAB, 08193 Bellaterra (Barcelona), Spain

3ICREA and Dept. of Physics, Autonoma University of Barcelona, Campus UAB, 08193 Bellaterra, Spain.

Acoustic attenuation at sub-THz frequencies at room temperature is largely unexplored even in well-characterized materials such as Si. Available data1 extending up to 100 GHz point to the existence of a local maximum of the intrinsic Q-factor below 1 THz. The question of whether this high Q-factor can be realized in nanomechanical systems has been addressed in recent studies of lifetime of fundamental thickness resonance modes in ultrathin silicon membranes.2,3 In this work, we extend the phonon

lifetime study to high-order thickness resonances of 0.4-1.5 m-thick membranes at frequencies ~0.25 THz. Short broad-band acoustic pulses were generated by 400 nm femtosecond laser pulses and detected at the opposite side of the membrane by probe laser pulses at the same wavelength. The detection process is preferentially sensitive to the Fourier-component of the acoustic pulse corresponding to twice the optical wavevector in the medium which leads to detection of a wavepacket centered at about 250 GHz 4 (see Fig. 1). The wavepacket bouncing back and force inside the membrane is composed of several high-order thickness resonance modes. The measured lifetime of these modes is found to be much shorter than the expected intrinsic phonon lifetime in Si. We believe that the main lifetime-limiting factor is inhomogeneous broadening caused by surface roughness with a large correlation length.

1B. C. Daly, K. Kang, Y. Wang, and D. G. Cahill, “Picosecond ultrasonic measurements of attenuation of longitudinal acoustic phonons in silicon”, Phys. Rev. B 80, 174112 (2009).

2A. Bruchhausen, R. Gebs, F. Hudert, D. Issenmann, G. Klatt, A. Bartels, O. Schecker, R. Waitz, A. Erbe, E. Scheer, J.-R. Huntzinger, A. Mlayah, and T. Dekorsy, “Subharmonic Resonant Optical Excitation of Confined Acoustic Modes in a Free-Standing Semiconductor Membrane at GHz Frequencies with a High-Repetition-Rate Femtosecond Laser”, Phys. Rev. Lett. 106, 077401 (2011).

3J. Cuffe O. Ristow, E. Chavez, J. Gomis-Bresco, P.-O. Chapuis, F. Alzina, M. Hettich, A. Shchepetov, M. Prunnila, J. Ahopelto, T. Dekorsy, and C. M. Sotomayor Torres, “Lifetimes of Confined Acoustic Phonons in Ultra-Thin Si Membranes”. presented at the 2011 MRS Fall Meeting in Boston.

4A. Devos, M. Foret, S. Ayrinhac, P. Emery, and B. Ruffl , “Hypersound damping in vitreous silica measured by picosecond acoustics”, Phys. Rev. B 77, 100201 (2008).

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FIGURE 1. Experimental configuration.

FIGURE 2. Preliminary data from a 400 nm-thick membrane: (a) transient reflectivity signal; (b) Fourier-transform reveals high-order thickness resonances of the membrane.

400 nm

pump

400 nm probe

to detector

membrane

0 50 100 150 200 250 300

7

7.5

8

8.5

9x 10

-7

time (ps)

sig

nal

acoustic pulse arrivals

Brillouin oscillations

150 200 250 300 3500

0.2

0.4

0.6

0.8

1

x 10-20

Frequency (GHz)

FF

T p

ow

er

(a)(b)

23rd

24th

25th

22nd

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WEDNESDAY

Mode shape and dispersion relation of bending waves in thin silicon membranes

Reimar Waitz1, Stephan Nößner1, Michael Hertkorn1, Olivier Schecker1,2, and Elke Scheer1

1 Universität Konstanz, D-78464 Konstanz, Germany 2now at: Robert Bosch GmBH, D-70839 Gerlingen-Schillerhöhe, Germany

We study the vibrational behavior of silicon membranes with a thickness of a few hundred nanometers and macroscopic lateral size1. A piezo stack is used for exciting transverse vibrations, which we monitor with a phase-shift interferometer using stroboscopic light. The observed wave pattern of the membrane deflection is a superposition of the mode corresponding to the excitation frequency and several higher harmonics. Using a Fourier transformation in time, we separate these contributions from each other and image up to the eighth harmonic of the excitation frequency (Fig. 1a-d). With this method we determine the dispersion relation of membrane oscillations in a frequency range up to 12 MHz (Fig. 1e, black dots). We develop a simple analytical model combining stress of a membrane and bending of a thin plate that describes both the experimental data and finite-elements (FE) simulations very well. The colored lines in Fig. 1e are calculated using the analytic formula. We derive correction terms to account for a finite curvature of the membrane and for the inertia of the surrounding atmosphere. Including these terms, we obtain excellent agreement between our analytic theory, the FE simulations, as well as the experimental results. Our findings pave the way for tailoring this kind of nanoscale membranes to the requirements of applications relying on particular properties of the vibrational excitations.

1R. Waitz, S. Nößner, M. Hertkorn, O. Schecker, and E. Scheer, “Mode shape and dispersion relation of bending waves in thin silicon membranes”, Phys. Rev. B 85, 035324 (2012).

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FIGURE 1. (a)-(d): Examples of measured eigenmodes of a membrane with size 714 µm x 691 µm x 340 nm. The excitation frequency is varied from 1 to 2 MHz. Higher frequencies are

accessed using harmonic excitations. Red and blue denote opposite sign of the phase with respect to the excitation. The darkness of the color is proportional to the deflection amplitude. (e): Dispersion relation. The black dots are experimental results calculated from modes like the ones shown in (a)-(d). The colored lines are calculated using the analytic formula. The apparent

scattering of the experimental data is of intrinsic nature. It results from the localization of modes to areas on the membrane of higher or lower stress and thus higher or lower frequency

for a given wave vector.

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WEDNESDAY

Confined coherent acoustic phonons in membranes

Thomas Dekorsy Department of Physics, Konstanz University, Konstanz, Germany

We investigate coherent acoustic phonons in different single-layer and double membrane systems by femtosecond pump-probe spectroscopy. We apply the method of high-speed asynchronous optical sampling which is based on two asynchronously locked femtosecond laser oscillators with approximately 1 GHz repetition rate. This method allows us to detect reflectivity changes below 10-7 within a few minutes of measurement times over 1 ns time delay with 50 fs resolution. 1,2 A model system for confined acoustic phonons are free-standing Si membranes.3 A superposition of coherent confined longitudinal acoustic modes of odd order is observed after impulsive optical excitation.4 The lifetime of these modes exceeds 5 ns at room temperature. This allows us to resonantly drive these modes by adjusting the repetition rate of the pump laser (1 GHz) to a sub-harmonic of the fundamental acoustic mode (19 GHz). By tuning the repetition rate we can map out the resonance excitation profile of the confined modes and accurately determine the Q factor.5 This method is promising for the investigation of coherent excitation and selective amplification of acoustic modes of single nanostructures.

In a double layer membrane system of aluminum and silicon we demonstrate the generation of an acoustic frequency comb combined of 24 modes of even and odd order spanning a frequency range from 12 GHz to 300 GHz. The lifetime of each mode can be accurately determined giving a quantitative measure of frequency dependent damping times over the full frequency range in a single measurement.

I like to thank all the people who contributed to this work: Axel Bruchhausen, Martin Schubert, Vitalyi Gusev, Florian Hudert, Oliver Ristow, Mike Hettich, Daniel Issenmann, Raphael Gebs, Albrecht Bartels, Oliver Schecker, Artur Erbe, Raimar Waitz, Adnen Mlayah, Jean-Roch Huntziger, and Elke Scheer.

1 A. Bartels et al., Rev. Sc. Instr.. 78, 035107 (2007).

2 R. Gebs et al., Opt. Express. 18, 5974 (2010).

3 C. M. Sotomayor Torres et al., Phys. Status Solidi C 1,2609 (2004).

4 F. Hudert et al., Phys. Rev. B 79, 201307 (2009).

5 A. Bruchhausen et al., Phys. Rev. Lett. 106, 077401 (2011).

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FIGURE 1. Sub-harmonic resonant driving of a coherent acoustic mode in a Si membrane with fundamental frequency of 19 GHz with 999.99 MHz repetition rate (top). Off-resonant

excitation (bottom) with 800 MHz laser repetition rate. Curves are vertically off-set for clarity.

FIGURE 2. Fourier transform of time-domain data in Fig. 1 for the case of of-resonant (800 MHz laser repetition rate) and resonant sub-harmonic excitation (999.99 MHz laser repetition rate).

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Confined coherent acoustic modes in aluminum/copper phthalocyanine thin films excited by femtosecond laser pulses

Huarui Sun,1 Vladimir A. Stoica,2 Max Shtein,3 Roy Clarke,2 and Kevin P. Pipe1,4 1 Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

2 Department of Physics, University of Michigan, Ann Arbor, MI, USA 3 Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA


Optical pump-probe techniques have been extensively used to study acoustic phonon dynamics in nanostructures. It has been shown that structures such as free-standing silicon membranes1, supported thin metal films2, and supported polymer layers3 exhibit confined longitudinal acoustic phonon modes when excited by a femtosecond pulsed laser. In this work we study the acoustic dynamics of such “membrane” modes by exciting an aluminum thin film that is in contact with a small molecular organic semiconductor (copper phthalocyanine, CuPc) thin film. The CuPc layer has a much smaller acoustic impedance than that of aluminum so it acts as an effective acoustic reflector to enhance the mode excitation and confinement. Acoustic modes of the Al/CuPc films up to the 5th order are observed, and the measured resonant frequencies show excellent agreement with the calculation. By varying the CuPc thickness, we are able to selectively increase or reduce the intensity of a specific mode. We find that the mode presents a bigger strength when the frequency is close to the normal mode of a single Al film. The non-monotonic dependence of the mode magnitude on frequency or the thickness results from the acoustic interference between both reflections at the Al/CuPc and CuPc/Si interfaces. We perform a finite difference time domain simulation to further compute the displacement field within the Al/CuPc films, and this provides insights to the physical origin of mode selection. The implications of these results are discussed in the contexts of acoustic resonators, acoustic Bragg reflectors, and interfacial thermal transport.

1F. Hudert, A. Bruchhausen, D. Issenmann, O. Schecker, R. Waitz, A. Erbe, E. Scheer, T. Dekorsy, A. Mlayah, and J.-R. Huntzinger, “Confined longitudinal acoustic phonon modes in free-standing Si membranes coherently excited by femtosecond laser pulses”, Phys. Rev. B 79, 201307(R) (2009). 2M. Hettich, A. Bruchhausen, S. Riedel, T. Geldhauser, S. Verleger, D. Issenmann, O. Ristow, R. Chauhan, J. Dual, A. Erbe, E. Scheer, P. Leiderer, and T. Dekorsy, “Modification of vibrational damping times in thin gold films by self-assembled molecular layers”, Appl. Phys. Lett. 98, 261908 (2011). 3A. V. Akimov, E. S. K. Young, J. S. Sharp, V. Gusev, and A. J. Kent, “Coherent hypersonic closed-pipe organ like modes in supported polymer films”, Appl. Phys. Lett. 99, 021912 (2011).

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Mechanical resonators in the quantum regime

Andrew Cleland1

1Department of Physics, University of California, Santa Barbara CA 93106 USA The superconducting quantum circuits group at UC Santa Barbara has spent the past ten years developing superconducting and nanomechanical systems for fundamental experiments in quantum mechanics.1,2,3,4 Our ultimate goal is to build a superconducting quantum computer. The Josephson junction, a fundamental superconducting device analogous to a transistor, provides an extremely nonlinear electrical circuit element that can be used as an “electronic atom”, and is the central active element in our approach to quantum computing. This unique device can detect and manipulate single quanta of energy, and has been used to demonstrate simple quantum algorithms. We have used this device to demonstrate full quantum control over microwave-frequency photons in electromagnetic resonators, and more recently demonstrated that we could measure the ground state of a macroscopic mechanical resonator, as well as create and manipulate individual phonons, the quanta of mechanical vibrations, in the same system. My talk will provide an introduction to the physics of superconducting quantum circuits, and outline how we can use these circuits to create and measure individual mechanical quanta; I will briefly outline an ongoing project to couple a superconducting circuit to a telecommunications optical signal. 1 M. Hofheinz et al., “Generation of Fock states in a superconducting quantum circuit “,Nature 454, 310-314 (2008) 2 M. Hofheinz et al., “Synthesizing arbitrary quantum states in a superconducting resonator”, Nature 459, 546-549 (2009) 3 A.D. O'Connell et al., “Quantum ground state and single-phonon control of a mechanical resonator”, Nature 464, 697-703 (2010) 4 M. Mariantoni et al., “Implementing the quantum von Neumann architecture with superconducting circuits”, Science 334, 61 (2011)

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Optomechanics in a GaAs Vertical Cavity for sub-THz Phonons and Visible Light

A. Fainstein,1 N. D. Lanzillotti-Kimura,1 B. Jusserand, 2 and B. Perrin2 1 Instituto Balseiro & Centro Atómico Bariloche, C.N.E.A., R8402AGP Bariloche, RN, Argentina

2 Institut des Nanosciences de Paris, UMR 7588 C.N.R.S. - Université Paris 6, 74015 Paris, France

Resonators that confine light and sound provide a platform to study novel quantum phenomena and for the development of new ultrafast devices. We show that GaAs/AlAs microcavities designed to confine photons are automatically optimal to confine acoustic phonons of the same wavelength, strongly enhancing their interaction. Optomechanical coupling at sub-THz acoustic frequencies is reported in these monolithic devices bridging the gap between optomechanics and optoelectronics in systems that have been used to demonstrate single-photon emitters and the most efficient (vertical cavity surface emitting) lasers. We study following the time evolution of the phonon strain in picosecond-laser experiments the impulsive generation of intense coherent and monochromatic acoustic phonons. Efficient optical detection is assured by the strong phonon backaction on the high-Q optical cavity mode.1,2

We demonstrate that these structures, that exploit the unsurpassed growth quality of molecular beam epitaxy, provide optomechanical devices that can attain very high mechanical and optical Q-factors (Q ~ 105), very low mechanical effective masses (meff ~ fg), large optomechanical coupling factors (gom ~ THz/nm), and ultra-high vibrational frequencies (sub-THz), while mantaining very efficient extraction efficiencies of both photons and phonons. We discuss the suitability of the proposed system for the demonstration of stimulated phonon emission through cavity parametric instability.

1N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent Generation of Acoustic Phonons in an Optical Microcavity”, Phys. Rev. Lett. 99, 217405 (2007).

2N. D. Lanzillotti-Kimura, A. Fainstein, B. Perrin, and B. Jusserand, “Theory of Coherent Phonon Generation in Optical Microcavities”, Phys. Rev. B 84, 064307 (2011).

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WEDNESDAY

Piezoelectric Optomechanical Crystals

Matt Eichenfield Sandia National Laboratories, Albuquerque, NM, USA

Optomechanical crystals (OMCs) are periodically patterned films with nanoscale dimensions with the ability to simultaneously control the properties of optical photons and microwave phonons by creating simultaneous bandgaps for equi-wavelength optical and acoustic modes. Geometric defects within OMCs thus allow the simultaneous localization of line and point defects, which allow these waves to interact in a deterministic and tailorable way, with an interaction strength that can be finely tuned all the way from zero to the maximum strength that the diffraction limit allows. Along with the ability to fabricate very low-loss confining structures, this gives the optomechanical waveguides and cavities created in OMCs exquisite measurement sensitivity, including the ability to optically transduce mechanical motion due to zero-point fluctuations. In this talk, I will discuss a new class of OMCs fabricated in piezoelectric nanoscale thin films. The introduction of piezoelectricity into this system allows an independent channel for creating and detecting phonons in OMCs. This allows new kinds of measurements and devices to be made from these exquisitely sensitive systems. As a particular example, I will discuss the design of microwave frequency optical frequency shifters and acousto-optic modulators in POMCs made from Aluminum Nitride; these devices can be integrated with CMOS to create DC-powered optoelectronic circuits that manipulate photons with microwave phonons and vice-versa.

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WEDNESDAY

Surface optomechanics: calculating surface acoustic wave generation on microsphere via photon-phonon interaction

John Zehnpfennig1,*, Gaurav Bahl2, Matthew Tomes2, and Tal Carmon2

1United States Military Academy, Photonics Research Center and EE&CS, West Point, NY, USA

2University of Michigan, Electrical and Computer Engineering, Ann Arbor, MI, USA

*[email protected]

We recently demonstrated Brillouin scattering in a glass-sphere microresonator where both the mechanical and optical modes are high-quality whispering-gallery modes. Vibrations at rates from 50 MHz1 to 12 GHz2 by forwared1- and backward2-Brillouin scattering were optically excited and interrogated. Further, we could also Brilouin cool1 such modes. Being relevant for optomechanical resonators1-3, we calculate here the form and rate of the mechanical whispering galleries. We calculate longitudinal, transverse and Rayleigh type whispering galleries, each of these mode families has members of higher order in the azimuthal, radial and polar directions that are also calculated. A reach world of mechanical whispering gallery resonances in microspheres are reported here4 which is now experimentally accessible.

While acoustical waves are known to be excited via photon-phonon interplay3 this Brillouin effect was rarely investigated in the context of mechanical resonances. Studies in Brillouin scattering recently evolved to the mm- and micron-scaled devices.1, 4 For example, Brillouin scattering nowadays enables optical excitation of mechanical whispering-gallery modes5 at 50 MHz to 12 GHz rates that are circumferentially circulating in a 100-micron silica sphere resonator.1, 2

Here we numerically calculate mechanical whispering-gallery modes similar to the ones that were experimentally observed.1, 2 Unlike optics where modes are usually restricted to two polarization states, our calculation reveals various mechanical whispering gallery modes including with longitudinal [L], transverse [T] and Rayleigh-type [R] deformations. For the Rayleigh6 whispering-gallery mode, particle motion is along an elliptical track.

Additionally, we change the number of acoustical waves resonating along the circumference from 10 to 2000, corresponding to observed vibrations at 50 MHz to 12 GHz rates. The polar- and radial-order of these modes was also parametrically studied as shown in Figure 2. We will present these calculations side-by-side with experimental observations.

Modes are confined to within a wavelength distance from the surface and were hence named surface modes. Similar to what is known in earthquake research; modes with transverse, longitudinal, and Rayleigh type deformation were calculated. These whispering gallery modes are not leaking through the support, suggesting that their dissipation can be reduced to the material limit without the need for a special sound-isolating supports. 1G. Bahl, J. Zehnpfennig , M. Tomes, and T. Carmon, "Stimulated optomechanical excitation of surface acoustic

waves in a microdevice", Nature Communications 2, 403, (2011). 2M. Tomes, and T. Carmon, "Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates",

Physical Review Letters, 102(11), 113601, (2009). 3R.W. Boyd, Nonlinear Optics, Academic Press, (2008).

4J. Zehnpfennig , G. Bahl, M. Tomes, and T. Carmon, "Surface optomechanics: calculating optically excited

acoustical whispering gallery modes in microspheres", Optics Express, 19(15), 9, (2011). 5L. Rayleigh, "The problem of the whispering gallery", Philos Mag 20(120), 1001–4, (1910).

6L. Rayleigh, "On waves propagated along the plane surface of an elastic solid", Proc London Math Soc, 1(1), 4,

(1885).

mailto:*[email protected]

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FIGURE 1. Illustration of the mechanical whispering gallery resonance in a sphere. Deformation of the outer surface describes the exaggerated

mechanical deformation. The cuts reveal also the internal deformation as indicated by colors.

FIGURE 2. High-order mechanical whispering gallery modes. Top: Increasing the mode order in the radial and polar directions for mechanical

whispering galleries in a silica sphere. Color stands for deformation; the sphere circumference is 20 in units of wavelength. Below: We depicted several of the top modes and present them in 3D. The presented section is one wavelength in the azimuthal direction. The equator is seen to

deform into a sine while for the Rayleigh mode, the sine deformation is in the radial direction and for the transverse mode the sine deformation is in the polar direction.

189

WEDNESDAY

Observation of Spontaneous Brillouin Cooling

Gaurav Bahl1*, Matthew Tomes1, Florian Marquardt2,3, Tal Carmon1 1Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan, USA

2Institut fur Theoretische Physik, Universitat Erlangen-Nurnberg, Erlangen, Germany 3Max Planck Institute for the Science of Light, Erlangen, Germany

While radiation-pressure cooling is well known [1-5], the Brillouin scattering of light from sound has been considered an acousto-optical amplification-only process. Here we experimentally demonstrate the cooling of a Brownian surface-acoustic-wave whispering-gallery resonance by using the Brillouin scattering process in a silica microsphere [6]. This work shows, for the first time, a new regime of operation for the Brillouin process where cooling of acoustical modes is allowed.

Light is coupled evanescently to a silica microsphere resonator [7] through a tapered optical fiber [8]. Photons in a whispering gallery optical mode of the sphere interact with a whispering gallery acoustical mode [9] that photoelastically forms an optical grating that is traveling at the speed of sound [10]. Pump photons can be scattered in both Stokes and anti-Stokes frequencies by the existing Brownian phonons of the mechanical mode. In our system, however, an optical resonance at the Stokes frequency does not exist and Stokes scattering can be suppressed. Instead, the presence of an optical resonance at the anti-Stokes frequency allows for resonant enhancement of the cooling process, stealing energy from the acoustical phonons, as illustrated in Figure 1(a), thereby cooling the mode. Light is coupled out of the resonator through the same tapered fiber and the power reflectance of the acoustic “grating” is measured with electrical and optical spectrum analyzers in order to determine linewidth and phonon profile.

1 O. Arcizet et al, Nature, vol. 444, pp. 71–74, Nov 2006.

2 S. Gigan et al, Nature, vol. 444, pp. 67–70, Nov 2006.

3 D. Kleckner and D. Bouwmeester, Nature, vol. 444, pp. 75–78, Nov 2006.

4 R. Riviere et al, Physical Review A, vol. 83, June 2011.

5 J. Chan et al, Nature, vol. 478, pp. 89-92, Oct 2011.

6 G. Bahl et al, Nature Physics, vol. 8, no. 3, pp. 203-207, Mar 2012.

7 M. L. Gorodetsky and V.S. Ilchenko, Optics Communications Vol. 113, Issues 1-3 (1994). 8 M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000). 9 J. Zehnpfennig, G. Bahl, M. Tomes, T. Carmon, Optics Express, Vol. 19, pp. 14240-8 (2011). 10 G. Bahl et al, Nature Communications, 2:403, doi:10.1038/ncomms1412 (2011).

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FIGURE 1. (a) To observe cooling, the process of heating via Stokes scattering from

Brownian phonons must be suppressed since heating sees positive feedback and

dominates any experiment. A pair of optical resonances must be found such that there is

an asymmetry leading to the enhancement of the anti-Stokes process instead. (b) We use

high order optical modes of a silica microsphere resonator to achieve this asymmetry. The

acoustic modes that are cooled are whispering gallery resonances. (c) This experimental

example shows the cooling of a 95 MHz mechanical mode. The electrical spectrum shown

is a result of the two beating optical signals (pump line and anti-Stokes line), and a

broadening of the acoustic profile as input pump power is increased.

191

WEDNESDAY

Anharmonic Phonon Decay as a Parametric Squeezing Process

Stephen Fahy,1,3 Eamonn D. Murray,2 and David A. Reis3,4 1Tyndall National Institute and Department of Physics, University College, Cork, Ireland

2Department of Chemistry, University of California, Davis, CA, USA

3Stanford Pulse Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

4Departments of Photon Science and Applied Physics, Stanford University, Palo Alto, CA, USA

We consider the anharmonic coupling of a phonon in a periodic solid to other modes throughout the Brillouin zone. Using an analysis, based on classical dynamics of the coupled modes, we show that, in addition to the well-known anharmonic decay process,1 the coupling of a coherent phonon to other modes also gives rise to squeezed phonon states throughout the Brillouin zone. These squeezed states are intrinsic to the anharmonically coupled motion and appear classically as correlations between the phases of distinct harmonic modes at any given point of the zone. The correlated motion is most prominent in, but is not confined to, those regions of the zone, to which resonant decay of the coherent mode occurs.

These squeezed states give rise to oscillations in the diffuse x-ray scattering signal at the frequency of the coherent mode, which are distinct, both from oscillations that arise from the direct variation of the x-ray structure factor due to the coherent phonon motion, and from oscillations arising from any harmonic softening of modes throughout the Brillouin zone.

We present classical dynamical simulations of ultrafast photo-excitation and decay of the A1g zone-centre coherent phonon mode in bismuth. The harmonic and anharmonic force constants in the photo-excited material are calculated using density functional theory.2 We find a phonon decay rate in good agreement with experiment and with second order perturbation theory. We calculate the diffuse x-ray scattering signal throughout the Brillouin zone for photo-excitation levels that are experimentally feasible and find that the amplitude of oscillations, arising from the non-linear squeezing effect, should be experimentally detectable using recently available time-resolved x-ray light sources.

1A. Debernardi, “Phonon linewidth in III-V semiconductors from density-functional perturbation theory”, Phys. Rev. B 57, 12848 (1998).

2 E. D. Murray, S. Fahy, D. Prendergast, T. Ogitsu, D. M. Fritz and D. A. Reis, “Phonon dispersion relations and softening in photoexcited bismuth from first principles”, Phys. Rev. B 75, 184301 (2007).

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WEDNESDAY

Ultrafast X-ray diffraction from coherent and incoherent phonons

Roman Shayduk,1 Daniel Schick,2 Peter Gaal,1 Hengameh Navirian,2 Mark Herzog,2 Wolfram Leitenberger,2 Jevgeni Goldshteyn1 and Matias Bargheer1,2

1 Helmholtz Center for Material and Energy, Berlin, Germany 2 Potsdam University for Physics and Astronomy, Potsdam, Germany

We excite epitaxial SrRuO3-related thin films and SrRuO3/SrTiO3 (SRO/STO) multilayers by a short 200fs infrared laser and probe the structure dynamics with ultra short X-rays. The experiments are done in a pump-probe scheme at 1kHz repetition rate using a table-top fs plasma X-ray source and as well at 200kHz at the dedicated beamline of storage ring BESSY1,2. The plasma X-ray source has a resolution of about 200fs and the synchrotron has a resolution of 100ps due to the electron bunch length, though higher X-ray flux is available at the synchrotron.

We synthesize quasi-monochromattic longitudinal acoustic phonons in the STO substrate by the multi-pulse laser excitation of thin epitaxial SRO films3. The coherent phonon frequency is determined by the laser multi-pulse period and can be varied in the range of 0.1-1THz.

Alternatively, coherent acoustic phonons can be synthesized via excitation of metallic layers in SRO/STO multilayers4. The frequency of the generated phonons in this case is determined by the multilayer structure. Due to the small thickness of the multilayer the coherent acoustic phonons couple to the STO substrate and leave the SL on timescales of 37ps after the excitation5. We observe the coherent acoustic phonons in the multilayer as well as their propagation into the STO substrate on timescales from 1ps to 3ns.

On timescales longer than 50ps after the excitation, only incoherent phonons remain in the multilayer in the form of heat. We determine the relevant timescales of the multilayer thermalization due to the process of heat diffusion. We demonstrate experimentally the ultrafast (order of 10ps) heat exchange between the SRO and STO sublattices in the SRO/STO multilayer. We also monitor the process of heat propagation through the multilayer into the

substrate on timescales from 100ps to 4s, from which the effective heat conductivity of the superlattice is estimated2.

1 F. Zamponi et al, “Femtosecond hard X-ray plasma sources with a kilohertz repetition rate”, App. Phys. A. 96, 51-58, (2009).

2 R. Shayduk et al, “Nanoscale heat transport studied by high-resolution time-resolved x-ray diffraction”, New Journal of Physics 13, 093032 (2011).

3 M. Herzog et al, “Detecting optically synthesized quasi-monochromatic sub-terahertz phonon wavepackets by ultrafast x-ray diffraction “, Appl. Phys. Lett. 100, 094101 (2012).

4 M. Bargheer at al, “Excitation mechanisms of coherent phonons unravelled by femtosecond X-ray diffraction”, Phys. Stat. Sol. B 243, 2389-2396, (2006).

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5 M. Herzog et al, “Analysis of ultrafast X-ray diffraction data in a linear-chain model of the lattice dynamics”, Appl. Phys. A 106, 489-499, (2012).

0 3 6 90.4

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FIGURE 2. The SRO/STO multilayer Bragg peak integrated intensity and the peak shift as a function of probe delay. On both plots black squares are experimental data points measured simultaneously. The blue curves are the theoretical curves for the case of no heat conduction in the multilayer. The red curves are the theoretical curves for the case with the heat conduction. The data demonstrates that heat exchange between the metal/dielectric layers in the SRO/STO multilayer occurs on timescales shorter than 100ps.

194

WEDNESDAY

Anharmonic phonons seen by ultrafast x-ray diffuse scattering

Mariano Trigo1, David A. Reis1 1PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

Our understanding of electron-phonon and phonon-phonon scattering is incomplete even in relatively well-known materials such as Si1. This is in part due to the lack of scattering probes with sufficient momentum and temporal resolution to access these processes in the time-domain. Here we present first ultrafast x-ray diffuse scattering images of photo-induced nonequilibrium phonons that show anharmonic decay over large areas of the Brillouin zone. These results are enabled by the recent availability of high-brightness x-ray sources at synchrotrons and free electron lasers that make possible the imaging of structural dynamics with atomic scale resolution and femtosecond to nanosecond time resolution. Our work shows that photoexcited polar semiconductors InP and InSb exhibit a subtle but long-lived nonequilibrium state corresponding to the delayed emission of transverse acoustic phonons that occur over several hundred picoseconds. Further, we will show preliminary results on the electron-phonon and phonon-phonon processes that occur on the natural femtosecond timescales that were obtained at the Linac Coherent Light Source (LCLS). These experiments demonstrate the ability of ultrafast x-ray diffuse scattering to probe phonon processes in the time-domain and hold promise as a viable alternative to dispersive inelastic x-ray scattering with the potential to revolutionize the phonon spectroscopy of non-equilibrium states of matter.

We thank our many collaborators on the APS and LCLS experiments, including M. Fuchs, J. Chen, M. Jiang, D. Fritz, M. Cammarata, H. Lemke, D. Zhu, T. Graber, R. Henning, M. Kozina, V. Vishwanath, Y. M. Sheu, A. Lindenberg, K. Gaffney, K. Sokolowski-Tinten, F. Quirin, S. Johnson, S. Ghimire, G. Ndabashimiye, T. Huber, J. Larssen, J. Wark, A. Higginbotham, C. Uher, G. Wang and F. Krasniqi. This work was supported by US Department of Energy office of Basic Energy Science through the Division of Materials Sciences and Engineering. Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. LCLS is an Office of Science User Facility operated for the US Department of Energy (DOE) Office of Science by Stanford University. Use of the Advanced Photon Source, an Office of Science User Facility operated for the US DOE Office of Science by Argonne National Laboratory, was supported by the US DOE under contract DE-AC02-06CH11357. Use of the Bio-CARS Sector 14 was supported by the National Institutes of Health, National Center for Research Resources, under Grant No. RR007707.

1David G. Cahill, Wayne K. Ford, Kenneth E. Goodson, Gerald D. Mahan, Arun Majumdar, Humphrey J. Maris, Roberto Merlin and Simon R. Phillpot, J. of Appl. Phys. 93, 15 (2003)

2M. Trigo, J. Chen, V. H. Vishwanath, Y. M. Sheu, T. Graber, R. Henning, and D. A. Reis. “Imaging nonequilibrium atomic vibrations with x-ray diffuse scattering”, Phys. Rev. B 82, 235205 (2010)

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FIGURE 1. (a) – (d) Laser-induced x-ray diffuse scattering from InP at room temperature for different x-ray-laser delays. The patterns show several Brillouin zones where the brightness is proportional to the increase in phonon population at a given momentum transfer induced by

photoexcitation.

FIGURE 2. (a) and (b) Contributions to the nonequilibrium component of the time-resolved diffuse scattering from InP with contours representing the contribution to the thermal diffuse

scattering by transverse acoustic phonons. (c) The same data with the Brillouin zones superimposed. (d) Time dependence of the non-thermal contribution.

196

WEDNESDAY

Vibrational Dynamics and Thermodynamics of Nanocrystalline Materials

S. Stankov,1 M. Miglierini,2,3 A. I. Chumakov,4 I. Sergueev,4 Y. Z. Yue,5,6 B. Sepiol,7 P. Svec,8 L. Hu,5,6 and R. Rüffer4

1Institute for Synchrotron Radiation, Karlsruhe Institute of Technology, Karlsruhe, Germany 2Department of Nuclear Physics and Technology, Slovak University of Technology, Bratislava,

Slovakia 3Center for Nanomaterials Research, Palacky University, Olomouc, Czech Republic

4European Synchrotron Radiation Facility, Grenoble, France 5Section of Chemistry, Aalborg University, Aalborg, Denmark

6Key Laboratory of Liquid Structure and Heredity of Materials, Shandong University, Jinan, China 7Faculty of Physics, University of Vienna, Vienna, Austria

8Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia

The atomic vibrations in nano-scale materials have attracted a considerable interest due to the observed striking differences with respect to the bulk counterparts1. The anomalies are an enhancement of the phonon density of states (DOS) at low and high energies and broadening of the phonon peaks. In addition, the energy dependence of the low-energy part of the phonon DOS has been a source of long-standing debates. The experimental and theoretical results are contradictory, reporting a linear2, a power low with n=1.53 and n=1.334, and a quadratic Debye-like behavior5. Consequently, anomalies in the vibrational thermodynamics have been observed6.

In order to further investigate these anomalies we have studied the vibrational properties of nanocrystalline Fe90Zr7B3 (Nanoperm) alloy via 57Fe nuclear inelastic scattering of synchrotron radiation. The atomic vibrations of the nanograins were separated from those of the interfaces for a wide range of grain sizes and interface thicknesses. Surprisingly, the results show that the atomic vibrations of the Fe nanograins do not vary with their size and even for 2 nm grains still closely resemble those of the bulk iron7, Fig. 1(a). The observed anomalies of the vibrational and thermodynamic properties originate solely form the atoms located at the nanocrystalline interfaces8, Fig. 1(b), and scale linearly to their atomic fraction Fig. 2.

S.S. acknowledges the support by the Helmholtz Association via the contract VH-NG-625.

1B. Fultz, Prog. Mater. Sci. 55, 247 (2010). 2U. Stuhr et al., Phys. Rev. Lett. 81, 1449 (1998). 3P. M. Derlet et al., Phys. Rev. Lett. 87, 205501 (2001). 4B. Roldan Cuenya et al., Phys. Rev. B 76, 195422 (2007). 5L. Pasquini et al., Phys. Rev. B 66, 073410 (2002). 6D. Wolf et al., Phys. Rev. Lett. 74, 4686 (1995). 7S. Stankov et al., Phys. Rev. Lett. 100, 235503 (2008). 8S. Stankov et al., Phys. Rev. B 82, 144301 (2010).

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FIGURE 1. Fe-projected phonon density of states of the nanograins for various grain sizes (a) and of the interfaces for various interface thicknesses (b) in Fe90Zr7B3 (reproduced from Ref. 7).

FIGURE 2. Vibrational entropy (a), lattice specific heat (b), mean atomic displacement (c), and mean-force constants (d) of Fe90Zr7B3 as a function of the intercrystalline fraction XIC (reproduced from Ref. 8).

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WEDNESDAY

Probing Zone Boundary Phonons at the Nanoscale

Gokul Gopalakrishnan1, Martin Holt

2, Kyle McElhinny

1, J. W. Spalenka

1, David

Czaplewski2, Tobias Schülli

3, Paul Evans

1

1 Materials Science and Engineering, University of Wisconsin, Madison, WI, USA

2 Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, USA

3 Structure of Materials Group, European Synchrotron Radiation Facility, Grenoble, France

The emerging ability to control the thermal properties of materials using nanotechnology arises

in large part from boundary scattering and confinement effects. Predictions that the phonon

dispersion can be modified by confinement have so far been tested only in the high-phonon-

energy regime of optical phonons near the center of the Brillouin zone. In macroscopic samples

the remainder of the zone can be probed by inelastic x-ray or neutron scattering which provide

the dispersion of large wave vector phonons. In individual or small ensembles of nanomaterials

inelastic signals become impractically weak and other methods must be identified to probe the

phonon dispersion.

Thermal diffuse scattering (TDS) collects information from scattering of x-rays by phonons with

wave vectors spanning the entire Brillouin zone, and with particular sensitivity to low-energy

vibrational modes. High brilliance x-ray sources at synchrotron radiation facilities now make it

possible to collect TDS signals from volumes of material matching the size of nanoscale

systems. Synchrotron x-ray TDS measurements performed on suspended silicon nanomembranes

probe large wave vector phonon modes near zone boundaries and reveal deviations from bulk-

like behavior in membranes with thicknesses of up to several tens of nanometers, beyond the

regime where confinement is predicted to significantly modify the dispersion of phonons.

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THURSDAY

Phonons in Mesoscale Structures: from super-resolution focusing with phononic crystals to

Anderson localization in mesoglasses*

John H. Page

Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada

Acoustic phonons in mesoscopic materials exhibit a wide range of interesting phenomena due to strong scattering from their internal structures. Ultrasonic techniques are well suited for investigating such phenomena since complete information about wave propagation (both amplitude and phase, in both time and space) can be measured directly. Moreover, samples with well controlled mesoscale structures can be readily fabricated due to the convenient length scales associated with ultrasonic waves at MHz frequencies. In this talk, I will illustrate recent progress in this field with two contrasting examples: focusing of ultrasound with phononic crystals and Anderson localization in disordered mesoglasses.

Since focusing of acoustic waves by negative refraction in phononic crystals was first demonstrated several years ago 1, there has been increasing interest in the possibility that focusing with resolution better than the diffraction limit may be achievable 2. By combining ultrasonic measurements and Finite Difference Time Domain simulations, we have shown since then that super-resolution focusing can indeed be realized in practice (Fig. 1) 3. I will examine the mechanisms influencing the resolution limit of our flat phononic crystal lens, and comment on prospects for phononic crystal lenses with improved resolution capabilities.

In disordered media, one of the most challenging and fascinating aspects of phonon transport is Anderson localization. The origin of this remarkable effect is the “trapping” of multiply scattered waves by interference due to strong disorder. Only recently has one of the most central questions - whether or not the Anderson localization of acoustic phonons can really occur in three-dimensional disordered materials – been unambiguously answered 4. Our demonstration of ultrasound localization in a disordered mesoglass is opening up new opportunities to study aspects of acoustic phonon localization that have not previously been amenable to experimental investigation, including a detailed investigation of its effects on the transverse spatial confinement of the modes (Fig. 2), as well as wavefunction multifractality, long and infinite range correlations, and coherent backscattering. This work is contributing to the current resurgence of interest in localization across several domains of physics 5.

*Work performed with A. Sukhovich, H. Hu, A. Strybulevych, W.K. Hildebrand, L.A. Cobus, E.J.S. Lee, S.E. Skipetrov, B.A. van Tiggelen, A. Derode, A. Aubry, J.-F. Robillard, J. Bucay, B. Merheb, A. Shelke, K. Muralidharan, P.A. Deymier and J.O. Vasseur. 1S. Yang, J.H. Page, Z. Liu, M.L. Cowan, C.T. Chan & P. Sheng, Phys. Rev. Lett. 93, 024301 (2004). 2A. Sukhovich, Li Jing and J.H. Page, Phys. Rev. B 77, 014301 (2008). 3A. Sukhovich, et al., Phys. Rev. Lett. 102, 154301 (2009). 4H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov & B.A. van Tiggelen, Nature Phys. 4, 945 (2008) 5e.g., see Physics Today, August 2009.

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FIGURE 1. Super-resolution focusing of ultrasound at 530 kHz by a flat 6-layer 2D phononic crystal consisting of 1-mm-diameter steel rods arranged in a triangular lattice and immersed in methanol. The medium outside the crystal is water. (a) FDTD calculations of the average pressure amplitude when a subwavelength source is placed just below the surface of the crystal. An image of the source is seen near x = 0 and z = 3.5 mm, as shown (b) and (c) for FTDT simulations and experiments, respectively. (d) and (e): Comparison of experiment and theory for the field amplitude through the peak of the focal spot along directions parallel and perpendicular to the lens surface. The experimental results and

theoretical predictions for the half width of the focal spot parallel to the surface, /2, are found to be

0.37 and 0.35.

FIGURE 2. (a) One of the mesoglass samples, made by brazing 4-mm-diameter aluminum beads together into a solid elastic network, in which 3D Anderson localization of ultrasound has been observed. (b) Instead of spreading diffusely with time (dashed black line), ultrasound emitted by a pulsed point source is confined in both space and time, an effect that is measured by transverse width w of the intensity profile at the far side of the sample. (Here w is less than the sample thickness L). Data for two samples

are shown for several transverse distances , revealing how localization causes the spatial intensity profile to saturate at long times, and providing direct evidence for Anderson localization4.

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

(b)

L / = 3.6

Exp't Theory

= 25 mm

= 20 mm

= 15 mm

L / = 1

Exp't Theory

= 30 mm

= 25 mm

= 20 mm

= 15 mm

w 2 /

L 2

Time (s)

(a)

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Anderson Universality in a Model of Disordered Phonons

Sebastian D. Pinski,1 Walter Schirmacher,2 and Rudolf A. Roemer1 1 Department of Physics & Centre for Scientific Computing, University of Warwick,

Coventry, CV4 7AL, UK 2 nstitut fu r h sik ni ersita t ain - D-55099 Mainz, Germany, EU

The Anderson model (AM) of localization has been a major topic of research for over 50 years. The resemblance of this model with that of the ‘scalar’ model of phonon locali ation (S L) due to disorder has been noticed in 1D systems.1 Past research on the SMPL has been heavily directed towards the vibrational density of states and unearthing the origins of the boson-peak, with the delocalized-localized transition assumed to be close to the upper band edge.2 We present work on a transformation between the AM and the SMPL that has enabled direct translation of the electron phase diagram with on-site potential disorder3 to that of a phonon phase diagram with mass disorder.4 This has been verified with high accuracy transfer matrix method (TMM) calculations.4 Phononic phase diagrams for both mass and force-constant disorder in the SMPL are presented for the first time and the implications of these diagrams are discussed. Finally, finite size scaling of the results obtained from TMM indicates that the critical exponent of phononic systems are equivalent to that of electronic systems.

1 S. Russ “Scaling of the locali ation length in linear electronic and ibrational s stems with long-range correlated disorder” Phys. Rev. B, 66, 012204 (2002)

2 S. N. Taraskin, J.J. Ludlam, G. Natarajan and S. R. Elliott “Propagation, hybridization and locali ation of ibrational excitations in disordered materials” Philosophical Magazine B, 82(2), 197–208 (2002).

3 B. Bulka . Schreiber and B. Kramer “Locali ation quantum interference and the metal-insulator transition” Z. Phys. B, 66, 21 (1987)

4 S. D. Pinski W. Schirmacher and R. A. Roemer “Anderson ni ersalit in a odel of Disordered honons” Europhys. Lett., 97, 16007 (2012)

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(a) (b)

FIGURE 1. Schematic representation of critical amplitude distributions obtained from exact diagonali ation for (a) mass disorder ∆m=4 at frequenc ω2 =4.134 and (b) force-constant disorder ∆k=1 at frequenc ω2 =12.526 in systems of size L3=703.

(a) (b)

FIGURE 2. Phase diagrams for (a) mass (∆m s. ω2) and (b) force-constant (∆k s. ω2) disorder. Spotted red shadings are the regions of localized states, cross-hatched red shadings enclose by a red lines (band edges) are inaccessible regions. The horizontal dash-dotted line indicates the border between stable and unstable regions the dotted lines denote ω2 = 0 and 6. Black diamonds and white circles are the three transition values obtained from finite size scaling and the other estimated transition points respectively. Additionally in (a) the grey shading denotes the critical region obtained from the transformation from the electronic phase diagram.3

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Decay of Spontanous Polarisation Echoes in Glasses

M. Bazrafshan, M. Schwarze, P. Fassl, A. Halfar, A. Fleischmann, and C. Enss

Heidelberg University, Kirchhoff-Institute for Physics, INF 227, D-69120 Heidelberg, Germany

Low temperature properties of glasses are governed by atomic tunneling systems. Many aspects are well described within the phenomenological standard tunneling model. Via their elastic and electric dipole moments tunneling systems interact mutually and with external fields. In recent years, the influence of two-level systems on the coherence of solid state qubits has drawn much attention. Similarly, the deteriorating effects of atom tunneling systems on the performance of kinetic inductance detectors and their rule in the 1/f noise in dc SQUID systems at very low temperatures have been studied intensively. The detailed understanding of the dynamics of atomic two level systems is therefore of vast importance for finding ways to improve such devices. One method to study the phase coherence of two level systems in glassy materials is to measure the phase memory time in two-pulse polarization echo experiments. Here the echo amplitude is measured as a function of the delay time between the two excitation pulses. Different dephasing mechanism contribute to the decay of the echo amplitude. In amorphous dielectrics at very low temperatures the dominating dephasing mechanism is spectral diffusion, which is the interaction of resonant tunneling systems with non-resonant thermally fluctuating ones. We have performed such echo decay measurements with an improved setup allowing us to observe echoes at very long delay times where the echo has decayed five orders of magnitude from its original amplitude. The data obtained in this way allows a precision test of the model of spectral diffusion and the distribution of parameters of the tunneling systems given by the standard tunneling model. We will show experimental results from measurements on BK7 and will discuss them in the framework of spectral diffusion and the standard tunneling model.

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Ordered and Disordered Contributions to Lattice Thermal Conductivity

Jason M. Larkin1 and Alan J. H. McGaughey1

1 Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

Understanding thermal transport in crystalline systems requires detailed knowledge of phonons, which are the quanta of energy associated with atomic vibrations. By definition, phonons are non-localized vibrations that transport energy over distances much larger than the atomic spacing. For disordered materials (e.g., alloys, amorphous phases), with the exception of very long wavelength modes, the vibrational modes are localized and do not propagate like phonons. The Einstein model assumes that the mean free path of these localized vibrations is the average interatomic distance and that their group velocity is equal to the speed of sound. The Cahill-Pohl model assumes that the mean free path of the localized modes is equal to half of their wavelength.1 While these approaches can be used to estimate a lower limit to the thermal conductivity of disordered systems, they only provide a qualitative description of the vibrations that contribute to the lattice thermal conductivity.

Using lattice dynamics calculations and molecular dynamics simulations on Lennard-Jones

crystalline, alloy, and amorphous systems, we predict and characterize the contributions from

phonons and localized vibrations to lattice thermal conductivity. The results are used to

motivate simple and computationally cheap models to predict the lattice thermal conductivity

of a range of disordered materials. 1D. G. Cahill S. K. Watson and R. O. ohl “Lower limit to the thermal conducti it of disordered cr stals” Phys. Rev. B 46, 6131 (1992).

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Ultrafast Optical Measurements of Acoustic Phonon Attenuation in Amorphous and Nanocrystalline Silicon

Brian C. Daly,1 Theodore B. Norris,2 B. Yan,3 J. Yang,3 and S. Guha3 1 Department of Physics and Astronomy, Vassar College, Poughkeepsie, NY, USA

2Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan, USA

3 Uni-Solar Ovonic LLC, Troy, Michigan, USA

The attenuation of high frequency sound waves in amorphous solids is not yet well understood. This is not surprising considering the uncertainty that remains in the study of thermal conductivity of amorphous solids, a topic that is directly related. We report measurements of the attenuation of coherent longitudinal acoustic phonons in amorphous and nanocrystalline hydrogenated silicon thin films (a-Si:H and nc-Si:H) using the method of picosecond ultrasonics. The films were grown using a very high frequency glow discharge method onto stainless steel substrates. The picosecond ultrasonic (ultrafast pump-probe) experiment and examples of reflectivity data are illustrated in Fig. 1. Optical pulses from a Ti:sapphire oscillator are absorbed by a thin Al transducer grown on the Si:H layer. The absorption of the pulses thermoelastically produces longitudinal strain pulses with a bandwidth of a few 100’s of GH that is then launched into the Si:H layer. These strain pulses travel back and forth in the Si:H layer, and the attenuation that is intrinsic to the Si:H can be determined by comparing the amplitude of the reflectivity changes caused by the first and second returning strain pulses. One advantage of using the steel substrate is that the acoustic mismatch between the steel and the Si:H is significant enough so that even for relatively thick samples (several microns) the second returning signal is still detectable. By varying the thickness of the samples and repeating the measurements, we can determine the loss at the Si:H/steel interface and account for this in the calculation of the intrinsic attenuation of a-Si:H or nc-Si:H.

Our preliminary results on a series of a-Si:H samples indicate a very low attenuation for an amorphous solid for acoustic phonons in the range of 50 – 100 GHz. Fig. 2 summarizes these results – a value of 340 cm-1 at 50 GHz and a value of 780 cm-1 at 100 GHz. There were no previous measurements in this frequency range on amorphous silicon, but a comparison with measurements on crystalline Si shows that the attenuation in the amorphous phase differs from that of the crystalline phase by less than an order of magnitude. In Fig. 2, we plot the calculated attenuation from a numerical model due to Fabian and Allen.1 In that work the authors modeled the attenuation using a randomized network of 1000 silicon atoms, realistic interatomic potentials, and a relaxation-time approximation calculation. They presented two models, one in which the internal strain of the amorphous network was included and one in which it was not. Curiously, our measured attenuation falls squarely in between these two calculations.

1J. Fabian and .B. Allen “Theor of sound attenuation in glasses: the role of thermal ibrations” Phys. Rev. Lett. 82, 1478 (1999).

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FIGURE 1. The inset shows a schematic of the sample in the ultrafast pump and probe experiment. The data represented here show the reflectivity changes caused by the detection of two acoustic phonon pulses that have made one and two round trips through a-Si:H films of differing thickness. The thicker film has a much longer delay time but also demonstrates significantly more acoustic attenuation. The data have been normalized so that the signal from the first echo is the same size in each case.

FIGURE 2. Attenuation versus frequency for longitudinal acoustic phonons. (■) – this work, (○) –

literature values for crystalline silicon, FA,IS – calculation from Ref. 1, internal strain included,

FA,No IS – calculation from Ref. 1, internal strain excluded.

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Heat transport by long mean free path vibrations in amorphous silicon-nitride near room temperature

A. D. Avery1, D. Bassett1, S. Mason1, and B. L. Zink1 1 Department of Physics and Astronomy, University of Denver, Denver, CO, USA

The study of thermal properties of glasses and other disordered or amorphous solids, despite a long and interesting history, continues to yield surprises. Results presented here, along with recent work of other groups1,2, adds yet another unexpected set of phenomena related to how heat is transported in amorphous materials. The typical view suggests that near room temperature, thermal conductance is dominated by phonons of relatively short wavelength that experience frequent phonon-phonon collisions. This limits the expected mean free path to lengths more comparable to inter-atomic spacings than to the size of micromachined features or even the thickness of thin film layers. The experiments we describe provide proof of the important role that surface scattering plays in heat conduction in disordered silicon-nitride thin film structures, confirming that vibrational excitations with long mean free paths carry a significant amount of heat even at room temperature. Though much remains to be explored, this result could impact a wide range of technologies ranging from integrated circuits to advanced detectors for which understanding and optimizing the heat flow through thin disordered insulating layers is crucial.

We present measurements of thermal transport in 500 nm thick micromachined suspended silicon nitride (Si-N) bridges at temperatures from liquid helium to above room temperature. The measured thermal conductivity of Si-N (for material grown by LPCVD in two different furnaces) deviates somewhat from previously reported measurements and also shows surprising dependence on surface variation at relatively high temperatures. Surface scattering is expected to affect thermal transport at low temperature but results presented here provide evidence that it also plays a role from 77-325 K. We discuss results of thermal transport in Si-N in cases of both intentional and unintentional surface variation. These include measurements of thermal transport in a large number of suspended Si-N bridges with no intentional surface modification, in bridges coated with discontinuous Au films, in bridges with a series of Au depositions starting at the discontinuous film limit, and in bridges coated with a series of alumina thin films. We find in all cases that modification of the surface lowers the measured thermal conductance of the Si-N bridge. This is strong evidence that vibrational excitations with long mean free paths carry significant heat even at these high temperatures. By measuring a series of film thicknesses the surface-scattering effects can be mitigated, and the resulting experimental values of the thermal conductivity of alumina and Au thin films compare very well to known values or predictions of the Wiedemann-Franz law.

1X. Liu, J. L. Feldman, D. G. Cahill, R. S. Crandall, N. Bernstein, D. M. Photiadis, M. J. Mehl,

and D. A. Papaconstantopoulos, Phys. Rev. Lett. 102, 035901 (2009)

2Y. He, D. Donadio, and G. Galli, Applied Physics Letters 98, 144101 (2011)

).

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FIGURE 1 a) Thermal model representing the thermal isolation platform. b) A tilted SEM micrograph

of the suspended Si-N thermal platforms. Here two 250 x 250 μm2 Si-N islands are connected to a Si frame by eight Si-N legs and also connected together by a 806 μm long, 35 μm wide & 500 nm thick

Si-N suspended bridge. Metal film thermometers and heaters, each with four leads directly to the thermometer element, are patterned on each island. A similar thermometer is also patterned on the

chip to monitor the reference temperature.

FIGURE 2. A plot of thermal conductance K vs. T for a Si-N bridge compares the initially meas red

al es red circles to those meas red after depostion of a discontin o s layer with a erage nominal thickness of 0 green circles , and after deposition of a third layer 35 thick that brings

the total nominal thickness to 5 . he shaded region indicates the spread of all al es of meas red for bridges on the same wafer. he addition of the first, discontin o s 0 ca ses a dramatic drop in K, much larger than the spread in as-measured KSi−N. The third, thicker Au layer

causes a significant increase due to the increased heat conduction by the now continuous Au layer.

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Ultra-high-frequency surface acoustic waves observed by ultrafast pump-probe spectroscopy

Elaine C. S. Barretto1, Martin Grossmann1, Oliver Ristow1, Mike Hettich1, Axel Bruchhausen2, Martin Schubert1, Vitalyi Gusev3, Elke Scheer1 and Thomas Dekorsy1

1 Department of Physics, University of Konstanz, D-78464 Konstanz, Germany 2 Instituto Balseiro & Centro Atómico Bariloche (CNEA), and CONICET, Argentina

3 Institut des Molécules et Matériaux du Mans, UMR CNRS 6283, Université du Maine, 72085 Le Mans, France

Picosecond generation and detection using metal gratings on transparent and semitransparent substrates is a well-known technique to excite and probe surface acoustic waves1, and by using sub-micron gratings very high frequencies can be obtained. Using aluminum gratings on bulk silicon, we obtained surface acoustic phonons of up to 90 GHz, which is to the best of our knowledge the highest acoustic frequency obtained so far for this system.

Several gratings were fabricated using standard electron beam lithography processing, with metal thickness of approximately 14 nm. The measurements were performed using asynchronous optical sampling2 (ASOPS), which is a pump-probe technique. The reflected signal from the structure was measured using a high speed photodetector. The low frequency components were removed from the signal, then FFT was applied to the time-resolved signal, and finally the peaks obtained in the frequency spectrum were extracted, which are shown in Figure 1. The data represents the values of the measurements (void symbols) and simulations (full symbols) obtained for the main acoustic modes for gratings with different pitches.

To identify the acoustic modes, finite element method simulations were performed using the software Comsol Multiphysics. Using eigenfrequency analysis, it was possible to identify that the first mode corresponds to the fundamental Rayleigh mode, and the second mode indicates a Leaky-SAW mode (a Rayleigh-like mode coupled to a bulk mode). A very good agreement between experiments and calculations is demonstrated.

Other acoustic modes with higher frequencies could also be detected. Figure 2 shows the spectrum obtained for the grating with 100 nm pitch, where an acoustic mode at 90 GHz can be clearly observed. Modes with such high frequencies can be used for several applications in the areas of thin film characterization, electron and phonon transport, among others.

This work was supported by the DFG through the SFB 767 (Germany) and by the Ministry of Science, Research and Arts of Baden-Württemberg (Germany).

1B. Bonello et al. “Surface acoustic wa es in the GH range generated b periodicall patterned metallic stripes illuminated b an ultrashort laser pulse” J.Acoust. Soc. Am. 110, 1943 (2001).

2A. Bartels et al. “ ltrafast time-domain spectroscopy based on high-speed asynchronous optical sampling” Rev. Sci. Instrum. 78, 035107 (2007).

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FIGURE 1. Experimental (void symbols) and numerical (full symbols) results for the main acoustic modes, Rayleigh and Leaky-SAW, for gratings with different periods.

FIGURE 2. Frequency spectrum obtained for the grating with 100 nm pitch. An acoustic mode at 90 GHz (arrow) can be clearly observed. The mode at 75 GHz corresponds to the Brillouin peak.

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Surface acoustic waves in MnAs thin films

J.-Y. Prieur1, J.-Y. Duquesne1, J. Agudo Canalejo1, V.H.Etgens1,2, M.Eddrief1, A.L. Ferreira1,3 and M. Marangolo1

1Institut des NanoSciences de Paris, UPMC-CNRS UMR 7588, 4 place Jussieu, 75252 Paris Cedex 5, France.

2 Fédération Lavoisier Franklin, UVSQ, 45 avenue des Etats Unis, 78035 Versailles cedex, France. 3Departamento de Fisica, UFPR, Centro Politécnico, Caixa Postal 19091, 81531-990, Curitiba PR,

Brazil.

Coupling of magnetization with non-magnetic fields is a subject of both fundamental and practical interest. It paves the way to new spintronic devices free from cumbersome magnetic control. In that respect, magnetoelastic materials offers the possibility to use acoustic waves to dynamically couple to the magnetization.

MnAs is a well known magnetostrictive and magnetocaloric solid. Epitaxied MnAs on GaAs(100) displays phase coexistence between 10 and 40 °C and a selforganized structural pattern of stripes, alternating ferromagnetic/hexagonal phase and paramagnetic/orthorombic phase1. We report here on the propagation of surface acoustic waves in a layered structure comprising a piezoelectric layer (1 µm) on top of a thin MnAs layer (100 nm) epitaxied on a GaAs(100) substrate. Attenuation and velocity changes have been measured, in the few 100 MHz range, versus temperature (between 0 and 80 °C) and magnetic field (between 0 and 0.2 T). Large variations are observed: see figure. We show our results can be explained by a strain induced triggering of the magnetocaloric effect in MnAs. Indeed, strains are responsible for internal magnetic field changes in magnetostrictive materials. Then, acoustic waves modulate the internal magnetic field in MnAs. In turn, this triggers heat release via the magnetocaloric effect. The net result is a giant thermoelastic effect, responsible for the acoustic behavior.

1R. Breitwieser, F. Vidal, I.L. Graff, M. Marangolo, M. Eddrief, J.-C. Boulliard and V. Etgens, Phys. Rev. B 80, 045403 (2009).

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FIGURE 2. SAW velocity changes versus applied magnetic field, at given temperatures (170 MHz)

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Acoustic control of carriers and spins in semiconductor wires

Hernández-Mínguez,1 M. Möller,2 S. Lazic1, S. Breuer1, C. Pfüller1, C. Somashini1, O.

Brandt1, M. M. de Lima, Jr.2, A. Cantarero2, L. Geelhaar1, H. Riechert1, P. V. Santos1

1Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin 2Institut de Ciència dels Materials, Universitat de València, 46980 Paterna (València), Spain

A surface acoustic wave (SAW) propagating on a piezoelectric semiconductor produces a moving type-II modulation of the band edges, which can capture electrons and holes and transport them with the wave velocity.[1] In semiconductor quantum wells (QWs), electrically generated SAWs with frequency on the order of a GHz have been used to transport photo-excited electrons and holes while maintaining the electrons spin polarization.[2, 3]

The acoustic transport can also implement another important functionality for quantum information processing, namely the generation of single photons. For that purpose, SAWs are used to pump a quantum dot (QD) inserted in a quantum wire (QWRs) with alternate trains of electrons and holes. The quantized nature of the QD states then leads to the emission of a single photon per SAW pulse. In this contribution, we review SAW-driven anti-bunched photon emission in two systems. The first consists of QWRs produced by molecular-beam epitaxy on (311)A GaAs substrates, which are electrically connected to a surrounding QW. Spectrally resolved photoluminescence (PL) of the QWR under acoustic pumping show sharp lines, which are attributed to emission from QDs created by potential fluctuations along the QWR axis. Under acoustic pumping, the QDs produce short (<0.5 ns) light pulses with the SAW repetition rate. The quantized nature of the emitted light was established by two-photon correlations studies using a Hanbury-Brown and Twiss (HBT) setup.[4] The second system consists of GaAs/AlGaAs core-shell nanowires (NW) terminated by InGaAs QDs and placed on a piezoelectric (LiNbO3) substrate. We show that the evanescent piezoelectric field generated by the SAW can be used for the contactless transport of carriers along the NW axis. If the carriers are photoexcited at NW end opposite to the QD, the acoustic transport leads to the emission of antibunched photons from the QD,[5] which has been verified using a HBT setup. Main advantages of these sources are the low jitter and high repetition rate, which can easily reach the GHz range. Mechanisms for the emission process will be discussed.[4]

The previous results demonstrate the potentials of phonons for the transport and manipulation of quantum states. One interesting issue to be discussed in the talk is the combination of acoustic spin transport with single-photon emission for the generation of polarized photons.

[1] C. Rocke et al., Phys. Rev. Lett. 78, 4099 (1997). [2] J. A. H. Stotz, R. Hey, P. V. Santos, and K. H. Ploog, Nat. Mater. 4, 585 (2005). [3] O. D. D. Couto, Jr. et al., Phys. Rev. Lett. 98, 036603 (2007). [4] O. D. D. Couto, Jr. et al., Nat. Phot. 3, 645 (2009), Lazic et al., N. J. Phys. 14, 13005 (2012) [5] A. Hernández-Mínguez et al., Nano Letters 12, 252 (2012).

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Acoustic Nanometrology of Ultrathin Films Using Coherent Extreme Ultraviolet Beams

Kathleen Hoogeboom-Pot,1 Damiano Nardi,1 Qing Li,1 Chris Deeb,2 Sean King,2

Marie Tripp,2 Erik H. Anderson,3 Margaret M. Murnane,1 and Henry C. Kapteyn1 1 JILA and Department of Physics, University of Colorado and NIST, Boulder, CO, USA

2 Intel Corp., 2501 NW 229th Ave, Hillsboro, OR, USA 3 Center for X-Ray Optics, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Photoacoustic spectroscopy is a powerful tool for characterizing thin films. We demonstrate a

new photoacoustic technique that allows us to characterize the mechanical properties of sub-

100 nm thin films using coherent extreme ultraviolet (EUV) light.

As shown in Figure 1, we focus an ultrafast laser pulse from a Ti:Sapphire amplifier onto nano-

patterned a-SiC:H thin film samples deposited on silicon. The nano-patterns are sets of 1D

nickel gratings of 15 nm thickness and periods ranging from 90 nm to 1500 nm. The impulsive

excitation of the periodic nano-grating generates both surface acoustic waves (SAWs) and

longitudinal acoustic waves (LAWs). SAWs propagate with a penetration depth of only a

fraction of their wavelength, making them extremely sensitive to the mechanical properties of

thin films and interfaces.1 LAWs travel vertically inside a material and probe mechanical

properties in the z-direction. Therefore, when both waves are fully confined within a thin film,

the 3D mechanical properties of the film can be precisely characterized.2

Coherent extreme ultraviolet pulses at 29 nm are then used to probe the propagation dynamics

of both classes of acoustic waves. The resulting photoacoustic signal on both short (ps) and long

(ns) time-scales yields important information. As displayed in Figure 2, fast oscillations followed

by an echo signal are observed in the first 100 ps and addressed to LAWs traveling respectively

inside the nanostructures and the ultrathin film. From these two dynamics we can extract the

LAW velocities in the two materials. On longer time-scales, SAW oscillations are clearly

detected. By combining the measured SAW frequency with the wavelength set by the period of

the nano-grating, the SAW velocity is accurately determined even for very short wavelength

SAWs with extremel shallow penetration. With this technique the ultrathin films’ elastic

properties as the Young’s modulus and oisson’s ratio are obtained in a single measurement.

This EUV photoacoustic technique can be extended to precisely characterize the mechanical

properties of sub-10 nm thin films used in current nanofabrication applications.

1 . E. Siemens et al. “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams” Appl. Phys. Lett. 94, 093103 (2009).

2Q. Li et al. “Characteri ation of ultrathin films b laser-induced sub-picosecond E V photoacoustics” to be published in SPIE Proc. Metrology, Inspection, and Process Control for Microlithography (2012).

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FIGURE 1. Schematic geometry of photoacoustic nanometrology of ultrathin films using coherent EUV detection.

FIGURE 2. Time-resolved EUV photoacoustic signal for a 100 nm thin a-SiC:H film with 1050 nm periodic nano-grating on top.

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High-Frequency Magneto-Acoustics

in Ferromagnetic Semiconductors

Alexey V. Scherbakov Ioffe Physical-Technical Institute of the Russian Academy of Sciences, St. Petersburg, Russia

We discuss the potential of high-frequency acoustics to control magnetic excitations in ferromagnetic materials. In our approach we inject a picosecond acoustic pulse into a thin ferromagnetic layer and excite coherent precession of magnetization, which we monitor directly in time domain. We analyze the dependences of the amplitude and frequency spectrum of the precession on the external magnetic field and structural properties of the layer. In the talk the detailed information about the mechanisms of dynamical magneto-acoustic effects is brightened up by new magneto-acoustic phenomena, like selective excitation of a standing spin wave mode by the spectrally broad acoustic pulse.

The structures studied are thin ferromagnetic semiconductor (FMS) layers of (Ga,Mn)As grown by low temperature MBE on GaAs substrates. This weak ferromagnet with strong magnetocrystalline anisotropy and ferromagnetic resonances in GHz frequency range is a perfect model object for high-frequency magneto-acoustics studies1. We generate the picosecond acoustic pulse by means of optical excitation of 100-nm thick Al film deposited on the back side of the substrate. The acoustic pulse travels through the substrate and reaches the FMS layer producing there local strain, which modifies the magnetic anisotropy and launches coherent magnetization precession. Time-resolved magneto-optical Kerr rotation (MOKR) measured in the experiments directly reflects the time evolution of magnetization.

Figure 1 shows an example of the MOKR signal measured at external magnetic field applied in the plane of the FMS layer. The pronounced beating is due to the superposition of standing spin waves excited by the acoustic pulse and contributing to the precession of the magnetization. The Fourier spectrum of the measured signal clearly shows two lowest spin wave modes (lower inset). The spectral content of the MOKR signals strongly depends on external magnetic field. For its certain direction and strength we detect only a single spectral line with the frequency corresponding to a certain spin wave mode. The selectivity in excitation induced by the acoustic pulse with a broad spectrum originates from the spatial matching of the eigenfunctions of a spin wave and a phonon of the resonance frequency.

We also demonstrate the extremely efficient excitation of magnetization precession by the pulse of TA phonons, which produce shear strain in the FMS layer. We realize such an excitation in the structure grown on high-index (311)-GaAs substrate. In this case the amplitude of precession may achieve 10% of saturation magnetization resulting in complicated spectral content of the MOKR signal due to the strong magneto-elastic coupling.

1A.V. Scherbako et al. “Coherent magneti ation precession in ferromagnetic (Ga n)As induced b picosecond acoustic pulses” Phys. Rev. Lett. 105, 117204 (2010).

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FIGURE 1. The MOKR signal reflecting magnetization precession induced by the longitudinal picosecond acoustic pulse in 200-nm width Ga0.95Mn0.05As layer at magnetic field of 450 mT

applied in the layer plane along easy magnetization axis. Acoustic pulse comes to the FMS layer at t=0 and completely leaves the layer at the time moment shown by a vertical arrow. The

upper inset shows the experimental schematics. The lower inset shows the FFT spectrum of the MOKR signal.

0 250 500 750 1000

MO

KR

sig

na

l (a

rb. u

nits)

Time (ps)

16 18 20 22 24 26

Am

plit

ud

e (

arb

. un

its)

Frequency (GHz)

Ti:Sp+ RegA

Balanced MOKR

detection

GaAs

(Ga,

Mn

)As

20 ns delay

Al film

15

0-fs

-pu

mp

linearly

pola

rize

d pr

obe

ps- acoustic pulse

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Polarization-Controlled Generation of Coherent Phonons in Plasmonic Nanostructures

N. D. Lanzillotti-Kimura,1 K. . O’Brien 1 J. S. Rho,1 H. Suchowski,1 and X. Zhang1 1 NSF Nano-scale Science and Engineering Center (NSEC), University of California at Berkeley,

94720 CA, USA

Plasmonics has emerged as a promising field in physics, with the potential to overcome the diffraction limit in classical photonics, and to develop a myriad of applications. Spatially localized surface plasmons show strong electronic resonances that allow their use for the design of optical nanoantennas and metamaterials, enabling new ways of capturing and controlling light.1 These resonances can be strongly dependent on polarization, allowing a selective coupling and control of the light with the nanostructures.2 Usually, short laser pulses are used to excite coherent acoustic phonons in metallic and semiconductor thin-films, multilayers, and microcavities. Great efforts have been made in the optimization of the light-matter interactions in these systems, and in the confinement of the acoustic and electric fields.3-5

Here, we propose the integration of plasmonics concepts into the field of nanophononics using metallic nanoantennas as coherent phonon generators and detectors. The polarization-dependent optical resonances and the phononic modes of metallic nanobars are determined by their geometry -size and shape- and material properties (index of refraction and sound velocity, respectively). We show how an array of metallic optical nanoantennas optimized to work at visible wavelengths can be tailored to generate and detect acoustic phonons of variable frequencies in the GHz range.

We report two-color pump-probe experiments which demonstrate that a nanostructured thin-film composed of crossed gold nanobars of different sizes (of the order of 100 nm) can generate acoustic phonons with GHz frequencies; and how the generated frequency can be controlled by the polarization of the pump. We also discuss how the selection of metals and the geometrical parameters of the individual bars enable the design and engineering of optimized hypersound sources, with tailored and tunable spectra. The presented results open new ways toward the design of novel nanophononic systems and the development of opto-acoustically functionalized surfaces.

1S. aier “ lasmonics: Fundamentals and Applications” Springer, Berlin, (2007).

2T. Ellenbogen K. Seo and K. B. Cro ier “Chromatic lasmonic olarizers for Active Visible Color Filtering and olarimetr ” Nanolett. 12, 1026 (2012).

3N. D. Lanzillotti-Kimura A. Fainstein B. errin et al “Enhanced optical generation and detection of acoustic nanowa es in microca ities” Phys. Rev. B 84, 211103 RC (2011).

4N. D. Lanzillotti-Kimura A. Fainstein B. errin et al. “Enhancement and nhibition of Coherent honon Emission of a Ni Film in a BaTiO3/SrTiO3 Ca it ” Phys. Rev. Lett. 104, 187402 (2010).

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Observation of Near-Field Interaction between Surface Plasmon Polaritons and Nanoacoustic Pulses

Szu-Chi Yang1, Hui-Hsin Hsiao1, Hung-Ping Chen1, Hung-Chun Chang1, Pei-Kuen Wei2, and Chi-Kuang Sun1,2,3

1 Department of Electrical Engineering and Graduate Institute of Photonics and Optoelectronics,

National Taiwan University, Taipei, 10617, Taiwan 2 Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Taipei, 115,

Taiwan 3 Molecular Imaging Center and Graduate Institute of Biomedical Electronics and Bioinformatics,

National Taiwan University, Taipei, 10617, Taiwan

Surface plasmon polaritons (SPPs) have been used for many applications such as sensors, superfocusing lenses, and building blocks of surface plasmonic circuits. With great application potentials, developing the capability to actively and accurately control and modulate the behavior of SPPs will further expand possibilities.

We recently used the femtosecond nanoacoustic technique in a 1-D gold nanograting on top of a GaN single crystal to confirm the existence of the plasmonic field distribution below the metal/dielectric interface [1]. The width of the applied longitudinal nanoacoustic pulse was on the nanometer scale and was shorter than the penetration depth of the SPP field in GaN. In order to explore the near-field acousto-plasmonic interaction on the nanometer scale both longitudinally and laterally, in this study we combine NSOM with femtosecond nanoacoustic techniques to investigate SPPs on a 1-dimentional gold nanograting. Measurements on the near-field acousto-plasmonic interaction with simultaneous high temporal (<200fs), lateral (<200nm), and longitudinal (<150nm) resolutions are thus obtained.

Thanks to the combination of NSOM and femtosecond nanoacoustic system, a real-time 3D imaging technique with high temporal, longitudinal, and lateral resolution can be constructed. Our results indicate that the extraordinary transmission (EOT) of nanogratings can be modulated with >11.6 GHz bandwidth by the nanoacoustic pulses. This plasmonic modulation is achieved through acoustically modulating the transmission of SPP field and the cavity modes. This result helps us understand how the acoustic waves interact with the EOT induced by SPPs and show great potential for future high speed, precision control of SPPs in nanostructure.

1H.-P. Chen, Y.-C. Wen, Y.-H. Chen, C.-H. Tsai, K.-L. Lee, P.-K. Wei, J.-K. Sheu, and C.-K. Sun, "Femtosecond laser-ultrasonic investigation of plasmonic fields on the metal/gallium nitride interface," Applied Physics Letters 97(2010).

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FIGURE 1. The position dependent transient near-field transmission differences measured by NSOM at different time delays, which indicate the ultrafast acousto-induced near-field

transmission change by the incoming nanoacoustic pulse.

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Subterahertz near-surface coherent phonons in a plasmonic grating structure

C. Brüggemann,1 V. Belotelov,2 B. Glavin,3 I. A. Akimov,1 J. Jäger,1 S. Kasture,4

A. V. Gopal,4 A. S. Vengurlekar,4 D. R. Yakovlev,1 and M. Bayer1 1 Experimentelle Physik 2, Technische Universität Dortmund, D-44227 Dortmund, Germany

2 Lomonosov Moscow State University, 119991 Moscow, Russia 3 V E Lashkaryov Institute of Semiconductor Physics, Kyiv 03028, Ukraine

4 Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India

We demonstrate here, that plasmonic excitations can be coupled efficiently to coherent high-frequency acoustic phonons (up to ~100 GHz). Such coupling is studied in a gold grating with a period of d =400 nm deposited on dielectric gadolinium gallium garnet substrate (Fig.1). The grating allows the optical excitation of surface plasmon polaritons (S ’s) pro ided that the wavelength and the incidence angle of the light are selected in a way to match energy and quasi-momentum conservation laws. The feature of such matching is a dip in the optical reflectivity spectrum.

Coherent phonons are generated in form of an optically excited picosecond strain pulse. Therefore an Al transducer film deposited on the surface of the sample opposite to the plasmonic grating is illuminated by an 800 nm femtosecond laser pulse (pump pulse). The phonons propagate through the gadolinium gallium garnet substrate and reach the grating, where they possess acoustic diffraction. This diffraction results in the generation of near-surface longitudinal acoustic (LA) waves in accordance with Bragg conditions: phonon wavelength md / ( m =1, 2, 3...). These phonons form standing elastic waves in the region near the surface where the electric field components of the SPP are essential.

The effect of the SPP interaction with those coherent near-surface acoustic waves is detected by probing the time-resolved reflectivity change of an optical pulse originating from the same laser and variably delayed relative to the pump pulse. An example of such a time-resolved reflectivity signal is shown in Fig.2a for the case where the incidence angle of the probe pulse corresponds to the SPP resonance. The corresponding Fourier spectrum in Fig.2b shows a sequence of equidistant peaks with frequencies up to 110 GHz. The peaks have maxima at frequencies which correspond to the near surface LA modes generated in accordance with Bragg conditions for phonon diffraction. The major role of plasmonic effects is confirmed by the absence of reflectivity changes in case of probe light incidence angles out of resonance with the SPP. The modulation of both, the dielectric function of the substrate and the stripe-gap spacings, are the responsible mechanisms for the SPP-phonon interaction. Consequently this leads to the strong dynamical changes of optical reflectivity.

The observed sub-THz acousto-plasmonic effects have high potential for applications in nanoplasmonics.

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FIGURE 1. The scheme of the experimental setup. A gold grating with a period of d=400 nm is grown on Gadolinium Gallium Garnet [111] substrate. A light pulse with wavevector k, corresponding to a wavelength of 800 nm, is incident on the grating and excites surface plasmon polaritons (S ’s). A picosecond strain pulse incident from the substrate side is used to modulate the strength of the SPP resonance. These changes are monitored by measuring the time resolved optical reflectivity.

FIGURE 2. a) Time resolved changes of the reflectivity, caused by the coherent phonons. b) Fast Fourier Transform of the time resolved reflectivity.

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Operation of a Non-equilibrium Phonon Source for Probing Nanoscale Phonon Transport

Richard D. Robinson1, Jared B. Hertzberg1, Obafemi Otelaja1, Mahmut Askit1 1 Department of Materials Science and Engineering, Cornell University, Ithaca, New York, USA

Non-thermal distributions of acoustic phonons may be locally excited in a solid by decay of excited-state electrons injected into an adjacent superconducting tunnel junction (STJ).1 Using this technique, we employ an aluminum tunnel junction to isolate and apply narrow frequency bands of phonons to silicon micro- and nanostructures. We detect the transmitted or scattered phonons using a second STJ attached to the structure.2 The completed system is operated at sub-kelvin temperatues and comprises a micro-scale spectrometer to investigate acoustic phonon transport through nanostructures. Using standard micro- and nano-fabrication techniques, this device may be replicated and modified to investigate a wide variety of nanostructure geometries. We will describe the operational performance of such a device, including the spatial resolution, frequency resolution, frequency range, dynamic range and signal-to-noise ratio. Spatial resolution is limited by fabrication methods, and we have achieved dimensions below 1 micron. Frequency resolution is set by device quality and signal-to-noise considerations, and we have achieved resolutions of ~10 GHz. Frequency range is governed by emission and absorption behaviors in the STJs and is expected to extend from ~80 to ~800 GHz. Calibration methods under study include the use of different types of superconducting materials in the tunnel junctions and the insertion of absorber materials into the phonon transmission path. This work is supported by the Energy Materials Center at Cornell (EMC2), award DOE (DE-SC0001086) and the National Science Foundation award DMR-1149036. Our devices were fabricated in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network.

1H. Kinder. "Spectroscopy with phonons on Al2O3:V3+ using the phonon bremsstrahlung of a superconducting tunnel junction," Phys. Rev. Lett. 28, 1564 (1972).

2J. B. Hertzberg, O. O. Otelaja, N. J. Yoshida, and R. D. Robinson. "Non-equilibrium phonon generation and detection in microstructure devices," Rev. Sci. Inst. 82, 104905 (2011).

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FIGURE 1. Example of microfabricated phonon spectrometer measurement. Phonons are emitted by aluminum superconducting tunnel junction (STJ), traverse a silicon microstructure 7

microns wide, and are detected by a second STJ.

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Probing Phonon Surface Scattering in Nanostructures Using a Microfabricated Phonon Spectrometer

Jared B. Hertzberg1, Obafemi Otelaja1, Mahmut Askit1 , Derek A. Stewart2 and Richard D. Robinson1

1 Department of Materials Science and Engineering, Cornell University, Ithaca, New York, USA 2 Cornell Nanoscale Facility, Cornell University, Ithaca, New York, USA

In insulating materials and many semiconductors, acoustic phonon modes are the dominant

carriers of heat. In nanostructures such as nanowires and nanosheets, the geometric

dimensions can be much smaller than the phonons' scattering length from conventional

phonon interactions (i.e., phonon-phonon, phonon-electron, or phonon-impurity scattering).

At these small scales the phonon transport then becomes dominated by scattering from

surfaces, and sensitively dependent on the surface morphology and roughness. In this talk, we

demonstrate a method to characterize the scattering rate and transmission factor of phonons

traveling lengthwise down a silicon nanosheet. Generation and detection of phonons is

accomplished by superconducting tunnel junctions attached to the silicon nanostructure and

operated at a temperature of 0.3K. Decay of excited states in the superconductor is employed

as a tunable narrow-band source of phonons for frequencies from ~80 GHz to ~800 GHz.1 This

tunable source enables investigation of the phonon mean free path as a function of the phonon

wavelength, the nanostructure dimensions, and the surface roughness, in nanosheets 100 to

200 nm thick. We will also describe efforts underway to quantify the surface roughness of the

structures and to model the scattering behavior. This work is supported by the Energy Materials

Center at Cornell (EMC2), award DOE (DE-SC0001086) and the National Science Foundation

award DMR-1149036. Our devices were fabricated in part at the Cornell NanoScale Facility, a

member of the National Nanotechnology Infrastructure Network.


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FIGURE 1. SEM image of prototype phonon spectrometer for study of phonon transmission

through silicon nanostructures.

FIGURE 2. Preliminary measurements of frequency-resolved phonon transmission through nanosheet-type silicon channels. Channels are 130 nm wide, 1 micron high and 0.4, 1 or 4

microns long.

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Simulating Low Temperature Phonon Transport and Scattering through Si Nanosheets

(authors: Mahmut Aksit1, Jared Hertzberg1, Obafemi Otelaja1, Derek Stewart2, Richard Robinson1)

1 Department of Materials Science and Engineering, Cornell University, Ithaca, New York, USA 2 Cornell Nanoscale Facility, Cornell University, Ithaca, New York, USA

Non-equilibrium phonons provide an effective means to measure the frequency dependence of phonon transport in materials. Superconducting tunnel junctions (STJ) have been used to generate and detect narrow frequency bands of non-equilibrium phonons1. Recently, our group implemented STJ based phonon spectrometry in micro-scale for the ultimate purpose of measuring frequency dependent phonon transport through nano-structures2. In the current work, Monte Carlo simulations are reported for phonon spectrometry through Si nanosheets. The nanosheets are thick (~120 nm) so acoustic confinement does not play a major role, but the rough surfaces and sheet length will influence the phonon transmissivity. The simulations are performed considering phonon behavior at low temperatures and only phonon-boundary scattering is taken into account as the source of deviation in the phonon path. The simulations are performed at the full system scale considering the geometry of the actual experimental arrangement (See Figure 1 below). The phonon frequency range is set to be between 80 GHz to 800 GHz (~75 nm to ~7.5 nm in phonon wavelengths). The important parameters for the simulations are found to be nanosheet surface roughness, nanosheet thickness and nanosheet length. The simulation results are compared with analytical Casimir-Ziman models for simple structures and also actual phonon transport measurements through the nano-fabricated Si nanosheets. This work is supported by the Energy Materials Center at Cornell (EMC2), award DOE (DE-SC0001086) and the National Science Foundation award DMR-1149036.

1H. Kinder. "Spectroscopy with phonons on Al2O3:V3+ using the phonon bremsstrahlung of a superconducting tunnel junction," Phys. Rev. Lett. 28, 1564 (1972).


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FIGURE 1. 3D Representation of the device for the micro-scale phonon spectrometry through Si Nanosheets.

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Vacuum Phonon Tunneling from STM Tip

Igor Altfeder and Andrey Voevodin

Air Force Research Laboratory, Wright-Patterson Air Force Base, OH, USA

Field-induced phonon tunneling, a previously unknown mechanism of interfacial thermal transport, has been revealed by ultra high vacuum inelastic scanning tunneling microscopy (STM). Using thermally broadened Fermi-Dirac distribution in the STM tip as in-situ atomic scale thermometer we found that thermal vibrations of the last tip atom are effectively transmitted to sample surface despite few angstroms wide vacuum gap. We have shown1 that phonon tunneling is dri en b interfacial electric field and thermall ibrating image charges “thermal mirages” and its rate is enhanced b surface electron-phonon interaction.

The sample for our study was Au(111) film on mica, which we annealed in UHV to 400C to clean it’s surface. The ST tip was electrochemicall etched 0.25 mm diameter t/ r wire which was also cleaned by UHV annealing using electron beam technique. The atomic level cleanness of the tip and sample surfaces has been confirmed by (a) STM observation of Au(111) atomic lattice and (b) observation of exponential tunneling current vs. vacuum gap width dependence. The base pressure in the UHV STM system (model UHV-300 from RHK Technology) was 5×10-11 Torr.

On this material, we performed Inelastic Electron Tunneling Spectroscopy (IETS) measurements at different sample temperatures, although the STM tip temperature was nominally always at 300 K. From IETS thermal broadening (Fermi-Dirac broadening) we found that the tip apex remains in thermal equilibrium with the sample. Thus, our measurements show that the terminating atom of the STM tip remains in thermal equilibrium with sample surface despite 3 Å wide vacuum gap separating this atom from the cold surface. We suggested that thermal equilibration occurs due to thermal vibration of image charge induced by STM tip on surface of our sample2. Our modeling confirmed that phonon tunneling induced b such “thermal mirage” of ST tip is sufficient to explain the obser ed effect.

In conclusion, we demonstrate that the temperature of the terminating atom of STM tip can be determined using innovative technique of UHV variable temperature inelastic electron tunneling spectroscopy. By advancing the understanding level of atomic scale thermal phenomena, our result, at the same time, has important implications for thermal transport at macroscopic heterointerfaces where nanoasperities often play crucial role. We have shown that field-induced thermal transport through atomically thin interfacial gap can exceed the

lanck’s radiation energ b a factor of 1010~ .

We thank Nader Hendizadeh and Kumar Jata for helpful discussions and support.

References

1 . Altfeder A. A. Voe odin A. K. Ro “Vacuum honon Tunneling” Phys. Rev. Lett. 105, 166101 (2010).

2 G. D. ahan “The tunneling of heat” Appl. h s. Lett. 98, 132106 (2011).

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FIGURE 1. Temperature dependent IETS spectra obtained on Au(111) surface at 210 K (green curve), 150 K (red curve), and 90 K (blue curve). The spectra reveal Au(111) surface phonon resonance at 12 meV and STM tip anti-resonance at 60 meV indicating that platinum tip is terminated by CO molecule. Insert: Gaussian fitting of IETS spectra was used to determine their FWHM and tip apex temperature related to each other as: FWHM=5.4 kT.

FIGURE 2. Screening charges induced on sample surface by local electric field of STM tip. Vibration of tip apex changes the spatial position of the field maximum. Thermal vibrations of the ST tip are transmitted to sample surface as forced “thermal“ ibrations of screening charges. Insert: energy diagrams for tip-sample inelastic tunneling processes: (a) phonon emission (see Au(111) resonance in Fig. 1), (b) resonant emission-reabsorption (see CO-Pt anti-resonance in Fig. 1).

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Power-law Time Decay of the Quantum Dot Photoluminescence Intensity

Karel Král1 and Miroslav Menšík2 1 Institute of Physics, Academy of Sciences of Czech Republic, Prague, Czech Republic,

2 Institute of Macromolecular Chemistry, Academy of Sciences of Czech Republic, Prague, Czech Republic

The experimentally well known effect of a slow decay of the photoluminescence is studied theoretically in the case of quantum dots with indirect gap. The slow decay of the photoluminescence is considered as a time decay of the luminescence intensity following the excitation of the quantum dot electronic system by a short optical pulse. In the presented theoretical treatment the process is studied as a single dot property. The interaction of the excited electrons with longitudinal optical phonons is considered in the self-consistent Born approximation. The theory is built on the nonequilibrium electronic transport theory. The relation of the numerical results to the experimental data is to be discussed. A possible connection of the presently considered effect to the blinking property of the quasi-zero dimensional nanostructures is also to be discussed.

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Raman and Surface - Enhanced Raman Scattering Studies of DNA: Analysis of Shifts in Vibrational Frequencie

Tsai-Chin Wu,1 Mitra Dutta,2 and Michael Stroscio1,2,3 1 Department of Bioengineering, University of Illinois, Chicago, IL, USA

2 Department of Electrical and Computer Engineering, University of Illinois, Chicago, IL, USA 3 Department of Physics, University of Illinois, Chicago, IL, USA

In many applications, it is desirable to have simple and efficient methods to detect the compositions of nucleotide acids. The use Raman spectroscopy to detect biomolecules has been challenging in many cases because of its weak signal intensity. In 1974, the first observation of SERS (surface-enhanced Raman scattering) by Fleischmann et al. [1], makes using Raman technique to study biomolecules more practical. Yet, all of the phenomena underlying SERS is not fully understood and the reproducibility of the enhancement has become a popular study topic. Herein, we studied SERS and peak shifts on thrombin-binding aptamer (TBA) in two different geometries. I. First substrate (schematic representation shown in Fig. 1) consists of a layer of silver with

thickness varying from 100 to 200 nm, coated on polystyrene latex nanospheres 390 nm in diameter [2]. The spectra of Fig. 2 reveal some noticeable peak shifts listed in Table 1.

II. Secondly, we place the double strand TBA between a gold thin film substrate and a gold

nanoparticle (schematic representation shown in Fig. 3). The is achieved by binding dsDNA TBA sequence with one end to gold particles, the other end to the gold substrate [3]. The experimental results to be presented shed the light on possibility of a hot spot between a nanoparticle and a thin film of gold.

SERS and Raman results for DNA aptamer will be presented. Acknowledgement We acknowledge Dr. Vasudev synthesizing the substrate depicted in Fig. 1.

References

[1] M. Fleischmann, P. J. Hendra and A. J. McQuillan. Raman spectra of pyridine adsorbed at a silver

electrode. Chemical Physics Letters 26(2), pp. 163-166. 1974. Available:

http://www.sciencedirect.com/science/article/pii/0009261474853881.

[2] M. Vasudev, Tsai-Chin Wu, S. Biswas, M. Dutta, M. A. Stroscio, S. Guthrie, M. Reed, K. P. Burris and

C. N. Stewart. Optoelectronic signatures of DNA-based hybrid nanostructures. Nanotechnology, IEEE Transactions on 10(1), pp. 35-43. 2011.

[3] G. Braun, S. J. Lee, M. Dante, T. Q. Nguyen, M. Moskovits and N. Reich. Surface-enhanced raman

spectroscopy for DNA detection by nanoparticle assembly onto smooth metal films. J. Am. Chem. Soc. 129(20), pp. 6378-6379. 2007.

http://www.sciencedirect.com/science/article/pii/0009261474853881

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Fig. 1. The cross-section of the substrate that the TBA is drop coated on; a layer of silver with thickness varies from 100 to 200 nm, coated on polystyrene latex nanospheres of 390 nm in diameter. Fig. 2. The Raman spectra of thrombin-binding aptamer with and without potassium ions compared on the subsrate depicted in Fig. 1.

Table 1. The peaks in Fig. 2.

w/ K w/o K Thymine Possible Thymine Assignment

Guanine Possible Guanine Assignment

488 531 512

634 618 632 N1C2Ob+N3C4Ob 656 in-phase ring strengching of the six-membered ring

except C4C5

780 771 776 Ring Breathing 952 946 960 N9Rs+N3Cs

2

1002 1000 992 C5-Mer* 1000

1136 1128 1184 Cb6H+C2Ns

3 1154 C8Ns7+N9Rs-C4N3

1425 1444 1442 C5-Meb*

1509 1476 1504 NHb* 1514 C4CS5-C4NS

9

1575 1570 1582 N3C4+N1Cs2+C6Cs

5-N1Cs6 1582 N3CS

4-CS5

1619 1627

1633 1638

1648 1659 1652 C4=Os+Cs-Cs6

1662 1681 1691 C2=Os 1680 C6=OS-C5CS6

1821 1837

1956 1964

Fig. 3. This illustration depicts the structure of the sample, double stranded TBA sequences sandwiched between 1.4 nm gold nanoparticles (GNP) and a 50 nm gold thin film.

500 1000 1500 20000

500

1000

1500

2000

Raman Shift(cm-1)

Inte

nsi

ty (

a.u

.)

without K ions

with K ions

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Localization phenomenon of surface acoustic waves into phononic crystal defect

Olga Boyko, Rémi Marchal, Jinfeng Zhao, Mathieu Rénier and Bernard Bonello

Institut des NanoSciences de Paris (INSP) UMR CNRS 7588, Université Pierre et Marie Curie, boîte 840

4 place Jussieu, 75252 Paris cedex 05, France

Surface acoustic waves are elastic waves that propagate along a material surface with

most of their energy density concentrated at the surface. SAW are largely used for the design of

classical resonator, filters and sensors in the MHz and GHz frequency ranges. Heterostructures

with periodic variations of their elastic properties may induce band gaps for acoustic waves,

slow down the velocity of their propagation and model the mechanical energy distribution. We

study in particular the third point and elaborate the periodic structures with punctual defect

allowing the selective resonance of SAW energy.

In this context, we have studied theoretically and experimentally the localization of

elastic energy within a defect. The heterostructures is the phononic crystal which consists in

arrays of holes periodically drilled throughout silicon plates (honey comb symmetry) and

featuring a vacancy (defect). The defect in periodic phononique crystal structure induces the

emergency of new frequencies in the gap of dispersion curve so-called the defect modes (Fig.

1). The honey comb symmetry of PhC allows the largest gap to compare with square symmetry,

thus, there are three defect modes inside the PhC gap. The theoretical analyses of mode

displacement shows that only two of them (B,C) could be detected in our experiment sensible

only to vertical component of displacement. The mode A is basically bulk mode.

Fig. 1. Three localized modes in band gap of PhC due to defect. In-set: Scanning electronic microscope

image of PhC with vacancy.

We use an all-optical experimental technique for both the generation and the detection

of the elastic guided waves [1]. The non-contact probing allows one to monitor the

0,01 0,02 0,03 0,04 0,05 0,06

12

14

16

18

20

22

Extended modes

Extended modes

(C)

(B)

Fre

qu

en

cy (

MH

z)

Wave vector (kxa/(2))

(A)

Band Gap

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displacements field inside the defects. The narrow band elastic guided waves, whose central

frequency corresponds to resonance modes (A,B) of the cavity are generated. The optical probe

scans the out-of-plane displacements along a central line in order to visualize the localized

wave within the cavity of the phononic structure. We report the standing wave generation

inside the cavity (Fig. 2 and Fig. 3) as result of following two different physical phenomena: the

first is the mechanical resonance of matter with vacancy, the second is the efficient refraction

of defect mode on the “walls” formed by phononic structure. As result, we have a cavity like

laser resonant cavity, with quality factor about 60.

Fig. 2. The vertical displacement of elastic wave inside the cavity along a central line: one observe the generation of

standing wave during approximately 1 microsecond.

Fig. 3. Spectral amplitude of elastic wave signal inside the cavity: the resonance frequency is centered on 14 MHz.

This work is supported by the European Community through the FET-Open project “TAILPHOX”

(grant n° 233883).

[1] J. Pierre, O. Boyko, L. Belliard, J. O. Vasseur, and B. Bonello, “Negative refraction of zero order flexural Lamb waves through a two-dimensional phononic crystal”, Appl. Phys. Lett. 97, 121919 (2010).

Po

siti

on

(m

)

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Phonon-assisted near-field activation of electron transfer between a solution and an electrode

T. Yatsui, K. Iijima, K. Kitamura, and M. Ohtsu

School of Engineering, the University of Tokyo, Tokyo 113-8656, Japan

An optical near-field is expected to realize phonon-assisted multiple excitation in nano-scale structures.1 Using the phonon-assisted process, higher catalytic activity is expected without heating. Thus, phonon-assisted activation can increase the catalytic activity of nanostructures, in addition to the contribution from increased surface area. To confirm this effect, we observed photo-induced current generation using platinum black electrodes (Fig. 1(a)).2

We observed current generation in ferricyanide solution under visible light irradiation (CW,

= 532 nm, Fig. 1(b)). Because the absorption band-edge wavelength of ferricyanide solution is 470 nm, the observed current generation did not originate from the photochemical reaction of the ferricyanide solution. We calculated the heat generation in platinum black, in which all the incident photons were absorbed (solid red line in Fig. 1(b)), and found that the heat generation was negligible with respect to that of the phonon-assisted process. Additionally, higher-order dependencies on the excitation power appeared with increasing current density, which was

fitted by the second-order function 2/i i aI bI (Fig. 1(b)), indicating that these activation of electron transfer originated from the optical near-field effect on the nanostructured surface of the electrode.1

Acknowledgements

This work was financially supported by a Grant-in-Aid for Young Scientists (A) from MEXT, by a research grant (Basic Research) from The TEPCO Memorial Foundation, and by a Research and Development Program of Innovative Energy Efficiency Technology from New Energy and Industrial Technology Development Organization (NEDO).

1 Arata Sato, Yuji Tanaka, Fujio Minami, and Kiyoshi Kobayashi, Journal of Luminescence 129 (12), 1718 (2009).

2 Lakshmi Krishnan, Steven E. Morris, and Glenn A. Eisman, Journal of The Electrochemical Society 155 (9), B869 (2008).

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Fig. 1 (a) AFM image of platinum black electrodes. (b) Relationship between irradiation power and current density. Solid diamonds: observed current generation. Black solid

curve: fitted curve, . Red solid curve: Calculated heat generation.

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Visible-light-induced water splitting by phonon-assisted optical near fields in ZnO nanorods

Takahiro Mochizuki, Kokoro Kitamura, Takashi Yatsui, and Motoichi Ohtsu

School of Engineering, the University of Tokyo, Tokyo 113-8656, Japan

The phonon-assisted optical near-field process was applied to a water-splitting reaction to increase the response of visible light, in which the photon energy was less than the band-gap energy.1 To generate the optical near field, we used thick (100-nm diameter) and ultra-fine (20-nm diameter) ZnO nanorods. The photocatalytic performance of ZnO was evaluated by photoelectrochemical (PEC) analysis using a three-electrode setup in 0.1 M NaOH electrolyte solution.2 The power dependence of the photocurrent in Fig. 1(c)–(e) shows the photocatalytic performance under ultraviolet (UV, 325 nm) and visible (473 nm and 532 nm) irradiation, respectively. Under UV irradiation, the photoresponse current of the ZnO nanorods was comparable to that of the reference bulk substrate with a flat surface, whereas under 473-nm irradiation, the photocurrent increased drastically with decreasing nanorod diameter. Compared with the bulk substrate, the ultra-fine nanorods showed a 70-fold enhancement in the photocurrent. Additionally, under 532-nm irradiation, photocurrent generation was observed only for the ultra-fine nanorods. Furthermore, the power dependence was fitted by the second-order function PC = aI + bI2 (PC: photocurrent, I: excitation power) shown by the solid curve in Fig. 1(e), indicating that the photocurrent generated by visible-light irradiation originated from multi-step excitation using the phonon-assisted process.

Acknowledgements

This work was financially supported by a Grant-in-Aid for Young Scientists (A) from MEXT, by a research grant (Basic Research) from The TEPCO Memorial Foundation, and by a Research and Development Program of Innovative Energy Efficiency Technology from New Energy and Industrial Technology Development Organization (NEDO).

1 A. Sato, Y. Tanaka, F. Minami, K. Kobayashi, J. Lumines. 129, 1718 (2009).

2 T. H. H. Le, K. Mawatari, Y. Pihosh, T. Kawazoe, T. Yatsui, M. Ohtsu, M. Tosa, and T. Kitamori, Appl. Phys. Lett. 99, 213105 (2011).

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Fig. 1. SEM images of (a) thick and (b) ultra-fine ZnO nanorods. The power dependence of the photocurrent measured by PEC analysis in 0.1 M NaOH (c) under 325-nm, (d) 473-nm, and (e) 532-nm irradiation of the bulk ZnO substrate (solid circles), thick nanorods (solid squares), and ultra-fine nanorods (solid triangles).

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POSTERS

Polarized optical properties of forsterite from room temperature up to the melting point

Myriam Eckes,1 Benoit Gibert,2 Domingos De Sousa Meneses,1,3 Mohammed Malki, 1,3 and Patrick Echegut1

1 CNRS, UPR 3079 CEMHTI, 1D Avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, France

2 Laboratoire Geosciences Montpellier, CC060, Université Montpellier 2, place Eugène Bataillon, 34095 Montpellier Cedex 5, France

3Polytech’Orléans, Université d’Orléans, Avenue du Parc Floral, BP 6749, 45067 Orléans Cedex 2, France

A complete knowledge of the thermo-physical properties of olivine minerals is necessary in the earth science field since they constitute a cornerstone for quantifying the thermodynamic properties of the Earth’s upper mantle rocks and more specifically, for determining the heat transfers by radiation. Forsterite (Mg2SiO4), the pure magnesium end member of the olivine group, crystallize in the orthorhombic system, has a symmetry corresponding to the Pbnm space group and owns two distinct crystallographic sites for magnesium cations (M1 and M2). Numerous literature results concerning thermodynamic and spectroscopic data show evidences of a change of vibrational behavior around 1000K. The temperature dependence of the thermodynamic properties at high temperature cannot be understood without invoking a sudden strengthening of the lattice anharmonicity1, 2. Despite the fact that forsterite has been investigated via a lot of different techniques and ab initio calculations, the origin of this anharmonicity is not completely clear. To contribute to the understanding of the change of behavior occuring at high temperature, infrared emittance spectra were acquired from room temperature up to 1900 K along the [100], [010] and [001] polarization directions. The fitting of the experimental data by using a semi quantum dielectric function model provides new results on lattice vibrations and phonon-phonon interactions in forsterite. In particular, a sudden enhancement of anharmonicity at high temperature is observed and is concomitant with the disappearance or brutal change of some modes around 1000K. The polarization along [001] direction is more specifically impacted and this changes can be linked to the magnesium mobility within M1 sites. Indeed, ab initio calculations3 and experimental data on tracer diffusion4 in forsterite show the presence of an enhanced diffusion of magnesium via M1 sites along [001] direction. Finally, this work allow for the extraction of the optical indices in the whole infrared range and in a wide range of temperature which are of high geophysical interest.

1P. Gillet, P. Richet, F. Guyot, G. Fiquet, J. Geophys. Research. B7, 96: 11805-11816 (1991).

2F. Guyot, Y. Wang, P. Gillet, Y. Ricard, Phys. Earth. Planet. Inter. 98, 17-29 (1996).

3J. Brodholt, Am. Mineral. 82, 1049-1053 (1997).

4S. Chakraborty, J. R. Farver, R. A. Yund, D. C. Rubie, Phys. Chem. Miner. 21, 489-500 (1994).

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Phonons versus short and medium range order in silicate glasses

Domingos De Sousa Meneses,1,2 Myriam Eckes,1 Cristiane N. Santos1 and Patrick Echegut1

1 CNRS, UPR 3079 CEMHTI, 1D Avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, France

2Polytech’Orléans, Université d’Orléans, Avenue du Parc Floral, BP 6749, 45067 Orléans Cedex 2, France USA

The chemical simplicity of binary silicate glasses makes them model systems that are suitable to

show how the localization of phonons in disordered materials can be use to characterize short

and intermediate range orders in the structure. We show that it is possible to extract from

infrared reflectivity measurements no solely quantitative information on short range order, i.e.

populations of Qn tetrahedral units (n : number of bridging oxygens) but also intermediate

range information like the presence and evolution of 3D network silicate clusters and silicate

sheet clusters. Examples will be given for alkaline silicates glasses and discussed at the light of

predictions obtained from structural glass models and literature results.

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POSTERS

Ultrafast Optical Measurements of Thermal and Mechanical Properties of Amorphous Silicon Carbide Films

Brian C Daly,1 Sean W King,2 J. Bielefeld2 1 Department of Physics and Astronomy, Vassar College, Poughkeepsie, NY, USA

2Intel Corporation, Portland Technology Development, Hillsboro, OR, USA

We report measurements of the thermal conductivity and sound velocity of a series of amorphous hydrogenated silicon carbide (a-SiC:H) films grown by plasma enhanced chemical vapor deposition (PECVD). Additional characterization measurements allow us to also determine the Young’s Modulus of these films. The physical properties of a-SiC:H are widely tunable via adjustments of the Si/C ratio or the hydrogen content, and as such it is an ideal material for studying the physics of amorphous systems in general. In particular, we will discuss the applicability of rigidity percolation theory in predicting mechanical and thermal properties of films of varying density and coordination number (average number of covalent bonds per atom). Our interest in this material system is also motivated by the technological interest in a-SiC:H for microelectronic and micro-electromechanical applications.

Our sound velocity measurements are made with the now well-established method of picosecond ultrasonics and the thermal conductivity measurements are made via time-domain thermoreflectance (TDTR). Both are performed using an ultrafast optical pump-probe setup employing a Ti:sapphire oscillator. Samples are prepared by coating them with 20 – 60 nm of Al to be used as a transducer layer. Pulses of light from the laser generate transient reflectivity

changes (R) that can be interpreted as the thermal and mechanical response of the sample layer. Figure 1a shows picosecond ultrasonic data for two a-SiC:H films of similar thickness (about 500 nm, measured by ellipsometry) but differing sound velocities. By measuring the time for a picosecond ultrasonic pulse to make a round trip within the a-Si:H layer, an accurate value for the longitudinal sound velocity can be calculated. Figure 1b shows TDTR data for two a-SiC:H films and for crystalline SiC as a reference material. The data can be fit using an algorithm due to Cahill,1 and thermal conductivity can be determined.

The a-SiC:H densities were varied from 1.0 g cm-3 to 2.5 g cm-3 by modifying the PECVD growth conditions. The thermal conductivity (range 0.0009 W/cmK to 0.042 W/cmK) and sound velocity (range 2370 m/s – 10460 m/s) both track roughly with the density. The thermal conductivity does not vary from the prediction of the minimum thermal conductivity2 by more than 20%. Determinations of Young’s modulus for the a-SiC:H layers are plotted versus density in Fig. 2. The data suggest the possibility of a critical value of the density (and coordination number) below which rigidity ceases to percolate throughout the amorphous network, resulting in very low values for the modulus.

1 D.G. Cahill, “Analysis of heat flow in layered structures for time-domain thermoreflectance,” Rev. Sci. Inst. 75, 5119 (2004).

2 D.G. Cahill and R.O. Pohl, “Heat flow and lattice vibrations in glasses,” Solid State Commun. 70, 927 (1989).

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FIGURE 1. (a) Picosecond ultrasonic data for Picosecond ultrasonic data for two a-SiC:H films with similar thickness but different sound velocities. SiC:H-9 has vL=6780 m/s. SiC:H-6 has

vL=3570 m/s. (b) TDTR data, SiC:H-1 and SiC:H-4 have =0.0009 W/cmK and =0.0045W/cmK

respectively. For comparison, we include a crystalline SiC sample (3C-SiC, =1.3 W/cm K).

FIGURE 2. Young’s modulus versus density for 12 a-SiC:H films. The data may indicate a

transition near 1.4 g cm-3 below which rigidity ceases to percolate in the amorphous network.

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Surface-Enhanced Raman Spectroscopy as a Tool for

Characterizing Nanostructures Containing Molecular Component

Ke Xu,1 Justin Abell,

2 Yiping Zhao,

3 Jun Qian,

4 Kimber Brenneman,

4 Xenia

Meshik,4 Mitra Dutta,

1 Michael Stroscio,

1,4

1 Department of Electrical and Computer Engineering, University of Illinois, Chicago, IL, USA

2 Nanoscale Science and Engineering Center, Department of Biological and Agricultural

Engineering, The University of Georgia, Athens, GA, USA 3 Nanoscale Science and Engineering Center, Department of Physics and Astronomy, The

University of Georgia, Athens, GA, USA 4 Department of Bioengineering, University of Illinois, Chicago, IL, USA

Raman spectroscopy, which is based on inelastic scattering of light that interacts with phonons or

molecular vibrations in the nanostructure, has been widely used to identify chemical and

biological molecules. Surface-Enhanced Raman Spectroscopy (SERS) greatly enhanced the

sensitivity of conventional Raman spectroscopy by a factor of >106 through the use of a

plasmon-generating substrate.1,2

This study investigated the use of Raman spectroscopy/SERS to

verify that synthesized nanostructures contain active molecular components critical to their

functioning. In particular, this study uses SERS to identify the signature spectrum of Methylene

Blue (MB) and uses Raman spectroscopy to verify the fictionalization of a DNA aptamer

terminated with MB.

SERS substrates consisting of silver nanorod arrays were prepared by oblique angle deposition.

Methylene Blue were diluted in deionized H2O to reach concentrations of 1.5 mM and 0.15 mM,

respectively. A drop of each concentration of MB was deposited on SERS surface and left dry at

room temperature. Another sample was prepared by attaching cocaine aptamer terminated with

MB to the surface of a graphene-based FET structure. All samples were then imaged with a

Renishaw Ramascope 2000 spectrometer using 0.23 mW power and 514 nm excitation

wavelength. The background signal was subtracted to obtain pure spectrum of target molecule.

The SERS spectrum of MB was observed clearly with all the main peaks consistent with

previously published results.3 Raman spectra of the cocaine aptamer with MB shows typical

peaks of both DNA1,4

and MB3, which proves that the aptamers have been successfully attached

to the graphene surface. These results demonstrate the effectiveness of the silver nanorod SERS

substrate in obtaining the Raman spectra of chemical and biological samples.

1 C. Otto, T. J. J. Van Den Tweel, F. F. M. de Mul, and J. Greve, “Surface-enhanced Raman

spectroscopy of DNA bases”, J. Raman Spec. 17, 289–298 (1986). 2 M. A. Stroscio and M. Dutta, Phonons in Nanostructure, Cambridge University Press, 2001.

3 G. Xiao and S. Man, “Surface-enhanced Raman scattering of methylene blue absorbed on cap-

shaped silver nanoparticles”, Chem. Phys. Lett. 447, 305-309 (2007). 4 M. Vasudev, T.-C. Wu, S. Bitwas, M. Dutta, M.A. Stroscio, S. Guthrie, M. Reed, K. P. Burris,

and C. N. Stewart, Jr., “Optoelectronic Signatures of DNA-Based Hybrid Nanostructures”, IEEE

Trans. Nanotechnol. 10, 35-43 (2001).

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FIGURE 1. SERS spectrum of MB with different concentration of (a) 1.5 mM, (b) 0.15 mM,

and (c) regular Raman spectrum of 1.5 mM MB drop on Si Substrate. An inset shows enlarged

SERS spectrum of (a) from 400 to 1200 (cm-1

) with main peaks identified.3

FIGURE 2. (a) Raman spectrum of the structure and (b) substrate deducted Raman spectra of

original, aptamer-attached, and cocaine-tested structure with peaks identified. 3,4

TABLE 1. Raman shifts and peak assignment for MB, DNA aptamer and graphene.

Methylene Blue(cm-1

) Band assignment DNA or Graphene(cm-1

) Band assignment

1628 ν(CC) ring+ν(CNC) ring 1598 G peak of graphene

1442 νasym(C-N) 1541 base Thymine

1393 α(C-H) 1498 NC-NC stretching in guanine

1302 ν(C-C) ring 1424 stretching of C-N bonds

1155 β(C-H) in Thymine

1075 νasym(C-S-C) 1367 D peak of graphene

1037 β(C-H) 1235 ring streching mode in Thymine

673 γ(C-H) 1084 symmetric stretching mode of

449 δ(C-N-C) PO2- backbone

300 500 700 900 1100 1300 1500 1700

Wavenumber (cm-1

)

Inte

nsi

ty (

a.u

.)

400 500 600 700 800 900 1000 1100 1200

(a)

(b)

(c)

14421393

1628

1302

1155

10751037

953

900

774673597503449

300 500 700 900 1100 1300 1500 1700

Wavenumber (cm-1

)

Inte

nsi

ty (

a.u

.)

400 500 600 700 800 900 1000 1100 1200

(a)

(b)

(c)

14421393

1628

1302

1155

10751037

953

900

774673597503449

300 500 700 900 1100 1300 1500 1700

Wavenumber (cm-1

)

Inte

nsi

ty (

a.u

.)

400 500 600 700 800 900 1000 1100 1200

300 500 700 900 1100 1300 1500 1700

Wavenumber (cm-1

)

Inte

nsi

ty (

a.u

.)

400 500 600 700 800 900 1000 1100 1200

(a)

(b)

(c)

14421393

1628

1302

1155

10751037

953

900

774673597503449

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Fabrication Methods for a Phonon Spectrometer Designed to Spectrally Resolve Hypersonic Phonon Transport through Nanostructures

Obafemi Otelaja, Jared Hertzberg, Mahmut Aksit, and Richard Robinson

Department of Materials Science and Engineering Cornell University, Ithaca, NY, USA

Phonons are the major heat carriers in semiconductors and insulators, and a better understanding of their nanoscale transport will inform the thermal engineering of materials properties. To this end, we demonstrate a scalable method of fabricating phonon emitters and detectors on silicon microstructures. Additionally we show silicon micromachining fabrication methods for nanosheet structures for studying phonon surface scattering effects. Al-AlxOy-Al superconducting tunnel junctions are utilized for emission and detection of non-equilibrium phonons with frequency ~100 GHz. The phonons travel ballistically along the <110> direction of a silicon mesa [1]. The mesas are formed by a silicon nitride-masked shallow depth anisotropic etching of silicon (100) in KOH, and are about 250 micron long, 10-50 microns wide and 1.5 microns high. A bilayer of lift-off resist and photoresist with stepper lithography is used to form the tunnel junction and wiring traces, with the “Dolan Bridges” hanging above the sidewall of the mesa [2]. A subsequent double angle shadow evaporation of aluminum with an oxidation step in between, and lift-off process forms the superconducting tunnel junctions. The phonon emitter and detector pair formed on the sidewall of the mesa allows the study of phonon transport across the mesa. This configuration creates a direct line of sight between the phonon emitter and detector. The ballistic transport path between the emitter and detector can be blocked by etching a trench into the mesa. Using an unpulsed-Bosch reactive ion etching method, we have also etched vertical sheets of silicon, 100-200nm wide and 0.4-4 micron long, into the mesas to study surface scattering effects. Our scalable method allows us to fabricate 6 emitter and detector pairs per chip and ~100 chips per wafer, and these allows us to run up to six experiments per cool down and multiple experiments per wafer. We show a simple and scalable configuration for studying phonon transport in silicon microstructures that may be adapted for studying various phononic structures. This work is supported by the Energy Materials Center at Cornell (EMC2), award DOE (DE-SC0001086) and the National Science Foundation award DMR-1149036.

References:

[1] J.B. Hertzberg, O. O. Otelaja, N. J. Yoshida, and R. D. Robinson. Rev. Sci. Instrum. 82, 104905 (2011).

[2] G. J. Dolan, Appl. Phys, Lett. 31, 337-339 (1977).

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Figure 1: Schematic of the spectrometer and possible experiment

Figure 2: STJ Phonon generator photoresist bridge formed on silicon mesa prior to evaporation

Figure 3: Silicon Nanosheets (4 micron long, 120nm wide) fabricated along the line of sight between STJ

phonon generator and detector

Phonon emitter

Phonon detector

Ballistic phonons

Mesa sidewall

STJ emitter

SQUID STJ

detector

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POSTERS

Probing interparticle vibration by phonon-plasmon coupling in a gold nanoparticles supracrystal

Pierre-Adrien Mante,1 Meng-Hsien Lin,2 Hung-Ying Chen,2 Shangjr Gwo2 and Chi-Kuang Sun1, 3, 4

1 Department of Electrical Engineering and Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan

2 Institute of Nanoengineering and Microsystems and Department of Physics, National Tsing-Hua University, Hsinchu 30013, Taiwan

3 Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan 4 Molecular Imaging Center and Graduate Institute of Biomedical Electronics and Bioinformatics,

National Taiwan University, Taipei, Taiwan

Metal nanoparticles have been intensively studied because of their interesting properties arising from their plasmon resonance. Numerous applications take advantage of these properties, such as sensitivity enhancement in optical techniques like SERS.1 Gold nanoparticles not only exhibit plasmonic properties but due to the size reduction, numerous changes in their physical properties are observed compared to the bulk, like their vibrational behavior.2 The vibrational behavior of individual noble metal nanoparticles has been intensively studied, and the detection by light of vibration modes can be enhanced by localized plasmon resonance due to the modulation by phonons of the plasmon resonance.

Recently, several studies have been devoted to the effect of aggregation of metal nanoparticles since novel physical properties arise from the interaction between nanoparticles. Breathing modes of aggregated nanoparticles has also been studied and it has been demonstrated that the coupling will results in a decrease of the frequency of the vibration.3 Interparticle vibration in an artificial crystal with long range ordering made of cobalt particles has been observed, but the question of the plasmon resonance has not been addressed.4

We present experimental results obtained by ultrafast optical pump-probe spectroscopy in 3D gold nanoparticle supracrystal exhibiting collective plasmon resonances. We demonstrate that laser induced phonons can modulate the collective plasmon resonances of plasmonic supracrystal due to the high sensitivity of the near-field coupling to interparticle distance. The wavelength dependent detection of the modulation allows us to selectively probe the elastic properties of the crystal in different directions.

1 P. L. Stiles, J. A. Dieringer, N. C. Shah and R. P. Van Duyne, ANNUAL REVIEW OF ANALYTICAL CHEMISTRY 1, 601, (2008)

2 N. Del Fatti, C. Voisin, F. Chevy, F. Vallée, C. Flytzanis, J. Chem. Phys. 110, 11484 (1999)

3 C. D. Grant, A. M. Schwartzberg, T. J. Norman, Jr. and J. Z. Zhang, J. Am. Chem. Soc. 125, 549, (2003)

4 I. Lisiecki, V. Halté, C. Petit, M.-P. Pileni and J.-Y. Bigot, Adv. Mater. 20, 4176 (2008)

249

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Finite difference modeling of laser generation of ultrasound in layered media in the coupled thermoelasticity

István A. Veres,1 Thomas Berer,1,2 and Peter Burgholzer1,2 1 Research Center for Non-Destructive Testing GmbH, Altenberger Str. 69, 4040 Linz, Austria

2 Christian Doppler Laboratory for Photoacoustic Imaging and Laser Ultrasonics, 4040 Linz, Austria

Generation of ultrasound by laser pulses has became an extensively used experimental technique due to its capability of contactless excitation of bulk, surface or guided elastic waves. The generation mechanism is usually based on a thermoelastic process and has been analytically investigated using different approximations. Thereby, the generation of the elastic waves is described by the coupled heat and wave equations.1 Although, analytic solutions are limited to idealized cases, such as a step-like temperature rise with point or line spatially distributed surface heating, broadly applicable numerical solutions have been rarely pursued. Here we introduce a combination of implicit-explicit finite difference techniques to simulate the generation of ultrasound by a laser source in the generalized coupled thermoelasticity, whereby also the thermal feedback by mechanical deformation is considered.2

Within the solution of the coupled system, the hyperbolic heat conduction equation is solved

by an implicit temporal integration technique (Wilson method). The resulting spatial distribution of the temperatures is applied to the explicitly integrated wave equation.3 In the simulation the thermal expansion excites the elastic waves, whereby the temperature field is updated in every time step by the thermal feedback of the mechanical stresses.

The influence of the coupling (i.e. thermal feedback) is investigated for pulsed laser sources. In the coupled thermoelasticity the elastic wave velocities are modified compared to the uncoupled case and the generated elastic waves are attenuated due to the thermomechanical coupling. The results show that for ultra high frequencies (i.e. ~100 GHz) the attenuation due to coupling becomes considerable as the attenuation increases with frequency. As a result of this effect the generated pulse on the epicentral axis is strongly broadened (Fig.1). The results are compared to available analytical solutions and show a good agreement. Furthermore, the presented method is applied to model the generation process by a line-focused laser source in homogeneous and layered media. Generated bulk and surface wave forms are presented for transversely isotropic and isotropic cases in heterogeneous media (Fig.2).

In conclusion the presented results show the applicability and flexibility of numerical methods to solve and investigate coupled, multiphysical problems.

1L.R.F. Rose, “Point-source representation for laser generated ultrasound”, J. Acoust. Soc. Am. 75, 723-732 (1984).

2A.J. Rudgers, “Analysis of thermoacoustic wave propagation in elastic media”, J. Acoust. Soc. Am. 88, 1078-1094 (1990).

3I.A. Veres, “Stability analysis of second- and fourth-order finite-difference modeling of wave propagation in orthotropic media”, Ultrasonics 50, 431-438 (2010).

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POSTERS

FIGURE 1. Epicentral waveforms generated by a line focused laser with 20 ps duration in transversely isotropic zinc (a) and in isotropic aluminum with copper coating (500 nm), showing

multiple reflections (b). The figures compare the coupled and uncoupled solutions. The generated waves posses different wave velocities and the high-frequency pulses are strongly

attenuated due to coupling.

FIGURE 2. Wave fields generated by line focused laser with 20 ps duration and 1µm half width in transversely isotropic zinc (top) and isotropic aluminum with copper coating (bottom). Quasi

longitudinal (QL) and Rayleigh waves (R) are present in zinc; longitudinal (L) and dispersive Rayleigh waves (R) are visible in the coated case.

251

POSTERS

Raman Scattering investigations of CdS thin films grown by Thermal Evaporation

Sidra Farid1, Michael A. Stroscio, 1,2,3, Mitra Dutta1,3

1 Department of Electrical and Computer Engineering, 2 Department of Bioengineering, 3 Department of Physics, University of Illinois at Chicago, IL, USA

Cadmium sulfide (CdS) thin films are important materials used extensively as the window layer in CdTe/CdS solar cell devices and appear to be a best available partner for the CdTe/CdS solar cells due to its ability to transmit maximum amount of light to the active layer1. The choice of buffer layer is constrained by the optical and electrical characteristics of the material as well as compatibility with the fabrication process. In this study, CdS thin films were deposited on ITO/glass substrate by thermal evaporation. To investigate the optical characteristics and crystal quality of the deposited films, Raman studies using an excitation source of 514 nm, have been done on the as grown CdS films at varying excitation powers and on annealed samples. Annealing was done at 450oC at constant times of 30 minutes in ambient oxygen. Raman Spectra for the as grown CdS films are shown in figure 1. As indicated, the spectra in the low frequency regime consist of two dominant peaks showing the longitudinal optical (LO) phonon mode at approximately 303 cm−1(1LO) and its overtone (2LO) at about 608 cm−1. The values for the LO phonon frequency for single crystal CdS in the literature2 have been given as 300 and 600 cm-1. Multiple over tones of LO phonon modes (3LO and 4LO) are also observed for the as grown samples excited with 24 mW laser power. In order to see the effects of Raman spectra on the laser excitation power, the power has been varied by using neutral density filters. It is observed that the intensity of the overtones changes quite markedly as the power is decreased from 24 mW to 6 mW as indicated in figure 2.

Figure 3 shows the Raman spectra of CdS films annealed at 450 oC for 30 minutes. It is observed that the films annealed at higher temperatures manifest sharper Raman peaks as compared to as grown samples. The degree of electron phonon coupling at particular wavelength can be quantified by calculating the ratio of the integrated overtone intensity to that of the fundamental, thus the ratio I2LO/ILO is an important tool in order to measure the disorder in the film3. For our case, this ratio decreases from 0.53 for the annealed films to .428 for as grown samples showing an improvement in crystalline quality. Another measure for the crystal quality improvement is the visibility of 3LO and 4LO peaks for the annealed samples excited at 12mW power which is almost negligible for the as grown samples. 1S. R. Kodigala, “Fabrication and Properties of Window Layers For Thin Film Solar Cells”, Thin Films and Nanostructures 35, 393–504 (2010). 2B. Tell, T. C. Damen and S.P.S Porto, “Raman Effect in Cadmium Sulfide”, Phys. Rev. 144, 771-774, (1966) 3S. Sahoo, A. K. Arora,”Laser-Power-Induced Multiphonon Resonant Raman Scattering in Laser-Heated CdS Nanocrystal”, J. Phys. Chem. B 114, 4199–4203 (2010)

http://www.sciencedirect.com/science/bookseries/15435016

http://www.sciencedirect.com/science/bookseries/15435016/35

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FIGURE 1. Raman spectra of as grown CdS thin films at varied laser power

FIGURE 2. Overtones of the Raman spectra of as grown CdS thin films

FIGURE 3. Raman spectra of as grown (bottom) and annealed CdS films(top spectra)

400 600 800 1000 1200

5000

10000

15000

20000

25000

30000

Ra

ma

n in

ten

sit

y(a

.u.)

Raman shift (cm-1)

As grown(12mW)

Annealed

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Surface-Enhanced Raman Spectroscopy Signatures of an RNA

Molecule: An Aptamer that Binds to the αVβ3 Integrin

Xenia Meshik,1 Kimber Brenneman,

1 Ke Xu,

2 Justin Abell,

3 Yiping Zhao,

4

Mitra Dutta,2 Michael Stroscio

1,2

1 Department of Bioengineering, University of Illinois, Chicago, IL, USA

2 Department of Electrical and Computer Engineering, University of Illinois, Chicago, IL, USA

3 Nanoscale Science and Engineering Center, Department of Biological and Agricultural

Engineering, The University of Georgia, Athens, GA, USA 4 Nanoscale Science and Engineering Center, Department of Physics and Astronomy, The

University of Georgia, Athens, GA, USA

Raman spectroscopy is a useful technique for identifying molecules by their unique vibrational signatures.

Surface-Enhanced Raman Spectroscopy (SERS) is capable of routinely amplifying the Raman signal by a

factor of >107 through the use of a plasmon-generating substrate.

1,2 This study investigated the SERS

spectrum of Apt-αVβ3, a 85-base long RNA molecule generated specifically for binding to the αVβ3

integrin on cellular membranes.3 Such RNA aptamers are of special interest since they exhibit highly

specific binding. The αVβ3 integrins normally interact with the RGDV peptide, a process that is amplified

in cancerous cells. Therefore, by occupying the binding site on the αVβ3 integrin, Apt-αVβ3 can potentially

aid in cancer treatment.

The Ag nanorod (AgNR) SERS substrate used in this study was fabricated using oblique angle deposition

(OAD). Apt-αVβ3 was dissolved in deionized H2O for a final concentration of 4 µM, placed in one well of

a patterned multiwell AgNR SERS chip, and washed out with diH2O after 24 hours. The sample was then

imaged with a Renishaw Ramascope 2000 spectrometer using 2.3 and 0.23 mW power and 514 nm

excitation wavelength. The background signal was subtracted to obtain the spectrum of Apt-αVβ3 alone.

The majority of the peaks lie in the 800-1600 cm-1

range consistent with previously published RNA/DNA

Raman spectra.1,4,5

Peaks corresponding to vibrational modes of guanine, cytosine, adenine and uracil can

all be identified.

These results demonstrate the effectiveness of the AgNR SERS substrate in obtaining the Raman spectra

of biological samples. Additionally, the unique Raman signature of Apt-αVβ3 was determined.

1 C. Otto, T. J. J. Van Den Tweel, F. F. M. de Mul, and J. Greve, “Surface-enhanced Raman spectroscopy

of DNA bases”, J. Raman Spec. 17, 289–298 (1986). 2 M. A. Stroscio and M. Dutta, Phonons in Nanostructures (Cambridge University Press, Cambridge,

2001). 3 J. Mi, Z. Zhang, P. H. Giangrande, J. O. McNamara II, S. M. Nimjee, S. Sarraf-Yazdi, B. A. Sullenger,

and B. M. Clary, “Targeted inhibition of αVβ3 integrin with an RNA aptamer inpairs endothelial cell

growth and survival”, Biochem. Biophys. Res. Commun. 228, 956-963 (2005). 4 B. Biese and D. McNaughton, “Surface-Enhanced Raman Spectroscopic Study of Uracil. The Influence

of the Surface Substrate, Surface Potential, and pH”, J. Phys. Chem. B 106, 1461-1470 (2002). 5 M. Vasudev, T.-C. Wu, S. Bitwas, M. Dutta, M.A. Stroscio, S. Guthrie, M. Reed, K. P. Burris, and C. N.

Stewart, Jr., “Optoelectronic Signatures of DNA-Based Hybrid Nanostructures”, IEEE Trans.

Nanotechnol. 10, 35-43 (2001).

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SERS Spectrum of Apt-αvβ3

0

200

400

600

800

1000

1200

200 700 1200 1700Wavenumber (cm

-1)

Inte

nsit

y (

a.u

.)

0

5000

10000

15000

20000

25000

30000

Inte

nsity

(a.u

.)

0.23 mW

2.3 mW

FIGURE 1. SERS spectrum of the Apt-αVβ3 obtained with varying laser power.

FIGURE 2. SERS spectrum of the Apt-αVβ3 obtained with 2. 3 mW laser power with peaks

identified.1,4,5

SERS spectum of Apt-αVβ3

0

200

400

600

800

1000

1200

1400

1600

1800

200 400 600 800 1000 1200 1400 1600 1800 2000

Wavenumber (cm-1)

Inte

nsit

y (

a.u

.)

489

838 914

1010

1194 1299

1340

1394 1426

1498

1602

489 – C-N bond bending in cytosine

838 – ring breathing

914 – C-N bond stretching in guanine

1010 – stretching of the phosphate

backbone

1194 – C-N bond stretching, C-H bond

bending in uracil

1299 – C-C bond stretching in cytosine

1340 – C-N bond stretching in adenine

1394 – C-H bond bending in uracil

1426 – C-N bond stretching in guanine

1498 – C-C bond stretching in cytosine

1602 – C=O bond stretching in

cytosine

255

POSTERS

Surface Enhanced Raman Spectroscopy of DNA Aptamer for Immunoglobulin E

Saadia Ranginwala,1 Kimber Brenneman,1Xenia Meshik,1 Justin Abell,2 Yiping Zhao,3 Michael Stroscio, 1,4, Mitra Dutta, 4

1 Department of Bioengineering, University of Illinois, Chicago, IL, USA

2 Nanoscale Science and Engineering Center, Department of Biological and Agricultural Engineering, The University of Georgia, Athens, GA, USA

3 Nanoscale Science and Engineering Center, Department of Physics and Astronomy, The University of Georgia, Athens, GA, USA

4 Department of Electrical and Computer Engineering, University of Illinois,Chicago, IL, USA

In this research, the vibrational spectrum of a DNA aptamer, that is reported to bind to the IgE antibody, is studied using surface enhanced raman spectroscopy (SERS). As is well known, the Raman signal can be routinely amplified by a factor greater than 106 times by employing the SERS technique, which relies on plasmons generated in the substrate. 1

In this study, the SERS spectrum of Immunoglobulin E (IgE) was investigated. The IgE aptamer is a 37 base pair long DNA molecule that binds specifically to IgE.2 The significance of studying IgE lies in the fact that IgE is only found in mammals, and is present in very low concentrations (1 nM), and can trigger a strong immune reaction.2 Patients with immune deficiency related diseases such as allergic asthma, atopic dermatitis, and even AIDS have IgE raised in their serum.2

Oblique angle deposition (OAD) was used to fabricate substrate the Ag nanorod (AgNR). The IgE aptamer was initially in solid form, and was then dissolved in deionized water to a final concentration of 5 micromolar, and was then applied to one well of the AgNR SERS chip.3 Then the sample was imaged with a Renishaw Ramascope 2000 spectrometer, with a power of 0.34 mW and 514 nm wavelength. The peaks lie in the range of 300-1200 cm-1 range, which correspond to previously reported SERS data.1 The peaks identified in this study were for vibrational modes in guanine, cytosine, and thymine. The results show that the AgNR SERS substrate is effective in producing Raman spectra of biological samples, and the spectra gives rise to the unique vibrational signature of Immunoglobulin E. Prominent features in these spectra will be discussed. 1C. Otto, T.J.J. Vand Den Tweel, F.F.M. de Mul, and J. Greve. “Surface-enhanced Raman

spectroscopy of DNA bases.” Journal of Raman Spectroscopy. 17. 289-298 (1986). 2Z.S. Wu, F. Zheng, G. Shen, R. Yu. “A hairpin aptamer-based electrochemical biosensing

platform for the sensitive detection of proteins.” Biomaterials.30. 2950-2955. (2009). 3Abell, J. L., Driskell, J. D. Dluhy, R. A., Tripp, R. A., Zhao, Y. P. “Fabrication and characterization of a

multiwell array SERS chip with biological applications.” Biosensors & Bioelectronics 24. 3663-3670

(2009).

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FIGURE 1. SERS spectrum of the IgE aptamer at a concentration of 5 micromolar.

366 C-N bending, N-N bending stretching in Guanine

560 N-C-N bending, C-N-C bending in Cytosine

778 Ring Breathing in Thymine

807 N-C bond stretching, Nitrogen Ring stretching, C-C bond stretching in Thymine

1140 N Ring stretching, C-C bending in Cytosine

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500

Inte

ns

ity (

a.u

.)

Wavenumber (cm-1)

SERS Spectrum of the IgE Aptamer

366

560

1140

778 807

257

POSTERS

Control of intervalley electron scattering and giant

piezoresistance of SiGe near the -L crossover

Felipe Murphy-Armando1 and Stephen Fahy1,2

1 Tyndall National Institute, University College Cork, Ireland 2 Department of Physics, University College Cork, Ireland

First-principles electronic structure methods1-3 are used to calculate the electron-phonon and alloy scattering in strained Si1−xGex alloys and to predict the piezoresistance of n-type material at various alloy compositions and strain configurations. We report extraordinarily large gauge

factors, G = dd, where is resistivity and is strain, for Ge compositions x ≈ 0.89 under cantilever type strain in the <111> direction, G>600. These gauge factors are three and a half times larger than the maximum possible for bulk Si, the most widely used and one of the most sensitive piezoresistive materials in use today. This large change in resistance due to strain is

achieved by tuning the relative positions of the L and valley minima, so that the occupancy of

the higher-conductance L valley relative to the lower-conductance valley and the suppression of inter-valley alloy and phonon scattering are highly sensitive to strain.

1F. Murphy-Armando and S. Fahy, “First principles calculation of alloy scattering in n-type Si1−xGex”, Phys. Rev. Lett 97, 096606 (2006).

2F. Murphy-Armando and S. Fahy, “First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys”, Phys. Rev. B 78, 035202 (2008).

3F. Murphy-Armando and S. Fahy, “First principles calculation of electron-phonon and alloy scattering in strained SiGe”, J Appl. Phys 110, 123706 (2011).

258

POSTERS

Phonon Induced Thermodynamic Properties of La1-xBaxCoO3

Rasna Thakur, Rajesh K. Thakur, and N.K. Gaur

Department of Physics, Barkatullah University, Bhopal 462026, India

Perovskite type cobaltate, La1-xBaxCoO3 (0 ≤ x ≤ 0.3) have been studied intensively because of

their wide range of unique physical properties. The fact that rare-earth perovskite-type

cobaltate are most suitable as a cathode material in solid oxide fuel cells (SOFC), makes the

thermal behavior of these compounds highly important. As these compounds are

predominantly ionic in nature hence the lattice contributions to the specific heat at constant

volume (Cv(lattice)) of pure (Fig. 1) and Ba doped LaCoO3 has been studied and thereby thermal

expansion (inset of Fig. 1) is computed as function of temperature by means of Rigid Ion Model

(RIM) and found to be in good agreement with experimental values [1, 2]. We have

systematically investigated the effect of phonons on thermal properties, Debye temperature

(D), molecular force constant (f), Reststrahlen frequency (), cohesive energy (), and

gruneisen parameter () for La1-xBaxCoO3 (0 ≤ x ≤ 0.3). Also the effect of phonons on the bulk

modulus is studied using the atoms in molecules (AIM) [2] theory for pure and Ba doped

LaCoO3. We have found that the computed properties reproduce well with the available

experimental data, implying that RIM represents properly the perovskite cobaltate La1-xBaxCoO3

(0 ≤ x ≤ 0.3). To our knowledge some of the properties for these complicated compounds are

reported for the first time.

1M. Kriener,M. Braden, H. Kierspel, D. Senff, O. Zabara C. Zobel, and T. Lorenz, Phys. Rev. B 79,

224104 (2009).

2K. Knizek, Z. Jirak, J. Hejtmanek, M. Veverka, M. Marysko, G. Maris, and T.T.M. Palstra, Eur.

Phys. J. B 47, 213–220 (2005).

3A.M. Pendas, A. Costales, M.A. Blanco, J.M. Recio, and V. Luana, Phys. Rev. B 62, 13970-78,

(2000).

259

POSTERS

0 100 200 3000

40

80

120

LaCoO3

0 200 400 600 800 10000

10

20

(

10

-6 K

-1)

T (K)

Exp.

Cal.

T (K)

C (

J/m

ole

K)

Exp.

Cal.

FIGURE 1. Computed specific heat (main panel) and thermal expansion (inset) of perovskite

LaCoO3 as a function of temperature. Present results are shown by line with solid circle

(−●−) and experimental values [1, 2] are shown by open circle (○).

260

POSTERS

Structural and Dielectric Study of Hexagonal Y0.9Sr0.1MnO3 Compound

Rajesh K. Thakur, 1 Rasna Thakur, 1 A. Bharathi, 2 and N.K. Gaur1

1Department of Physics, Barkatullah University, Bhopal 462026, India

2Condensed Matter Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India

Strontium doped YMnO3 compound have been prepared in single-phase form by using high temperature solid state reaction method. Although hexagonal manganites have been studied for many years [1, 2], very recently there has been a resurgence of interest in these materials [3]. The structural and dielectric properties of the prepared sample have been carried out in the wide range of temperature and frequency. The XRD pattern of the prepared Y0.9Sr0.1MnO3 compounds could be refined by using P63cm space group. A typical plot of the XRD pattern is shown in Fig.1, which reveals single phase formation of the compounds with hexagonal structure. The obtained lattice parameter for Sr doped YMnO3 are a = b = 6.1374 Å and c = 11.39 Å. The frequency dependence of dielectric is shown in the Fig. 2. It is clear from the graph that with increasing temperature the permittivity shifts to higher value and saturation in it has been observed with increasing frequency. Temperature and frequency variations of dielectric permittivity measurements show that the present hole doped YMnO3 compound exhibits a competing interaction in between the ferromagnetic double - exchange and antiferromagnetic super-exchange interactions, further a weak signature of ferromagnetic ordering at lower temperature has been witnessed. Our resistivity measurement reveals that the material is highly insulating at lower temperature just below the reported AFM transition in this class of materials.

1A Waintal and J Chenevas, Mater. Res. Bull. 2, 819–22 (1967). 2N Fujimura, T Ishida, T Yoshimura and T Ito, Appl. Phys. Lett. 69, 1011–13 (1996). 3M Bieringer and J E Greedan, J. Solid State Chem. 143, 132–9 (1999).

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FIGURE 1. XRD pattern of pure YMnO3compound with 2ϴ ranges from 200 to 600.

FIGURE 2. Frequency dependence of dielectric permittivity (ε) of ceramic Y0.9Sr0.1MnO3

at different temperature.

262

POSTERS

Specific Heat and Transport Properties of BaRuO3

N.K. Gaur, 1 Rasna Thakur, 1 Rajesh K. Thakur, 1 and Archana Srivastava 2

1Department of Physics, Barkatullah University, 462026, Bhopal, India 2Department of Physics, Sri Sathya Sai College for Women, Bhopal 462024, India

We have investigated the specific heat and transport properties of BaRuO3 perovskite probably

for the first time by means of Rigid Ion Model (RIM). The lattice contributions to the specific

heat and thermal expansion of BaRuO3 as a function of temperature (0 K≤ T ≤ 1000 K) are

reported. The systematic trend of variation of specific heat (Fig. 1) and the closer agreement

with the experimental data [1] reveal the suitability and appropriateness of RIM, for BaRuO3

perovskite. A meticulous attention was given to the investigation of the assumption that these

cobaltate perovskites are Debye-like solids and obeys T3 law at low temperature (T < D/50).

Present investigations reaffirm the presence of strong electron–phonon interactions in this

compound. The calculated lattice specific heat gives Debye temperature 272 K, 382 K and 358 K

which is consistent with experimental value (260 K, 389 K and 361 K) for 9R BaRuO3, 4H BaRuO3

and 6H BaRuO3 [1] respectively. The Atoms in Molecules (AIM) theory [2] is used to determine

the bulk modulus of these compounds. Further, the value of Gruneisen parameter is calculated

which is within the range 2-3 as reported earlier for perovskite family [3]. In addition, the

results on thermal expansion () cohesive energy (), molecular force constant (f), Restsrahlen

frequency (), Debye temperatureD) and Gruneisen parameter () are also presented. Our

results on cohesive and thermal properties revealed by using RIM reproduce well with the

available experimental data.

1J.G. Zhao, L.X. Yang, Y. Yu, F.Y. Li, R.C. Yu, Z. Fang, L.C. Chen and C.Q. Jin, J. Solid State

Chem. 180, 2816-2823, (2007).

2A.M. Pendas, A. Costales, M.A. Blanco, J.M. Recio, V. Luana, Phys. Rev. B 62, 13970-78, (2000).

3P.G. Radaelli, S.W. Cheong, Phys. Rev. B 66, 094408 (2002).

263

POSTERS

0 100 200 3000

40

80

120

BaRuO3

Sp

ecif

ic h

eat

(J/m

ole

K)

T(K)

Exp.

Cal.

FIGURE 1. The specific heat of BaRuO3 as a function of temperature (0 K≤ T ≤ 300 K) where solid lines with solid

circles (−●−) are the present results.

264

POSTERS

Time-resolved imaging of surface phonons reflected at microscale circular grooves on silicon surfaces

Motonobu Tomoda,1 Oliver B. Wright,1 Paul Otsuka,1 Osamu Matsuda,1 Yoshiaki Nishijima,2 Kosei Ueno,2 Juodkazis Saulius,2 Hiroaki Misawa2 and István A. Veres3

1 Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan 2 Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan

3 Recendt Research Center for Nondestructive Testing, Linz, Austria

Gigahertz surface phonons are important in nondestructive testing, in sensors and in filtering applications. These applications often make use of microstructures on surfaces, such as electrode films or holes. Although the reflection of bulk waves from flat boundaries can be understood analytically, the reflection of surface phonons from edges and grooves is not amenable to such calculations, and is less well understood. Here we measure GHz surface phonon reflection at grooves in Si wafers as a function of incident angle and frequency.

We fabricated circular grooves of typical diameter 100 μm, depth 13 μm and width 10 μm by a micromachining technique on (100) Si surfaces. Surface phonon pulses are optically generated at a small circular spot (~1 μm) inside the circle by ultrashort light pulses. Time-resolved movies of the propagating surface phonons inside of the circle boundary were obtained by the use of scanned probe light pulses.1,2 The surface phonons propagate outwards, and are then reflected at the circular boundary (Fig. 1).

The movies are analyzed to find the acoustic reflection coefficients from the boundary. The results were also checked by the use of a time domain finite element method.

1D. M. Profunser, E. Muramoto, O. Matsuda and O. B. Wright, “Dynamic visualization of surface acoustic waves on a two-dimensional phononic crystal”, Phys. Rev. B 80, 014301 (2009). 2T. Tachizaki, T. Muroya, O. Matsuda, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation”, Rev. Sci. Instr. 77, 043713 (2006).

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POSTERS

FIGURE 1. (a) Optical reflectivity image of a circular groove boundary of internal diameter 100 μm. The substrate is Si (100) covered with a 40 nm polycrystalline Cr film. (b) Snapshot of the phonon pulse propagation. The times after pumping are indicated by the arrows: 6.2 ns is the outgoing wave front, and 18.6 ns is the reflected wave front.

266

POSTERS

Influence of growth temperature on cross-plane thermal conductivity of ZrN, ScN and (Zr,Sc)N thin films measured by

Time-Domain Thermoreflectance

Gilles Pernot,1 Polina Burmistrova,2 Yee Rui Koh,1 Tim Sands,2 and Ali Shakouri1,2 1 Baskin School of Engineering, University of California, Santa Cruz, CA, USA

2 Birk Nanotechnology Center, Purdue University, West Lafayette, IN, USA

As previous researches have demonstrated1, nitride metal/semiconductor multilayers are

promising for thermal-to-electrical energy conversion. By optimizing the metal-semiconductor

Schottky barrier to maintain good electronic properties and the multilayer period to reduce the

cross-plane thermal conductivity, a high thermoelectric figure-of-merit can be obtained.

Experimental studies of different superlattice structures2 reveal a minimum of thermal

conductivity for a period of about 3 to 7nm. The effects of interface roughness can also be

optimized by changing the growth condition such as temperature. To understand the mechanism

of heat transport in multilayers, measurements on reference samples grown in the same

experimental conditions are required. This can clarify the thermal conductivity reduction

mechanisms.

In this paper, we report the experimental cross-plane thermal conductivity of nitride crystalline

materials grown at different temperatures using a femtosecond pump-probe thermoreflectance

technique. About 1.5 microns thick film of metal ZrN, semiconductor ScN and alloy (Zr,Sc)N

samples were grown on a (100) MgO substrate by DC reactive magnetron sputtering at 500C,

600C and 850C. In Figure 1, thermal conductivity versus growth temperatures is reported.

Thermal conductivity of ZrN is in good agreement with the one reported by Rawat et al. whereas

ScN and (Zr,Sc)N films show an important discrepancy compared to the values measured for

thin films. Our measurements clearly show the typical reduction in alloy's thermal conductivity.

As expected, the change in the growth temperature also affects the cross-plane thermal

conductivity. For all of the materials, we report a thermal conductivity reduction of about 2

between high and low temperatures. Furthermore, High-resolution x-ray diffraction (HRXRD),

Scanning electron microscopy (SEM) and High-resolution transmission electron microscopy

(TEM) of the films and 4-probe electric measurements are performed to study the role of the

crystal structure and the defects on the observed thermal conductivity and the correlations

between electrical and thermal transport coefficients.

1 V. Rawat, T. Sand, “Growth of TiN/GaN metal/semiconductor multilayers by reactive pulsed laser deposition”, J. Appl. Phys. 100, 064901 (2006).

2 V. Rawat et Al, “Thermal conductivity of (Zr,W)N/ScN metal/semiconductor multilayers and

superlattices”, J. Appl. Phys. 105, 024909 (2009).

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500 600 700 800 900

10

20

30

40

50

(1450nm)

(297nm)

ZrN

ScN

(Sc,Zr)NT

he

rma

lCo

nd

uctivity (

W/m

K)

Growth Temperature (C)

Data from

Rawat et Al

(306nm)

FIGURE 1. Cross-plane thermal conductivity of ZrN, ScN and (Zr,Sc)N alloy for grown at different temperatures. (inset) Data from Rawat et Al2 for 1.45um ZrN film, 306nm thin ScN film and

297nm thin (Sc,Zr)N film.

268

POSTERS

Characteristics of a coherent longitudinal optical phonon in a GaAs buffer layer optically covered with a GaSb top epitaxial

layer investigated with use of terahertz spectroscopy

Hideo Takeuchi,1 Syuichi Tsuruta,2 and Masaaki Nakayama2 1 Department of Electronic Engineering Systems, The University of Shiga Prefecture, Hassaka-cho

2500, Hikone, Shiga 522-8533, Japan 2 Department of Applied Physics, Osaka City University,3-3-138 Sugimoto, Sumiyoshi-ku, Osaka

558-8585, Japan

Terahertz (THz) spectroscopy is an interesting tool for the investigation of dynamics of coherent phonons. In emission processes of the THz electromagnetic wave from longitudinal optical (LO) phonons, the coherent LO phonon is initially induced by the surge current of photogenerated carriers that causes an instantaneous change in the band bending through the screening effect. Subsequently, the induced coherent LO phonon emits the THz wave. The above-mentioned THz-wave emission mechanism suggests that the substantial trigger of driving the coherent LO phonon is not the pump-beam illumination but the photogenerated-carrier induced band bending. Accordingly, it is expected that, even in the case where a given layer is optically covered with upper layers, the THz wave from the coherent LO phonons is generated through a change in the band bending. In the present paper, we explore the feasibility of the above-mentioned phenomenon. The present sample, an undoped GaSb/undoped GaAs epitaxial structure, was grown on a (001)-oriented semi-insulating GaAs substrate by molecular beam epitaxy. The thicknesses of the GaSb top layer and GaAs buffer layer were 900 nm and 200 nm, respectively. Initially, we performed Raman scattering measurements at room temperature (RT). The excitation-beam photon energy was 1.58 eV. In the Raman scattering spectrum, only the GaSb transverse optical phonon and LO phonon are observed; namely, the GaAs buffer layer is optically covered with the GaSb top layer. Next, we performed THz-wave measurements at RT. The pump-beam photon energy was 1.57 eV. In the THz waveform, the monocycle signal, which results from the surge current, is followed by an oscillation pattern. The oscillation pattern shows a beat profile; namely, the multiple oscillation modes are observed. The Fourier power spectrum shows the GaAs LO phonon band peaking at 8.6 THz in addition to the GaSb LO phonon band at 7.0 THz. It is, therefore, confirmed that the THz wave from the coherent LO phonons in the GaAs layer optically covered with the upper GaSb layer is generated through a change in the band bending. We note that the frequency of the GaAs LO phonon is 8.8 THz in the single crystal. Accordingly, the shift of the phonon frequency -0.2 THz indicates the presence of a tensile strain. The estimated tensile strain is 1.810-2, according to Ref. 1. We also estimated the decay times of the coherent GaAs and GaSb LO phonons, taking advantage of the time-domain THz-wave measurement. In order to estimate the decay times, we performed the time-partitioning Fourier transform. The decay times of the coherent GaAs and GaSb LO phonons are 2.0 and 3.3 ps, respectively. Accordingly, it is concluded that the THz-wave measurement is useful way to investigate the characteristics of the coherent LO phonon in the layer optically covered with the upper layer.

1 M. Nakayama et al., J. Appl. Phys. 58, 4342 (1985).

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FIGURE 1. Raman spectrum of the GaSb/GaAs epitaxial structure at room temperature (RT).

FIGURE 2. (a) THz waveform of the GaSb/GaAs structure at RT. (b) Fourier power spectrum of the THz waveform. The bands peaking at 7.0 and 8.6 THz are attributed to the coherent GaSb and GaAs LO phonons, respectively.

FIGURE 3. (a) Time-partitioning Fourier transform spectra at various time windows. (b) Peak intensity of each phonon band plotted as a function of time delay. The peak intensity of the GaAs LO phonon band decays faster than that of the GaSb LO phonon.

5.0 6.0 7.0 8.0 9.00

Frequency (THz)

Inte

nsi

ty (

arb.

un

its)

GaSb LO

GaSb TO

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0

-1

0

1

2

Am

pli

tud

e (p

A)

Time Delay (ps)

(a)

1.0 2.0 3.0

-1

0

1

Time Delay (ps)

0 2.0 4.0 6.0 8.0 10.0

0

Frequency (THz)

Inte

nsi

ty (

arb

. u

nit

s)

GaSb LO

GaAs LO(b)

0 2.0 4.0 6.0 8.0 10.00

Time Window[ ps, 8.0 ps]

= 0.0 ps

= 1.2 ps

= 2.0 ps

(a)

Inte

nsi

ty (

arb

. u

nit

s)

2

5

Frequency (THz)-1.0 0 1.0 2.0 3.0

10-4

10-3

Time Delay (ps)

Pea

k I

nte

nsi

ty (

arb

. u

nit

s)

GaAs LOGaSb LO

(b)

270

POSTERS

Longitudinal and Transverse Acoustic Phonon Excitations in Gold Nanowires under Uniaxial Strain

Tamanaco Francisquez,1 Carlos Sabater, Giovanni Saenz-Arce2 and Carlos Untiedt1 1 Department of Applied Physics, University of Alicante, San Vicente del Raspeig, Alicante, Spain

2 Department of Physics, Universidad Nacional, 86-3000, Heredia, Costa Rica

Gold nanowires have been fabricated with the help of a mechanically controllable break-junction and scanning tunneling microscope techniques at low temperatures by repeated indentation between two gold leads1. During the formation and rupture of the nanowires, point contact spectroscopy2 was carried out at different stages of the gold nanowire formation/rupture trace and at different strains along stable conductance plateaus. The derivatives of the differential conductance (d2I/dV2 versus V) display the characteristic gold point-contact spectrum features of phonon excitations, which shift upon stretching the nanowire along the conductance plateaus, similar to previously reported shifts of the features in atomic wires/contacts3,4 and molecular junctions5. We also investigated the relationship between the plastic deformation of the nanowire as is stretched and the magnitude of the electron-phonon scattering response obtained from point-contact spectroscopy, finding that greater plastic deformations yield larger electron-phonon scattering magnitudes in the differential conductance measurements for both longitudinal and transverse acoustic phonon excitations.

1Agraït, N., Yeyati, A. & van Ruitenbeek, J. “Quantum properties of atomic-sized conductors”. Physics Reports 377, 81-279 (2003).

2Jansen, A., Gelder, A. & Wyder, P. “Point-contact spectroscopy in metals”. Journal of Physics C:

Solid State Physics 13, 6073 - 6118 (1980).

3Agraït, N., Untiedt, C., Rubio-Bollinger, G. & Vieira, S. “Onset of Energy Dissipation in Ballistic

Atomic Wires”. Physical Review Letters 88, 216803 (2002).

4Böhler, T., Edtbauer, a & Scheer, E. “Point-contact spectroscopy on aluminium atomic-size

contacts: longitudinal and transverse vibronic excitations”. New Journal of Physics 11, 013036

(2009).

5Djukic, D. et al. “Stretching dependence of the vibration modes of a single-molecule Pt-H_2-Pt

bridge”. Physical Review B 71, 161402R (2005).

271

POSTERS

Time Resolved Vibrational Properties of Single

Si3N4 Nanostructures

Oliver Ristow,1 Mike Hettich,1 Martin Grossmann1, Martin Schubert,1 Elaine Barretto1, Jochen Grebing,2 Axel Bruchhausen,1 Denis Mounier,3 Artur Erbe,2 Elke

Scheer,1 Vitalyi Gusev3 and Thomas Dekorsy1 1 Department of Physics and Center of Applied Photonics, University of Constance,

D-78457 Konstanz, Germany

2 Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany

3LPEC, UMR-CNRS 6087, ENSIM, PRES UNAM, Université du Maine, 72085 Le Mans, France

Phonons in one dimensional confined nanostructures have been investigated in recent times using various techniques such as Brillouin light scattering or pump-probe spectroscopy. Using high speed asynchronous optical sampling1 earlier studies showed confined longitudinal phonons in silicon membranes2. In this work we present investigations of the vibrational properties of further dimensionally reduced nanostructures, focusing on nano-mechanical resonator structures. These structures consist of a Si3N4 beam, with typical dimensions of a few hundred nm width and up to 5 µm length. The beam is suspended between two bases (Fig. 1), a top layer of 20 nm gold acts as optical transducer. By using a 50x microscope set-up we are able to achieve diffraction limited focal spot size, giving us the opportunity to spatially resolve the vibrational dynamics within the structure. We compare the vibrational properties of free standing beams (Fig. 1, left) with those of similar structures which were released from the substrate and then soft-landed (Fig.1 top). Figure 2 (right top) shows the Fast Fourier Transform (FFT) of a series of measurements scanning across such a landed beam, giving evolution to only one frequency. Figure 2 (right bottom) shows the frequencies obtained from a comparable free standing beam. Here several frequencies occur, which cannot be found at the landed beam. The changes in the vibration spectra can be compared with finite element simulations using the COMSOL software package. The simulations indicate that the suppression of these modes is influenced by the coupling of the beam to the substrate.

A second system studied are micromechanical disk resonators (Fig 3, top). These structures were fabricated using the same material system as the cantilevers. Mechanical eigenmodes in the GHz range could be found. The obtained frequency spectrum of a 1 µm diameter disk is given in Fig.3, right. Assuming a radial symmetry of the individual modes, the simulations agree very good with the experimental data.

1

A.Bartels et al. “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling“ Rev. Sci. Instrum. 78, 035107 (2007) 2 A.Bruchhausen et al. “Subharmonic Resonant Optical Excitation of Confined Acoustic Modes in a Free-Standing Semiconductor

Membrane at GHz Frequencies with a High-Repetition-Rate Femtosecond Laser”,Phys. Rev. Lett. 106, 077401 (2011)

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FIGURE 2. Top: Schematics of a beam structure on the substrate, as given in Fig.1 right. The arrow indicated the scan direction.

Right top: Evolution of the mode spectrum obtained from scanning across a beam structure lying on the substrate.

Right bottom: Mode spectrum obtained from a free standing beam structure, as indicated in Fig. 1 left.

FIGURE 1. Left: Scanning electron micrograph (SEM) picture of a freestanding Si3N4 beam structure.

Top: SEM picture of a soft-landed beam structure on the

substrate.

FIGURE 3. Top: SEM picture of a microdisk resonator structure.

Right: Frequency spectrum of a 1 µm disk resonator, compared with COMSOL simulations. Shown in color is the relative displacement amplitude.

273

POSTERS

Acousto-optic coupling under the conditions of plasmonic resonance in lateral grating structures

Vladimir Belotelov1 and Boris Glavin2 1 Lomonosov Moscow State University, 119991 Moscow, Russia

2 V E Lashkaryov Institute of Semiconductor Physics, Kyiv 03028, Ukraine

The field of acousto-optics emerged many decades ago. Since then, considerable efforts have been made to optimize the coupling of acoustic and electromagnetic waves. The development of nanotechnologies brought about new approaches to the problem. For example, extensive studies, both experimental and theoretical, were performed for layered semiconductor heterostructures, where simultaneous confinement of acoustic and light fields gives rise to considerable enhancement of the light scattering by vibrations.1 Here, we address an alternative approach to the problem, which relies on the plasmonic effect in metal/dielectric structures. The advantage of this approach is sub-wavelength confinement of the electric field of the electromagnetic wave,2 which is difficult to achieve in semiconductor structures with relatively low refractive index contrasts.

In particular, we performed theoretical analysis of a structure where a metallic grating is deposited on top of a dielectric substrate. In such a system an incident light beam can excite surface plasmon-polaritons for particular angles of incidence and wavelength. We have shown that plasmon-polariton coupling to light can be modified efficiently by acoustic vibrations due to both photoelasticity and perturbation of the grating geometry. Naturally, the system is sensitive mostly to vibrations within the near field optical zone just below the grating, where the magnitude of the electric field is enhanced strongly due to the plasmonic effect. We addressed the possible types of acoustic excitations for which the acousto-optical coupling is most efficient. Among them, the best candidates are quasi-surface waves as well as near-surface waves, which propagate along or close to the surface. For realistic material parameters they can cause acousto-optical modulation at sub-terahertz frequencies. In practice, both of the mentioned acoustic waves can be excited using picosecond acoustics, where the bulk-surface wave transformation is realized due to acoustic diffraction at the grating. We also performed an analysis of more sophisticated structures where an additional optical waveguide layer is introduced below the grating. We show that such a design provides more flexibility for the optimization of the acousto-optical coupling due to the interplay of the plasmonic and waveguide resonances.

1 N.D. Lanzillotti-Kimura, A. Fainstein, B. Perrin, B. Jusserand, L. Largeau, O. Mauguin, A. Lemaitre, Phys. Rev. B 83, 201103 (2011).

2 L. Novotny and B. Hecht, Principles of Nanooptics (CUP, 2006).

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Brillouin Study of the Bandgap Structure of

Laterally-patterned Phononic Crystals

H. H. Pan,1 V. L. Zhang,1H. S. Lim,1 S. C. Ng,1 M. H. Kuok,1

S. Jain,2 and A. O. Adeyeye2 1Department of Physics, National University of Singapore, Singapore 117542

2Department of Electrical and Computer Engineering, National University of Singapore,

Singapore 117576

Photonic crystals are periodic composites comprising two or more materials of different refractive indices, as opposed to different elastic properties for phononic crystals. Phononic crystals are novel materials that enable the manipulation of the flow of phonons. The periodic variations of density and elastic property of phononic crystals result in the formation of phononic bandgaps which prevent acoustic waves with certain frequencies from propagating through the crystals. Thus, phononic crystals, besides being of great fundamental scientific interest, are expected to show enormous promise in a wide variety of applications.1 In this work, the phononic crystal studied is composed of a one-dimensional periodic array of alternating Cu and Ni80Fe20 (Py) nanostripes on a SiO2/Si substrate. Brillouin light scattering, an excellent technique for probing acoustic waves in nanostructured materials,1,2 has been employed to map the frequency band structure in the artificial crystal. Numerical simulations of the phononic dispersions within the finite element framework yield good agreement with experiments.

1 W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals”, Nat. Mater. 5, 830 (2006).

2 J. R. Dutcher, S. Lee, B. Hillebrands, G. J. McLaughlin, B. G. Nickel, and G. I. Stegeman, “Surface-Grating-Induced Zone Folding and Hybridization of Surface Acoustic Modes”, Phys. Rev. Lett. 68, 2464 (1992).

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FIGURE 1. Phononic dispersion relations of Cu/Py phononic crystal. Experimental data are denoted by symbols. Measured bandgaps are represented by shaded bands, and Brillouin zone boundaries by vertical dashed lines.

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Multifractal analysis of instantaneous normal modes at mobility edges

Ten-Ming Wu Institutet of Physics, National Chiao-Tung University, Hsinchu, Taiwan, R.O.C.

The localization-delocalization transition (LDT) due to disorder has been studied for many years

with the Anderson model (AM) for electron transport on a lattice. However, the complicated

electronic interactions make the electron transport in real materials deviated from the AM.

Observed recently in experiments with atomic matter waves, the LDT is also expected to occur

in the vibrational spectra of topologically disordered systems, like glasses and liquids, with the

transition named as mobility edge (ME). In this presentation, we investigate the ME in the

instantaneous normal mode (INM) spectrum of a fluid, in which the disorder is originated from

particle positions, and compare the properties at a ME with those of the AM.

The INMs of a fluid are referred as eigenmodes of the Hessian matrices evaluated at fluid

configurations generated with simulations. For fluid structures, which no longer possess a

reference of lattice, the Hessian matrices are an ensemble of the Euclidean random matrices,

with elements subject to some constrains, and the INM spectrum consists of both positive and

negative eigenvalues in general. With the level-spacing (LS) statistics and the approach of finite-

size scaling, we have identified two MEs in the INM spectrum of a repulsive Lennard-Jones

fluid,1 with one in the positive-eigenvalue branch and the other in the negative-eigenvalue one;

the locations of the two MEs are further confirmed with the multifractal analysis2. We also

show that the INMs at each ME exhibit a multifractal nature, with two examples presented in

Fig. 1, and the multifractal INMs at the two MEs yield the same generalized fractal dimensions

and singularity spectrum.3 Compared with the AM in three-dimensional space, our results

indicate that the nearest-neighbor LS distribution, the critical exponent and the singularity

spectrum of the INMs at the two MEs agree well those calculated by the eigenstates of the AM

at the critical disorder. These good agreements provide numerical evidences for the universality

of the LTD due to disorder.

1B. J. Huang and T. M. Wu, “Localization-delocalization transition in Hessian matrices of topologically disordered systems”, Phys. Rev. E 79, 041105 (2009).

2B. J. Huang and T. M. Wu, “Numerical studies for localization–delocalization transition in vibrational spectra”, Comput. Phys. Commun. 182, 213 (2011).

3B. J. Huang and T. M. Wu, “Multifractality of instantaneous normal modes at mobility edges”, Phys. Rev. E 82, 051133 (2010).

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FIGURE 1. Geometric structure of a multifractal INM with a positive eigenvalue (a) or a negative eigenvalue (b) for the repulsive LJ fluid of N=96000 particles. In each structure, particles with vibrational amplitudes larger than the average value N-1/2 are presented by spheres centered at the particle positions, with the color of a sphere indicating the magnitude of vibrational amplitude of the particle. The numbers of spheres shown in (a) and (b) are about 5700 and 7000, respectively.

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Nanoscale thermal transport measurements: Bridging ultrafast and steady-state

Brian G. Green, Barry L. Zink, and Mark E. Siemens Department of Physics and Astronomy, University of Denver, Denver, CO, USA

Thermal transport dynamics of materials at mesoscopic (~1-500nm) length scales, with critical

dimensions only hundreds of atoms in size, is a field of critical importance and serious

experimental challenges. Mesoscale transport couples the nanoscale (quantized) and bulk

(diffusive) transport regimes, but a full understanding is complicated by material

inhomogeneity, impurities, and disorder. For this reason, it is essential to make experimental

transport measurements in carefully-controlled samples. Transport can be measured using a

variety of techniques that each have their own strengths, weaknesses, and experimental

barriers, but no one technique can fully characterize electron and phonon transport.

In this work, we make a direct comparison of two techniques at opposite ends of probing

timescale and volume: ultrafast thermoreflectance measurements with pulsed lasers and

steady-state transport measurements using micromachined thermal isolation platforms. Both

measurements are performed on carefully isolated nanostructures, as shown in Fig. 1, in order

to draw concrete conclusions about transport properties. Specifically, we compare thermal

conductivities measured by ultrafast and steady-state measurements and use any

inconsistencies to provide insight into the fundamental phonon and electron transport.

Preliminary transient thermoreflectance results from a thermally isolated Si-N bridge coated

with a 200 nm molybdenum film are shown in Fig. 2. These data show a strong TTR signal

corresponding to optical heating (first few picoseconds after “time zero” where the pump and

probe beam arrive at the sample at the same time) and subsequent cooling (∼ 1000 picosecond

timescale) due to thermal diffusion away from the optically heated region. These results are

consistent with thermal diffusion in the molybdenum film, and fitting to a 1D model yields a

thermal diffusivity of κ = 3.1 × 10−5 m2/s. Assuming bulk values for density and heat capacity,

we calculate a thermal conductivity of kMo = 80 W/mK, which is between the higher bulk value

(kMo,bulk = 138 W/mK) and a lower value measured by DC electrical thermometry on the same

sample (kMo,DC = 55 W/mK).

We are investigating possible reasons for this discrepancy by comparing ultrafast and steady-

state measurements on thinner films and variable base temperatures. We look forward to

gaining empirical insight into the fundamental physics of sub-continuum carrier interactions

and the transfer processes in nano-to-macro scale energy flow, as well as practical learning of

how to resolve inconsistencies between different modes of probing thermal transport.

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FIGURE 1. Integrated setup for combination transient thermoreflectance/Joule heating and electrical thermometry on thermally isolated nanoscale bridges.

FIGURE 2. Preliminary results of TTR dynamic measurements on an isolated Si-N bridge coated with 200 nm of molybdenum, using the experimental setup shown in Fig. 1. The temperature in

the bridge decays exponentially with a time constant τ = 1280 ps, corresponding to thermal diffusion in the film with a thermal conductivity of 80 W/mK, as indicated in the table at right.

Pumpbeam

Polarizing BSObjective

BS

CCD

Probe beam

50/50 BS

½ WP

Pulsedlaser

Optical isolator

Modulator

Sample

Time-delay stagePump beam

Probe beam

Photo-diode

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Inelastic Phonon Tunneling Via a Quantum Point Contact

Douglas M. Photiadis

Naval Research Laboratory, Washington, DC, USA

The coupling of the vibrations of a suspended structure attached to a substrate by a point contact gives rise to a fundamental loss mechanism for the structure. This loss mechanism has generally been referred to as attachment loss or anchor loss, but by analogy with the corresponding geometries involving electromagnetic radiation tunneling and electron tunneling, the transport of phonons from the suspended structure, a phonon cavity, to the substrate can be usefully considered to be phonon tunneling1. It has long been thought that such tunneling phenomena provide the dominant source of extrinsic energy loss of a weakly coupled suspended structure.

Based on a theoretical analysis of the equations of elasticity, we have found2 that a new phenomenon, inelastic phonon tunneling, can make a significant contribution to the total energy transport in the limit in which the scale of the point contact becomes much smaller than the dominant wavelength of the substrate. This transport mechanism corresponds to a nonlinear process in which phonons in the cavity are strongly coupled to excitations in the substrate because of the large strains in the nearfield of the point contact. The theoretical result we have obtained is universal, independent of the geometry, because it depends only on the elastic nearfield to the point contact. For an oscillator of effective mass M attached to a substrate, inelastic phonon tunneling places an absolute lower limit on the Q-1 of the oscillator,

where is of order the internal friction of the substrate, 0 is the resonance frequency of the

suspended structure and is a natural frequency determined by the mass of the oscillator, the size of point contact, and the material properties of the substrate.

This work was supported by the Office of Naval Research.

1 Garrett D. Cole, Ignacio Wilson-Rae, Katharina Werbach, Michael R. Vanner & Markus Aspelmeyer, “Phonon-tunnelling dissipation in mechanical resonators,” Nature Comm. DOI: 10.1038/ncomms1212 (2011). 2 Douglas M. Photiadis, “The effect of dissipation on the resistive admittance of an elastic medium,” J. Acoust. Soc. Am. In press. (2012).

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Study of Local Heating and Thermoelectric Effects in Quantum Point Contacts and Molecular Junctions

Woochul Lee,1 Kyeongtae Kim,1 Wonho Jeong,1 and Pramod Reddy1,2 1 Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

2 Department of Materials Science, University of Michigan, Ann Arbor, MI, USA

We present experimental results from our study of energy dissipation and thermoelectric properties of one-dimensional (1D) atomic and molecular junctions. Using custom-fabricated scanning thermal microscopy (SThM) probes, which have thermocouples integrated into the tips of atomic force microscope probes, we have probed the thermoelectric properties and energy dissipation characteristics of atomic and molecular junctions. Specifically, our studies performed in an ultra high vacuum environment elucidate the dependence of thermoelectric properties of junction on their molecular structure and end group chemistry. Further, our studies of energy dissipation describe the local temperature rise in the metal atomic contacts as well as in the contacts of molecular junctions as a function of molecular length, and contact chemistry. Finally, we will briefly describe our recent efforts into experimentally probing thermal transport in single molecule junctions.

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Guided Phonon Transmission Through Nanoribbon Constrictions

Drew A. Cheney, Jennifer R. Lukes Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania,

Philadelphia, PA, USA

In this study, we theoretically investigate guided phonon transport through nanoribbon constrictions. Mode-by-mode ballistic phonon transmission rates are calculated using the harmonic lattice-dynamics based scattering boundary method.1 In part one of this study, we explore how the constriction impedes the transport of out-of-plane guided phonon modes. We compare our results for the transmission of these modes with results obtained from a popular eigen-mode expansion method based on a continuum, scalar model for phonon transport.2 Our results show that the accuracy of the continuum model erodes as the nanoribbon and constriction width become smaller and as the phonon wavelength approaches the interatomic spacing. In part two of this study, we expand our investigation by calculating mode-by-mode transmission for all phonon modes including in-plane coupled phonon modes which are similar to Lamb modes in elastic plate waveguides. Using Landauer theory, the phonon transmission coefficients are used to calculate ballistic thermal conductance through the constriction. We explore the effect of constriction size and shape on the transmission of particular phonon modes as well as on the aggregate, temperature dependent thermal transport across the constriction. Various shapes and sizes of constriction are compared in their ability to impede phonon transport across the constriction and limit ballistic phonon conductance. The relative contribution of each phonon mode to thermal transport is determined and the most dominant modes are identified. In addition, we comment on the role of evanescent modes, which are localized near the constriction, in determining the mode-by-mode phonon transmission.

1J. Wang, and J.S. Wang, “Mode-dependent energy transmission across nanotube junction calculated with a lattice dynamics approach”, Phys. Rev. B 74, 054303 (2006).

2P. Yang, Q. Sun, H. Guo, and B. Hu, “Thermal transport in a dielectric T-shape quantum wire”, Phys. Rev. B 75, 235319 (2007).

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High-frequency acousto-electric response of Schottky diodes

Daniel M. Moss,1 Andrey V. Akimov,1 Boris A. Glavin,2 Mohamed Henini,1 and Anthony J. Kent1

1 School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK 2 V E Lashkaryov Institute of Semiconductor Physics, Kyiv 03028, Ukraine

Acousto-electonics is a well-established field which found extensive applications in signal processing at frequencies about or below 1 GHz. Here we demonstrate that strong acousto-electric coupling is attainable at much higher frequency for GaAs Schottky diodes. The diode is driven by picosecond strain pulse excited by the femtosecond laser pulse applied to a metallic film transducer deposited at the bottom of the substrate. The electrical response of the diode is measured by the digital sampling oscilloscope. The characteristic time dependence of the response, measured at temperature of 5K and various diode reverse biases is shown in Fig.1. Similar responses were observed at elevated temperatures, up to 300 K. The performed analysis suggests that the observed signal can not be attributed to the strain-induced variation of the semiconductor band-gap, which is responsible for static piezo-resistivity of p-n and Schottky junctions. We have found that for dynamical spatially non-uniform strain an alternative mechanism appears due to the screening of the deformation potential caused by the pulse by the free carriers. Due to the spatially nonuniform distribution of carriers, the total charge required to screen the effect of strain changes while the pulse travels through the structure, giving rise to the displacement current of the diode. Theoretical analysis, taking into account the properties of the circuit, shows that for not too high frequencies the response traces the value of strain at the edge of the depletion layer. The key experimental feature supporting this model is the bias dependence of the position of the peaks of the diode response (Fig.1), which correlates well with the time when the forward and reflected strain pulses reach the edge of the depletion layer. The numerical simulations considering realistic shape of the strain pulse influenced by the crystal anharmonicity and dispersion provide good agreement with experimental observations, in terms of both shape and magnitude of the electrical response.

We estimated also the frequency cut-off in the system, which is roughly determined by the characteristic screening length in the semiconductor, being for realistic parameters in the range of a hundred GHz.

The obtained results suggest feasibility of high-frequency acousto-electronic applications for both electronic devices and high-frequency phonon detection.

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FIGURE 1. Dynamical current response of the Schottky diode to the strain pulse at different reverse biases and temperature of 5K. The dashed lines indicate the time instants when the forward and reflected strain pulses cross the edge of the diode depletion layer. The inserts show the signal for larger time interval, demonstrating contribution from the strain pulses

reflected back and forth across the sample (left), and experimental (squares) and calculated (line) bias dependence of the pulse arrival time to the edge of depletion layer (right).

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Do Zone-Center Acoustic Modes of a Superlattice Always Avoid Boundaries?

A. A. Maznev 1 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Acoustic modes of superlattices (SLs) at zone-center bandgaps present an interesting class of waves with very low group velocity and high phase velocity. Trigo et al.1 observed that these waves tend to “avoid” boundaries of a finite SL and suggested that this property is universal and holds for any boundary conditions. However, there exists an obvious counter-example: a rigid wall placed at the midplane of any layer does not disturb the displacement pattern in a symmetric zone-center mode; consequently, in this case the mode is not “surface-avoiding”. Similarly, it is possible to terminate an SL at a free surface in such a way that makes the zone-center mode satisfy the boundary condition. Thus the behavior of near-zone-center modes at a boundary depends on how, exactly, the SL is terminated. We will discuss the effect of this phenomenon on eigenmodes of SL slabs and on laser excitation of acoustic waves in a semi-infinite SL.

1M. Trigo, T. A. Eckhause, M. Reason, R. S. Goldman, and R. Merlin, “Observation of Surface-Avoiding Waves: A New Class of Extended States in Periodic Media”, Phys. Rev. Lett. 97, 124301 (2006).

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Single mode phonon scattering at CNT-graphene junction in pillared graphene structure

Jonghoon Lee,1,2,* Vikas Varshney,1,2 Joshua Brown,3 Ajit K. Roy,1 and Barry L. Farmer1

1 Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, USA

2 Universal Technology Coorporation, 1270 N. Fairfield Rd., Dayton, Ohio 45432, USA 3 College of Engineering and Science, Louisiana Tech. University, Ruston, LA 71272, USA

Phonon scattering at the carbon nanotube-graphene interface in the pillared graphene structure is studied using the phonon wave packet method for all acoustic modes and selected optical modes including radial breathing mode. The graphene interface, whose surface normal is parallel to the nanotube pillar axis, is found to distribute the incoming phonon energy to both sides of the interface more of less equally, thus providing a strong diffusive scattering site. Although a small amount of mode mixing occurs during scattering, the incident phonon polarization constitutes the major part of the polarizations in the post-scattering vibrations. Unlike previous studies on phonon scattering in carbon nanotube systems, the phonon group velocity is found to play an insignificant role in determining the phonon energy transmission coefficient. This study provides a microscopic understanding of the decisive role played by the junction on the thermal transport in pillared graphene structure and presents an example of phonon dynamics control with a designed interface.

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FIGURE 1. Schematic of the unit-cell pillared grapheme structure (left) and its junction structure (right) used in this work. Four CNT pillars are labeled with numbers.

(a) (b)

FIGURE 2. The coordinate deviation of the first basis atom of each unit cell is plotted for the wave packet of a radial breathing optical mode at two different time frames of before and after

the interface scattering. The grapheme interface is located at z=0. The amplitude of the wave packet before the collision is about 2 pm. Defferent colors indicate three different directions of

x,y,z.

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Acoustic Phonon Temperature of Nanoscale Molecular Devices during Electromigration

Wonho Jeong,1 Kyeongtae Kim,1 Woochul Lee,1 and Pramod Reddy1,2 1Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

2Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

Three terminal single molecule transistor devices are usually created by taking advantage of electromigration in gold nanowires.1 Such devices have been extensively used for studying charge transport in nanometer-sized molecular junctions. However, their use is somewhat limited by the large local temperature rise that is expected to occur during the electromigration process, which is central to the creation of the single molecule transistor devices. These large temperature rises could potentially degrade the organic molecules through which charge transport is to be studied.1 In order to understand local heating in these devices, we directly measured the rise in the phonon temperature by thermally imaging biased devices—with nanoscale resolution—using a novel scanning thermal imaging technique2 developed by us. The obtained results indeed show that very large local temperature rises occur during electromigration. To overcome this problem, we have developed and verified a new design that includes fins to attenuate the temperature rise during electromigration, thus making them better suited for a variety of studies.

1T. Taychatanapat, K. I. Bolotin, F. Kuemmeth, and D. C. Ralph, “Imaging Electromigration during the Formation of Break Junctions”, Nano Lett.7, 652 (2007).

2K. Kim, W. Jeong, W. Lee, and P. Reddy, “Ultra-High Vacuum Scanning Thermal Microscopy for Nanometer Resolution Quantitative Thermometry”, In Submission (2012).

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Detection of shorter-than-skin-depth acoustic pulses in a

metal film via transient reflectivity

Kara J. Manke,1 Alexei A. Maznev,1 Christoph Klieber,1 Vasily V. Temnov,1

Sueng-Hyub Baek,2 Chang-Beom Eom,2 and Keith A. Nelson1

1 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA 2Department of Materials Science and Engineering, University of Wisconsin, Madison, WI, USA

In picosecond ultrasonics, the generation and detection of ultrashort acoustic pulses is typically performed with thin metal film transducers. Conventional wisdom suggests that the ability to resolve a short acoustic pulse by transient reflectivity is limited by the optical skin depth. Consequently, aluminum, which has a short skin depth of ~7 nm in the visible range, is typically considered a material of choice for picosecond acoustic transducer films. Recently Mante et al.1 demonstrated the detection of acoustic pulses significantly shorter than optical skin depth in semiconductor InP. In this report we show that the detection of sub-skin-depth acoustic pulses is also possible in common metals such as gold. We studied ~200 nm gold films that had been grown on thin (4-12 nm) SrRuO3 (SRO) films on SrTiO3 (STO) substrates. A short acoustic pulse was generated by illumination of the SRO film with an 800 nm femtosecond laser pulse. The acoustic pulse propagated through the gold film and was detected at the free surface via transient reflectivity of a 400 nm probe pulse (Figure 1). We show that the transient reflectivity response of the gold film to a short acoustic pulse can be decomposed into two components: one entirely determined by the optical skin depth of the probe light and independent of the acoustic pulse duration, and another representing the integral of the acoustic strain profile (Figure 2). The superposition of the two components leads to an intricate shape of the observed waveforms. Our results demonstrate that the optical skin depth does not impose a limit on the acoustic detection bandwidth of picosecond ultrasonics measurements.

1P.-A. Mante, A. Devos, and A. Le Louarn, “Generation of terahertz acoustic waves in semiconductor quantum dots using femtosecond laser pulses”, Phys. Rev. B 81, 113305 (2010).

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FIGURE 1. a) A schematic diagram of the sample structure and the experimental arrangement (not to scale).

FIGURE 2. a) A transient reflectivity waveform generated by a short acoustic pulse at the surface of a gold film. The experimental data have been overlaid with a simulated curve. b) and

c) The two components of the modeled response.

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Phonon Density of States and Phonon Dispersion Simulation for Si, (4H)SiC, and GaN Materials

Srikanta Bose1 and S. K. Mazumder1

1 Laboratory for Energy and Switching-Electronics System, Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA.

(E-mail:[email protected])

Abstract- The increase in demand for power density in excess of 107 W/cm2 from the high power electronics units, draws attention for better thermal management which ultimately comes down to the use of materials which should perform well not only electrically and but thermally as well. The reliability and performance of the whole power electronics unit mostly depends on the high voltage switches which should be made up of semiconductor materials, efficient both electrically and thermally. Recently, the authors have proposed a GaN-AlN-(4H)SiC based optically-triggered bipolar npn transistor concept (for power electronics applications) with GaN serving as the p-base that is subjected to the photonic excitation.1 The key advantage of such a vertical heterostructure is to address the high electric field, high current density, high operation frequency and to sustain high temperature and in addition, the device structure takes the advantage of superior optical absorption of GaN for optical triggering to avoid the presence of any electromagnetic interferences (EMI) that may affect the whole power electronics unit. To assess, the thermal behavior of the proposed heteroepitaxial material system GaN-AlN-(4H)SiC),1 initially, in a small-scale level, in this work, a first-principle simulation study is conducted for the phonon density of states and the phonon dispersion for the Si, (4H)SiC, and GaN materials with atoms in the respective unit cells and is shown in Fig. 1. The simulation is carried out on a TeraGrid Supercluster2 (of National Center for Supercomputing Applications) using CASTEP first-principle simulation module of Materials Studio 5.0 software.3 From the study, it is observed that (Fig. 1(b)), with the increase in vibration frequency, the available phonon density of states (PDOS) for occupancy is comparatively more for the (4H)SiC material than its competitors GaN and Si, which implies (4H)SiC has good thermal conductivity and is a better candidate for high temperature operation. The above behavior is also reflected in the phonon dispersion plot at Γ(G)-band. However, if we look at the GaN’s PDOS and dispersion plot (Fig. 1(c)), it can be safely said that GaN is the most optimized future material for not only high voltage power electronics with high frequency electrical operation,1 but also has sufficient PDOS to sustain thermal vibrations at high temperatures. As explained earlier, our goal is not to evaluate the thermal behavior of individual materials but to know the thermal behavior of the heteroepitaxial material system GaN-AlN-(4H)SiC, as proposed in our recent work, Bose et al. 1 and hence, further first-principle work is being carried out. 1 S. Bose and S.K. Mazumder, “Atomistic and electrical simulations of a GaN-AlN-(4H)SiC

heterostructure optically-triggered vertical power semiconductor device”, Solid State Electronics, vol. 62, pp. 5-13 (2011).

2 http://www.ncsa.illinois.edu/UserInfo/Resources/Hardware/Intel64Cluster/TechSummary

3 http://accelrys.com/

http://www.ncsa.illinois.edu/UserInfo/Resources/Hardware/Intel64Cluster/TechSummary

http://accelrys.com/

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FIGURE 1(a).

FIGURE 1(b).

FIGURE 1(c).

FIGURE 1. (a) Phonon density of states (left) and the phonon dispersion (right) for the Si material with atoms in unit cell, (b) Phonon density of states (left) and the phonon dispersion (right) for the (4H)SiC material with atoms in unit cell , and (c) Phonon density of states (left) and the phonon dispersion (right) for the GaN material with atoms in unit cell. Acknowledgement: The authors are thankful to the US. National Science Foundation (Award no. 0823983), for necessary financial support.

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Graphene Applications in Thermal Interface Materials

K. M. F. Shahil1,2, V. Goyal1,3, R. Gulotty1 and A. A. Balandin1 1Nano-Device Laboratory, Department of Electrical Engineering and Materials Science and

Engineering Program, University of California, Riverside, CA 92521 USA 2 Intel Corporation, Hillsboro, Oregon 97124, USA

3 Texas Instruments, Dallas, Texas 75243, USA

Continuous down scaling of electronic devices and circuits, increased speed and integration densities resulted in problems with thermal management of nanoscale device and computer chips1. Further progress requires more efficient heat removal methods and stimulates the search for thermal interface material (TIMs) with enhanced thermal conductivity. The commonly used TIMs are filled with the particles such as silver or silica. Conventional TIMs require high volume fractions of the filler (~70%) to achieve thermal conductivity of ~1–5 W/mK. Recently, it was discovered that graphene has extremely high intrinsic phonon thermal conductivity2-4. To use this property for thermal management, we utilized the inexpensive liquid-phase exfoliated graphene and multi-layer graphene (MLG) as filler materials in TIMs (Fig. 1). Thermal properties of the graphene composites were measured using the “laser flash” technique (Fig. 2). It was found that thermal conductivity enhancement factor exceeded ~23 at 10% of the graphene volume loading fraction5. This enhancement is larger than anything that has been achieved using other fillers. We have also tested graphene flakes in the electrically-conductive hybrid graphene-metal particle TIMs. Thermal conductivity of resulting hybrid composites was increased by a factor of ~5 in a temperature range from 300 K to 400 K at a small graphene loading of 5-vol.-%. The strong enhancement of thermal conductivity in both types of the graphene-based TIMs was attributed to the high phonon thermal conductivity of graphene, low Kapitza resistance between graphene and matrix, and the large range of the length-scales of the graphene and metal filler particles6.

The work in Balandin Group was supported, in part, by the Office of Naval Research (ONR), and by the Semiconductor Research Corporation (SRC) and Defense Advanced Research Project Agency (DARPA) through FCRP Center on Functional Engineered Nano Architectonics (FENA). 1A. A. Balandin, “Chill Out: New Materials Can Keep Chips Cool”, IEEE Spectrum, 29, 35 (2009).

2A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao & C. N. Lau, “Superior Thermal Conductivity of Single-Layer Graphene”, Nano Lett. 8, 3, 902 (2008).

3S. Ghosh, W. Bao, D. L. Nika, E. P. Pokatilov, C. N. Lau, & A. A. Balandin, “Dimensional crossover of thermal transport in few-layer graphene”, Nature Mat., 9, 555 (2010).

4A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials”, Nature Mat., 10, 569 (2011).

5K.M.F. Shahil and A.A. Balandin, “Graphene-multilayer graphene nanocomposites as highly efficient thermal interface materials,” Nano Lett., 12, 861 (2012).

6V. Goyal and A.A. Balandin, Thermal properties of the hybrid graphene-metal nano-micro-composites: Applications in thermal interface materials, Appl. Phys. Lett., 100, 073113 (2012).

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Figure 1: Synthesis of the graphene-based nanocomposite TIMs. (a) graphite source material; (b) liquid-phase exfoliated graphene in solution; (c) SEM image of graphene flake; (d) SEM image of a large multi-layer graphene (n<5) flake extracted from the solution; (e) AFM image of the flake with varying n; (f) Raman spectroscopy image of bilayer graphene flakes extracted from the solution; (g) optical image of graphene-based composite prepared for thermal measurements; (d) SEM image of the surface of the resulting graphene based TIMs indicating.

Figure 2: (a) Measured thermal conductivity enhancement factor as a fraction of the graphene filler volume loading fraction; (b) experimentally determined dependence of thermal conductivity of TIMs on temperature for different loading fractions.

295

POSTERS

Non-Contact Specific Heat Measurements of Glasses at Low Temperatures Utilizing Dielectric Polarization Echoes

A. Halfar, M. Bazrafshan, A. Fleischmann, and C. Enss 1

Heidelberg University, Kirchhoff-Institute for Physics, INF 227, D-69120 Heidelberg, Germany

Specific heat measurements of amorphous dielectrics at very low temperatures have been a challenging problem for decades. The main reason is that it is difficult to match all necessary conditions in terms of thermal coupling, electrical contact, as well as suitable heater and thermometer addenda at the same time. In particular, parasitic heat inputs through wires are a general problem in such measurements at low and ultra-low temperatures. To avoid such unwanted effects new contact-free techniques for investigating the thermal properties of glasses have been developed in recent years. With a new technique based on the amplitude of coherent polarization echoes as intrinsic temperature information and an optical heating method we have extended the temperature range, in which the specific heat of glasses can be measured reliably, to well below 10 mK. In this experiment the glass sample is located in a microwave cavity attached to the mixing chamber of a dilution refrigerator and is heated via an optical fibre by a pulsed LED mounted at the 1K pot. The properties of glasses at such temperatures are governed by atomic tunneling systems. These degrees of freedom allow for the generation of polarization echoes whose temperature dependent amplitude is used as a thermometer in the specific heat experiments. First heating sequences have been recorded using a BK7 glass as sample. We discuss this new technique and first results obtained with it.

296

POSTERS

Phononic Diode Structures Produced in a FIB Microscope

J. J. Hu,1,2 John B. Ferguson,2 Chris Muratore,2 and Andrey A. Voevodin2 1 University of Dayton Research Institute, Dayton, OH, USA

2 AFRL/Materials and Manufacturing Directorate, Wright-Patterson AFB, Dayton, OH, USA

Asymmetric thermal flow structures are proposed to benefit systems where thermal cycling or varying environmental loads have significant impact on thermal performance. For example, spacecraft radiators are used to reject waste heat to the space environment. Under normal operating conditions, the radiator has a clear view of deep space and effectively rejects spacecraft heat. However if the radiators should heat up temporarily (e.g. solar loading), the radiator becomes a heat source instead of a heat sink thereby jeopardizing the survivability of the spacecraft. Several recent publications have investigated theoretical aspects that utilize a directional difference in heat flow dependent on a thermal gradient. These structures have utilized graphene1, graphene nanoribbon2 and nanostructures3 for deterministic interactions with ballistic phonons. There is an urgent need to develop and characterize the basic elements like diodes for evaluating their directional behaviour of thermal transportations. In this paper, the focused ion beam (FIB) techniques were employed to fabricate the asymmetric diode microstructures, which have great potentials for rectifying heat flow carried by phonons.

Figure 1 shows an example of asymmetric diode microstructures that was produced on a silicon wafer using a FIB microscope in comparison to previous modeling graphene ribbon shapes with a rectification ratio of up to or greater than approximately 100%.1,2 The control of heat flux by these graded microstructures can be well explained by the phonon spectra change in the asymmetric shapes. Figure 2 shows another example of 2-dimensional array of about 50 nm diameter holes produced by FIB, where the distance between two adjacent columns decreases gradually from right to left. Such a short distance may result in multiplication of phonon scatterings between the nano holes at the left end. Here the experimental results demonstrate the feasibility of using FIB to make various micron and nano scale structures which impart a phonon transport property not seen in the bulk materials. Further experimental measurements on transporting heat are going to be performed on fabricated phonon diodes and their function in thermal applications will be discussed.

1N. Yang, G. Zhang, and B. W. Li, “Thermal rectification in asymmetric graphene ribbons”, Appl. Phys. Lett. 95, 033107 (2009).

2J. N. Hu, X.L. Ruan, and Y.P. Chen, “Thermal conductivity and thermal rectification in graphene

nanoribbons: a molecular dynamics study”, Nano Lett. 9, 2730 (2009).

3B. W. Li, L. Wang, and G. Casati, “Thermal diode: rectification of heat flux”, Phys. Rev. Lett. 93, 184301 (2004).

http://pubs.acs.org/doi/abs/10.1021/nl901231s

http://pubs.acs.org/doi/abs/10.1021/nl901231s

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FIGURE 1. Asymmetric diode structures produced by using a FIB microscope similar to the asymmetric graphene shapes being proposed by Yang, Zhang and Li.1

FIGURE 2. Array of nano holes with continuously decreasing spacing were patterned in silicon that can increase phonon scatterings along the horizontal path.

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Flexural Phonon Dispersion and Distributed Bond Charge Model for Graphene and Covalent Two-Dimensional Crystals

Yuriy A. Kosevich1,2 1 Semenov Institute of Chemical of Physics, Russian Academy of Sciences, Moscow, Russia

2 Materials Science Institute, University of Valencia, Valencia, Spain

The recent identification of graphene structures with high degree of crystallinity,1 extraordinary high

stiffness and strength,2 calls for an understanding of the applicability of classical continuum models in

two dimensions. Since in graphene the carbon atoms are disposed in a geometric structure that closely

resembles the basal planes of bulk graphite, the in-plane elastic constants can be inferred directly from

the well-studied graphite. But the determination of the bending constant of a two-dimensional crystal

requires going beyond the macroscopic theory of elasticity and understanding the microscopic nature of

corresponding energy and forces. The existing models of bending constant and dispersion of flexural

phonon modes in graphene and graphite relate the bending elastic energy with the distortion of the

many-body bond-angle interactions, which necessitates the breakdown of the plate phenomenology

and Kirchhoff hypothesis for the strain distribution in the bending distortion and in flexural phonon

mode.3,4 Here we present a model for the bending constant of graphene or another covalent two-

dimensional crystal, which is based on the distributed bond charge model. In contrast to the adiabatic

bond charge model for diamond-type semiconductors, 5 our model relies on the finite spatial extent of

the bond charges across the in-plane covalent bonds, which results in finite effective thickness of the

monolayer crystal. The proposed model is based only on the two-body ion-bond charge, ion-ion and

bond charge-bond charge central interactions. The latter property allows recovering qualitatively the

plate phenomenology and correspondingly the Kirchhoff hypothesis. In the case of strong bond charge-

bond charge central interactions, the only two fitting parameters describe the longitudinal and flexural

phonon modes in the covalent two-dimensional crystal, and the relation between the dispersion of the

flexural phonon mode and longitudinal velocity in the elastic layer is recovered. The proposed model

does not relate the bending stiffness of a monolayer crystal with the orbital misalignment or bond-angle

effects, and explains the small value of the effective “mechanical thickness” of monolayer graphene.

1 J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth “The structure of suspended graphene sheets”, Nature 446, 60 (2007).

2 C. Lee, X. D. Wei, J. W. Kysar, and J. Hone “Measurement of the elastic properties and intrinsic strength of monolayer graphene”, Science 321, 385 (2008).

3 Q. Lu, M. Arroyo, and R. Huang “Elastic bending modulus of monolayer graphene”, J. Phys. D: Appl. Phys. 42, 102002 (2009).

4 D.-B. Zhang, E. Akatyeva, and T. Dumitrica “Bending utrathin graphene at the margins of continuum mechanics”, Physical Review Letters 106, 255503 (2011).

5 W. Weber “Adiabatic bond charge model for the phonons in diamond, Si, Ge, and a-Sn”, Physical Review B 15, 4789 (1977).

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Piezoelectricity in polar semiconductor nanowires

Banani Sen,1 Michael Stroscio,1,2,3 and Mitra Dutta1,2 1 Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago,

IL, USA 2 Department of Physics, University of Illinois at Chicago, Chicago, IL, USA

Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA

There is currently great interest in nanodevices based on nanoscale piezoelectric components. In view of this interest, this article provides a detailed treatment of the piezoelectric effect in zincblende and wurtzite nanowires based on the full piezoelectric tensor. The piezoelectric

potential is calculated from the piezoelectric polarization, P in terms of the strain, S and the piezoelectric tensor e ; this piezoelectric potential is induced in the nanowire as given by the following relations [1-2]:

000

00000

00000

511

5

5

zzz

x

x

eee

e

e

e for wurtzites

4

4

4

00000

00000

00000

x

x

x

e

e

e

e for zincblendes.

SeP

dPV0

1

It is found that bending mode which is easier to realize in practice over stable compressional modes generates maximum piezo energy for zincblende semiconductor nanowires. In case of wurtzite nanowires, the compressional modes generate much higher energy. This analytical paper reports the importance of the crystal orientations the nanowires to maximize the piezoelectric effect.

1 B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, New York, 1973).

2M. A. Stroscio and Mitra Dutta, Phonons in Nanostructures, (Camb. U. Press, 2001).

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Stretching |Vzz| (V)

Bending |Vzz| (V)

Wurtzite AlN ZnO GaN AlN ZnO GaN

15.1 11.3 4.9 0.4 0.4 0.2

Zincblende 0 0 0 1.3 1.9 1.1

TABLE 1. Piezoelectric potential generated in case of 50 nm thick and 600 nm long nanowires.

Strain applied along different directions resulting into 0.1% strain along c-axis.

FIGURE 1. Piezoelectric potential generated in case of 50 nm thick and 600 nm long nanowires

of wurtzite and zincblende crystal structure. The wurtzite wires are stretched and zincblende

wires are bent w.r.t z-axis resulting into 0.1% strain along c-axis.

Wurtzite Zincblende

Wurtzite Zincblende

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Pressure effects on Kapitza conductance at the Silicon-Superfluid Helium interface

Aymeric Ramiere,1 Jay Amrit,1 and Sebastian Volz2 1 Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur UPR CNRS 3251,

Université Paris-Sud, B.P. 133, F-91403 Orsay Cedex, France

2 Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion UPR CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes F-92295 Chatenay-Malabry, France

Preliminary measurements of the thermal boundary resistance (inverse of Kapitza conductance) between a Silicon single-crystal (111) and superfluid helium are presented as the pressure in the superfluid is varied. In the presence of a heat flux, the temperature jump due to phonon reflection at the Si/He boundary is measured in the Si crystal close to the interface. The superfluid temperature is held constant to within less than 1 mK. Details of the cell design and experimental technique are discussed elsewhere1.

Experiments are carried-out from superfluid vapor pressures (a few torrs) up to 25 bars. While the acoustic impedance of the superfluid undergoes correspondingly an ~80% change, the measured thermal boundary resistance remained constant to within ~7% over the entire pressure range at temperatures below 1K. These results demonstrate that the heat conductance across the Si/He interface involves one or more mechanisms localized at the interface. Discrepancies to acoustic and diffuse mismatch theories are discussed. Comparison is made to interfaces between solid materials having large disparities in the Debye temperatures2.

1J. Amrit, “Impact of surface roughness temperature dependency on the thermal contact resistance between Si(111) and liquid 4He”, Phys. Rev. B 81, 054303 (2010)

2R. J. Stoner and H. J. Maris, “Kapitza conductance and heat flow between solids at temperatures from 50 to 300 K”, Phys. Rev. B 48, 16373 (1993)

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Two-dimensional Phononic Thermal Conductance in Thin Membranes in the Casimir Limit

Ilari J. Maasilta1 1 Nanoscience Center, Department of Physics, University of Jyväskylä, Finland

We discuss a computational analysis of phononic thermal conduction in the suspended membrane geometry, in the case where heat can flow out radially in two dimensions from a central source1. As we are mostly interested in the low-temperature behavior where bulk scattering of phonons becomes irrelevant, we study the limit where all phonon scattering takes place at the membrane surfaces. Moreover, we limit the discussion here to the case where this surface scattering is fully diffusive, the so called Casimir limit.

We present a derivation of an integral equation for the temperature profile from power balance at the surfaces. Our analysis shows that in the two-dimensional case, no analytic results are available, in contrast to the well known 1D Casimir limit. Numerical solutions are presented for the temperature profiles in the membrane radial direction, for several different membrane thicknesses and heater diameters. We find that there is no universal temperature profile, but instead it depends on the aspect ratio between the membrane radius and thickness, and on the heater size. The results can be applied, for example, in the design of membrane-supported bolometric radiation detectors.

1I. J. Maasilta, “Two-dimensional phononic thermal conductance in thin membranes in the Casimirlimit”, AIP Advances 1, 041704 (2011).

303

POSTERS

Doping effect on electrical and thermal properties

of half doped La0.5Ce0.5Mn1-x(Fe,Co)xO3 manganites

Irfan Mansuri1,2

and Dinesh Varshney1 and M. W. shaikh

1

1School of Physics, Vigyan Bhavan, Devi Ahilya University, Khandwa Road Campus,

Indore 452001, India 2Deparment of Physics, Shri Venkateshwar Institute of technology, Sanwer road, Indore –

453331, India

Abstract

The temperature dependent electrical and thermal properties of La0.5Ce0.5Mn1-xTMxO3

(TM = Fe, Co; 0.0 x 0.1) manganites are investigate. The metal-semiconducting

transitions (TMS) are observed for La0.5Ce0.5MnO3 manganite and if we doped transition

metals at Mn site it becomes in semiconducting nature [1]. In the La0.5Ce0.5MnO3

manganites the temperature dependence of resistivity shows a minimum behavior at low

temperatures (T 60 K), explained by the enhanced electron-electron and the Kondo-like

spin dependent scattering. In the metallic region explain by the combined effect of spin-

fluctuation, electron-electron and electron-phonon scattering mechanism of

La0.5Ce0.5MnO3 manganites (Figure 1). However above TMS, the small polaron conduction

(SPC) model is found to be operative for La0.5Ce0.5Mn1-xTMxO3 (TM = Fe, Co; 0.0.05 x

0.1) samples [2]. The thermopower data documents hole as charge carriers and

successfully retrace by electron-magnon and spin wave fluctuation mechanism at low

temperature domain for La0.5Ce0.5MnO3 sample and at high temperature SPC model fits

the observed data (Figure 2). A transition from decreasing high temperature thermal

conductivity (due to local anharmonic distortions associated with small polarons), an

increasing thermal conductivity (due to decreasing of phonon-phonon scattering) at low

temperatures (Figure 3) [3].

[1] Dinesh Varshney, I Mansuri and N. Kaurav J. Phys.: Condens. Matter 19, 246211 (2007)

[2] Y KKuo, K M Sivakumar, J I Tasi, C S Lue, J W Huang, S Y Wang, Dinesh Varshney, N

Kaurav and R K Singh, J. Phys.: Condens. Matter 18, 2955 (2006)

[3] N. Panwar. D.K Pandya, A.Rao, K.K Wu., N. Kaurav, Y.-K.Kuo, and S.K.Agarwal Eur.

Phys. J. B 65, 179 (2008)

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Figure 1: The metallic electrical resistivity as a function of temperature of

La0.5Ce0.5MnO3.

Figure 2: Thermopower as a function of temperature of La0.5Ce0.5Mn1-x (Fe, Co)xO3 (0.05

x 0.1) compounds.

Figure 3: Thermal conductivity as a function of temperature of La0.5Ce0.5Mn1-x(Fe,

Co)xO3 (0.0 x 0.1) compounds.

75 100 125 150 175

1.5

2.0

2.5

3.0

3.5

225 240 255 270 285 3000.8

1.6

2.4

3.2

4.0

4.8

La0.5Ce0.5MnO3 mcm)

T (K)

T (K)

m

cm)

La0.5Ce0.5MnO3

50 100 150 200 250 300

2

4

6

8

10

225 250 275 300 325

15

30

45

60

Fe0.05

C o0.05

Fe0.05

T (K)

S (V/K)

x = 0

T (K)

S (V/

K)

TM = Fe, Co

La0.5Ce0.5Mn1-xTMxO3

0 50 100 150 200 250 300 350

10

20

30

40

50

60

70

80

2 0

3 0

4 0

5 0

6 0

7 0

8 0

5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0

L a 0 .5 C e 0 .5 M n O 3

T (K )

(m

W/cm

-K)

T (K)

Fe0.05Co0.05

Fe0.10

La0.5Ce0.5Mn1-x(Fe,Co)xO3

(mW/

cm-K)

x = 0

305

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Observation of optically excited mechanical vibrations in a fluid containing microresonator

Kyu Hyun Kim1, Gaurav Bahl1, Wonsuk Lee1,2, Jing Liu2, Matthew Tomes1, Xudong Fan2, Tal Carmon1


2 Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA

In the field of label-free optical sensing, researchers have studied optical resonators for detecting nanoparticles, bio-analytes, and gases [1-3]. In parallel, mechanical sensors using resonance frequency shift in cantilever are studied as chemical and biological sensors [4, 5]. Here we bridge between optomechanics and microfluidics by optically exciting mechanical vibrations in a silica bubble that contains liquid or gas. Our device might support capillary-based [6] or on-chip [7] bubble that will be used as an optomechanical resonator containing bio-analytes (in liquid) or quantum condensates (e.g. BEC). We name our device a microfludic

optomechanical (FOM) resonator.

We evanescently couple light via a fiber to excite the optical whispering gallery mode of a silica bubble in the middle of a capillary (Fig. 1 a, c). The centrifugal radiation pressure applied by the circulating light excites the mechanical modes [8, 9] of this water contained-bubble. It is helpful that light is supplied via a telecom fiber while liquids flow through the capillary inlet, which are both standard and commercially available products in optics and biology labs. Furthermore, excitations as well as interrogations of mechanical modes are done with evanescent light without physically touching the bubble resonator with no external feedback. We observe vibrations starting at the mW-scale optical input that are sustained as long as we keep our laser source on.

For a stability test, a 31 MHz vibration in a water-containing bubble show a standard deviation of 112 Hz over a 35 second period. We measure a 35 Hz linewidth for 20 MHz

vibration with water contained inside the bubble. The FOM system that we present here might enable coupling between optomechanical oscillation and quantum condensates inside the bubble to enable experiments as suggested in [10]. Additionally, on-chip microbubble resonators [11] could benefit from our contactless optical excitation method and improve their mechanical Q. 1Shopova, S.I., et al., “On-Column Micro Gas Chromatography Detection with Capillary-Based Optical Ring

Resonators.” Anal. Chem., 80(6): p. 2232-2238 (2008).

2Vollmer, F. and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules.”

Natutre Methods, 5: p. 591-596 (2008).

3He, L., et al., “Detecting single viruses and nanoparticles using whispering gallery microlasers.” Nature

Nanotechnol., 6: p. 428-432 (2011).

4Burg, T.P., et al., “Weighing of biomolecules, single cells and single nanoparticles in fluid.” Nature, 446(7139): p.

1066-1069 (2007).

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5Waggoner, P.S. and H.G. Craighead, “Micro- and nanomechanical sensors for environmental, chemical, and

biological detection.” Lab Chip, 10(7): p. 1238-1255 (2011).

6Lee, W. et al., “A quasi-droplet optofluidic ring resonator laser using a micro-bubble.” Appl. Phys. Lett., 99,

091101-091103 (2011).

7Eklund, E.J. and Shkel, A.M., “Glass Blowing on a Wafer Level”, JMEMS., 16, 2, 232-239 (2007).

8Carmon, T. et al., “Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon

mode,” Phys. Rev. Lett. 94, 223902 (2005).

9Carmon, T. and K. Vahala, “Modal Spectroscopy of Optoexcited Vibrations of a Micron-Scale On-Chip Resonator at

Greater than 1 GHz Frequency.” Phys. Rev. A., 98(12): p. 123901-1-4 (2007).

10Singh, S., Jing, H., Wright, E. & Meystre, P. “Quantum state transfer between a Bose-Einstein condensate and an

optomechanical mirror.” e-print. arXiv:1202.6100v1 (2012).

11Prikhodko, I. P., et al., “Microscale Glass-Blown Three-Dimensional Spherical Shell Resonators.” JMEMS., 20, 691-

701 (2011).

FIGURE 1. (a) Schematic of experimental setup. (b) A SEM image of a FOM capillary resonator. (c) Cross sectional view of the resonator when light is coupled. (d) A calculated mode for 26

MHz vibration in air-filled FOM resonator.

FIGURE 2. We measure optically excited vibration at the 9MHz to 140 MHz band in water filled bubble resonators (red). A resonance with air inside is given as a comparison (blue).

(a)

(b)

(c)

10 20 30 40 50 60 70 80 90 100-70

-60

-50

-40

-30

-20

-10

0

Frequency, MHz

Po

wer,

dB

m

Air-filled

Water-filled26.645 MHz

22.48 MHz

10 20 30 40 50-70

-60

-50

-40

-30

-20

-10

0

Frequency, MHz

Po

wer,

dB

m

8.555 MHz

100 200 300 400 500 600 700 800 900 1000-70

-60

-50

-40

-30

-20

-10

0

Frequency, MHz

Po

wer,

dB

m

139.69 MHz

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Finite element calculation of real and complex band structures for surface acoustic waves

István A. Veres1, Peter Burgholzer1,2, Alex A. Maznev3, Arthur G. Every4 , Osamu Matsuda5 and Oliver B. Wright5

1 Research Center for Non-Destructive Testing GmbH, Altenberger Str. 69, 4040 Linz, Austria 2 Christian Doppler Laboratory for Photoacoustic Imaging and Laser Ultrasonics, 4040 Linz, Austria

3 Department of Chemistry, Massachusetts Institute of Technology, Cambridge,

Massachusetts 02139, USA 4

School of Physics, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa 5Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, 060-8628, Japan

Phononic crystals can be one of the simplest realisations of left-handed metamaterials showing negative refraction or stopbands. These effects provide possibilities in the control of elastic waves and they are typically investigated through the band structure of the crystal. Besides analytic solutions, numerical methods, such as the Finite Differences Time Domain or the Finite Element Method (FEM), can be applied in the calculation of these band structures.

For surface phononic crystals it is common to calculate the dispersion curves using finite-depth models, since the surface modes become separated from the Lamb-wave dispersion curves. The current work makes use of the same idea presenting 2D and 3D frequency domain FEM models to calculate the band structure of surface acoustic waves using a unit cell with periodic boundary conditions. Such calculations are normally limited to the real band structure in k-space, although group velocities in real space are often necessary in the description of phononic crystals as the propagation of energy is aligned to the group velocity vector. It will be shown that using FEM solutions, the group velocities can be calculated directly from the resulting generalized eigenvalue problem. The results presented in Fig.1-2 are for a surface grating, i.e. for a phononic crystal with one-dimensional periodicity.

Although complex band structures carry important information about evanescent waves, they are rarely pursued. Numerical solutions using FEM usually calculate the unknown frequencies for an arbitrary wave number and result in the real band structure of the crystal. It is possible, however, to modify the FEM solution and calculate the complex wave number for an arbitrary frequency, revealing the full band structure of the crystal. This complex band structure is particularly important for SAWs, since the folded surface modes become evanescent beyond the sound cone. This behavior and the complex interconnections between the real propagating modes are clearly visible for the presented dispersion relation in Fig.2.

The results show that by using FEM solutions, not only real but also complex band structures and group velocities can be calculated for surface phononic crystals.

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FIGURE 1. a) Equal frequency contours of the Rayleigh wave (RW) in a grating, calculated using a 3D unit cell model. The 1D periodicity of the crystal leads to the opening of a stop band in the kx direction. The corresponding group velocity contours are shown in (b). The flattening of the RW mode in the ky direction leads to a double horn structure of the group velocity surface.

FIGURE 2. a) Real band structure for the grating in the kx direction using a 2D unit cell model. Magenta curves are Lamb waves; blue curves show the SAW dispersion modes: Rayleigh wave (RW), Sezawa wave (SW) and the folded Rayleigh wave (RW-BH). b) Complex dispersion relation for the same surface phononic crystal showing only the relevant surface modes: blue curves are the real SAW dispersion modes, red curves are the complex ones.

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POSTERS

Electronic and Vibrational Properties of Multilayer Graphene

Himadri R. Soni, Sanjeev K. Gupta and Prafulla K. Jha

Department of Physics, Bhavnagar University, Bhavnagar, 364 001, India

In the frame work of density functional theoretical calculations, the electronic and lattice dynamical properties of multilayers graphene have been investigated and analyzed using the plane wave pseudopotentials within the local density approximation functional. Carbon is arguably the most versatile element in the periodic table. It has wide variety of structures. It forms 3D sp3 bonded solid like diamond, 2D sp2 hybridized like graphene nanotubes, nanoribons, fullerenes with 60 carbon atoms etc. The electronic, structural and physical properties of such carbon based systems are interesting. Graphene is a two dimensional honeycomb lattice of carbon which has a pseudogap in the bandstructure by particular arrangements of touching Dirac cones.

We find that the electronic properties exhibit large sensitivity to the number of layers. The single layer graphene exhibits isotropic and linear bands in the low energy region, which intersect at K- point. The dispersion curves are parabolic for bilayer graphene while it consists the combination of linear and parabolic in the case of trilayer graphene and four layer graphene. With the increase of layers the pairs of π/π* bands increase.

Compared to single layer graphene, the optical phonon E2g mode and out of plane, ZA mode at Γ-point splits in the bi-, tri- and fourlayer graphene. We observe a shift for highest optical branch at Dirac K- point. We find that the different derivatives of graphene have different phonon dispersion relations. Raman scattering has been widely used for probing the G- band in graphene layers that corresponds to the zone centre (Γ- point) phonons and identify the number of layers in multilayer graphene.

Fig. 1 (a) Electronic band structure along with density of states of single layer graphene. The

dashed and continuous line in bandstructure represents GGA and LDA calculations respectively.

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POSTERS

Fig. 2 (a) Phonon dispersion curves alongwith phonon density of states of single layer graphene,

(b) highest optical phonon dispersions near Γ- point (c) highest optical phonon dispersions near

K- point and (d) zone centre splitting (out of plane ZA phonon mode) of single layer graphene.

The dashed and continuous lines represent GGA and LDA correlations respectively.

References

1H. Wang, Y. Wang, X. Cao, M. Feng, and G. Lan, “Vibrational properties of graphene and

graphene layers”, J. Raman Spectroscopy 40, 1791 (2009).

2F. Tuinstra, and J. L. Koenig, “Raman Spectrum of Graphite”, J. Chem Phys 53, 1126 (1970).

3R. Wong, D. Zhang, W. Sun, Z. Han, and C Liu, “A novel aluminum-doped carbon nanotubes

sensor for carbon monoxide”, J. Molecular Structure: Theochem 806, 93 (2007).

4A. Z. Alzahrani, and G. P. Srivastava, “Graphene to graphite: electronic changes within DFT

calculations”, Braz. J. Phys 39, 694 (2009).

5Y. H. Ho, J. Y. Wu, Y. H. Chiu, J. Wang, and M. F. Lin, “Electronic and optical properties of

monolayer and bilayer graphene”, Phil Trans R Soc A 368, 5445 (2010).

6S. K. Gupta, H. R. Soni, and P. K. Jha, Carbon (In communication).

1400

1500

1600

1700

1800

(b)

0.21000

1100

1200

1300

1400

1500

1600

K

(c)

0.8 1.0-100

0

100

200

(d)

0.250

200

400

600

800

1000

1200

1400

1600

1800

ZA

TA

ZO

LA

TO

LO

Fre

qu

en

cy

(c

m-1

)

KM

LDA

GGA

(a)

PHDOS

311

POSTERS

Polarized and depolarized scattering from free-standing metal nanoparticles:

Probing confined acoustic phonon

Venu Mankad1, Prafulla K. Jha1* and T. R. Ravindran2 1Department of Physics, Bhavnagar University, Bhavnagar 364 001, India.

2Material Science Group, Indira Gandhi Centre for Atomic Research,

Kalpakkam 603102, India

During the past few years, nanometer-sized particles have attracted considerable interest

primarily motivated by the capability of tailoring their physical properties simply through control

of their size, shape, and environment. A number of novel applications of these nanocrystals is

foreseen in the coming years including in aerospace, nanocomposites, biomedical, bioelectrical,

nanoswitches and superfast microelectronics. Noble metal nanoparticles [1] such as Ag or Au

have been subjects of extensive research due to the strong absorption resonance in the visible

range resulting from the surface dipolar plasmon i.e collective oscillations of their free electron

cloud. The plasmon-vibration coupling between the dipolar plasmon and the vibrational

excitations has been clearly established through low frequency Raman scattering [2].

Low frequency inelastic scattering (LOFIS) is a Raman signal that arises near the elastic

scattering as a consequence of acoustic phonon wave’s propagation in a small, quasi-spherical

particle. The results of Raman scattering from confined acoustic phonon modes in free standing

metal nanoparticles (size 3 to 6 nm) are in good agreement with theoretical calculations using

Lamb’s theory and CSM. The observed low frequency peaks in experimental Raman spectra are

assigned to the spheriodal l=0 and l=2 modes. A blueshift of Raman peaks with decreasing size

is observed in both experimental and theoretical studies. Additional low frequency bands in

Raman scattering of gold nanoparticles are assigned to the l=1, n=0 spheroidal modes.

References:

1. U. Kriebig , M. Vollmes, Optical Properties of Metal Clusters (Springer, Berlin, 1995);

U. Kriebig and U. Genzel, Surf. Sci. 156, 698 (1985).

2. D. A. Weitz, T. J. Gramila, A. Z. Genack J. I. Gersten Phys. Rev. Lett. 45, 355 (1980).

B

http://publish.aps.org/search/field/author/Weitz_D_A

http://publish.aps.org/search/field/author/Gramila_T_J

http://publish.aps.org/search/field/author/Genack_A_Z

http://publish.aps.org/search/field/author/Gersten_J_I

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A

Figure-1: TEM Micrograph for A) AuNP and B) Ag NP

Figure-2: Low frequency Raman Raman scattering of a) d=3.0 Ag nanoparticle b) d=3.4 Au

B

10 20 30 40 500

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First Principles Study of Structural, Electronic and Dynamical Properties of Lanthanum Nitrides

Sanjay D. Gupta1, Prafulla K. Jha1 and Sankar P. Sanyal2

1Department of Physics, Bhavnagar University, Bhavnagar – 364 001, India

2Department of Physics, Barkatullah University, Bhopal – 462 026, India Email: [email protected]

The discovery of a new class of materials of binary nitrides attracted keen attention due to record breaking amount of non-metal exceeding that in the majority of earlier metal nitrides [1,2]. The main attention in these nitrides is due to its structure and theoretical assessment of the stability of the predicted phases, which is important from their possible synthesis, simulation of certain properties and the nature of chemical bonding. LaN2 is an exothermic phase compared to the simple 1:1 nitride LaN and elemental nitrogen, and it also has a smaller volume. In the present work, first principles theoretical calculations is performed to investigate the structural, electronic, and dynamical properties of Lanthanum nitride (LaN2 and La2N) in most favorable monoclinic (ThC2 type) crystal structure [3]. The metalicity of the lanthanum nitride from electronic band structure, total and partial electronic density of states have been discussed in detail for both prescribed structures. The total energy calculations and phonon band structure at equilibrium ground states has been employed to analyze for phase stability in LaN2 and La2N in monoclinic crystal structures at ambient pressure using the density functional theory. Phonon modes throughout Brillouin zone are positive only in the case of La2N; however, it is negative in LaN2 structure. This indicates that LaN2 is energetically stable and La2N is dynamically stable in monoclinic structure.

1. L. Toh, Transition metal carbides and nitrides (New York: Academic Press, 1971).

2. G. V. Vajenine, G. Auffermann, Y. Prots, W. Schnelle, R. K. Kremer, A. Simon, R. Kniep, Inorg. Chem., 40, 4866 (2001).

3. M. Wessel and R. Dronskowski, J. Am. Chem. Soc.132, 7 (2010).


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0

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Figure 1 Phonon dispersion relation in La2N crystal

Figure. 2 Phonon dispersion relation in LaN2 crystal

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Probing Zone Boundary Phonons at the Nanoscale

Gokul Gopalakrishnan1, Martin Holt

2, Kyle McElhinny

1, J. W. Spalenka

1, David

Czaplewski2, Tobias Schülli

3, Paul Evans

1

1 Materials Science and Engineering, University of Wisconsin, Madison, WI, USA

2 Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, USA

3 Structure of Materials Group, European Synchrotron Radiation Facility, Grenoble, France

The emerging ability to control the thermal properties of materials using nanotechnology arises

in large part from the ability to manipulate the behavior of phonons. These are the fundamental

excitations of the crystal lattice and as such are affected by size-dependent phenomena, including

confinement and scattering by charge carriers or boundaries. Predictions that the phonon

dispersion can be modified by confinement have so far been tested only in the high-phonon-

energy regime of optical phonons near the center of the Brillouin zone. In macroscopic samples

the remainder of the zone can be probed by inelastic x-ray or neutron scattering which provide

the dispersion of large wave vector phonons. In individual or small ensembles of nanomaterials

inelastic signals become impractically weak and other methods must be identified to probe the

phonon dispersion.

Thermal diffuse x-ray scattering (TDS) collects information from scattering of x-rays by

phonons with wave vectors spanning the entire Brillouin zone, and with particular sensitivity to

low-energy vibrational modes. High brilliance x-ray sources at synchrotron radiation facilities

now make it possible to collect TDS signals from volumes of material matching the size of

nanoscale systems. Synchrotron x-ray TDS measurements on suspended silicon nanomembranes

probe large wave vector phonon modes near zone boundaries and reveal deviations from bulk-

like behavior in membranes with thicknesses of up to several tens of nanometers, beyond the

regime where confinement is predicted to significantly modify the dispersion of phonons.

316

POSTERS

Interfacial Thermal Conductance between Singlewalled-Carbon Nanotubes and Between Multiwalled-Carbon

Nanotubes by Molecular Dynamics

Meng Shen,1 William Evans,2 Pawel Keblinski1,2 1 Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY,

USA 2 Rensselaer Nanotechnology Center, Rensselaer Polytechnic Institute, Troy, NY, USA

We use molecular dynamics simulations to compute Van der Walls junction thermal conductance between singlewalled carbon nanotubes (SWCNTs) as a function of the crossing angle. While with the increasing angle, the junction conductance decreases, the conductance per unit area, i.e., interfacial thermal conductance is constant. Also larger-diameter SWCNT are characterized by the same interfacial thermal conductance. By contrast, recent experimental studies by D. Y. Li and collaborators 1 have shown that that the interfacial thermal conductance between multiwalled carbon nanotubes (MWCNTs) increases with the diameter of the nanotubes. To elucidate this behavior we studied a simplified model involving an interface between two stacks of graphene ribbons that mimics the contact between multiwalled nanotubes. Our results, in agreement with experiment, show that the interfacial thermal conductance indeed increases with a number of graphene layers, corresponding to larger diameter and larger number of walls in MWCNT. These results, combined with our observation of almost diameter independent interfacial conductance of single-walled carbon nanotubes (SWCNT), indicate that the increase of interfacial conductance of MWCNT with diameter is attributed to the stacking of multiple graphene layers.

1Prof. D. Y. Li, private communication (Nov. 14, 2011).

317

POSTERS

Phonon Trapping in Ultrathin Bi Films Studied by Ultrafast Electron Diffraction

T. Frigge, B. Krenzer, A. Kalus, A. Hanisch-Blicharski and

M. Horn-von Hoegen

Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, 47057 Duisburg, Germany

The shrinking dimensions of electronic devices demand fundamental research on the heat transport phenomena on the nanoscale. The heat transport from such structures into a substrate is usually measured in a pump-probe setup through the thermal response upon short laser excitation. Here we present ultrafast time resolved electron diffraction in reflection geometry (tr-RHEED) as a valuable tool to study fundamental mechanisms of heat transport in nanoscale heterostructures. Grazing incidence of 7-30 keV electrons ensures surface sensitivity. The analysis of different diffraction orders allows to clearly distinguish between different structures, such as films, clusters or surface reconstructions. In a pump probe setup the sample is excited by an 800 nm laser pulse of 50 fs duration and subsequently probed with ultrashort electron pulses. The transient temperature evolution is observed through the decrease of intensity by the Debye-Waller effect (Fig. 1). The thermal boundary conductance is then determined from the exponential recovery of the diffraction intensity. As a model system to demonstrate finite size effects in heat transport we used single-crystalline ultrathin Bi(111) films on Si(001) in a thickness range from 2.5 nm up to 12.2 nm, grown in-situ by molecular beam epitaxy under ultra high vacuum conditions. For thicknesses larger than 6 nm we observe a linear behaviour between cooling time and film thickness, which is in good agreement with the commonly used models for heat transfer, AMM and DMM. For thicknesses less than 6 nm, however, the cooling time shows a clear deviation between theory and experiment of more than 250% (Fig. 2). AFM and XRD characterisation of the morphology of the Bi films exhibit a rms roughness of less than 0.2 Å, resulting in a specularity parameter of the surface and interface of approximately one. This is evidence that diffuse scattering is absent at the surface and interface. The phonon momentum is conserved within the phonon transmission process and the AMM dictates the heat transport across the interface. The strong deviation is then explained by Snells law, where phonons outside a critical cone which is defined by the critical angle for total internal reflection are trapped inside the film. Thermalisation in the phonon system becomes the bottleneck for heat transfer across the interface. As a result we observe a pronounced non-equipartition situation in the phonon system: inside the critical cone the phonons are depleted and outside the critical cone the phonons are trapped in the Bi film.

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Figure 1. Transient surface temperature as function of time delay for a 7.7 nm thin Bi film on Si(001)

Figure 2. Comparison between measured and expected cooling times for different film thicknesses

319

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Interactions of AlGaN/GaN High Electron Mobility Transistors with Surface Acoustic Waves

Lei Shao1, Meng Zhang2, Animesh Banerjee2, Pallab K. Bhattacharya2, and Kevin P. Pipe1,2 1 Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

2 Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2122

AlGaN/GaN high electron mobility transistors (HEMTs) offer a number of advantages for high-power and high-speed RF and microwave applications. In addition, GaN-based materials exhibit strong piezoelectric effects, leading to their use in surface acoustic wave (SAW) devices. In this work, we examine the direct interaction of SAWs and HEMTs, i.e., the generation or detection of SAWs by a two-dimensional electron gas (2DEG) that is dynamically modulated in the various regimes of transistor operation (e.g., cut-off, linear, and saturation) for a 3-terminal HEMT.

We first detect SAWs emitted by HEMTs using integrated interdigital transducers (IDTs) that have geometries resonant with the HEMT source/gate/drain electrode geometry. Such an integrated HEMT/IDT system could nondestructively sample the degradation of its epitaxy and 2DEG in real time. Moreover, the piezoelectric conversion of emitted SAWs could also provide a means for resonant cooling or energy harvesting in high-power applications. By characterizing the integrated HEMT/IDT structure, we show that the maximum HEMT-IDT SAW transmission occurred at VGS,DC where the HEMT’s transconductance is maximized1; at this bias point, there is maximum time variation of the carrier density in the 2DEG, to which we ascribe increased SAW generation through screening of the piezoelectric field.2 Such screening has been predicted by self-consistent Schrödinger-Poisson calculations to be quite significant.3

We then demonstrate the detection of SAWs by AlGaN/GaN HEMTs, showing how SAWs emitted by an integrated IDT can be used to provide dynamic strain modulation of a HEMT. In addition to providing a means for high-speed and high-sensitivity detection of SAWs, such an effect could be used to modulate HEMT material properties over short periods of time, without potentially the degradation effects that often occur when such strain is incorporated through lattice mismatch. We show that a SAW induces a modulation in IDS for the HEMT that is controlled by VGS, and that detection is maximized when the HEMT is in the saturation regime.1

Finally, in order to study the SAW emission spectrum of a HEMT, we use an optical reflectance method to detect ultrasonic surface displacements. We show that various resonant modes polarized along different crystal directions are emitted by a HEMT under normal operation. The DC dependences and frequency shifts of these resonant modes suggest their generation mechanisms. This ultrasonic detection can be utilized to sample the epitaxial quality of a HEMT 2DEG channel and the GaN/substrate interface. In addition, the various polarized SAW modes emitted by a HEMT structure make such a device a candidate for multi-channel sensor designs.

1 L. Shao et al, Appl. Phys. Lett. 99, 243507 (2011).

2J.-H. Song et al, Appl. Phys. Lett. 83, 1023 (2003).

3B. Jogai et al, J. Appl. Phys. 94, 3984 (2003).

320

POSTERS

Thermal conductance at the interface between Lennard‐Jones crystals by molecular dynamics

Samy Merabia1 and Konstantinos Termentzidis2

1LPMCN, CNRS UMR5586, Un. Claude Bernard Lyon I, Villeurbanne, France 2EM2C, CNRS UP288, Ecole Centrale Paris, Chatenay‐Malabry, France

In the current work, we compare the results of non‐equilibrium (NEMD) and equilibrium (EMD) methods to compute the thermal conductance at the interface between solids. We propose to probe the thermal conductance using equilibrium simulations measuring the decay of the thermally induced energy fluctuations of each solid. We also show that NEMD and EMD give generally speaking inconsistent results: Green Kubo simulations probe the Landauer conductance between two solids, which assume phonons on both sides of the interface to be at equilibrium. On the other hand, we show that non‐equilibrium simulations (NEMD) give access to the out‐of‐equilibrium interfacial conductance consistent with the interfacial flux describing phonon transport in each solid. We analyze finite size effects for the two determination of the interfacial thermal conductance, and show that the equilibrium simulations suffer from severe size effects as compared to NEMD. We have also compared the predictions of the two above mentioned methods ‐EMD and NEMD‐ regarding the interfacial conductance of a series of mass mismatched Lennard‐Jones solids. We show that the Kapitza conductance obtained with EMD can be well described using the classical diffuse mismatch model (DMM). On the other hand, NEMD simulations results are consistent with a out‐of‐equilibrium generalisation of the acoustic mismatch model (AMM). These considerations are important in rationalizing previous results obtained using molecular dynamics, and help in pinpointing the physical scattering mechanisms taking place at atomically perfect interfaces between solids, which is a prerequisite to understand interfacial heat transfer across real interfaces.

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Figure 3. Interfacial conductance determined by NEMD and EMD as a function of the mass mismatch between the two solids. The simulations results are compared to the different theoretical expressions AMM, DMM and their generalisations for out of equilibrium systems.

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Directed Matrix Seeding of Embedded Semiconductor Nanocomposites for High Efficiency Thermoelectrics

M. V. Warren,1 G. Wang,2 V. A. Stoica,3 R Clarke,3 C. Uher,2,3 R. S. Goldman1,2,3

1Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

2Department of Physics, University of Michigan, Ann Arbor, MI, USA 3Department of Applied Physics, University of Michigan, Ann Arbor, MI, USA

Nanocomposite materials have been identified as promising candidates for high figure-of-merit thermoelectric materials. Due to the increased control of the density of states and hence, the energies of charge carriers, nanocomposite materials are predicted to have a significantly higher thermoelectric power factor (S2σ, where S is the Seebeck coefficient and σ is the electrical conductivity) compared to bulk materials. Nanoscale inclusions of metallic and semi-metallic particles are predicted to enhance the Seebeck coefficient via electron energy filtering. One approach to nanocomposite synthesis is matrix-seeded growth, which involves ion-beam-amorphization of a semiconductor film, followed by nanoscale re-crystallization via annealing. We recently showed that indium ion implantation into GaAs, followed by thermal annealing, leads to an enormous increase in the GaAs Seebeck coefficient.1 Annealing these films at high temperatures (600ºC) results in recrystallization of the amorphous layer without nanocrystal formation. For the lowest annealing temperatures (450ºC), metallic indium nanocrystals nucleate within the amorphous GaAs matrix, which are expected to enhance the Seebeck coefficient. Similarly, bismuth ion implantation into GaAs leads to the formation of an amorphous layer containing crystalline remnants; upon annealing, metallic Bi nanocrystal formation is expected. We will discuss measurements of the nanostructure, Seebeck coefficient, electrical resistivity, and thermal conductivity of both In- and Bi-implanted GaAs films. Together, these measurements allow us to examine correlations between the nanostructure and the thermoelectric figure of merit, providing new insights into the potential of embedded semiconductor nanocomposites for thermoelectrics. 1. M.V. Warren, A.W. Wood, J.C. Canniff, F. Naab, C. Uher, and R.S. Goldman, “Evolution of structural and thermoelectric properties of indium-ion-implanted epitaxial GaAs”, Appl. Phys. Lett. 100, 102101 (2012).

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