Physics of Semiconductor Nanostructures

41
Physics of Semiconductor Nanostructures Reference Books & Articles: [1] "The physics of low-dimensional semiconductors: an introduction", by John H. Davies, Cambridge university press (1998). URL: http://userweb.elec.gla.ac.uk/j/jdavies/ldsbook (Chapter 1,3,4,6,9,10) [2] Thesis “Correlations in semiconductor quantum dots” , Marek Korkusinski, June 2004, University of Ottawa (Chapter1,2,3 ) [3] Thesis “Collective Excitations and Coulomb Drag in Two-Dimensional Semiconductor Systems” , Shun-Jen Cheng, September 2001, Universität Würzburg (Chapter2 ) [4] “ A Guide to Feyman Diagrams in the Many-Body Problem, R.F. Mattuck (Dover Books) (1992) [5] “Electronic structure of quantum dots”, S. M. Reimann and M. Manninen, Reviews of Modern Physics, 74, 1283 (2002) [6] “Magnetism in condensed matter”, Stephen Blundell, Oxford University Press (2001) (Chapter 1 &2) [7] “Quantum theory of the optical and electronic properties of semiconductors”, H. Haug and S. W. Koch, World Scientific (Chapter 1) [8] “Excitonic artificial atoms: engineering optical properties of quantum dots”, Pawel Hawrylak, Phys. Rev. B 60, 5597 (1999). 鄭鄭鄭 (http://www.cc.nctu.edu.tw/~sjcheng/Frameset05.htm) Department of Electrophysics, National Chiao Tung University Evaluation: 1. Exercises: 50% 2. Oral presentation: 50% 2006 Spring Semester

description

Physics of Semiconductor Nanostructures. 鄭舜仁 ( http://www.cc.nctu.edu.tw/~sjcheng/Frameset05.htm ) Department of Electrophysics, National Chiao Tung University. 2006 Spring Semester. Reference Books & Articles: - PowerPoint PPT Presentation

Transcript of Physics of Semiconductor Nanostructures

Page 1: Physics of Semiconductor Nanostructures

Physics of Semiconductor Nanostructures

Reference Books & Articles:

[1] "The physics of low-dimensional semiconductors: an introduction", by John H. Davies, Cambridge university press (1998). URL: http://userweb.elec.gla.ac.uk/j/jdavies/ldsbook (Chapter 1,3,4,6,9,10)

[2] Thesis “Correlations in semiconductor quantum dots” , Marek Korkusinski, June 2004, University of Ottawa (Chapter1,2,3 )

[3] Thesis “Collective Excitations and Coulomb Drag in Two-Dimensional Semiconductor Systems” , Shun-Jen Cheng, September 2001, Universität Würzburg (Chapter2 )

[4] “ A Guide to Feyman Diagrams in the Many-Body Problem, R.F. Mattuck (Dover Books) (1992)[5] “Electronic structure of quantum dots”, S. M. Reimann and M. Manninen, Reviews of Modern Physics, 74, 1283 (2002)

[6] “Magnetism in condensed matter”, Stephen Blundell, Oxford University Press (2001) (Chapter 1 &2)

[7] “Quantum theory of the optical and electronic properties of semiconductors”, H. Haug and S. W. Koch, World Scientific (Chapter 1)

[8] “Excitonic artificial atoms: engineering optical properties of quantum dots”, Pawel Hawrylak, Phys. Rev. B 60, 5597 (1999).

鄭舜仁(http://www.cc.nctu.edu.tw/~sjcheng/Frameset05.htm)

Department of Electrophysics, National Chiao Tung University

Evaluation:1. Exercises: 50%2. Oral presentation: 50%

2006 Spring Semester

Page 2: Physics of Semiconductor Nanostructures

Semiconductor nanostructures

Mesa-etched dot Self-Assembled Quantum Dots

Three-dimensional STM image of an uncovered InAs quantum dot grown on GaAs(001). J. Marquez, et al, Appl. Phys. Lett. 78 (2001) 2309.

- - - - -- - - - --+

1m~100nmGate-defined dot

Quantum ring

1µm~100nm

~20nm

~20nm

Page 3: Physics of Semiconductor Nanostructures

Semiconductor nanostructures

Colloidal nanocrystals

~ few nm

Page 4: Physics of Semiconductor Nanostructures

Carbon nanotubes: One dimensional system

(Courtesy Cees Dekker, Delft Institute of Technology, the Netherlands.) This research was reported in the 7 May 1998 issue of Nature.

Here are some real-world nanotube materials, produced by laser ablation of a graphite target containing metal catalyst additives. On top is an atomic force microscopy image of a chiral tube with a diameter of 1.3 nanometers (Technical University, Delft: www.pa.msu.edu/cmp/csc/nanotube.html).

Page 5: Physics of Semiconductor Nanostructures

OutlineOutline:1. Introduction to semiconductor nanostructures [1,2](1w)2. Formation of semiconductor nanostructures [1,2](0.5w)

gate-defined quantum dots (QDs)self-assembled QDssynthesized nanocrystals (NCs)quantum wires, quantum rings…

3. Single-particle properties [1,2,3](2w)band theory in solidsk.p theory envelope function approximationquantum diskparabolic modelspherical quantum dots (QDs)quantum rings*strain effects *asymmetric nanostructures

4. Electric and magnetic fields [1] (1w)nanostructures in magnetic fieldsnanostructures in magnetic fields :Stark effectsFermi’s golden ruleThe Aharonov-Bohm effect*Quantum Hall effects in 2D and 0D systems*

5. Many-particle problems [1,4] (3w)Hartree & Hartree-Fock approximation(0.5w)Second quantization(2.5w)Configuration interaction methodTechnique of exact diagonalization*Many electrons in QDs

6. Transport properties[5,6] (2w)Coulomb Blockade spectroscopy(1w)Hund’s rule(1w)Quantum Hall droplets in QDs*

7. Optical properties[1,7,8](2w)Dipole approximation & Fermi’s golden rulesemission and absorption spectrumFine structure of the optical spectrum of QDs

8. Magnetic properties[6](2w)Magnetism of QDsSemi-magnetic QDsSpintronics

總授課時間約 14週Oral presentation: 2週Home work: 4~6次

[#]: reference#; *: optional; (nw): n weeks

Page 6: Physics of Semiconductor Nanostructures

OutlineOutline:1. Introduction to semiconductor nanostructures [1,2](1w)2. Formation of semiconductor nanostructures [1,2](0.5w)

gate-defined quantum dots (QDs)self-assembled QDssynthesized nanocrystals (NCs)quantum wires, quantum rings…

3. Single-particle properties [1,2,3](2w)band theory in solidsk.p theory envelope function approximationquantum diskparabolic modelspherical quantum dots (QDs)quantum rings*strain effects *asymmetric nanostructures

4. Electric and magnetic fields [1] (1w)Electrostatic potentialStark effectsFermi’s golden ruleThe Aharonov-Bohm effect*Quantum Hall effects in 2D and 0D systems*

5. Many-particle problems [1,4] (3w)Hartree & Hartree-Fock approximation(0.5w)Second quantization(2.5w)Configuration interaction methodTechnique of exact diagonalization*Many electrons in QDs

6. Transport properties[5,6] (2w)Coulomb Blockade spectroscopy(1w)Hund’s rule(1w)Quantum Hall droplets in QDs*

7. Optical properties[1,7,8](2w)Dipole approximation & Fermi’s golden rulesemission and absorption spectrumFine structure of the optical spectrum of QDs

8. Magnetic properties[6](2w)Magnetism of QDsSemi-magnetic QDsSpintronics

總授課時間約 14週Oral presentation: 2週Home work: 4~6次

[#]: reference#; *: optional; (nw): n weeks

Page 7: Physics of Semiconductor Nanostructures

Introduction to semiconductor nanostructures

• Semiconductor (SC).

• Fabrication

• Scale of nanometer.

• Interesting Physics in SC nanostructures:

- transport measurement

- optical spectroscopy

- magnetic (& spin) properties

• Observations & Measurements

• Possible Applications

Page 8: Physics of Semiconductor Nanostructures

Physics of Semiconductor Nanostructures

What’s SC?Why SC?

What’s “structure”?What’s “nano-scale”?Why nanostructures?

Why study the physics?What’s interesting physics?How to study the physics?Understand better the physics, then…

Page 9: Physics of Semiconductor Nanostructures

insSCmetal

Conductor

(Cu, Ag..)

Semiconductor

(Si, GaAs..)

Insulator

(SiO2,..)

Resistivity

(Ohm.cm)26 10~10 92 10~10 2214 10~10

Metal, Insulator, and Semiconductor

Page 10: Physics of Semiconductor Nanostructures

Band Diagram of Solids

1s

2s

2p

3s

2N

2N

6N

N

Single atom Solid

Valence band

conduction band

Energy

position

Page 11: Physics of Semiconductor Nanostructures

Metal, Insulator, and Semiconductor

Valence Band (VB)

Conduction Band (CB)

metal insulator semiconductor

T>0 doping

+ + + + + +

Energy gap (Eg)

insSCmetal RRR

Page 12: Physics of Semiconductor Nanostructures

Semiconductor Heterostructures*

A B

Confinementpotential

* 2000 Nobel prize in physics

Page 13: Physics of Semiconductor Nanostructures

Is Nanometer small or large?A10101 9 mnm

Lattice constant: nm01 10~10

F of bulk: nm21 10~10

Effective Bohr Radius: nm110~

Length scales in semiconductors (SC’s)

Coherent length:

Mean free path:

0.1nm

1m

100nm

10nm

1nm

100m

10m

E

mes

osco

pic

a

22 1

FFF kE

(see “Electronic transport in mesoscopic systems”, S. Datta, Cambridge Univ. Press)

Page 14: Physics of Semiconductor Nanostructures

Low-Dimensional Systems

Quantum Well (quasi-2D)

Quantum Wire (quasi-1D)

Quantum Dot (quasi-0D)

<<100nm, in usual.

Page 15: Physics of Semiconductor Nanostructures

Formation of Quantum Dots

- - - - -- - - - -

-+

etching

~10nm

1m~100nm

Self-assembled dots

Gate-defined dot Pillar dot

1m~100nm

Page 16: Physics of Semiconductor Nanostructures

Advanced ApplicationsFundamental InterestAtom physics,Many-body physics,Quantum opticsetc…..

Quantum-dot lasers,Photodetectors,Single electron devices,Single photon devices,Quantum computing,etc….

Semiconductor nano-technology,Material engineering,etc…

E

dN/dE (density of states)

bulk

~100meV(for GaAs)

10nmNano-scale

Room temp.kT~25meV

Aspects of Nanostructures

Nano-Technology

Page 17: Physics of Semiconductor Nanostructures

I

V

I

V+_

w

Current transport through a classical resistance

Conductance (G)

WL

WG

GVI

law sOhm'

Page 18: Physics of Semiconductor Nanostructures

Quantum Point Contact

(see also J.H. Davies Fig.5.22/p186)

B.J. van Wees, PRL 60, 848(1988).

Page 19: Physics of Semiconductor Nanostructures

Quantum Point Contact

Vg

1

2

3

4

5

)/2( 2 heG_

: metal (gate): two-dimensional electron gas

h: Planck’s constantI

VgVg

~250nm

+V

W

807.25812

resistance sKlitzing' von

2e

hRK

*see also quantum Hall effect (Nobel prizes in ’85,’98) p228 in textbook.

Page 20: Physics of Semiconductor Nanostructures

Quantum Point Contact (metal)

Quantized conductance through individual rows of suspended gold atoms H. OHNISHI, et al., Nature 395, p780 (‘98)

F of metal: nm10 10~10

~0.9nm

)( ,, SCFMF

Page 21: Physics of Semiconductor Nanostructures

Coulomb Blockade in Quantum Dot (Q.D.)

J. Weis, et al. Phys. Rev. Lett. 71, 4019-4022 (1993)

IG

Vg

Vg Vg

Quantum dot

“single” electron transister (SET)

G

S D G

S D

(a review article about Q.D.: S.M. Reimann and M. Manninen, Review of Modern Physics, 74,1283 (2000))

Page 22: Physics of Semiconductor Nanostructures

Quantum Hall Droplet

Vg

dotSource

Drain

N-1

B

B

B

E

2 2

Spin polarization

T.H.Oosterkamp, PRL, 82, 2931 (1999)

Page 23: Physics of Semiconductor Nanostructures

Photoluminescence (PL) from Quantum Wells

Page 24: Physics of Semiconductor Nanostructures

Photoluminescence (PL) from (parabolic) Quantum Well

R.C. Miller, et al. Phys. Rev. B 29, 3740 (’84)Also see sec. 4.3 in textbook

40meV

Page 25: Physics of Semiconductor Nanostructures

PL from Ensemble of Quantum Dots

Sylvain Raymond and cowokers, NRC, Canada

~20nm

Artificial atoms!!!

Page 26: Physics of Semiconductor Nanostructures

Magneto-PL from Ensemble of Quantum Dots

B

s

p+

p-

d+ d

d-

Sylvain Raymond et al. PRL(2004)

Page 27: Physics of Semiconductor Nanostructures

- Fermi’s golden rule- intitial state: ground state.- final state: GS & “all” excited states

ffi EENGSiPNfNA )(|,)1(,|),( 2

i

ii chP ,,

The interband polarization operator

Hawrylak, ChengM.Bayer et al, Nature 405, 923 (2000)

B=0 experiment theoryX6

Gs-to-GS

Single-Dot PL Spectrum

Page 28: Physics of Semiconductor Nanostructures

PL from Single Quantum Dot

Robin Williams and cowokers, at NRC, Canada

20meV

~20nm

Page 29: Physics of Semiconductor Nanostructures

U. Banin, Y. Cao,D. Katz, and O. Millo, Nature vol.400, 542 (1999)

InAs NC

Coulomb Blockade spectrum of a Single Nanocrystal

Page 30: Physics of Semiconductor Nanostructures

Experiment Calculation

Chemical potential

( ) ( 1)N GS GSE N E N

µ4

N=1 2 3 4 5 6 7 8

Page 31: Physics of Semiconductor Nanostructures

Semiconductor Nanocrystals

Page 32: Physics of Semiconductor Nanostructures

B0

M

B

Paramagnetism

B0

M

B

Diamagnetism

M

SQUID

B

Page 33: Physics of Semiconductor Nanostructures

Paramagnetism of QDs: experimental results

0 10000 20000 30000 40000 50000-0.0006

-0.0003

0.0000

0.0003

0.0006

0.0009

(em

u m

ol-1

Oe-1

)

Magnetic Field (Oe)

PbSe QD0 50 100 150 200

0

2000

4000

6000

8000

10000

100 Gauss 1000 Gauss 10000 Gauss

1/ (

mol

Gau

ss /

emu)

Temperature (K)

0 40 80 120 160 200-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

(em

u / m

ol G

auss

)

Temperature (K)

100 Gauss 1000 Gauss 10000 Gauss

Cd0.996Mn0.004Se

1

M

SQUID

B

T

CdMnSe QD

B

Wen-Bing Jian et al, to be published Wen-Bing Jian et al

Low-field paramagnetism

0

0

magnetic susceptibility

: paramagnetism

: damagnetism

M

B

Page 34: Physics of Semiconductor Nanostructures
Page 35: Physics of Semiconductor Nanostructures

Observation of Nanostructures

• Scanning Electron Microscope (SEM)

Electron beam10-40kV

Resolution>10nm *

* See, for instance, “University Physics”, by Harrison Benson, John Wiley & Sons, Inc.

Page 36: Physics of Semiconductor Nanostructures

Observation of Nanostructures

• Transmission Electron Microscope (TEM)

Electron beam50-100kV

Resolution>0.5nm

Observation of Nanostructures

diffraction

Page 37: Physics of Semiconductor Nanostructures

Scannning Tunneling Microscope (STM)* * Nobel prize in 1986

Three-dimensional STM image of an uncovered InAs quantum dot grown on GaAs (001). J. Marquez, et al, Appl. Phys. Lett. 78 (2001) 2309.

I=const

Resolution:0.001nm (vertical)0.1nm (horizontal)

Observation of Nanostructures

Page 38: Physics of Semiconductor Nanostructures

Possible Applications

。 Quantum dot infrared photodetectors, QDIPs

。 Optical memories

。 Single-Photon sources

-- Aslan, B.,Liu, H.C., Korkusinski, M., Cheng, S.-J., and Hawrylak, P., Appl. Phys. Lett. 82, 630 (2003)

--Petroff, P.M., in:Single Quantum Dots: Fundamentals, Application, and New Concepts, Peter Michler (Ed.) (Spring,Berlin,2003);-- Lundstrom, T., Schoenfeld, W. Lee, H., and Petroff, P.M., Science 286,2312(1999)

--Michler, P., Kiraz, A., Becher, C., Schoenfeld, W.V., Petroff, P.M., Zhang, L., Hu, E, and Imamoglu, A., Science 290, 2282 (2000)

--Moreau, E., Robert, I., Manin, L., Thierry-Mieg, V., Gerard, J.M., and Abram, I., Phys. Rev Lett. 87,183601 (2001)

--Santori, C., Pelton, M., Solomon, G., Dale, Y., and Yamamoto, Y., Phys. Rev. Lett. 86, 1502 (2001)--M.Pelton et al, Phys. Rev. Lett.89, 233602 (2002)

Page 39: Physics of Semiconductor Nanostructures

0.0

0.2

0.4

0.6

0.8

1.0

100 150 200 250 300 3500.0

0.2

0.4

0.6

0.8

1.0

Nor

mile

zed

phot

ores

pons

e

P-polarizationT=6 K

sample A sample B sample C

P

S

IR

45o

z

Figure 2

(b)

(a)

Sca

led

phot

ores

pons

e

Photon energy (meV)

S-polarizationT=6 K

sample A sample B sample C

0.0

0.2

0.4

0.6

0.8

1.0

30 40 50 60 70 800.0

0.2

0.4

0.6

0.8

1.0

Nor

mili

zed

phot

ores

pons

e

P-polarizationT=6 K

sample A sample B sample C

Figure 3

(b)

(a)

Nor

mili

zed

phot

ores

pons

e

Photon energy (meV)

S-polarizationT=6 K

sample A sample B sample C

I

•Intra-band photocurrent spectrum

Page 40: Physics of Semiconductor Nanostructures

Possible Applications

。 QD lasers

。 Terahertz radiation

--Arakawa, Y., and Sasaki, H., Apl. Phys. Lett. 40, 939 (1982); Fafard, S., Hinzer, K., Raymond, S., Dion, M.,McCAffrey, J., Feng, Y., and Vharbonneau, S., Science 22, 1350 (1996); Maximov, M.V., Shernyakov, Yu.M., Tsatsul'nikov, A.F., Lunev, A.V., Sakharov, A.V., Ustinov, V.M., Egorov, A.Yu., Zhukov, A.E., Kovsh, A.R., Kop'ev, P.S.,Asryan, L.V., Alferov, Zh.I., Ledentsov, N.N., Bimberg, D., Kosogov, A.O., and Werner, P., J. Appl. Phys. 83, 5561 (1998); Ledentsov, N.N., Ustinov, V.M., Shchukin, V.A., Kop'ev, P.S., Alferov, ZH.I., and Bimberg, D., Semiconductors 32, 343 (1998); Fafard, S., Wasilewski, Z.R., Allen, C. Ni., Hinzer, K., McCaffrey, J.P., and Feng, Y., Appl. Phys. Lett.75, 986 (1999)

--Anders, S., Rebohle, L., Schrey, F.F., Schrenk, W., Unterrainer, K., and Strasser, G., Appl. Phys. Lett. 82, 3862 (2003)

--Apalkov, V.M. and Chakraborty, T., Appl. Phys. Lett. 78, 1820 (2001)

--Wingreen, N.S. and Stafford C.A., IEEE J. Quant. Electron. 33, 1170 (1997)

。 Single electron transistor, quantum computation,…

Page 41: Physics of Semiconductor Nanostructures

NCs for Biosensing