Embedding Plasmonic Nanostructure Diodes Enhances Hot ElectronEmissionMark W. Knight,†,§ Yumin Wang,†,§ Alexander S. Urban,†,§ Ali Sobhani,†,§ Bob Y. Zheng,†,§

Peter Nordlander,†,‡,§ and Naomi J. Halas*,†,‡,§

†Department of Electrical and Computer Engineering, ‡Department of Physics and Astronomy, and §Laboratory for Nanophotonics,Rice Quantum Institute, Rice University, Houston, Texas 77005, United States

*S Supporting Information

ABSTRACT: When plasmonic nanostructures serve as themetallic counterpart of a metal−semiconductor Schottky interface,hot electrons due to plasmon decay are emitted across the Schottkybarrier, generating measurable photocurrents in the semiconductor.When the plasmonic nanostructure is atop the semiconductor, onlya small percentage of hot electrons are excited with a wavevectorpermitting transport across the Schottky barrier. Here we show thatembedding plasmonic structures into the semiconductor substan-tially increases hot electron emission. Responsivities increase by25× over planar diodes for embedding depths as small as 5 nm. The vertical Schottky barriers created by this geometry make theplasmon-induced hot electron process the dominant contributor to photocurrent in plasmonic nanostructure-diode-baseddevices.

KEYWORDS: Plasmon, nanoparticle, nanowire, hot electron, embedded, Schottky

The new concept of plasmon-based optoelectronics,exploiting combinations of electrical transport properties

and optically excited coherent electron oscillations known asplasmons, is rapidly giving rise to a new generation ofelectrically active optical elements and devices.1 This newclass of devices already includes tunable infrared photo-detectors,2−4 complementary metal−oxide−semiconductor(CMOS) compatible on-chip sensors,5,6 and broadband solarcells,7−9 many of which rely on harvesting the energetic (“hot”)electrons generated by plasmon decay. Following opticalexcitation, a plasmon mode can undergo either radiative(scattering) or nonradiative decay (absorption). When aplasmon decays nonradiatively, the energy of a plasmonquantum is initially transferred to a single, hot electron−holepair.10,11 For an isolated plasmonic nanostructure, the hotelectron will rapidly thermalize with the surrounding electrongas.12,13 However, when a hot electron of sufficient momentumis generated in a metallic nanostructure in direct contact with asemiconductor where an interface potential, known as aSchottky barrier, has been established, the electron may havesufficient momentum to traverse this barrier (Figure 1a). In aplasmonic nanostructure diode, the hot electrons originatingwithin the optically excited metallic nanostructure cancontribute to the semiconductor photocurrent, and bereplenished, when the nanostructure is included within anelectrical circuit. This effect can induce significant photocurrentat photon energies below the bandgap of the semiconductor yetabove the Schottky barrier, where the latter can be controlledby selection of the specific metal and semiconductorconstituents of the interface. Silicon photodetectors based on

plasmonically driven hot electron flow have been demonstratedusing nanoantennas,2,14,15 strip waveguides,3−6 and nano-structured metallic films.7,16 TiO2-based devices have beenused to demonstrate hot electron photoconversion through thevisible spectrum.7

Schottky barrier detectors are traditionally based on a planarmetal−semiconductor interface, where the metal film orstructure is deposited onto the semiconductor as the deviceis fabricated. While this geometry is most straightforward tofabricate, it allows electrons to emit over the potential barrieronly when they fall within a specific cone in momentum space(k-space), corresponding to emission directly into the semi-conductor (Figure 1b).17,18 For these electrons, the internalquantum transmission probability (ηi) can be approximatedusing the modified Fowler equation:17,19

ηϕ

≈−

Chv q

hv

( )i F

B2

(1)

where CF is a coefficient that depends on device-specific details,qϕB is the Schottky barrier energy, and hν is the energy of theincident photon. For excitation of the surface plasmon by anormal incidence electromagnetic field, injection over thisSchottky barrier would require a change in momentum for thecoherent electrons of the optically excited plasmon. Oneapproach to overcoming this restriction and increasing

Received: January 15, 2013Revised: February 21, 2013

Letter

pubs.acs.org/NanoLett

© XXXX American Chemical Society A dx.doi.org/10.1021/nl400196z | Nano Lett. XXXX, XXX, XXX−XXX

conversion efficiencies is to embed the plasmonic structurewithin the semiconductor (Figure 1c).20,21 Embedding wouldessentially form a 3D Schottky barrier on the vertical sides ofthe plasmonic element, in addition to the planar Schottkyinterface created when the plasmonic element is fabricated ontop of the semiconductor device.In this Letter, we show that the photocurrent generated by

an active plasmonic device element can be significantlyenhanced by this embedding approach, with photocurrentenhancements exceeding the geometrical increase in contactarea. To examine the effect of semiconductor embedding onhot electron Schottky injection, a simplified plasmonicgeometry of planar gold nanowire “belts” of precisely controllednanoscale widths and nanometer scale depths, with 10 μmlengths, were fabricated and studied. This geometry was chosenin preference to discrete nanoantennas for simplicity infabrication, modeling, and to ensure consistent electricalcontact with all structures in the completed devices. It hasrecently been shown that analogous chemically fabricated goldnanobelts, when excited with optical polarization transverse tothe long axis of the structure, support localized plasmonresonance frequencies that redshift strongly with increasing

nanobelt width.22 Here we observe a sizable increase inphotocurrent relative to nonembedded plasmonic elements byembedding the nanowires just a few nanometers into thesemiconductor substrate. Moreover, the size dependence of thiseffect, strongest for the narrowest nanowires, indicates that theballistic hot electrons produced by plasmon decay are the majorcontributor to the observed enhanced photocurrent inembedded plasmonic nanostructure-diode structures. Both theobserved embedding depth and size dependence are keyparameters that need to be optimized when designing higherquantum efficiency photocurrent harvesting devices based onthe plasmonic nanostructure-diode concept.The embedded nanowires were fabricated using a combina-

tion of planar lithography and dry etching. Fabrication wasperformed on a 1−10 Ohm-cm, ⟨100⟩ Si substrate protected by10 nm of thermal oxide. This oxide thickness was chosen toeliminate shunting between the substrate and the top electricalcontacts, while remaining sufficiently thin to permit facileetching of the underlying silicon. Electron beam lithographywas used to pattern a 400 nm layer of ZEP-520A (ZeonChemicals), which was developed for 60 s in n-amyl acetate(ZED-ND50, Zeon Chemicals) and 10 s in methyl isobutylketone (MIBK, Zeon Chemicals). The samples were cleanedwith an isopropyl alcohol (IPA) rinse and dried under an N2stream. The high dry etch resistance of the ZEP resist allowedthe creation of trenches in the Si substrate using reactive ionetching (RIE with a chamber pressure of 25 mTorr, 150 Wforward power, 6 SCCM O2, and 60 sccm CF4). Theseparameters gave an Si etch rate of ∼0.50 nm/s, measured byatomic force microscopy (AFM). Etch times were selected toyield nominal pit depths in the Si substrate of 5, 15, and 25 nm.Immediately prior to removal from the RIE chamber, weperformed a final 5 s RIE etch using only CF4 to expose a freshSi surface. Post-etch exposure to atmosphere was limited to <60s to minimize interfacial oxidation during transfer to theelectron beam (e-beam) evaporator. Following e-beamdeposition of 2/35 nm of Ti/Au, liftoff was performed at 60°C for 2.5 h, followed by sonication and an IPA rinse. Electricalcontact to the plasmonic nanowires was achieved using a pad-and-wire geometry deposited on top of the SiO2 layer in asecond lithography step using 2/50 nm Ti/Au (Figure 2a−c).Ohmic contact to the underlying Si was accomplished usingIndium solder.Photocurrent measurements were performed using a custom

beam scanning microscope with polarization control and lock-in detection. Plasmonic device arrays measuring 10 × 10 μmwith a 500 nm pitch were illuminated at near-normal incidencewith the diffraction-limited output of an ultrabroadband visible-infrared frequency laser (Fianium). Frequency selectivity wasachieved using an acousto-optic tunable filter (AOTF, CrystalTech). Photocurrent spectra were measured using a lock-inamplifier (Signal Recovery, 7280DSP) for both a solid Au padand the plasmonic nanowires. The excitation power spectrum,which was used to determine device responsivities, wasmeasured after transmission through a NIR objective(Mitutoyo, 20×). All measurements were performed with theincident light polarized transverse to the long nanowire axis; theplasmonic devices yielded no significant photocurrent whendriven using light polarized along the length of the nanowire.The photoresponse of the solid Au pads was polarization-independent.Modeling of the absorption spectra of these devices was

performed using the finite difference time domain method

Figure 1. Plasmon-induced hot electron production for embeddednanostructures. (a) Transport over a Schottky barrier begins whenplasmon decay generates a hot electron in the metal that undergoesballistic transport to the interface. An electron with sufficientmomentum can transfer into the semiconductor, where it relaxesinto the conduction band. (b) Planar devices support electrontransport only through the bottom interface, while (c) fully embeddeddevices support electron transport through all three Schottkyinterfaces. Electrons can only emit across the Schottky junctionwhen their k-vector lies inside the emission cone and their energyexceeds the barrier height (qϕB).

Nano Letters Letter

dx.doi.org/10.1021/nl400196z | Nano Lett. XXXX, XXX, XXX−XXXB

(FDTD, Lumerical). The theoretical geometries were definedusing the nominal experimental dimensions for the nanowires, apitch of 500 nm, and literature values for all dielectricfunctions.23,24 To match the experimental results, periodicboundary conditions were employed with a period matchingthe experimental pitch of the nanowires.Scanning electron microscope images of the completed

devices are shown at an 80 degree tilt angle, enabling directvisualization of the embedded nanowire structures (Figure 2a−c). Minimally embedded rods can be seen extending well abovethe 10 nm SiO2 layer. Increased etch times allow for partial(Figure 2b) or nearly complete (Figure 2c) embedding. For allembedding depths a top contact, seen as a broad 50 nm thickAu stripe, was used to make robust electrical contact with thenanowires.Enhancement spectra (Figure 2d) were obtained by

normalizing the photocurrent from a nanowire array (Figure2e, left) with the photocurrent generated by illuminating a solidAu pad fabricated onto the same device (Figure 2e, right). Thisexperimental normalization accounts for the wavelength

dependence of transmission across the Schottky interface,allowing us to isolate the plasmonic contribution (S) of thephotocurrent response (R):2

ν η ν=R S( ) ( )i (2)

The enhancement spectra exhibit a consistent increase inamplitude with increasing embedding depth of the nanowire,most clearly observable for nanowires of the widest transversedimensions (Figure 2d). The spectra consistently exhibit asingle broad resonance that tunes weakly to lower energies withincreasing aspect ratio (ratio of width to thickness). Theenergies of our measured dipolar peak locations agree well withFDTD calculations (Figure 2f). As the transverse dimension ofthe nanowire is increased, its overall optical cross section alsoincreases, which leads to an increasing photocurrent withincreasing nanowire width. The highest aspect ratio devicesexhibited a measured photocurrent response around 25 timesstronger than for a front-illuminated Au pad, corresponding toa strong plasmonic enhancement of the photocurrent responserelative to a planar Schottky interface.The effect of embedding the plasmonic structures on the

photocurrent enhancement can be examined in greater detail byexplicitly comparing the responsivity of nominally identicalplasmonic nanowires at different embedding depths (Figure3a). For an incident wavelength of 1500 nm, we find anincrease in responsivity with increasing embedding depth,especially for the narrowest wires, increasing substantially as theembedding depth increases. We also observe a rapid rise inresponsivity as the transverse nanowire dimension (andtherefore its electromagnetic cross section) increases, with asubsequent decrease in intensity as the nanobelt width isincreased beyond the optimal nanowire width for plasmonexcitation at this incident wavelength. In contrast with theexperimental responsivity curves, calculated absorption forthese nanowire structures exhibits only minimal variationbetween embedding depths both in the spatial distribution ofabsorption within the wires (Figure S1) and in the overallmagnitude of the absorption (Figure S2). The nearly constantabsorption cross section of the nanowires indicates that thenumber of photons absorbed in these devices is independent ofthe embedding depth of the structure into the semiconductor.With approximately the same number of photons absorbed inall devices, the initial population of hot electrons created by agiven photon flux will be similar for all device depths.Therefore, the experimentally observed differences in respon-sivity can be directly attributed to an enhancement in chargeinjection over the vertical Schottky barrier by the embeddednanowire structures.We can estimate the increase in hot electron photocurrent

efficiency by examining the ratio of photocurrent between theembedded and nonembedded devices, which yields a lowerbound on the photocurrent enhancement achieved byincorporating a 3D Schottky interface (Figure 3c, black points).These enhancement curves show a strong (∼10×) enhance-ment for narrow nanowires, with enhancement decreasing tounity as the wire width increases; this contrasts strongly withcalculated absorption enhancements and geometrical enhance-ments, both of which are close to unity for all sizes (Figure 3c,blue curves). The additional enhancement observed exper-imentally, which greatly exceeds the simple geometric increasein contact area (Figure S2), suggests that the initial hot electronpopulation resulting from plasmon decay exhibits an aniso-tropic distribution of wavevectors. For such an electron

Figure 2. (a−c) Three representative SEM images of devices withwidths of 120 ± 10 nm embedded ∼5 nm (blue), 15 nm (green), and25 nm (red) into the silicon substrate. The images were taken at an80° tilt angle; the Au is colored for clarity. Scale bars are 100 nm. (d)Measured photocurrent spectra for increasing widths, where eachspectrum is the photocurrent from (e) a nanowire array normalized tothe response from a solid Au pad. The dotted white circle indicates thelaser spot FWHM of 3 μm. Scale bar is 2 μm. (f) Calculatedabsorption peak wavelengths (black line) agree closely withexperimentally observed enhancement peaks.

Nano Letters Letter

dx.doi.org/10.1021/nl400196z | Nano Lett. XXXX, XXX, XXX−XXXC

population localized in k-space, the vertical Schottky interfacesare expected to dominate the overall photocurrent, since fewunscattered (and therefore energetic) hot electrons would fallwithin the bottom emission cone (Figure 1c).Based on the calculated absorption efficiencies, we can

estimate that a typical embedded nanowire driven nearresonance exhibits an internal quantum efficiency of 0.05−0.1%, which is 10× greater than previously reported forsimilarly resonant Au plasmonic nanorod antennas on silicon.2

This enhancement varies somewhat from device to device, withvariations in the RIE etch causing the nonembedded “control”devices to be slightly embedded. Resolving these fabricationlimitations should result in even greater enhancement factorsfor this device geometry.For embedded structures, an exponential decrease of

photocurrent enhancement with increasing nanowire width isobserved which corresponds to a spatial decay length of ∼24nm (Figure 3c, black lines). This is consistent with literaturevalues for the mean free path of ballistic electrons in Au.25,26

We believe this spatial dependence originates, as with the

magnitude of the enhancement, in an initial hot electronpopulation localized in k-space by Landau damping, which willinitially yield electrons propagating with a k-vector matchingthe plasmon mode.27 Since collisions reduce the energies andalter the propagation directions of the hot electrons, thisanisotropic distribution will dephase with a characteristic lengthon the order of the mean free path and prevent many of theinitially created hot electrons from reaching the metal−semiconductor interface with sufficient momentum to undergoemission. Changing the width of the nanowire effectivelyprobes the number of hot electrons remaining with their initialenergy and k-vector and provides an indirect mechanism fordetermining the mean free path of the hot electrons producedby plasmon decay. As the width of the nanowire is increased,the probability of unscattered electrons propagating throughthe wire and reaching the vertical Schottky interface is reduceduntil, for the widest nanowires, electron transmission over theSchottky barrier is dominated instead by transmission over thebottom Schottky interface. In this limit, the photocurrentemission probability in an embedded structure approaches thatof an unembedded structure.We attribute the measured photocurrent enhancements to

the 3D Schottky interface geometry, rather than modificationsof the barrier height, as a result of consistent I−V characteristicsmeasured for structures at all embedding depths (Figure 4a).

Transport measurements were performed at room temperature(295 K) on 10 × 10 μm solid Au squares fabricated in parallelwith the embedded plasmonic nanowires. The Schottky barrierparameters were extracted from the I−V response usingthermionic emission theory:19,28

η=

−−

⎡⎣⎢⎢

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤⎦⎥⎥I I

q V V

kTexp

( )1sat

photo

(3)

Figure 3. Effect of nanowire embedding on photocurrent measure-ments. (a) Measured responsivities and (b) calculated plasmonabsorption at λ = 1500 nm for embedding depths of 5 nm (blue), 15nm (green), and 25 nm (red). (c) Photocurrent enhancement, definedas the ratio of photocurrent from embedded nanowire to anonembedded nanowire, for two wavelengths: 1300 nm (triangles)and 1500 nm (circles). The experimental data is fit with exponentialsusing a decay constant of 24 nm (black lines). Calculated absorptionenhancements (dashed blue line, λ = 1300 nm) and geometricalenhancements of the Schottky contact area (solid blue line) varyweakly with embedding depth.

Figure 4. (a) I−V curves for 10 × 10 μm Au Schottky contactsembedded by ∼0 nm (blue), 5 nm (green), and 10 nm (red). (b) I−Vresponse of a device array under λ = 1700 nm illumination for incidentpowers of 0 mW (gray), 100 mW (black), 200 mW (red), 300 mW(green), and 400 mW (blue). The wire width was 160 nm. Points areexperimental values; solid lines are fits from thermionic emissiontheory with an ideality factor of 1.13. (c) The photovoltage (Vphoto)shifts linearly with increasing incident laser power.

Nano Letters Letter

dx.doi.org/10.1021/nl400196z | Nano Lett. XXXX, XXX, XXX−XXXD

and

ϕ= ** −

⎛⎝⎜

⎞⎠⎟I SA T

q

kTexpsat

2 B

(4)

where S is the Schottky contact area, qϕB is the barrier height,A** is the reduced effective Richardson constant, T is theoperating temperature in Kelvin, and k is Boltzmann’s constant.The ideality factor, η, describes the deviation of the measureddiode response from the expected response of an ideal diodewithin thermionic emission theory. Extracting η and qϕB fromthe I−V curves was accomplished using the saturation current(Isat) determined from a least-mean-squares fit to theexperimental data, the 10 × 10 μm area (S) specified duringlithography, and standard values for k and q. The reducedeffective Richardson constant (A**), which accounts for theeffective carrier mass in the Si, was taken to be 110 A/(cm2·K2).19,29,30 All of the measured diodes yielded idealityfactors of 1.13 and a Schottky barrier height of 52 meV. Thisbarrier height was also determined independently on both thesolid devices and the plasmonic nanowires using Fowler plots19

and found to be ∼50 meV, in good agreement with the valuesextracted using thermionic emission theory. These measuredvalues correspond well with literature values for Ti/Si barrierdevices,19,31 indicating that the Ti adhesion layer determinesboth the vertical and the horizontal interface potentials. Thisbehavior is anticipated due to the preferential generation of hotelectrons in the titanium, as well as the greater transmissionprobability at Ti/Si interfacesrelative to Auarising fromthe difference in Schottky barrier potentials. The consistency inboth ideality factor and barrier height between devices withvarying degrees of embedding suggests that differences betweendevices do not result from an altered electrical response.Power-dependent I−V curves show a linear increase in

photovoltage with increasing photon flux (Figure 4b,c). Fittingthese I−V curves with thermionic emission theory, using thebarrier height and ideality factor determined withoutillumination, gives the induced photovoltage (Vphoto). Figure4b shows a typical response using plasmon resonant λ = 1700nm illumination on a device array with wire widths of 160 nm.Over our experimentally accessible power range (0−400 μW)the photovoltage shift is linear, with an induced voltage of 37mV/mW. This power-dependent photovoltage, which willlikely be improved with further refinement of the fabricationtechnique, may allow the construction of optically activatedmicropower or control sources compatible with integration intolarger CMOS devices.In conclusion, we have examined the effect that embedding

plasmonic nanostructures within a semiconductor has onincreasing the photocurrent efficiency in a plasmonicnanostructure-diode device. Embedding the nanostructureinto the semiconductor introduces vertical Schottky interfaces,which permit emission of ballistic electrons over the Schottkybarriers into the semiconductor, increasing the internalquantum efficiency of this geometry for photodetection. Wehave shown that embedded nanowires, under normal incidencecan have 25× greater efficiency than comparable planarSchottky devices. These results suggest that 3D Schottkybarriers can be a key design feature for increasing the efficiencyof plasmon-based photodetection. A broad array of devices canpotentially benefit from the integration of such verticalSchottky interfaces, including hot electron-based optical sensorswith direct electrical readout, on-chip plasmon-based optoelec-

tronic circuitry, infrared detectors, active metamaterials,32 andenhanced solar cells.

■ ASSOCIATED CONTENT*S Supporting InformationIllustration of the localization of hot electron generation at theedges of the nanowires (Figure S1) and comparison of themeasured photocurrent enhancements to theoretical geometricand electromagnetic enhancements (Figure S2). This materialis available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: halas@rice.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe would like to acknowledge J. Britt Lassiter and Surbhi Lalfor productive discussions. This work was supported by theRobert A. Welch Foundation under Grants C-1220 (N.J.H.)and C-1222 (P.N.), the National Security Science andEngineering Faculty Fellowship (NSSEFF) N00244-09-1-0067, the Air Force Office of Scientific Research (AFOSR)FA9550-10-1-0469, NSF MRI (ECCS 1040478), the ArmyResearch Office, and the Office of Naval Research.

■ REFERENCES(1) Warren, S. C.; Walker, D. A.; Grzybowski, B. A. Langmuir 2012,28, 9093−9102.(2) Knight, M. W.; Sobhani, H.; Nordlander, P.; Halas, N. J. Science2011, 332, 702−704.(3) Akbari, A.; Berini, P. Appl. Phys. Lett. 2009, 95, 021104.(4) Akbari, A.; Tait, R. N.; Berini, P. Opt. Express 2010, 18, 8505−8514.(5) Goykhman, I.; Desiatov, B.; Khurgin, J.; Shappir, J.; Levy, U.Nano Lett. 2011, 11, 2219−2224.(6) Berini, P.; Olivieri, A.; Chen, C. K. Nanotechnology 2012, 23,44011.(7) Mubeen, S.; Hernandez-Sosa, G.; Moses, D.; Lee, J.; Moskovits,M. Nano Lett. 2011, 11, 5548−5552.(8) Wang, F. M.; Melosh, N. A. Nano Lett. 2011, 11, 5426−5430.(9) Atwater, H. A.; Polman, A. Nat. Mater. 2010, 9, 205−213.(10) Endriz, J.; Spicer, W. Phys. Rev. Lett. 1970, 24, 64−68.(11) Fuchs, R.; Kliewer, K. L. Phys. Rev. B 1971, 3, 2270−2278.(12) Inagaki, T.; Kagami, K.; Arakawa, E. Phys. Rev. B 1981, 24,3644−3646.(13) Inagaki, T.; Kagami, K.; Arakawa, E. T. Appl. Opt. 1982, 21,949−954.(14) Fukuda, M.; Aihara, T.; Yamaguchi, K.; Ling, Y. Y.; Miyaji, K.;Tohyama, M. Appl. Phys. Lett. 2010, 96, 153107.(15) Zhu, S. Y.; Chu, H. S.; Lo, G. Q.; Bai, P.; Kwong, D. L. Appl.Phys. Lett. 2012, 100, 061109.(16) Wang, Y. M.; Su, X. D.; Zhu, Y. Y.; Wang, Q. J.; Zhu, D. L.;Zhao, J. W.; Chen, S.; Huang, W. X.; Wu, S. Appl. Phys. Lett. 2009, 95.(17) Fowler, R. H. Phys. Rev. 1931, 38, 45−56.(18) Scales, C.; Berini, P. IEEE J. Quantum Elect. 2010, 46, 633−643.(19) Sze, S. M.; Ng, K. K. Physics of Semiconductor Devices, 3rd ed.;John Wiley & Sons, Inc.: Hoboken, NJ, 2007; p 815.(20) Raissi, F. IEEE T. Electron Devices 2003, 50, 1134−1137.(21) White, T. P.; Catchpole, K. R. Appl. Phys. Lett. 2012, 101,073905.(22) Anderson, L. J. E.; Payne, C. M.; Zhen, Y. R.; Nordlander, P.;Hafner, J. H. Nano Lett. 2011, 11, 5034−5037.(23) Johnson, P. B.; Christy, R. W. Phys. Rev. B 1972, 6, 4370−4379.

Nano Letters Letter

dx.doi.org/10.1021/nl400196z | Nano Lett. XXXX, XXX, XXX−XXXE

(24) Palik, E. D. Handbook of Optical Constants; Academic Press: SanDiego, 1998.(25) Crowell, C. R.; Sze, S. M. Phys. Rev. Lett. 1965, 15, 659−661.(26) Ventrice, C. A.; Labella, V. P.; Ramaswamy, G.; Yu, H. P.;Schowalter, L. J. Phys. Rev. B 1996, 53, 3952−3959.(27) Shalaev, V. M.; Douketis, C.; Stuckless, J. T.; Moskovits, M.Phys. Rev. B 1996, 53, 11388−11402.(28) Bethe, H. A. Theory of the Boundary Layer of Crystal Rectifiers;MIT Radiat. Lab. Rep. 43-12: Cambridge, MA, 1942.(29) Crowell, C. R. Solid-State Electron. 1965, 8, 395−399.(30) Crowell, C. R. Solid-State Electron. 1969, 12, 55−59.(31) Cowley, A. M. Solid-State Electron. 1970, 13, 403−414.(32) Urzhumov, Y.; Lee, J. S.; Tyler, T.; Dhar, S.; Nguyen, V.;Jokerst, N. M.; Schmalenberg, P.; Smith, D. R. Phys. Rev. B 2012, 86,075112.

Nano Letters Letter

dx.doi.org/10.1021/nl400196z | Nano Lett. XXXX, XXX, XXX−XXXF