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ArticleJournal of

Nanoscience and NanotechnologyVol. 14, 5177–5180, 2014

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Electron and Phonon Coupling Dynamics in Low-GapSemiconductor: Quantum versus Classical Scale

Kyung-Gu Min1, Ki-Ju Yee2, Christopher J. Stanton3, Jin-Dong Song4, and Young-Dahl Jho1�∗1School of Info. and Comm., Gwangju Institute of Science and Technology, Gwangju 500-712, Korea

2Department of Physics, Chungnam National University, Daejeon 305-764, Korea3Department of Physics, University of Florida, Gainesville, Florida 32611-8440, USA

4Center for Opto-Electronic Convergence Systems, Korea Institute of Science and Technology,Seoul 136-791, Korea

We have studied the characteristics of longitudinal-optical-phonon-plasmon coupled (LOPC) modeby using the ultrashort pulsed laser with 45 THz bandwidth as a function of thickness in InAsepilayers, ranging from 10 to 900 nm. We have observed the LOPC modes split into the upper(L+ mode) and the lower (L− mode) branches only in the classical scale, but the longitudinal-optical(LO) phonon peak was persistently observed. The shorter decay time of the plasmon-like L+ modesrather than the phonon-like L− modes should be associated with carrier–carrier scattering whichis further considered with diffusion properties in the low-gap semiconductors. This result leads tothat the absence of the LOPC modes in a scale less than exciton Bohr radius manifests the role ofelectron diffusion rather than the carrier screening via drift motion in surface depletion region.

Keywords: Longitudial Optical Phonon, Plasmon, Diffusion, Coupling.

1. INTRODUCTIONPhonons, i.e., collective vibrations in a lattice, are oneof the most often found quasi-particle involved in electri-cal, thermal, and optical phenomena in condensed matter.Investigations of coherent-phonon generation mechanismsin bulk and quantum-confined semiconductors have beenmade possible in the last two decades and identifiedas either displacively coupled type, as in the case ofabove-the-gap excitations,1 or impulsively coupled typevia impulsive stimulated Raman scattering (ISRS) in trans-parent materials.2 For example, both bulk GaAs under theabove-the-gap excitation condition and semimetals such asSb, Bi, and Te show displacive screening mechanism innature.3�4 The corresponding phase of the so-called dis-placively excitation of coherent phonons (DECP) is knownto be cosine-like in contrast to the sine-like one in the caseof ISRS.In polar semiconductors, excitation by ultrafast laser

pulses triggers the coherent lattice vibrations based on thepotential screening in the depletion layer sometimes simul-taneously with the collective motion of electrons which iscalled as plasmon. In n-doped GaAs, coherently excited

∗Author to whom correspondence should be addressed.

phonon-plasmon coupled modes have been observed underthe excitation of femto-second laser pulses.5 Accordingly,the coupled modes between the plasmon and the longi-tudinal optical (LO) phonon split into a lower and anupper branch, the L− and the L+ modes, respectively.The frequency variation and anti-crossing behavior ofthose two branches of the LO-phonon-plasmon coupled(LOPC) modes as a function of doped or photo-excitedcarriers have been both theoretically and experimentallyestablished.3�6

While controlling the lattice vibrations have emerged aschallenges faced by the semiconductor physics commu-nity,7 influences of transport properties such as diffusioncoefficients and mobility on phonon-related phenomenaare still not completely understood even in bulk materi-als. Particularly in the narrow-gap semiconductors suchas InAs, an effective charge separation in the directionperpendicular to the surface due to the large diffusioncoefficient difference between electron and hole (or photo-Dember effect) plays a key role in carrier transport whichis further enhanced with large excess carrier energy andshort absorption depth. In this study, in order to character-ize the influence of transport phenomena on the formationof the LOPC modes, we have experimentally investigated

J. Nanosci. Nanotechnol. 2014, Vol. 14, No. 7 1533-4880/2014/14/5177/004 doi:10.1166/jnn.2014.8298 5177

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Electron and Phonon Coupling Dynamics in Low-Gap Semiconductor: Quantum versus Classical Scale Min et al.

Figure 1. Sample structure with corresponding band gap values in InAsepilayer grown on AlAs0�32Sb0�68 buffer layer and GaAs substrate.

amplitudes and phase changes of coherent optical phononsas a function of active layer thickness which ranges from10 nm (smaller than exciton Bohr radius) to 900 nm (largerthan diffusion length of about 400 nm, considering themeasured value of mobility).

2. EXPERIMENTAL DETAILSWe performed reflective electro-optic sampling (REOS) inInAs epilayers. A mode-locked Ti-sapphire laser was usedto generate pulses with 15 fs duration at the center wave-length of 800 nm. This ultrafast laser pulse enables usto resolve frequency components up to 45 THz. The lin-early polarized probe beam monitors REOS signal �R/Rwhich is induced by the perpendicularly polarized pumpbeam. The photo-excited carrier density was estimated tobe about 4×1018 cm−3 (much larger than the n-type dop-ing density of about 6×1016 cm−3�, considering the pumpbeam power (50 mW focused onto 50 �m) and absorp-tion depth (∼ 140 nm).8 As shown in Figure 1, InAs epi-layers have been grown on GaAs substrate (∼ 300 �m)along the [100] direction. The InAs layer thicknesses were10, 20, 70, 370, and 900 nm. The samples could beclassified into two groups: Group A has thickness of 10and 20 nm which is thinner than exciton Bohr radius of36 nm.9 Group B has thickness of 70, 370, and 900 nmwhich was thicker than exciton Bohr radius. A 2.2 �m-thick AlAs0�32Sb0�68 buffer layer with larger bandgap of1.8 eV was inserted between InAs epilayers and GaAssubstrate for reducing the lattice mismatching so that thephoto-excited carriers are concentrated within InAs layers.With sample thicknesses, the electron mobility, estimatedfrom Hall measurements, monotonically increased from6×102 to 8×103 cm2/Vs, leading to increasing diffusionlength from 80 nm (in 10 nm-thick sample) to 400 nm(in 900 nm-thick sample).10 We ignore the lateral diffusionin our experimental condition due to the large ratio of spotsize to diffusion length.

3. RESULTS AND DISCUSSIONFigure 2(a) shows the oscillatory component of REOS sig-nal (�R/R) as a function of InAs thickness. The inten-sity of oscillatory component which is dominated by LO

0 2 4 6 8 0 10 20 30 40 50

10 nm

20 nm

70 nm

370 nm

900 nm

∆R/R

(a.

u.)

Time delay (ps)

L+

Am

plitu

de (

a. u

.)

Frequency (THz)

900 nm 370 nm 70 nm 20 nm 10 nm

L–

LO phonon(a) (b)

Figure 2. (a) Transient REOS signals in InAs with different thick-ness. (b) Fourier transformed spectra obtained from time-domain signals,revealing the LOPC modes in thick samples.

phonon density increases monotonically with thickness.The beating features in Figure 2(a) are due to the coexis-tence of the LO phonon (∼ 7.2 THz in our samples) andthe LOPC modes. As shown in Fourier transformed spec-tra in Figure 2(b), the LOPC modes were revealed at thehigher frequency side (L+ with about 28 THz) and thelower frequency side (L− with about 6.5 THz) only inthe Group B. Considering the photo-excited carrier densityof 4× 1018 cm−3 and the transverse optical (TO) phononfrequency in InAs (∼ 6.5 THz), the L+ and the L− modecoincide with the plasmon frequency and TO phonon fre-quency in the high-density limit, respectively.11

Figure 3 shows the results from wavelet analysis of theoscillatory parts in REOS for (a) Group A and (b) GroupB. The most intriguing feature in group A as shown inFigure 3(a) was the absence of the LOPC modes whereasthe LO phonon peak was persistent with slight frequencychange which could be associated with interfacial strain.12

In Group A which was thinner than the exciton Bohrradius (∼ 36 nm) and the absorption length (∼ 140 nm),we could further observe estimated LO phonon frequen-cies from GaAs and AlAs0�32Sb0�68 around 9 and 11 THz,respectively.13 In group B, now with thickness largerthan the exciton Bohr radius, three frequency peaks wererevealed; The TO-phonon-like L− (plasmon-like L+� wascentered near 6.5 THz (28 THz), while the LO-phononwas observed near 7.2 THz which matches well with thecase of strain-free bulk samples.11

Another notable feature in Figure 3(b) was that the LOphonon component survived in longer time scale comparedto the L− and L+ mode. From the exponential decay fit-tings in wavelet spectra, the decay times of the L− modein Group B were estimated to be from 370 to 540 fs,slightly shorter than those of LO phonons from 1.0 to1.7 ps. The decay times of the L+ mode were muchshorter to be from 60 to 85 fs, compared to the othertwo modes. The much faster decay time of L+ could be

5178 J. Nanosci. Nanotechnol. 14, 5177–5180, 2014

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Min et al. Electron and Phonon Coupling Dynamics in Low-Gap Semiconductor: Quantum versus Classical Scale

Figure 3. Wavelet spectra with sample thicknesses (left-hand panel):(a) Group A and (b) Group B. Fourier transformed spectra (right-handpanel) indicate the time-integrated frequency components. The dottedlines indicate the LO phonon and the L− mode while the red-coloredfittings based on Gaussians are employed for L+ mode.

originated from the inherent electron–electron scatteringof plasmon mode, in contrast to the other modes domi-nated by phonons. Therefore, the experimentally acquireddecay times taken from the L+ mode in Group B corre-spond to the momentum relaxation time (∼ 100 fs) of theplasmons at 800 nm. In a simplified picture ignoring thenon-parabolic band structures and the inter-valley scatter-ings which is inherent in the narrow-gap semiconductors,

10 100 10006.0

6.5

7.0

25

26

27

28

29

30< Group B >

ωL

LO phonon

L+ mode

Fre

quen

cy (

TH

z)

Thickness (nm)

ωT

L– mode

< Group A>

aB

Figure 4. The frequency of the LOPC modes with sample thickness:L+ mode (black), LO phonon (red), and L− mode (blue). The upper andlower dotted lines denote the previously reported values of LO phonon(�L� and TO phonon (�T � frequencies in strain-free bulk InAs, respec-tively. The aB (dashed line) denotes exciton Bohr radius (36 nm).

the electron–electron scattering time � is further associatedwith diffusion properties via the Einstein relationship, D=� ·kT /q = �q�/m∗� ·kT /q, where D is the diffusion coef-ficient, � denotes the carrier mobility, k is Boltzmann’sconstant, T is the absolute temperature, and q is the electri-cal charge of a particle.14 On the other hand, the empiricaldecay times in the L− and the LO phonon modes are notassociated with � , thus, couldn’t be directly related to thecarrier diffusion phenomena.Figure 4 traced the frequency peaks of three modes in

the different samples. In Group A with thin InAs layers,the LO phonon frequencies slight deviated from strain-free bulk values with the LOPC modes being absent.In Group B, on the other hand, the apparent featuresof the L+ and L− modes showed that frequencies wereincreased with thicker InAs layers and thus with largerdiffusion regions. Conventionally the increasing tendencyof frequency values of the L+ and L− modes has beenextensive studied both theoretically15 and experimentally.11

However, the increasing frequency behavior in Figure 4,even with the constant photo-excited carrier density withnegligibly small doping density, is not fully understoodyet although the larger diffusion coefficients with thickersamples could intuitively imply more efficient electronicdiffusion which was further confirmed from the increas-ing amplitude of THz waves with thickness and band dia-gram simulation (not shown here).16 On the other hand, LOphonon frequencies didn’t change as a function of thick-ness in Group B.

4. CONCLUSIONWe have investigated the salient features of the LOPCmodes as a function of InAs thickness. Only in a thicknessregime where the length scale is larger than the excitonBohr radius, the LOPC modes were observed with slightspectral shift. Much shorter decay time of plasmon-like

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Electron and Phonon Coupling Dynamics in Low-Gap Semiconductor: Quantum versus Classical Scale Min et al.

mode compared to those of other modes was associatedwith dephasing dynamics via electron–electron scatterings.

Acknowledgment: This work was supported by theBio-Imaging Research Center at GIST and NationalResearch Foundation of Korea (NRF) funded by theMinistry of Education, Science, and Technology (2012-042232). The research in KIST was mainly supported bythe KIST institutional program including Dream projectand partially by 2011K000589 and by GRL Programthrough MEST.

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Received: 18 February 2013. Accepted: 18 March 2013.

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