Anisotropic ultrafast electron dynamics induced by high-field terahertz pulses in n-doped InGaAs
F. Blanchard, D. Golde, F. H. Su, L. Razzari, G. Sharma, R. Morandotti, T. Ozaki, M. Reid, M. Kira, S. W. Koch, F. A. Hegmann
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov Anisotropic ultrafast electron dynamics induced by high-field terahertz pulses in n -doped InGaAs F. Blanchard, D. Golde, F. H. Su, L. Razzari, G. Sharma, R. Morandotti, T. Ozaki, M. Reid, M. Kira, S. W. Koch, and F. A. Hegmann ∗ INRS-EMT, Advanced Laser Light Source, Universit´e du Qu´ebec, Varennes, Qu´ebec J3X 1S2, Canada Department of Physics and Materials Sciences Center,Philipps-University, Renthof 5, 35032 Marburg, Germany Department of Physics, University of Alberta, Edmonton, Alberta T6G 2G7, Canada Department of Physics, University of Northern British Columbia,Prince George, British Columbia V2N 4Z9, Canada (Dated: September 28, 2018)The anisotropic effective mass of electrons is directly measured using time-resolved THz-pump/THz-probe techniques in a n -doped InGaAs semiconductor thin film. A microscopic theoryis used to attribute this anisotropy in the THz probe transmission to the nonparabolicity of theconduction band. Self-consistent light-matter coupling is shown to contribute significantly to theTHz response. PACS numbers: 73.50.Fq, 78.47.jh
Terahertz (THz) field induced transport effects canstrongly influence the behavior of fast semiconductorcomponents operating under extreme conditions [1, 2].The internal dynamics of the charge carriers in such de-vices is, among other things, determined by the bandstructure of the solid. Consequently, a complete under-standing of the underlying physical processes requiresa detailed knowledge of the band structure. In recentyears, the development of extremely strong pulsed THzsources and ultrafast coherent detection methods [3–10]has made it possible to continuously alter the lattice mo-menta of the electrons in the solid and, thus, to exploretheir properties within the entire Brillouin zone. This canpotentially yield new tools for characterizing the bandstructure and analyzing transport kinetics.Using various techniques of time-resolved THz nonlin-ear spectroscopy [4, 5, 10–26], effects like THz-inducedintervalley scattering [15, 16] and ballistic transport ofelectrons across half of the Brillouin zone [21] have beeninvestigated in semiconductors. Currently, also THz-pump/THz-probe (TPTP) techniques seem very attrac-tive in probing nonlinear carrier dynamics induced byintense few-cycle THz pulses in semiconductors. For in-stance, TPTP has been applied to induce impact ioniza-tion in InSb [14, 17] as well as intervalley scattering indoped GaAs, Si, and Ge [18].For III-V semiconductor compounds, the conductionband energy ε k is parabolic and symmetric only for lowelectronic momenta ~ k implying the same effective elec-tron mass in all directions, as illustrated in Fig. 1(a)at k = (0 , k = ( K x , ε k be-comes strongly nonparabolic [27] producing strongly di-rectional, i.e. anisotropic, effective masses, as shown inFig. 1(b) along the x - (black line) and y - (blue line) di-rections for a typical isotropic, nonparabolic band as a function of the corresponding electron energy. In otherwords, due to the nonparabolicity of ε k , the two com-ponents of the effective mass are equivalent only at thebottom of the band but they strongly deviate from eachother at higher carrier momenta.Traditionally, the effective mass is measured using FIG. 1. (color online) (a) The electric field of the THz pumppulse drives the electronic distribution (black circles) high inthe band to an average momentum of k = ( K x , m x or m y inthe x - or y -direction, respectively. (b) Effective mass nor-malized to the effective mass at the bottom of the band asfunction of the electron energy ε K x for co- (black line) andcross-linear (blue line) configurations. The effective mass iscomputed from Eqs. (2) and (3) using a nonparabolicity factorof α = 1 .
33 eV − . (c) Schematic of a polarization dependentTHz-pump/THz-probe (TPTP) experiment. For the co-linear(CL) configuration, both THz pulses are polarized in the x -direction whereas the probe polarization is along the y -axisfor cross-linear (XL) TPTP. FIG. 2. (color online) Experimental setup. (a) Electric fieldprofile of the THz pump beam emitted by the ZnTe opticalrectification source. Inset: amplitude spectrum of the THzpulse. (b) Schematic of the experimental setup. (c) Electricfield profile of the transmitted THz probe beam at variousdelay times between the main positive peaks of the THz pumpand THz probe pulses. magnetic cyclotron resonance (CR) [28, 29]. In partic-ular, nonparabolicity was first observed in bulk InSb us-ing CR [28], and the same technique was used to studynonparabolicity in bulk In . Ga . As [29], showing anincrease in the electron effective mass as a function of CRenergy (up to 30 meV at 4.2 K). However, CR probes theaverage effective mass (often called cyclotron mass) for agiven orbit in k -space and for a certain level of energy, butis not capable of probing the above mentioned anisotropyof the effective mass at a specific point in k -space.In this Letter, we present a new technique to directlymonitor the anisotropic effective mass of the electrons.We implement a polarization dependent TPTP exper-iment as shown schematically in Fig. 1(c). Here, astrong THz pump pulse accelerates the electrons in the x -direction which are then probed by another weaker THzpulse polarized either in the x - (co-linear) or y - (cross-linear) direction. We show that the anisotropy in theelectron masses yields distinctly different THz responsesfor the co- and cross-linear configurations because themeasured THz probe signal is proportional to the in-verse effective mass in the probed direction. While thenonlinear THz response in doped semiconductors aris-ing from band nonparabolicities has already been re-ported [30, 31], our experimental results demonstrate theanisotropic nature of band nonparabolicity.In our experiments, a large aperture ZnTe optical rec-tification source [7] was used to generate high-power,few-cycle, THz pump pulses with energies of 0 . µ J and0 . − n -type In . Ga . As epilayer (carrier concentra-tion of approximately 2 × cm − ) on a 0.5-mm-thicksemi-insulating InP substrate. A 10 × × . ZnTecrystal placed just after the first off-axis parabolic mirrorand just before the sample was used to generate a THzprobe beam that overlaps the THz pump beam at thefocus on the sample. An additional ZnTe crystal 0.5 mmthick was used to detect the THz probe pulses transmit-ted through the sample by free-space electro-optic sam-pling. The spot size diameters on the sample for theTHz pump beam and THz probe beam were 1.6 mm and2.5 mm, respectively (the probe beam path has a largerf-number than the THz pump beam). Both the ZnTesource crystal and the ZnTe detection crystal for the THzprobe beam could be rotated to produce (and detect)probe polarization states either parallel or perpendicu-lar to the THz pump beam. At the sample position, theTHz pump and THz probe peak electric fields were esti-mated to be about 200 kV/cm and 2 kV/cm, respectively.The THz probe itself is in the low-field regime and there-fore does not induce any nonlinear response in the sam-ple [15, 16]. We note that the non-collinear geometry ofthe TPTP experiment allowed the THz pump and probebeams transmitted through the sample to be geometri-cally separated. Cross-talk between the two THz beamswas therefore avoided by simply placing a metallic beamblock in the path of the transmitted THz pump beamafter the second off-axis parabolic. In addition, lock-indetection of the transmitted THz probe pulse amplitudewas synchronized to an optical chopper inserted in theTHz probe source beam. As shown in Fig. 2(c), the am-plitude of the transmitted THz probe waveform increaseswhen it overlaps with the THz pump pulse at zero rela-tive time delay, while the phase is relatively unaffected.This allows the transmission of the main positive peakof the THz probe pulse to be monitored as function ofpump-probe delay time. We also note that all the ex-periments were performed under a dry nitrogen purge atroom temperature.Figure 3(a) shows the normalized transmission of themain peak of the THz probe pulse as a function of pump-probe delay time, which is a common method for probingultrafast carrier dynamics in semiconductors in optical-pump/THz-probe experiments [16, 32, 33]. The presenceof the THz pump pulse results in an increase in trans-mission of the peak electric field of the THz probe pulse.The blue shaded area in Fig. 3(a) shows the transmissionchange for cross-linear polarization of pump and probebeams, while the black line shows the same measurementperformed for the co-linear polarization configuration. Inthe latter case, a fast, large amplitude oscillation is ob-served on top of a slower component similar to that shownas the area plot. As previously mentioned, we have ex-cluded the possibility that these fast oscillations are dueto cross-talk between the pump and the probe at the N o r m a li z ed t r an s m i ss i on (a) −2 0 2 4 611.21.41.6 Delay time (ps) N o r m a li z ed t r an s m i ss i on (b) −1 0 1 200.511.5 FIG. 3. (color online) Measured (a) and calculated (b) nor-malized peak transmission of the THz probe pulse as functionof the pump-probe delay. The solid lines and the blue shadedareas show the results for co- and cross-linear TPTP configu-rations, respectively. The dashed line and the yellow shadedarea in (b) represent corresponding calculations omitting theradiative backcoupling effects. detection level. In particular, when the probe beam isblocked, no residual signal from the pump beam is de-tected; both beams have to be present inside the sam-ple in order to observe the large amplitude oscillationsfor co-linear polarization shown in Fig. 3(a). Moreover,moving the sample to an off-focus position (or completelyremoving it from the THz beam) eliminated any modula-tion signal of the THz probe transmission. Finally, sim-ple interference cannot justify the observed anisotropy,due to the negligible contribution of the probe signal tothe overall electric field amplitude. As discussed earlierfor Fig. 2(c), the lack of any significant phase shift inthe transmitted THz waveform implies that the observedsignal is due to modulation of the peak amplitude of theTHz probe pulse. To further corroborate this conclu-sion, no signal was observed as a function of pump-probedelay time when the THz detection point was set to azero-crossing of the THz probe waveform.We next apply a microscopic theory to rigorously re-veal the microscopic origin of the detected anisotropy.The propagation of a THz field E ( z, t ) follows from thewave equation (cid:20) ∂ ∂z − n c ∂ ∂t (cid:21) E ( z, t ) = µ δ ( z ) ∂∂t J ( t ) , (1) where n b is the background refractive index, c is thespeed of light, µ is the vacuum permeability, and J ( t )is the excited current density. Since the thickness of thesample is much smaller than the THz field’s wave length,the z -dependence of J is very accurately described viaa δ -function. The temporal evolution of J follows thenfrom J ( t ) = − | e | ~ V P k ( ∇ k ε k ) f k where f k defines the mi-croscopic electron distribution and V is the quantizationvolume of the semiconductor. For not too large k -values,the conduction band energy dispersion is well-describedby the relation [27] ε k (1 + α ε k ) = ~ k m ∗ , (2)where α is the nonparabolicity factor of the band and m ∗ is the effective mass at the bottom of the band. The k -dependent effective mass, i.e. m − i ( k ) ≡ ~ d ε k d k i , (3)in Fig. 1(b) is computed using Eq. (2) with the standardInGaAs value α = 1 .