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Abstract
The experimental THz-excitation spectroscopy technique for determining heterojunction band offsets is suggested. When photoexcited electrons gain sufficient energy to pass the potential barrier corresponding to a conduction band offset, an amplitude of THz-emission pulse sharply increases, which allows for direct measurements of the offset value. The technique is applied for determining GaAsBi-GaAs band offsets. The deduced conduction band offset of GaAsBi-GaAs heterojunction has about 45% of an energy gap difference at the Bi concentrations x < 0.12 investigated.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The conduction and valence band offsets, ΔEc and ΔEv, at a heterojunction of two semiconductors set up the potential barriers for electrons and holes, which essentially affect performance of practically all contemporary micro- and opto-electronic devices. The band alignment problem, due to its importance both for solid-state physics and device engineering, is widely investigated (see, e. g., reviews [1–5]) theoretically and by various experimental techniques – optical spectroscopy, photoemission spectroscopy, transport methods, and ballistic electron emission microscopy. The principle instrumental tool is the optical spectroscopy of quantum wells (QW). However, the energies of interband transitions between QW electron and hole subbands are not sufficiently sensitive to band-offset values – different ratios of the conduction band offset to the energy gap difference, Q = ΔEc/ΔEg, usually correspond to similar sets of the interband-transition energies. As a result, a reliable determination of band offsets for a given heterostructure is not a straightforward task and usually requires integrated studies by optical and other, more sensitive to band-offsets, techniques.
In the present paper we suggest a novel technique for a direct band-offset determination based on a terahertz excitation spectroscopy (TES). The THz emission in semiconductors is due to a spacial separation of charge carriers photoexcited by a short laser pulse. When charge carriers are photoexcited in a heterostructure of semiconductors, an amplitude of the emitted THz-pulse will experience a sharp increase at the photon energies when photoelectrons (holes) gain sufficient kinetic energies to overcome the potential barrier corresponding to a heterojunction band-offset (Fig. 1). This allows for a direct determination of band-offsets from the spectral positions of THz-emission onsets.
Fig. 1 Scheme of optical transitions corresponding to the threshold photon energy E1 for THz-emission. The THz pulse is emitted when an electron excess energy is sufficient to overcome the ΔEc potential barrier.
The TES technique assumes ballistic propagation of photoexcited carriers in a thin enough layer of a narrower-gap semiconductor. The layer width should be smaller either than the optical penetration length, for photocarriers to be uniformly distributed, or than the distance the carriers travel while THz-pulse emission takes place.
In the present study, the TES technique is applied for a determination of band offsets of GaAsBi-GaAs heterojunction. The dilute bismides – the III-V semiconductors with a few percent of Bi – are in a focus of recent theoretical and experimental studies, which are motivated by a potential use of bismides in GaAs-based near-IR photodetectors, highly-efficient solar cells [6], and laser diodes with reduced temperature-sensitivity of emission-wavelength [7]. Despite the wide-range studies, the GaAsBi-GaAs band offsets are not unambiguously determined. Our measurements, carried out by TES technique, show that the GaAsBi-GaAs conduction band offset is of about 45 % of the bandgap difference at Bi content up to about 12 %.
2. THz excitation spectroscopy
The main mechanism of THz emission in semiconductors is due to a spacial separation of electrons and holes photoexcited by a short, typically ∼ 100 fs, laser pulse. The photoexcited electrons move quasi-ballistically leaving less-mobile holes behind themselves and, as a result, induce a dynamically varying electric dipole that eventually leads to a THz-pulse emission [8]. In a bulk semiconductor, the THz-pulse is generated when a photon energy of the laser pulse exceeds the energy gap of semiconductor [9], ħω ≥ Eg.
When a heterostructure comprised of two different-bandgap materials, with a thin narrower-bandgap material at a surface, is illuminated, the THz-emission will be generated when photoexcited charge carriers in a top (surface) layer will gain an excess energy to pass the potential barrier corresponding to a conduction (valence) band offset (Fig. 1). Indeed, when the thickness of a top layer is much smaller than the optical absorption depth, photoexcited electrons and holes will be uniformly distributed in the layer. The energy barriers at the heterojunction will prevent their spatial separation, and no electric dipole and subsequent THz-pulse will be generated. With an increase of the exciting photon energy, photoexcited electrons will eventually gain energy enough to pass to the widegap semiconductor and an onset of THz-emission will start at the threshold energy ħω = E1 which is determined by the conduction band offset ΔEc,
Here Eg is the bandgap of a top-layer semiconductor, m and mh are the effective electron and hole masses. As it is seen from Eq. (1), the band offset can be directly determined from the spectral position of THz-emission onset.
2.1. Onset of THz-emission
The amplitude of THz-emission pulse is proportional to the electron (hole) flux density along the heterojunction normal (taken as the z-axis),
Here vz = nkz /m is the electron velocity along the z-axis, fk is the electron distribution function, and T(ε⊥) is the transmission coefficient of the potential barrier (see inset to Fig. 2),
is the electron kinetic energy of the z-motion, and U = ΔEc is the potential barrier corresponding to a conduction band offset.
Fig. 2 The theoretical spectral shape of THz-emission onset: The A(ε0) function for an electron photoexcitation from the hh band (α0 = −1) at ϑE = 80°. The inset presents the transmission coefficient of potential barrier.
The distribution function of electrons photoexcited by a short laser pulse is determined by the Gaussian energy-dependence G(ε) and the angular dependence F(nk), which is due to the optical orientation [10] of their quasimomenta k,
Here ε0 = (ħω − Eg)/(1 + m/mh) is the electron energy, determined by the photon energy ħω of the excitation pulse, is the standard deviation parameter determined by the pulse duration Δt, the α0 parameter is equal to −1 or +1 for an electron excitation from heavy-and light-hole branches, correspondingly, P2(x) is the second Legendre polynomial, and χ is the angle between the k-vector and the electric vector of the exciting light, cos χ = nk nE. The constant C of the distribution function in Eq. (4) is determined by the normalization condition 2(2π)−3 ∫ d3k fk = n, where n is the concentration of photoexcited electrons, and can be expressed (at ε0 ≫ s) as C = n/ϱ(ε0), where is the electron density of states at ε0 energy.
The general expression (2) for the flux density, by integrating in the spherical coordinate system with the polar axis taken along z-direction, can be reduced to the form
Here is the F(nk) function averaged over the azimuthal angle,
ϑE is the polar angle of the electric vector of exciting light pulse.
The introduced dimensionless A(ε0) function [Eq. (5)] determines an expected spectral shape of an onset of THz-emission. Neglecting the energy spread of photoexcited electrons (s = 0) and assuming that the transmission coefficient of potential barrier corresponds to the step function [T(ε⊥) = 0, for ε⊥ < U, and T(ε⊥) = 1, for ε⊥ > U], one obtains the linear onset of THz-emission (dashed line in Fig, 2), which is predicted by Eq. (5) at ε0 − U ≪ U,
The energy dependence of the transmission coefficient (3) gives rise to a superlinear behavior of THz-emission onset (thinner full curve in Fig, 2), which can be successfully modeled by a power-law dependence
with the p ≈ 1.25 exponent. At immediate vicinity to the ε0 = U energy, the onsets starts with the p = 3/2 exponent, which corresponds to an initial rise of the transmission coefficient (3). However, this holds true in a very short range of electron energies and subsequently the A(ε0) rise becomes less steep. The energy spread of photoexcited electrons (s ≠ 0) smears the THz-emission edge by its Gaussian convolution, as it seen from the final theoretical spectral shape of the A(ε0) function presented by a thick full curve in Fig. 2.3. Experimental
3.1. TES measurements
The THz excitation spectroscopy measurements have been carried out in the quasi-reflection geometry with samples illuminated at 45° to their surface normal. Experimental setup is shown schematically in Fig. 3. The setup is based on an amplified ytterbium-doped potassium gadolinium tungstate (Yb:KGW) laser system (PHAROS, Light Conversion Ltd.) operating at 1030 nm with the pulse duration of 160 fs and the pulse repetition rate of 200 kHz. Average power of 6 W from the laser is directed into a cavity-tuned optical parametric amplifier (OPA, ORPHEUS, Light Conversion Ltd.) that generates 140–160 fs duration pulses with a central wavelength tunable from 640 nm to 2600 nm. In the THz-TDS arrangement activated by the laser system, the investigated samples were excited by the OPA output beam, while the sample-emitted THz pulses were detected by the GaAsBi photoconducting antenna (TeraVil Ltd.). The THz detector was illuminated by a small fraction (average power of ∼ 5 mW) of Yb:KGW-laser beam delayed by different times with respect to the optical beam exciting an investigated sample. All experiments were performed at room temperature. The average power of the optical pulses incident on a sample was of about 10 mW.
The THz pulses emitted by GaAs0.941Bi0.059As-GaAs heterostructure at the 1.19–1.89 eV photon energies of OPA beam and the pulse spectrum for ħω = 1.89 eV are presented in Fig. 4.
Fig. 4 THz pulses emitted by GaAs0.941Bi0.059As-GaAs photoexcited by OPA beams with photon energies in the 1.19–1.89 eV range (a) and the Fourier spectrum of the pulse obtained for ħω = 1.89 eV (b).
3.2. Growth of heterostructures
The GaAsBi-GaAs heterostructures were molecular-beam-epitaxy (MBE) grown on semi-insulating (001) GaAs substrates at temperatures between 320 and 350 °C. Prior to the bismide layer of d = 100 nm deposition, the native oxide of GaAs-wafer was removed at 630 °C temperature and under maximum arsenic flux. For smoothing of the wafer surface, a 10–20 nm thick GaAs buffer layer was grown. The atomic composition of the GaAs1−x Bix layer was varied by adjusting the growth temperature and/or the Bi to As molecular flux ratio.
3.3. Characterization of GaAsBi layers
The atomic compositions x, Bi contents, of the grown GaAs1−x Bix layers (Table 1) were determined by X-ray diffraction (XRD) measurements, carried out with SmartLab Rigaku diffractometer, by monitoring shifts of the (004) diffraction peak with respect to its position in GaAs [Fig. 5(a)] and by reciprocal space mapping (RSM) of the (115) diffraction peak.
Table 1. Physical parameters of GaAs1−xBix layers (their atomic compositions x and bandgaps Eg), measured onsets of THz-emission E1 and determined conduction band offsets ∆Ec of investigated GaAsBi-GaAs heterostructures.
Fig. 5 (a) XRD rocking curves of the (004) diffraction peak of several GaAsBi-GaAs samples, x = 0.068, 0.086, and 0.117. (b) Reciprocal space map of the (115) diffraction peak of GaAsBi-GaAs sample with the highest Bi content, x = 0.117.
The recorded RSM patterns clearly indicated [Fig. 5(b)] that epitaxial GaAsBi layers, which were of d = 100 nm thickness, remained to be strained even at the highest Bi content, x = 0.117, achieved in the present study. To determine atomic compositions of strained GaAsBi layers, the Vegard’s law for the lattice constant of unstrained GaAsBi,
and the known expressions of strain-tensor components were employed. Here aGaAs = 5.653 Å and aGaBi = 6.234 Å are the lattice constants of GaAs and GaBi [11], Δa = aGaAsBi − aGaAs, a = (aGaAsBi + aGaAs)/2, C11 and C12 are the elastic constants, which were taken to be equal to those of GaAs [12], C11 = 122.1 GPa and C12 = 56.6 GPa.The bandgaps of GaAsBi layers were determined from the spectral positions of their photoluminescence peaks, which were recorded by a standard PL setup with DPSS 532 nm excitation laser. The energy gaps determined (dots in Fig. 6) monotonously decrease with an increase of Bi content and follow the theoretical estimate of Eg(x) dependence (full curve in Fig. 6)
Here Eg,0(x) is the energy gap of bulk, unstrained GaAsBi [13], ac = −7.17 eV, av = −1.16 eV, and b = −2 eV are the deformation potential constants (taken to be equal to those of GaAs).
Fig. 6 Dependence of the GaAs1−x Bix bandgap on the atomic composition x. Full curve presents the theoretical estimate of strained-layer Eg(x) dependence (11). Dashed curve corresponds to the bandgap dependence of unstrained, bulk GaAsBi [13].
4. GaAsBi-GaAs band-offsets
The band offsets of GaAsBi-GaAs heterojunction is a widely debated problem. The valence band anticrossing (VBAC) model shows [13] that a restructuring of GaAs1−x Bix valence band occurs as a result of an anticrossing interaction between the extended states of GaAs valence band and the resonant states of Bi atoms. In addition to the VBAC-induced valence band movement, the recent theoretical studies [14] have predicted that the conduction band also experiences shift, contributing to approximately 40 % of the GaAsBi-GaAs bandgap difference ΔEg. Experimental data on the GaAsBi-GaAs conduction band offset are few and range from 23 %, as determined by X-ray photoemission spectroscopy [15] on samples with less than 2.5 % Bi, to nearly 48 % at 2.1% < x < 5.9 %, as found from a photoreflectance study [16] of GaAsBi-GaAs quantum wells. Moreover, the authors of a recent multi-quantum well photoluminescence study [17] have suggested that GaAsBi-GaAs band offsets correspond to a staggered, type-II, rather than to a more common straddling, type-I, alignment.
The THz-pulse excitation spectra measured on GaAsBi-GaAs heterostructures are presented by dots in Fig. 7. As it is seen, an increase of the signal occurs at energies E1 above the GaAsBi bandgap Eg and the spectral shape of THz-emission onsets is close to its theoretical estimate A(ε0) [Eq. (5), blue curves in Fig. 7]. Since the optical absorption coefficient in GaAsBi layers does not exceed 2 · 104 cm−1 for photon energies up to about Eg + 0.3 eV [18,19], the photoexcited electrons and holes are uniformly distributed in the investigated d = 100 nm GaAsBi layers, and THz-pulse is not generated until electrons gain sufficient energy to overcome the conduction-band-offset barrier.
Fig. 7 THz-pulse excitation spectra (dots) of investigated GaAsBi-GaAs heterostructures. Red curves present photoluminescence spectra of the samples. Blue ones correspond to theoretical spectral shapes A(ε0) of THz-emission onset [Eq. (5)].
With an increase of the photon energy, the THz-pulse amplitude experiences a drop at a photon energy of 1.42 eV, when a photoexcitation begins in GaAs substrate. With a further increase of ħω, the THz excitation spectrum shows [Fig. 7(c)] additional features E2 and E3 which are due to a photoexcitation of electrons in GaAsBi and GaAs layers with excess energies sufficient to pass to GaAs L-valleys [19].
The threshold energies of THz-emission E1 can be determined by fitting the emission onsets with the A(ε0)-function. The E1 values obtained are presented in Table 1. The deduced value of the broadening parameter s was of about 36 meV.
The measured shifts of the THz-emission onsets from the bandgap values, E1 − Eg, allow for a straightforward determination of the conduction band offsets [see Eq. (1)]. The values obtained at the m = 0.067 m0 and mh = 0.55 m0 effective electron and hole mases (taken to be equal to those of GaAs) are presented in Table 1 and by open dots in Fig. 9.
Fig. 8 Energy spectra of several investigated strained GaAsBi layers (thick curves). Dashed curves present spectra of unstrained GaAsBi.
Fig. 9 Positions of the strained-GaAsBi conduction and valence bands (dots) with respect to those of GaAs (dashed lines). Large open and small full dots are obtained disregarding and taking into account an influence of strains on energy-band dispersions.
The shifts of THz-emission onsets, as seen from Eq. (1), are related both with the band offsets and parameters of energy-band dispersions,– the effective electron and hole masses. Since the band dispersions are affected by strains, a determination of the strained-heterostructure band offsets, in principle, should be carried out taking into account the strain-induced band dispersions.
To estimate an influence of energy spectrum parameters on a band-offset determination, we modeled the strain-induced dispersion of the heavy-and light-hole branches by a simplest, 4 × 4 Hamiltonian approach [20],
and the conduction band dispersion by the Kane spectrum,Here γ1, γ2, γ3 are the Luttinger parameters and P is the Kane parameter.
The dispersion of energy bands for several of the investigated GaAsBi layers, calculated by Eqs. (12)–(15) at the γ1 = 6.98, γ2 = 2.06 and 2m0P2/ħ2= 21.23 eV parameter values (corresponding to those of GaAs), is presented in Fig. 8. The altered dispersion, at the chosen set of parameters, only slightly affected the band-offset values [small full dots in Fig. 9]. By varying the parameters within relevant limits, one can estimate the influence of the band dispersion parameters on the ΔEc-determination accuracy to be below ~ 25 %.
The determined positions of the GaAsBi conduction and valence bands with respect to those of GaAs are presented graphically in Fig. 9. The band offsets for a given heterojunction of the type-I alignment are conventionally characterized by the Q-parameter which is defined as a ratio of the conduction band offset to a difference of the energy gaps in unstrained semiconductors, Q = ΔEc,0/ΔEg,0. The curves in Fig. 9 present estimates of the strained-GaAsBi energy band positions corresponding to the Q = 0.45 value. As it is seen, the experimental values closely follow the theoretical estimates what allows us to conclude that the conduction band offset of the GaAsBi-GaAs heterojunction, at the Bi concentrations x < 12 % investigated, is close to Q = 0.45± 0.05. The Q = 0.45 value is very close to that, Q = 0.48, determined by Kudrawiec et al. [16] from a photoreflectance study of GaAsBi-GaAs quantum wells with x < 5.9 % bismuth concentrations.
5. Discussion
The determined GaAsBi-GaAs band offsets at the x < 0.1 bismuth concentrations, as it is seen from Fig. 9, are close to their values corresponding to Q = 0.45, while the offsets at x = 0.117 distinctly deviate from the Q = 0.45 estimates. Most probably this is due to the band bending effects induced by a redistribution of charge carriers in the GaAs0.883Bi0.117-GaAs heterostructure.
Although the MBE-grown epitaxial GaAsBi layers were not intentionally doped, an incorporation of Bi leads to a formation of acceptor levels (see, e. g., [21]) positioned up to 90 meV above the valence band edge [22]. The Hall coefficient RH measurements carried out on investigated GaAsBi-GaAs samples indicated the 5 · 1015 cm−3 hole concentration in the x = 0.117 sample and much lower, 1 · 1011 – 5 · 1014 cm−3, effective charge carrier concentrations nH = −1/(ecRH)in the x = 0.03 – 0.086 samples. The presumable energy diagram of the GaAs0.883Bi0.117-GaAs heterostructure is presented in Fig. 10. The diagram was calculated under an assumption of the NA = 1 · 1016 cm−3 acceptor concentration with the εA = 90 meV binding energy in the d = 100 nm GaAsBi layer and a standard doping of SI-GaAs substrate by deep EL2 donors, ND = 1.5 · 1016 cm−3, εD = 0.684 eV. (The intermediate d = 10 nm GaAs buffer layer was assumed to be undoped.) As seen from Fig. 10, the band bending in GaAsBi layer, ΔV, induced by a charge-carrier redistribution, reduces the potential barrier for electrons, Ueff = ΔEc − ΔV. Taking into account the calculated ΔV = 0.07 eV value, one obtains the corrected GaAs0.883Bi0.117-GaAs conduction band offset of 0.19 eV which is close to the 0.24 eV value expected at Q = 0.45.
In summary, the suggested THz excitation spectroscopy technique allows for a straightforward direct determination of band offsets under the flat-band conditions in constituent layers of heterostructure, what is expected at low thicknesses of the narrower-gap layers and at low doping levels. When a charge carrier redistribution affects the potential profile of heterostructure, the band bending should be taken into account in a determination of band-offset values.
The main advantage of the suggested TES technique with respect to other experimental methods of band-offset determination is a direct relation between the offset values and the experimentally traced spectral TES features, what ensures a high sensitivity of the technique. The technique is contactless and does not require complicatedly sampled structures. An accuracy of the technique is limited by the spectral resolution of the current stage THz spectroscopic equipment. Keeping in mind that an instrumentation of THz spectroscopy is rapidly developing, one can expect the TES technique to become both reliable and precise tool for a band-offset determination.
Funding
Research Council of Lithuania (grant No. 09.3.3-LMT-K-712-01-0032).
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