Intervalley Deformation Potential Research Articles

Effects of size quantization in the spectra and Γ − M transitions in (GaAs)m(AlAs)n(001) superlattices

Based on the pseudopotential method and the phenomenological model of coupling forces, electron scattering by short-wavelength phonons in the conduction band of superlattices (GaAs)m(AlAs)n with thin layers (n, m ≤ 10) is studied. Intervalley deformation potentials for transitions between the lower states of the Γ and M valleys of superlattices, which are analogs of the sphalerite transitions of Γ̲−X̲ and X̲−X̲̃, are calculated. The intensity of the Γ − M transitions is determined mainly by the longitudinal optical vibrations of the Al atoms and depends strongly on the mixing of the states Γ̲ and X̲. The capture of phonons and electrons in AlAs layers leads to an increase in the deformation potentials of X̲−X̲̃ transitions.

Thermoelectric transport properties of silicon: Toward anab initioapproach

We have combined the Boltzmann transport equation with an ab initio approach to compute the thermoelectric coefficients of semiconductors. Electron-phonon, ionized impurity, and electron-plasmon scattering mechanisms have been taken into account. The electronic band structure and average intervalley deformation potentials for the electron-phonon coupling were obtained from the density functional theory. The linearized Boltzmann equation has then been solved numerically beyond the relaxation-time approximation. Our approach has been applied to crystalline silicon. We present results for the mobility, Seebeck coefficient, and electronic contribution to thermal conductivity as functions of the carrier concentration and temperature. The calculated coefficients are in good quantitative agreement with experimental results.

Calculation of the electron Hall mobility and Hall scattering factor in 6H-SiC

The calculated electron Hall Mobility and Hall scattering factor in n-type 6H-SiC based on numerical solutions to the Boltzmann transport equation are presented. These results were obtained by solving the Boltzmann equation exactly for the electron Hall mobility using the contraction mapping principle and the electron drift mobility with Rode’s iterative method. The relative importance of the various scattering mechanisms for these calculations is discussed, and a new set of values for the acoustic deformation potential, intervalley deformation potential, and intervalley phonon energy is found, which simultaneously fit experimental Hall mobility and Hall scattering factor data. The calculated Hall mobility and Hall scattering factor are in good agreement with experimental results. In addition, predicted values of the Hall scattering factor for various temperatures and doping concentrations are given.

Electron–phonon effects on the direct band gap in semiconductors: LCAO calculations

Using a perturbative treatment of the electron–phonon interaction, we have studied the effect of phonons on the direct band gap of conventional semiconductors. Our calculations are performed in the framework of the tight-binding linear combination of atomic orbitals (LCAO) approach. Within this scheme we have calculated the temperature and isotopic mass dependence of the lowest direct band gap of several semiconductors with diamond and zincblende structure. Our results reproduce the overall trend of available experimental data for the band gap as a function of temperature, as well as give correctly the mass dependence of the band gap on isotopic. A calculation of conduction band intervalley deformation potentials is also reported. Finally, calculated Debye–Waller factors are compared with X-ray and EXAFS experimental results.

A multi-valley model for hot free-electron nonlinearities at 10.6μm in highly doped n-GaAs

When the frequency of infrared light and the plasma frequency of highly doped n -GaAs are in resonance ( e.g. for a doping concentration N = 7 × 10 18 cm −3 and a wavelength m), the free-electron induced optical nonlinearity is soundly pronounced. At such high doping concentrations it is necessary to extend the rigid quantum mechanical description of the free-electron induced nonlinearity to a multi-valley model. The central valley of GaAs was treated as a fully nonparabolic degenerated electron gas, whereas the satellite valley was modeled as an anisotropic electron gas of arbitrary degeneracy. The following intra- and intervalley absorption mechanisms were taken into account: impurity assisted, thermal and hot polar optical phonon assisted intravalley absorption on one hand and intervalley phonon assisted absorption in equivalent and nonequivalent intervalley absorption on the other hand. The dependence of the different absorption and energy relaxation mechanisms on the doping concentration, free electron heating, optical power density and the equivalent LL -intervalley deformation potential are discussed. We demonstrated for the first time that the behavior of the optical intervalley nonlinearity, i.e. the nonlinear absorption and nonlinear intervalley transfer, strongly depend on the equivalent LL -intervalley deformation potential. In the linear regime the model calculations are in good agreement with experimental results.

Optical absorption in GaTe under high pressure

This paper reports on the pressure dependence at room temperature of the absorption coefficient of the layered semiconductor gallium telluride. The absorption edge in the explored pressure range ~up to 6.1 GPa! can be accounted for through the superposition and interaction of a direct gap and an indirect gap. The pressure shift of the direct gap is strongly nonlinear, starting at low pressure with a coefficient of 285.7 60.4 meV/GPa and exhibiting a minimum at around 2.9 GPa. The exciton binding energy decreases under pressure, which can be related to the increase of the dielectric constant. The broadening of the exciton line is explained through phonon-assisted intervalley scattering of conduction-band electrons after the crossover between direct and indirect gaps, with an estimation of the related intervalley deformation potential. @S0163-1829~99!16035-1#

Photoluminescence of short-period GaAs/AlAs superlattices: A hydrostatic pressure and temperature study

The temperature and pressure dependence of type-I and -II transitions from photoluminescence (PL) spectra in a series of $(\mathrm{GaAs}{)}_{m}/(\mathrm{AlAs}{)}_{m}$ superlattices show that the temperature dependence of energy bands can be described very well with a Bose-Einstein-type equation. From these measurements the parameters that describe the temperature dependence of excitonic transition energies and the corresponding broadening of the PL line are deduced. The pressure dependence of the PL linewidths of the type-I exciton as a function of pressure and temperature yield the intervalley deformation potential. Beyond the type-I--type-II crossover, the PL linewidth increases as a function of both pressure and temperature. The electron-phonon deformation potential for $\ensuremath{\Gamma}\ensuremath{-}X$ scattering is found to be temperature dependent.

Temperature Dependence of the Intervalley Deformation Potential of GaAs/AlAs Superlattices Under Hydrostatic Pressure

ABSTRACTWe have studied the pressure dependence of the type-I and type-II transitions in (GaAs)m/(AlAs)m superlattices by photoluminescence (PL) spectroscopy. From the study of PL linewidths of the type-I exciton as a function of pressure and temperature, we determine the intervalley deformation potential. Beyond the type-I and type-II crossover, the PL linewidth increases both as a function of pressure and temperature. We find that the electron-phonon deformation potential for Γ-X intervalley scattering varies with temperature.

Femtosecond kinetics of photoexcited carriers in germanium.

Thermalization, intervalley scattering, and cooling of photoexcited carriers are observed in the indirect-band-gap semiconductor Ge through time-resolved direct-band-gap transmission and luminescence with 100-fs resolution. The transmission experiment, which uses \ensuremath{\lambda}=1.53 \ensuremath{\mu}m, 120-fs pulses from a 76-MHz optical parametric oscillator takes advantage of the indirect-band-gap character of Ge to unambiguously determine the \ensuremath{\Gamma}\ensuremath{\rightarrow}L intervalley scattering time at 295 K. The measured \ensuremath{\Gamma}\ensuremath{\rightarrow}L transfer time for electrons at the \ensuremath{\Gamma} valley edge is 230\ifmmode\pm\else\textpm\fi{}25 fs yielding 4.2\ifmmode\pm\else\textpm\fi{}0.2\ifmmode\times\else\texttimes\fi{}${10}^{8}$ eV/cm for the ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}\mathrm{\ensuremath{-}}\mathit{L}}$ intervalley deformation potential. The luminescence experiments were performed at 10 K using a standard time and spectrally gated up-conversion technique employing an 82-MHz, 80-fs pulse width Ti:sapphire laser operating at \ensuremath{\lambda}=750 nm. From the luminescence experiments conducted with peak carrier densities of ${10}^{18--}$${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, we observe that \ensuremath{\Gamma}\ensuremath{\rightarrow}L,X scattering competes with carrier-carrier scattering so that nonthermalized carriers are observed for up to several hundred femtoseconds after an excitation pulse. Because the initial carrier kinetic energy is quite high we find that in addition to phonon-assisted L-L intervalley scattering, X-L and X-X processes must be included to account for a 1-ps carrier-cooling time. A value of 5\ifmmode\times\else\texttimes\fi{}${10}^{8}$ eV/cm is obtained for the ${\mathit{D}}_{\mathit{X}\mathrm{\ensuremath{-}}\mathit{X}}$ deformation potential.

Phonon-assisted Gamma -X transfer in (001)-grown GaAs/AlAs superlattices.

A theory of phonon-assisted intervalley \ensuremath{\Gamma}-X transfer in periodic heterostructures GaAs/AlAs is developed on the basis of the envelope-function approximation. Matrix elements of intervalley transitions are expressed through the overlap integrals of \ensuremath{\Gamma} and X envelope functions with use of \ensuremath{\Gamma}-X intervalley deformation potential constants of bulk GaAs and AlAs. The phonon spectrum of an ideal GaAs/AlAs periodic heterostructure is studied in a microscopic approach. It is shown that phonons responsible for intervalley transitions are GaAs-like and AlAs-like X-point LO phonons, confined within GaAs and AlAs layers, respectively. \ensuremath{\Gamma}-X transfer times due to phonon-assisted scattering are calculated for the problem of photoexcited-electron relaxation in the type-II GaAs/AlAs superlattices and compared with the transfer times due to the phononless transition mechanism (\ensuremath{\Gamma}-X mixing). Both phonon-assisted \ensuremath{\Gamma}-X scattering and \ensuremath{\Gamma}-X mixing are important for the determination of \ensuremath{\Gamma}-X transfer times. The calculated values of \ensuremath{\Gamma}-X transfer times and their dependence on GaAs and AlAs layer thicknesses are in agreement with the experimental data.

Self-consistent calculation of intervalley deformation potentials in GaAs and Ge

We use the ab initio tight-binding method with ad-hoc site diagonal potentials to calculate electronic and structural properties of semiconductors. By distorting the lattice to simulate L or X phonons, intervalley deformation potentials, D, for electron and hole transfer in GaAs and Ge are obtained self-consistently. In most cases, self-consistency increases the value of D by only about 10%. The values obtained, however, are larger than those from fitted tight-binding or empirical pseudopotential methods and in good agreement with recent experiments.

An ensemble Monte Carlo study of high-field transport in β-SiC

The high-field transport of electrons in β-SiC is investigated by use of an ensemble Monte Carlo technique. We consider scattering by acoustic deformation potential, polar optical phonon, two different equivalent intervalley phonons (one first-order and one zero-order interaction), impurity scattering and impact ionization. The intervalley coupling constants and deformation potential constant are estimated by fitting the ohmic mobility to the measured experimental values over the temperature range 50–1000 K. Polar runaway occurs above 5 × 10 5 V/cm. The distribution can be partially stabilized by impact ionization processes, but the runaway is still observed. For a nonparabolic band model, the drift velocity has a gentle peak around 4 × 10 5 V/cm. The peak value is 1.9 × 10 7 cm/s, which is comparable to the experimental value observed in 6H-SiC (2.1 × 10 7 cm/s).

Intervalley Gamma -X deformation potentials for top valence bands in III-V zincblende semiconductors by ab initio pseudopotential calculations

The authors have calculated Gamma -X hole-phonon scattering matrix elements for the top valence bands in nine III-V zincblende semiconductors AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs and InSb, by ab initio pseudopotential calculations. At the same time, the authors have calculated the eigenfrequencies and eigenvectors of transverse acoustic (TA) and optic (TO) phonons at X in these materials, which agree very well with the available experimental results. They have evaluated the Gamma -X intervalley deformation potentials (IVDPs) for the longitudinal phonons, and transverse phonons, respectively. The IVDPs for the TAX phonon are very small, as expected from symmetry. The IVDPs for the TOX phonon do not vary appreciably from one semiconductor to another, averaging about 5 eV AA-1. IVDPs for the longitudinal phonon with X1 symmetry are generally larger than those of X3 symmetry. This is due to more screening to the long-range electron-phonon interaction for the X3 phonon by electron redistribution, resulting in smaller IVDPs.

Ensemble Monte Carlo simulation of intervalley scattering in AlxGa1-xAs.

An ensemble Monte Carlo simulation of the femtosecond response of photoexcited electrons in indirect-gap ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As is performed. The time evolution of electron populations in the conduction-band valleys is studied. By comparing with recent femtosecond infrared-absorption experiments, a value for the L-X intervalley deformation potential was derived through parameter fitting. The effect of binary phonon modes due to the alloy structure of the semiconductor is incorporated into the simulation of both the ultrafast scattering processes and the indirect photogeneration process. The value found for the L-X intervalley deformation potential, ${\mathit{D}}_{\mathit{X}\mathit{L}}$=1.7\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}${10}^{8}$ eV/cm, can be assumed as a lower bound for the deformation potential in GaAs.

L6-X6 intervalley scattering time and deformation potential for Al0.6Ga0.4As determined by femtosecond time-resolved infrared absorption spectroscopy.

Hot electrons in ${\mathrm{Al}}_{0.6}$${\mathrm{Ga}}_{0.4}$As were produced in the ${\mathit{X}}_{6}$ valley from a photoexcited indirect transition by a 585-nm femtosecond pump pulse. The time evolution of the population of electrons in the bottom of the ${\mathit{X}}_{6}$ alley was monitored by a femtosecond infrared probe pulse. The ${\mathit{L}}_{6}$\ensuremath{\rightarrow}${\mathit{X}}_{6}$ intervalley scattering time of \ensuremath{\sim}200 fs and the ${\mathit{L}}_{6}$${\mathit{X}}_{6}$ intervalley deformation potential of \ensuremath{\sim}2.7\ifmmode\times\else\texttimes\fi{}${10}^{8}$ eV/cm were determined from the measured kinetic data.

Pressure-induced resonance broadening of exciton line shapes in semiconductors: Direct determination of intervalley scattering rates in GaAs.

We show that the exciton photoluminescence line shape in the GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells under pressure is broadened by hybridization of the \ensuremath{\Gamma} exciton with the X and the L continua via electron-phonon coupling. Furthermore, we demonstrate the pressure tuning of the resonance-broadening effect which can be used to extract the electron-phonon coupling parameters directly. For GaAs we estimate the intervalley electron-phonon deformation potential ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}\mathit{X}}$ to be 10.7\ifmmode\pm\else\textpm\fi{}0.7 eV/\AA{}. The resonance effect should be observable in other semiconductors as well.

Monte Carlo investigation of acoustic, intervalley and intravalley deformation potentials for GaAs

Influence of the acoustic, intervalley, and intravalley deformation potentials of GaAs on the electron mobility, peak velocity, threshold electrical field, and negative differential mobility at 300 K has been studied using Monte Carlo simulations. The Monte Carlo results compared to the experimental measurements suggest a value as large as 12.7 eV for the acoustic deformation potential. However, it has been shown that information provided by the available experimental results is insufficient to determine the intervalley and intravalley deformation potentials.

Monte Carlo simulation of transport in technologically significant semiconductors of the diamond and zinc-blende structures. I. Homogeneous transport

Monte Carlo simulations of electron transport in seven semiconductors of the diamond and zinc-blende structure (Ge, Si, GaAs, InP, AlAs, InAs, GaP) and some of their alloys (Al/sub x/Ga/sub 1-x/As, In/sub x/Ga/sub 1-x/As, Ga/sub x/In/sub 1-x/P) and hole transport in Si were performed at two lattice temperatures (77 and 300 K). The model uses band structures obtained from local empirical pseudopotential calculations and particle-lattice scattering rates computed from the Fermi golden rule to account for band-structure effects. Intervalley deformation potentials significantly lower than those which have been previously reported are needed to reproduce available experimental data. This is attributed to the more complicated band structures, particularly around the L- and X-symmetry points in most materials. Satisfactory agreement is obtained between Monte Carlo results and some experiments. >

Effective intervalley deformation potentials in the description of time-resolved and hot-electron luminescence

The concept of effective intervalley deformation potentials (IDPs) has been introduced to account for the k -dependence of the IDPs under actual experimental conditions. These effective IDPs obtained in GaAs, from the Γ L and Γ X scattering times, calculated using a theoretical description of the electron-phonon interaction in the rigid pseudo-ion approximation, compare well with different experimental results. This explains the wide range of experimental values of the IDPs quoted in the literature and is also useful in model simulations of the dynamics of hot-electron phenomena.

Microscopic theory of intervalley scattering in GaAs: k dependence of deformation potentials and scattering rates

The ‘‘rigid-pseudoion’’ model is applied to intervalley scattering processes in GaAs. The intervalley deformation potentials (IDPs) that we obtain at high-symmetry points are in good agreement with previous calculations. We find that the IDPs show a strong dependence on the wave vector of the intervalley phonon, therefore a numerical integration over the Brillouin zone (e.g., with the tetrahedron method) is necessary to obtain realistic scattering rates that can be compared with those obtained from experiments. We calculate the lifetimes of electrons at the L and X valleys as a function of temperature (L: 2.2±0.5 ps; X: 130±20 fs at room temperature) and discuss our results in comparison with recent ultrafast laser experiments and Monte Carlo simulations. Finally, the IDPs show an anisotropy that might be important when simulating electrical transport in hot-electron devices.