Dynamical Response of Electrons in GaAs at 300 K

Abstract

Numerical calculations are made on the time response of the high-field electron distribution function a t T = 300 K in GaAs both for instantaneously and periodically varying electric fields.According to Rees the method of calculation is an iterative process due to Kellogg for solving a homogeneous Fredholm integral equation of the second kind derived from the Boltzmann equation. The time evolution of the average drift velocity, the mean energy of the electrons in the central valley, and the fraction of electrons in the satellite valleys is presented for an instantaneous appli. cation E ( t ) = E O ( t ) of the electric field. Finally the time dependence of the average drift velocity and the satellite valley population fraction is calculated for a sinusoidal electric field E(t) = E,, x x sin ot with Eac = 5 kV/cm and o = 2.2 x 1011 rad/s. The results obtained are discussed, taking into account the band structure and the effective scattering processes. Es werden numerische Berechnungen zum zeitlichen Verhalten der Verteilungsfunktion heiDerElektronen fur T = 300 K in GaAs sowohl bei stufenformiger als auch bei periodischer VerLnderung des elektrischen Feldes durchgefuhrt. Die Methode der Berechnung besteht nach Rees darin, die in eine homogene Fredholmsche Integralgleichung der zweiten Art umgeformte Boltzmann-Gleichung durch ein Kelloggsches Iterationsverfahren zu losen. Fur stufenformig verLnderliches elektrisches Feld E(t) = E . O(t) wird die zeitliche Entwicklung der mittleren Driftgeschwindigkeit, der mittleren Energie der Elektronen im Zentraltal sowie der Elektronenubergangsrate in die Satellitentiler des GaAs angegeben. Fur ein periodisch verLnderliches elektrisches Feld der Form E ( t ) = Eac . sin ot wird die ZeitabhLngigkeit der mittleren Driftgeschwindigkeit und der Elektronenubergangsrate in die Satellitentiiler fur E,, = 5 kV/cm und o = 2,2 x 10l1 rad/s berechnet. Die erhaltenen Resultate werden an Hand der Bandstruktur und der wirksamen Streuprozesse diskutiert.

Hot-electron transient and terahertz oscillations in graphene

“…Finally, in compound semiconductors, the oscillation onset is restricted by two conflicting conditions: On the one hand, the low value of the OP energy (hω OP : 0.04 eV) is comparable to the thermal broadening of the carrier distribution at room temperature so that the back-and-forth motion of the distribution between the optic phonon and the zero-point energy is immediately damped. 8,10,11 On the other hand, at low temperature, ionized impurity scattering becomes dominant and produces strong damping, which can only be reduced by lowering the dopant density, thereby lowering the carrier density, and weakening the oscillation amplitude. In this respect, the high conductance of graphene and the high optic phonon energy provide the conditions for room-temperature observation.…”

“…9 However, their manifestation in these materials is different in several respects: First, owing to the carrier parabolic energy-momentum dispersion, the oscillation periodicity in GaAs is instead given by τ GaAs = 2m * hω GaAs OP /eF . 8,10,11 Second, and more importantly, in III-V semiconductors, the oscillation onset is restricted by two conflicting conditions: On the one hand, the low value of the OP energy (hω OP ∼ 0.04 eV) (Ref. 12) is comparable to the thermal broadening of the carrier distribution at room temperature so that the back-and-forth motion of the distribution between the optic phonon and the zero-point energy is immediately damped.…”

“…For this purpose, we use the Boltzmann formalism, and solve for the steady state and the time-dependent carrier distribution in the presence of OP scattering. 8,10,11 Since both intravalley and intervalley scattering can be treated within the deformationpotential interaction model, 13 we use an overall transition rate accounting for both mechanisms. We also account for low-energy scattering such as impurities and acoustic phonons by using the relaxation time approximation, 14 but we ignore the dissipation effects due to the environment such as remote phonons, 15 detrimental to the occurrence of the oscillations, which limits their observations optimally to suspended graphene or nonpolar substrate.…”

Hot Electron Terahertz Oscillations in Graphene: Crater and Terraces in the Carrier Distribution Function

“…For this purpose, we use the Boltzmann formalism, and solve for the time-varying carrier distribution in the presence of OP scattering. [8][9][10] We also account for low energy scattering such as impurities and acoustic phonons, by using the relaxation time approximation. In weak concentrations (n c 10 11 cm −2 ), electron-electron interactions do not play a major role in transport in graphene, 11 and are not included in this analysis.…”

“…Finally, in compound semiconductors, the oscillation onset is restricted by two conflicting conditions: On the one hand, the low value of the OP energy (hω op : 0.04eV ) is comparable to the thermal broadening of the carrier distribution at room temperature so that the back and forth motion of the distribution between the optic phonon and the zero point energy is immediately damped. [8][9][10] On the other hand, at low temperature, ionized impurity scattering becomes dominant and produces strong damping which can only be reduced by lowering the dopant density, thereby lowering the carrier density, and weakening the oscillation amplitude. In this respect, the high conductance of graphene, and the high optic phonon energy provide the conditions for room temperature observation.…”