Phonon-scattering-limited electron mobilities inAlxGa1−xAs/GaAs heterojunctions

Abstract

We study the bulk-phonon-scattering contribution to the transport properties of a two-dimensional electron gas formed at the interface of an ultrapure ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs heterojunction. Assuming that the electrons only occupy the lowest subband, we calculate the mobility as a function of temperature for the temperature range T=1--300 K, within the variational-subband-wave-function model for carrier confinement. Our work encompasses three physically distinct temperature ranges with respect to phonon scattering: the Block-Gr\"uneisen (BG), equipartition (EP), and inelastic regimes. In the EP regime we calculate (i) the individual and total scattering rates ${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}1}$, and momentum relaxation rates ${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}^{\mathrm{\ensuremath{-}}1}$, due to deformation-potential and piezoelectric coupled acoustic-mode phonons, with screening of these rates taken into account within the static random-phase approximation; (ii) the acoustic-phonon-scattering limited drift mobilities ${\mathrm{\ensuremath{\mu}}}_{\mathrm{ac}}$ for different densities ${\mathit{n}}_{\mathit{s}}$ as a function of temperature T; (iii) the level of validity of Matthiessen's rule; and (iv) the dimensionless Hall ratio ${\mathit{r}}_{\mathit{H}}$. In addition, we investigate in detail the temperature dependence of the low-temperature mobility and find excellent agreement with experimental data for the linear coefficient \ensuremath{\alpha}=d${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}1}$(T)/dT of the temperature dependence as a function of density.We carry out similar calculations in the BG regime and compare the results with the corresponding ones in the EP regime. Finally, to evaluate the mobility in the inelastic regime at high temperatures above T\ensuremath{\approxeq}40 K, where the scattering from polar LO phonons becomes important, we compute the first-order perturbation distribution \ensuremath{\varphi}(E) as a function of the carrier energy E by directly solving the linearized Boltzmann equation by an iterative method. We compare these results with the commonly used closed-form approximations for \ensuremath{\varphi}: the low-temperature relaxation-time approximation ${\mathrm{\ensuremath{\tau}}}_{\mathrm{LT}}$, and the high-energy relaxation-time approximation ${\mathrm{\ensuremath{\tau}}}_{\mathrm{HE}}$, and check their level of validity.