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 ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$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-Grüneisen (BG), equipartition (EP), and inelastic regimes. In the EP regime we calculate (i) the individual and total scattering rates ${\mathrm{\tau }}_{\mathit{s}}^{\mathrm{-}1}$, and momentum relaxation rates ${\mathrm{\tau }}_{\mathit{t}}^{\mathrm{-}1}$, 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 ${\mathrm{\mu }}_{\mathrm{ac}}$ 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 α=d${\mathrm{\mu }}^{\mathrm{-}1}$(T)/dT of the temperature dependence as a function of density.