Low-field galvanomagnetic transport at an n-AlGaAs/GaAs heterojunction: I. Analysis

Abstract

An analysis is presented for computing the low-field galvanomagnetic coefficients of the quasi-two-dimensional electron gas confined to the GaAs side of a modulation-doped AlGaAs/GaAs heterostructure. The model of confinement uses Ando's prescription for band bending and a variational wavefunction, with modification for finite-depletion regions in the active and doped layers, and with provision for a spacer layer. The method for solving the Boltzmann equation is based on the accurate numerical procedure developed for polar bulk semiconductors, namely expansion of the distribution function in degrees of anisotropy and in powers of the electric and magnetic field strengths, followed by iterative solution of the resulting coupled difference equations for the departures of the distribution from equilibrium. Analytic expressions are given for the rates of lattice scattering by acoustic deformation potential and piezo-electric mechanisms and by the polar optical mechanism, and for impurity scattering by both background and remote ionised impurities. The degeneracy of the electron distribution has been taken into account, as well as some effects of carrier screening and nonparabolicity of the bands. The predictions of this analysis for a realistic heterostructure are reported in the accompanying paper.