An exact solution of the linearized Boltzmann equation with applications to the Hall mobility and Hall factor of n-GaAs

Abstract

An exact method is given for solving the linearized Boltzmann equation for arbitrary magnetic field strengths in the presence of polar mode scattering and elastic scattering mechanisms. The perturbed distribution function shows slope discontinuities at all multiples of the polar phonon energy. The Hall mobility of n-GaAs is calculated and the results obtained are within 10% of the experimental values throughout the temperature range 9-400K. The calculated Hall number is also in good agreement with experiment at high magnetic fields but is about 5% too large at low fields.