Solution of the Boltzmann equation for calculating the Hall mobility in bulk Ga Nx As1-x

The ladder method for solving the linearized Boltzmann equation is developed to deal with a nonparabolic conduction band. This is applied to find the low field Hall mobility of electrons in bulk Ga Nx As1-x using the band-anticrossing model, which predicts highly nonparabolic energy dispersion relations. Polar optical, acoustic phonon, piezoelectric, ionized impurity, neutral impurity, and nitrogen scattering are incorporated. In finding an exact solution to the linearized Boltzmann equation, we avoid the unrealistic assumption of a relaxation time for inelastic scattering via polar optical phonons. Nitrogen scattering is found to limit the electron mobility to values of the order 1000 cm2 V-1 s-1, in accordance with relaxation time approximation calculations but still an order of magnitude higher than measured values for dilute nitrides. We conclude that the nonparabolicity of the conduction band alone cannot account for these low mobilities.