Analytical method for selecting random scattering angle for polar or acoustic phonon scattering of central valley conduction band electrons in GaAs

The introduction of nonparabolicity to the electron conduction band structure of GaAs produces scattering angle probability distributions which seem to be non-invertible for finding the scattering angle ß from a uniformly distributed random number r. The paper shows that an exact analytical inversion can be obtained for the acoustic phonon-electron scattering process in the central (000) valley based on scattering transition rates. For the polar optical phonon-electron scattering process, an exact inversion is proven to be impossible in the (000) valley, but analytical inversions are found in regions formed by constant energy surfaces in momentum k space. These results can be applied to Monte Carlo numerical techniques for finding electron transport behaviour in GaAs devices.