Solution of Boltzmann's equation for semiconductors using a spherical harmonic expansion. (Acoustic phonon scattering)

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Abstract
A method of solution of the steady state Boltzmann equation for small fields using a spherical harmonic expansion of the nonequilibrium part of the distribution function has been derived for acoustic phonon scattering in nondegenerate semiconductors. The method is easy to apply for arbitrarily complicated scattering functions and has some other advantages over previous treatment. It is possible to extend the method to include other scattering mechanisms and the effects of a magnetic field. Applications to silicon and germanium are discussed. As a by-product, a new sum rule for Clebsch-Gordan coefficients is derived.