Scattering of Electrons by Phonons and Impurities in Semiconductors

A theory is developed for the mobility of an electron in an $n$-type semiconductor under the combined scattering of phonons and impurities. An attempt is made to combine the two processes in a rigorous manner by treating the effects of impurities as though due to an applied external field. Although in principle a solution for any value of $\tau$, the phonon scattering relaxation time, should be possible, this paper only arrives at a limiting law for the mobility at small values of $\tau$. In the region of applicability satisfactory agreement with experiment is achieved.