Scattering of Electrons by Lattice Vibrations in Nonpolar Crystals

Abstract

A theoretical analysis of the scattering of electrons by lattice vibrations in nonpolar crystals is made which permits an estimate of the relative importance of acoustical-mode and optical-mode scattering in monatomic nonmetals. This comparison is achieved by expanding the matrix elements for scattering in powers of the electron wave number. Individual terms are examined in the light of crystal symmetries and the nature of the band minimum associated with the carriers. The order of the first nonvanishing term is obtained in each case. The temperature dependence of the mobility as indicated by these results is compared with that observed in the cases of electrons and holes in silicon and germanium. The observed dependence upon temperature is understandable in terms of the expected relative importance of acoustical- and optical-mode scattering in the cases of holes in silicon and germanium and electrons in germanium. In the case of electrons in silicon, optical modes are not expected to contribute appreciably and the strong temperature dependence must arise from some other mechanism, presumably intervalley scattering. The relation between the results obtained here and those of deformation-potential theory is discussed briefly.