Many-Valley Dipole Scattering of Electrons in Germanium and Silicon

The theory of dipole scattering is developed for germanium and silicon, whose conduction-band structure can be described by a simple many-valley model. A formalism is used which employs a linear approximation to the distribution function, and is due to Herring and Vogt. It is shown that, in the approximation, an alternative approach due to Samoilovich et al. gives an identical result. The relaxation-time ratio $\frac{{\tau }_{\parallel }}{{\tau }_{\perp }}$ is computed as a function of energy and it is shown analytically that, as $E\to \infty$, $\frac{{\tau }_{\parallel }}{{\tau }_{\perp }}\to 3.69$. This is approximately the square root of the corresponding result for point ions. Thus the scattering due to dipoles is less sensitive to the anistropy of the energy surfaces than in the point-ion case. This can be explained by considering the form of the cross sections presented by each type of scattering center. Finally, some numerical work on the mobility and the effective anisotropy parameter is presented.