Influence of the acoustic phonon scattering anisotropy on the distribution function and the electronic transport in n-Si

The Herring-Vogt transformation is ordinarily used in many-valley semiconductors to reduce the ellipsoidal surfaces of constant energy in each valley α to spheres. As a result effective electric and magnetic fields, E^*and H^*respectively, are introduced in each valley α. For E^*⊥H^*these two fields are the only parameters needed to describe the properties of the electrons in the valley α for isotropic scattering. For that reason and to simplify the Monte Carlo calculations previous authors have mostly introduced the equivalent isotropic acoustic phonon scattering (APS). The present Monte Carlo calculations are performed for n-Si at 27K. It is shown that the electronic properties in valley α (the mean velocity v^*,the mean energy {Mathematical expression}, the intervalley scattering time τ, etc.) depend on the orientation of the E^*and H^*to the principal axes of the valley α, if the APS anisotropy is taken into account. In particularly, τ may changes by one order of magnitude under the rotation of vectors E^*or H^*.But the dependence of τ on {Mathematical expression} is almost universal function, which depends only on the scalar H^*. For a fixed {Mathematical expression} the heating of the high energy electrons increases and τ decreases considerably as H^* increases. The negative differential conductivity of N-type for H=0 and S-type for a strong magnetic field are more pronounced for current along [100] axis if the APS anisotropy is taken into account.