Room-Temperature Conductivity Anisotropy and Population Redistribution in $n$-Type Silicon at High Electric Fields

Theoretical expressions have been derived for the high-field mobility of carriers in $n$-type Si for any arbitrary direction of field. The distribution function of the electrons in a valley has been assumed to be Maxwellian, and scattering by intravalley acoustic and two types of intervalley phonons have been considered. The conductivity anisotropy for room temperature obtained from theory is of the same order as found experimentally. The population ratio is, however, found to be in disagreement with the values obtained from the analysis of experimental results. A plausible explanation for this disagreement is also presented.