High-Field Transport in $n$- Type GaAs

We have solved the coupled Boltzmann equations for the electron distributions in ${\Gamma }_1$ and $X_1$ minima of GaAs under a set of approximations that are fair for fields around the beginning of the negative-differential-resistance region, but should be quite good at higher fields. Intervalley, polar and other relevant intravalley scattering processes have been included. Nonparabolicity of the central minimum has been taken into account. The effect of space-charge scattering has also been considered. From the distributions, we have calculated as functions of field the average drift velocity, the variation of the valley populations, diffusion constants, and mobilities in each of the valleys, etc. The validity of the principal approximations made, such as neglect of the $L_1$ minima, is discussed. The present experimental situation is examined, and some tentative explantations are offered for the large differences between the various measurements of drift velocity versus field.