In the approximation of displaced Maxwell electron distribution functions, the relative importance of the various lattice scattering processes to energy and momentum relaxation is investigated theoretically for $n$-type GaAs as a function of electric field, taking into account the nonparabolic structure of the (0,0,0) valley. In this valley, at room temperature, energy and momentum relaxation is found to be governed by polar optical scattering below ∼7 kV/cm and by nonequivalent intervalley scattering between the (0,0,0) and (1,0,0) valleys above (for a deformation potential of 5×${10}^8$ eV/cm). In the (1,0,0) valleys, polar intravalley and equivalent and nonequivalent intervalley scattering are significant for the energy relaxation in like manner, whereas equivalent intervalley scattering is predominant for the momentum relaxation (for an equivalent intervalley scattering constant of ${10}^9$ eV/cm). The conservation equations for energy, momentum, and particle number are used to calculate the field-dependent relative population of the (1,0,0) valleys, the mobilities, the electron temperatures, the diffusion coefficients, and the field dependence of the average drift velocity; the effect of nonparabolicity on these results is discussed. Evidence is found against a nonequivalent intervalley-scattering deformation potential as low as 1×${10}^8$ eV/cm.

• Received 4 October 1968

DOI:https://doi.org/10.1103/PhysRev.178.1319