Distribution Functions for Hot Electrons in Many-Valley Semiconductors

The Boltzmann equation for electrons in many-valley semiconductors, with scattering by acoustical and optical lattice vibrations, is solved for high electric fields in the following two cases: (1) Intervalley-scattering is completely negligible. Then, in each particular valley, the distribution of the electrons over the energy is Maxwellian for energies of the electrons larger than the energy of an optical phonon. The corresponding electron temperature varies approximately with the square of the electric field strength and depends on the angle between the electric field and the longitudinal axis of the particular valley under consideration. The electron temperatures are therefore in general different in different valleys. The deviations of the electron distribution from the Maxwellian one for energies of the electrons smaller than the energy of an optical phonon are small. (2) If allowance is made for a transfer of electrons between different valleys a finite difference in the populations is set up even for infinitesimally small intervalley scattering rate. In addition to this, for finite intervalley rate, the electron distribution deviates from the original Maxwellian one. The deviation increases with increasing intervalley rate constant, increasing lattice temperature, and increasing difference of the average electron energies in the different valleys. Both of these effects of intervalley scattering are important for the explanation of the field dependence of the Sasaki effect.