Modified Form of Energy Distribution Function for Hot Carriers in Polar Semiconductors at High Temperatures: Inclusion of Higher-Order Terms

Abstract

We examine the convergence of the Legendre-polynomial expansion of the distribution function for hot carriers in polar semiconductors at high temperatures and come to the conclusion that degeneracy makes the expansion converge more rapidly and that the inclusion of higher-order terms is indeed important especially at high electric fields, and opposes the cooling effect of nonparabolicity. A comparative study of some important galvanothermomagnetic transport coefficients (GTMTC) reveals an essentially unchanged electric-field variation; nevertheless, the isothermal electrical conductivity and the isothermal Hall coefficient exhibit an almost linear dependence at moderately high electric fields. The rest of the GTMTC exhibits a small quantitative effect along with a reduced sensitivity to the electric field. The theoretical results are applicable to hot-electron experiments at lattice temperatures much higher than the Debye temperature where the Boltzmann-equation-solution approach is applicable and also under conditions where the distribution starts diverging from the nearly isotropic to the elongated distribution.