High-Field Effects in Degenerate Nonparabolic Semiconductors: Collision Integral and Isotropic Distribution Function

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Abstract
Collision integrals for various modes of lattice scattering for nonparabolic semiconductors with an arbitrary degree of degeneracy of charge carriers have been derived, taking Pauli's exclusion principle into account. These expressions are used to obtain the isotropic part of the momentum distribution function of transport carriers subjected to a dc field for different cases of interest. This formulation avoids the use of the concept of effective carrier temperature in the calculation of transport and other properties of arbitrarily degenerate semiconductors. It is pointed out that the assumed form of the distribution function with effective carrier temperature and drift velocity in the case of parabolic piezoelectric semiconductors, which is used to investigate acoustic-wave amplification in the presence of high dc fields, is not justified for a wide upper range of applied dc fields. This is so because above a certain critical value of the dc field the distribution function obtained by solving the Boltzmann transfer equation is not normalizable. It is shown that the distribution function corresponding to the piezo-electric mode of lattice scattering can be normalized for any finite value of the applied dc field if the nonparabolicity of energy bands is taken into account (apart from the influence of nonequilibrium phonons on the normalization of the carrier distribution function).