Evaluation of some transport integrals. IV. Nonparabolic bands

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Abstract
Formulas are presented for the practical evaluation of transport and related integrals for conduction in a single nonparabolic band of the simplest type: k ∝(ε+ε2/εg)1/2. It is shown that when Maxwell‐Boltzmann statistics apply, these integrals may be evaluated in terms of modified Bessel functions plus a single additional function. For the Fermi‐Dirac region, approximation formulas for small εg are given, complementing those for large εg found in the literature. It is shown how further approximations may be found using the Laplace transform technique. As an example, the Faraday rotation due to free carriers is considered. It is pointed out that nondegeneracy of the carriers does not mean that effects of nonparabolicity are negligible.

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