Highlighting non-parabolic bands in semiconductors

Abstract

The parabolic approximation to the dispersion relation is a simplification that has often been adopted for the electronic band structure of most semiconductors near the edges of the fundamental bandgap. A non-parabolic approximation can be justified which will better describe the properties of semiconductors of narrow bandgaps for which a reduction to a quadratic form is not accurate enough, nor always warranted. It also stands for a better approximation in III–V compounds and for more complex thermoelectric materials. Some of the consequences of adopting non-parabolic bands will be highlighted, as well as approximate expressions for statistical properties. It is emphasized that many properties of semiconductors are not difficult to calculate with non-parabolic bands, which may have a wider range of applications in actual materials. These calculations can then be introduced in solid state physics and statistical physics courses through projects and homework problem sets. Specific examples are discussed designed to clarify basic physics concepts in semiconductors.