Effective-Mass Theorems, Envelope Function, and Semiclassical Dynamics

Abstract

The subject treated in this chapter is of extreme importance to understand electron transport properties in semiconductors and in solid state in general. In fact, it will be shown that, in spite of the crowded presence of atoms in solids, electrons can move freely, in absence of imperfections, owing to the wave nature of their dynamics combined with the periodicity of the atom positions. The periodic potential in the crystal has the effect that the momentum of the electron is no more a good quantum number and it must be substituted by the crystal momentum. Furthermore, the relation between kinetic energy and momentum, which for free electrons is given by the parabolic dependence p ² /2m _o , must be substituted by the relation between energy and crystal momentum, given by the band Є _n (k).