The increasing demand on ultra miniturized electronic devices for ever improving performances has led to the necessity of a deep and detailed understanding of the mathematical theory of charge transport in semiconductors. Because of their very short dimensions of charge transport, these devices must be described in terms of the semiclassical Boltzmann equation coupled with the Poisson equation (or some phenomenological consequences of these equations) because the standard approach, which is based on the celebrated driftdiffusion equations, leads to very inaccurate results whenever the dimensions of the devices approach the carrier mean free path
