TABLE OF CONTENTS The transport of carriers in semiconductors can be understood as the propagation of charged particles in an almost periodic lattice potential. The description of such transport phenomena from a mesoscopic point of view must be based on solid-state physics.
It is the aim of this chapter to give an overview of the quantum mechanical foundations of the particle transport in semiconductors. We present the Bloch-Boltzmann-Peierls equations, which constitute the governing set of evolution equations for the carrier and phonon distribution functions in such materials, and study their main properties. More detailed information on these topics are found, for example, in the books [Markowich et al. (1990); Lundstrom (2000); Ziman (2001); Tomizawa (1993); Fetter and Walecka (1971); Wei mantel and Hamann (1995); Ashcroft and Mermin (1976)].
Electrons in a semiconductor crystal move in a periodic crystal potential, which is formed by the potential of the atomic nuclei and that due to the other electrons. When studying the transport of electrons in such a crystal, one must consider an extremely complicated many-body problem [Fetter and Walecka (1971); Czycholl (2000)]. However, if attention is only paid to the motion of an electron in the crystal by assuming that the effects of the atomic nuclei and the remaining electrons on the selected electron can be approximated by a prescribed potential V( r) depending on the position r, the many-body problem reduces to the problem of a single electron. The potential V( r) must be...
