Transport Properties

Electrons are spin 1/2 particles and therefore obey the Pauli exclusion principle which states that no two spin 1/2 particles can occupy the same one particle quantum state. Consequently their populations are arranged in a Fermi-Dirac distribution. According to Fermi-Dirac statistics at zero temperature T = 0 K, the electrons in a metal fill all possible states up to the Fermi level. The density of states can be calculated from a band structure model and in this highly degenerate case, an energy integration from the bottom of the conduction band to an energy for which all the electrons are accommodated determines the Fermi level. In intrinsic semiconductors, at T = 0 K electrons fill the valence bands and none occupy the conduction bands. Semi-metals and highly doped semiconductors at finite but low temperatures are also degenerate but their population distributions are somewhat different from those of a metal. In this chapter we will discuss the statistics and transport properties of narrow gap semiconductors.