Semiconductor Statistics

Abstract

In this chapter we present the three basic statistics which are commonly used in the derivation of distribution functions for gas molecules, photons and phonons, electrons in a metal, and electrons and holes in a semiconductor Without using these basic statistics, it is impossible to deal with the problems of interactions of a large number of particles in a solid. Since a great deal of physical insight can be obtained and learned from statistical analysis of the particle distribution functions in a solid, it is appropriate for us to devote this chapter to finding the distribution functions associated with different statistical mechanics for particles such as gas molecules, photons, phonons, electrons, and holes. The three basic statistics which govern the distribution of particles in a solid are: (1) Maxwell-Boltzmann (M-B) statistics,(2) Bose-Einstein (B-E) statistics, and (3) Fermi-Dirac (F-D) statistics. The M-B statistics are also known as the classical statistics, since they apply only to particles with weak interactions among themselves. In the M-B statistics, the number of particles in each quantum state is not restricted by the Pauli exclusion principle. Particles such as gas molecules in an ideal gas system and electrons and holes in a dilute semiconductor are examples which obey the M-B statistics. The B-E and F-D statistics are known as the quantum statistics because their distribution functions are derived based on quantum mechanical principles. Particles which obey the B-E and F-D statistics usually have a much higher density and stronger interaction among themselves than the classical particles.