Semiconductors in Equilibrium

Abstract

A relation between equilibrium concentrations of electrons and holes and the value of the Fermi energy is obtained within Boltzmann approximation and used to derive the mass action law. A distinction between the conductivity effective mass and the density of states effective mass is made. The concentration of charge carriers in an intrinsic semiconductor is obtained. The common method to control the type and concentration of charge carriers is by doping a semiconductor with donor and acceptor impurities. The concentrations of ionized and neutral impurities are derived and related to the concentrations of the charge carriers via the charge neutrality equation. The three ionization regimes in a semiconductor are the intrinsic regime, the complete ionization regime, and the freeze-out regime. They are realized depending on the temperature of the material. Analytical expressions for the charge carrier concentrations at not too high temperatures are obtained.