Carrier Statistics

Abstract

The total number of free electrons and holes in a semiconductor as well as their distribution over the energy levels depend on the doping level, the density of states in the conduction and the valence band, and the temperature, which enters via the distribution functions of statistical physics (Fermi–Dirac or Boltzmann, depending on carrier concentration). Interesting insights are provided by the “law of mass action” which tells that the product of electron and hole concentrations in thermal equilibrium is independent of the doping level. It follows that the lowest possible total carrier concentration at a given temperature is realized in the intrinsic case and that a “highest possible resistivity” of a semiconductor material can be specified, strongly depending on the bandgap. This highest possible resistivity can be realized for certain applications in so-called “semi-insulating” materials. Carrier statistics explain why Si cannot be used for high-temperature electronics. For this application, high bandgap materials like SiC are required.