Summary of the Basic Free Electron Transport Characteristics in Donor Doped Silicon

Abstract

A present summary is assigned to present the transport characteristics of the free randomly moving (RM) electrons in silicon at any doping level by phosphorous donors. The application of the Fermi-Dirac statistics and stochastic description of the free RM electrons lead to obtaining the general expressions of conductivity, the effective density of the free RM electrons, their diffusion coefficient and the drift mobility, which are valid for silicon with any doping level. It is shown that drift mobility of the free RM electrons considerably exceeds the Hall mobility at heavy doping, and that the Einstein relation is fundamental and is conserved at any level of degeneracy. It is estimated what part of electrons in the conduction band of heavily doped silicon is not free and is coupled with phosphorous ions. The main conclusions and formulations can be applicable for holes in acceptor-doped silicon, and other homogeneous materials with one type of the free RM charge carriers as well.