An Overview of Transport of Electrons in Donor- Doped Silicon at Any Degree of Degeneracy of Electron Gas1

The general expressions, based on the Fermi distribution of the free electrons, are applied for
calculation of the kinetic coefficients in donor-doped silicon at arbitrary degree of the degeneracy of
electron gas under equilibrium conditions. The classical statistics leads to large errors in estimation of
the transport parameters for the materials where Fermi level is located high above the conduction
band bottom unless the effective density of randomly moving electrons is introduced. The obtained
results for the diffusion coefficient and drift mobility are discussed together with practical
approximations applicable for non-degenerate electron gas and materials with arbitrary degree of
degeneracy. In particular, the drift mobility of randomly moving electrons is found depend on the
degree of degeneracy and can exceed the Hall mobility considerably. When the effective density is
introduced, the traditional Einstein relation between the diffusion coefficient and the drift mobility of
randomly moving electrons is conserved at any level of degeneracy. The main conclusions and
formulae can be applicable for holes in acceptor-doped silicon as well.