TITLE:
Transport of Electrons in Donor-Doped Silicon at Any Degree of Degeneracy of Electron Gas
AUTHORS:
Vilius Palenskis
KEYWORDS:
Donor-Doped Silicon, Electrical Conductivity, Thermal Noise, Einstein Relation, Diffusion Coefficient, Drift Mobility, Hall Mobility
JOURNAL NAME:
World Journal of Condensed Matter Physics,
Vol.4 No.3,
August
15,
2014
ABSTRACT: 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 lead to large errors in estimation of the transport
parameters for the materials where Fermi level is located high above the
conduction band edge 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 to
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.