Current, carrier concentration, Fermi energy, and related properties of binary compound polar semiconductors with nonparabolic energy bands

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Abstract
Using Kane’s energy–wave-vector relation (k.P model), it is shown that the nonparabolic band structure of binary compound polar semiconductors (BCPSCs) is, in fact, a perturbed parabolic band structure. The formula for this ‘‘parabolic’’ band structure is used to derive current, carrier concentrations, Einstein equation, and others. The formula for the Einstein equation is found to be of the same form as that for wide-gap semiconductors. Simplified relations for nonparabolicity coefficients have been derived. It is shown that these coefficients compare well with similar coefficients derived earlier from different considerations. Numerical calculations of effective mass, density of states, Fermi energy, and electron-impurity interaction energy have been carried out for a number of representative compounds. Good correspondence of theoretical results with available experiments indicates that the present model is quite useful for describing properties of BCPSCs.