The Einstein relation for degenerate semiconductors with nonuniform band structures

Modification of the Einstein equation for semiconductors with nonparabolic energy bands and doped nonuniformly with impurity atoms is suggested. The suggestion is based on a new approximation of the Fermi-Dirac integral of order 1/2, namely, F/sub 1/2/( eta /sub n/), where eta /sub n/ is the reduced Fermi level for electrons. The relation reduces to that for semiconductors with parabolic energy bands and doped uniformly with impurity atoms under appropriate boundary conditions. A comparison of the calculated and exact results for F/sub 1/2/( eta ) is found to be very encouraging.<
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