Calculation of Fermi Energy and Bandtail Parameters in Heavily Doped and Degenerate n-Type GaAs

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Abstract
The second-order perturbation method of Parmenter and the theories of Kane and of Halperin and Lax are employed to calculate self-consistently the conduction band density of states in heavily doped n-type GaAs using a screened Coulomb potential for impurity atoms. The three models all show that the total number of states in the tail is small compared to the total number of electrons even though the detailed structure of the bandtails are substantially different. Consequently, the position of electron Fermi level relative to the shifted band edge and other bandtail parameters such as the carrier screening length and the bandshift due to Coulomb interaction can be calculated with sufficient accuracy using parabolic density of states. Because of omission of the kinetic energy of localization, Kane's theory predicts a larger density of states in the tail than does the theory of Halperin and Lax. The condition for the validity of the calculation is that the impurity concentration be approximately equal or greater than 6×1017 cm−3 at 300°K or 2×1017 cm−3 at both 77° and 20°K.