Calculation of semiconductor intrinsic properties using a nonparabolic three-band model

The intrinsic carrier concentration and the Fermi level are calculated using an approximation of the three-band k·p model. The approach is suitable for temperatures from 0 to 400 K and includes the contribution of electrons in the lowest conduction band, heavy holes, and light holes. An approximation for the nonparabolic Fermi-Dirac integral is used in the calculation of carrier concentrations. The resulting expressions are simple and depend explicitly on temperature, semiconductor band gap, carrier effective masses, and nonparabolicity factors. Consequently, the present approach seems suitable for the calculation of intrinsic properties of any semiconductor material for which the three-band k·p model is applicable. The model is compared with a numerical integration of the k·p model for Hg _1-xCd_xTe (0.17<x<1) and with experimental measurements (0.2<x<0.29). We also present a comparison between the model and a numerical evaluation of the three-band model for InGaAs. Because of their simplicity the new expressions seem suitable for both numerical and analytical modeling of semiconductor devices and materials.