APPROXIMATIONS FOR CARRIER DENSITY IN NONPARABOLIC SEMICONDUCTORS

We propose simple, analytic approximations that describe properties of semiconductors with nonparabolic energy bands. The approach is based on the two-level k.p model of the semiconductor statistics which includes effects of band nonparabolicity and carrier degeneracy. The new expressions are in the form of a correction to the classical, Boltzmann's approximation of the semiconductor statistics and do not introduce any new adjustable parameters. These relations can be applied to both narrow- and wide-bandgap nonparabolic semiconductors. First, we derive expressions for semiconductor intrinsic properties, n.p product, and the Einstein relation. Then, we solve a one-dimensional Poisson's equation and obtain an analytical model of the total semiconductor charge. Finally, we calculate the low-frequency capacitance of a nonparabolic MIS structure and compare the results with an accurate numerical model and experimental measurements of a HgCdTe capacitor. The solution includes the contribution of both types of carriers and the effect of impurity freezeout. The new approximations should be useful for characterization and modeling of semiconductor devices with nonparabolic energy bands.