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Considerations for predicting freezeout and exhaustion under a variety of nontrivial conditions

A numerically robust method for evaluating the temperature dependent carrier concentrations and related Fermi levels has been proposed. The method is applicable to simple cases for which analytic solutions are available as well as more complex cases in which numerical methods are required due to nonstandard effects including bandgap widening, compensation and degeneracy induced by high levels of doping. The tests presented in the earlier paper [1998] did not focus on the use of the algorithm under conditions of high level doping. A degeneracy correction factor was defined as the essential ingredient in the algorithm that gauges the levels of degeneracy. For the trivial case of nondegenerate conditions the degeneracy factor is approximately one. The critical component in the application of the algorithm for degenerate conditions is to obtain a functional evaluation of the degeneracy factor in terms of normalized acceptor and donor energy level differences.