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 is considered. 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. Known tests do 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 is the application of the algorithm for degenerate conditions to obtain a functional evaluation of the degeneracy factor in terms of normalized acceptor and donor energy level differences.