Analytic Tests for a Robust Numerical Algorithm for Predicting Semiconductor Freeze-out and Exhaustion

In this report a complete analytic description for the temperature dependence of the majority carrier in a single impurity doped equilibrium semiconductor is proposed. This model should provide an attractive alternative to commonly used rules predicting the temperature boundaries for the exhaustion regime. This model is used to provide a confidence test for a less restrictive robust numerical model recently proposed in the literature. Both the analytic description and results for the numerical algorithm are compared under a variety of assumed conditions including band-gap narrowing. Limitations of the analytic model are also clarified. Key-Words Semiconductor, simulation, exhaustion, freeze-out