An Exact Analysis For Freezeout And Exhaustion In Single Impurity Semiconductors

In this paper, a complete analytical description for an exact expression for temperature dependence of the majority carrier in a single-impurity, equilibrium semiconductor is proposed. Analysis establishes that the problem is solvable exactly by identifying the only physically possible root to a cubic equation. This model provides an attractive alternative to approximate standard classroom approaches for this topic covered in senior and first year graduate level solid state courses in physics and electrical engineering.