1. When the Boltzmann approximation is valid for computing the electron concentration, is it also valid for computing the hole concentration? Give two examples, one showing the true and the other, the false answer.
2. The electron concentration, N=NCexp[-(EF-EC)/kT], and hole concentration, P=NVexpl-(EC.-EF)/kT), were derived based on four assumptions. What are these assumptions? Why are they made? And how are they justifiable?
Partial answers: large crystal, spherical energy band, large band width, Boltzmann. For engineering inclined students who want to get the analytical expressions and accurate numerical criteria for these four approximations, do the following four problems or look up their solutions in an advanced semiconductor physics textbook. The derivations require only straight forward algebra and elementary mathematics and functions.)