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This and the next problem summarize the equation and methodology used by physicists to calculate NDD, NAA, ED and gD in a semiconductor from a set of N versus T data from very low temperatures to above Ti.

Using the mass action law for all the equilibrium reactions present In this problem, derive the general cubic equation for the electron concentration. In a nondegenerate semiconductor that has NDD > NAA ≠ 0 which is valid at all temperatures.

Obtain the quadratic equation and the explicit analytical solution for N which is valid at all temperatures below the intrinsic temperature.

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