Question

The equilibrium electron concentration is given by the product of density of states and probability function, n(E) = g_c(E)F(E)n(E)=gc​(E)F(E) whereg_c(E)gc​(E) and F(E)F(E) are the conduction band density of states and Fermi-Dirac probability function, respectively

Using the full expression of Fermi-Dirac function, calculate the energy relative to the conduction band edge, E-E_cE−Ec​, at which the electron concentration becomes maximum. This semiconductor has a bandgap of 1.124 eV and the temperature is 300 K. Further assume that the Fermi level, E_FEF​ is located precisely at the middle of the bandgap, i.e. E_C - E_F = \frac{E_g}2EC​−EF​=2Eg​

Answer 1

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