Fermi Dirac level:

Sol. The Fermi level is simply a reference energy level. It is the energy level at which the probability of finding an electron n energy unit above it in the conduction band is equal to the probability of finding a hole n energy units below it in the valence band. Very simply, it can be considered to the average energy level of the electrons, as illustrated in fig. (a). For simplification let us assume that (i) widths of energy bands are  small in comparison to forbidden energy gap between them (ii) all levels in a band have the same energy, bandwidths being assumed to be small (iii) energies of all levels in valence band are E0, as shown in fig. (a) and (iv) energies of all levels in conduction band are EG. Let the zero energy reference level be taken arbitrarily at the top of the valence band, as shown in fig. (b). Now number of electrons in conduction band, where P represents the probability of an electron having energy EG. Its value may be determined from Fermi Dirac probability distribution function given as where P (E) is the probability of finding an electron having any particular value of energy E.