Doping changes the Fermi energy of a semiconductor. Consider silicon, with a gap of 1.11 eV between the top of the valence band and the bottom of the conductionband. At 300 K the Fermi level of the pure material is nearly at the midpoint of the gap. Suppose that silicon is doped with donor atoms, each of which has a state 0.10eV below the bottom of the silicon conduction band, and suppose further that doping raises the Fermi level to 0.075 eV below the bottom of that band (see the figurebelow). For (a) pure and (b) doped silicon, calculate the probability that a state at the bottom of the silicon conduction band is occupied. (c) Calculate the probabilitythat a donor state in the doped material is occupied.Conduction bandFermiDonor1.11 eVlevellevelValence band

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