PHT.301 Physics of Semiconductor Devices  

Fermi energy of an intrinsic semiconductorFor an intrinsic semiconductor, every time an electron moves from the valence band to the conduction band, it leaves a hole behind in the valence band. The density of electrons in the conduction band equals the density of holes in the valence band. Here N_{c} is the effective density of states in the conduction band, N_{v} is the effective density of states in the valence band, E_{F} is the Fermi energy, E_{c} is the conduction band edge, E_{v} is the valence band edge, k_{B} is Boltzmann's constant, and T is the temperature in K. Rearranging this equation yields, Take the logarithm, Solve for E_{F}, The Fermi energy is in the middle of the band gap (E_{c} + E_{v})/2 plus a small correction that depends linearly on the temperature. The correction term is small at room temperature since E_{g} ~ 1 eV while k_{B}T ~ 0.025 eV. For Si and Ge, N_{c} > N_{v} and the correction term is negative while for GaAs N_{c} < N_{v} and the correction term is positive. 