PHT.301 Physics of Semiconductor Devices

Fermi energy of an intrinsic semiconductor

For 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_BT ~ 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.