Generation–recombination noise in uniformly doped semiconductors with contacts of finite surface recombination velocities

The formula for the voltage noise spectrum due to generation–recombination (G–R) rate fluctuations is derived for uniformly doped majority-carrier n-type semiconductor samples with contacts of finite surface recombination velocities. In the derivation of the formula, a new boundary condition with finite surface recombination velocities considered is used instead of the ohmic boundary condition. The G–R voltage noise spectra are calculated to become saturated and equal in the high electric field region irrespective of surface recombination velocities. However, the behaviors of slow surface recombination velocities in the low electric field region differ from those of fast ones. The profiles of the electron density fluctuations of slow ones differ significantly from those of fast ones in the low-field region. In the high field region, a steep rise in the magnitude of the electron density fluctuation occurs near the voltage contact toward which electrons drift. The various location dependencies of the contribution of noise sources to the voltage power spectral density are also derived for low and high field regions as well as low and high surface recombination velocities, and analytical expressions are developed for the voltage power spectral densities and electron density fluctuations.