Impedance of a semiconductor surface at flat band condition

The ac surface impedance of a homogeneously doped semiconductor is calculated for the dc bias resulting in flat energy bands and assuming thermal equilibrium of the dc carrier distributions. This special case is distinguished by the availability of a complete solution for any bulk lifetime for the small signal linearized case. Two basic modes of ac carrier distributions arise which represent, respectively, a Boltzmann distribution, and (in the limit of long lifetime of minority carriers) the distribution associated with minority carrier injection. The relative intensities of the two modes are determined by the boundary conditions for the electron and hole currents. Two cases are treated in some detail: 1) photoconductivity induced by modulated light at the flat band condition, and 2) electron-hole generation in surface states of the Shockley-Read type by an applied ac field. The results are applied mainly to the case that the signal frequency is low compared with the inverse bulk relaxation time. However, interesting changes in the induced carrier distributions arise if both frequencies become about equal.