A theoretical treatment is given of two dispersion phenomena in the field-effect experiment: (1) dispersion arising from the finite time required to generate minority carriers, and (2) relaxation of the fast surface states. It is shown that the in-phase part of the field-effect mobility is given (for an $n$-type semiconductor) by ${\mu }_{\mathrm{FE}}=-{\mu }_n+\frac{A}{(1+{\omega }^2{{\tau }_1}^2)}-\frac{B}{(1+{\omega }^2{{\tau }_2}^2)}$, where ($\frac{\omega }{2\pi }$) is the frequency of the applied field, $A$ and $B$ are constants, and ${\tau }_1$ and ${\tau }_2$ are characteristic times, all four quantities being functions of the body resistivity, surface potential, and of the densities, energy levels, and capture cross sections of the fast states. Under certain conditions, ${\tau }_1$ is equal to the fundamental decay-mode lifetime of the sample, while ${\tau }_2$ is expected to be much shorter, and depends primarily on the cross sections and the position of the state level in the gap. A comparison of the theory with recent experimental results of Montgomery shows (1) that reasonable agreement can be obtained, and (2) that the presence of any significant number of states in the region close to the center of the gap is unlikely.

• Received 29 March 1957

DOI:https://doi.org/10.1103/PhysRev.107.478