The complex capacitance of Si inversion layers in the quantized resistance regime

We report the results of an examination of the complex capacitance of Si inversion layers at low temperatures and kHz frequencies in the quantized resistance regime. We also discuss the results for the capacitance without a magnetic field and in a non-quantizing magnetic field. We find that the one-dimensional diffusion model as discussed by Stern is adequate for the discussion of the latter cases, but does not describe the quantizing case. A description is given which may be a basis for deriving the density of states and the contribution of both the localized and extended states.