Impedance of thin semiconductor films in low electric field

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Abstract
Impedance and admittance of a thin semiconductor film in the direction perpendicular to the film is calculated as a function of the sample length, doping, and temperature for voltages smaller than the thermal voltage. The calculation is based on the approximate solution of the Boltzmann equation in the relaxation time approximation. When the sample length is smaller than the mean free path, the conductance becomes independent of the sample length. In this limit the inductive susceptance is proportional to the sample length. When the sample length becomes comparable to the mean free path, the inductive susceptance reaches the maximum value, and then decreases. Our calculation shows that for high mobility GaAs samples at 77 K, the size effect may be important for films thinner than 5 μm. The results of the calculation are interpreted in the frame of a simple equivalent circuit which includes the bulk resistance, in series with the resistance due to the finiteness of the sample length, in series with the inductance L due to the inertia effect of the carrier transport, and all in parallel with the geometric capacitance C. The sample inductance L is approximately equal to (ω2pC)−1 where ωp is the plasma frequency. This simple model agrees fairly well with the results of the numerical calculation. The calculation, based on the model demonstrates that the predicted effects can be observed for realistic values of the contact resistance.