Depletion layer and contact capacitance in non-uniformly doped semiconductors

We consider the dependence of the capacitance C of the semiconductor depletion layer versus the contact bias V. When the concentration of doping impurities varies in the plane parallel to the contact, we show that the standard Schottky dependence C?2(V) is no longer a straight line. We compute the effective concentration Neff from the slope of the dependence C?2(V) by using the perturbation and variation methods and compare Neff with previous theoretical and experimental data.