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.