Method of determining C-V profiles in semiconductor substrates and active layers

A method for calculating C-V profiles by transforming the one-dimensional Poisson equation from a two-sided boundary value problem to an initial value problem is described. An analytic solution is used outside a reference plane deep in the substrate, and the rest of the solution is obtained by numerically integrating outward to the surface. This strategy speeds the calculation of quantities such as the carrier density and the apparent density that would be measured by a C-V profiler. For the same computation time, errors are smaller than those of Newton-Raphson methods because of the inherent speed and accuracy of the predictor-corrector algorithms used. By fitting Q-V pairs to a cubic spline, the C-V profiles are obtained efficiently with a moderate number of integrations. C-V profiles and threshold voltages can be calculated rapidly and accurately by this technique for a variety of semiconductor structures.<
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