Model database for determining dopant profiles from scanning capacitance microscope measurements

To help correlate scanning capacitance microscope measurements of silicon with uniformly doped concentrations, model capacitance curves are calculated and stored in a database that depends on the probe-tip radius of curvature, the oxide thickness, and the dopant density. The oxide thicknesses range from 5 to 20 nm, the dopant concentrations range from 1017 to 1020 cm−3, and the probe-tip radius of curvature is set to 10 nm. The cone-shaped probe is oriented normal to the sample surface, so that the finite-element method in two dimensions may be used to solve Poisson’s equation in the semiconductor region and Laplace’s equation in the oxide and ambient regions. The equations are solved within the semi-classical quasistatic approximation, where capacitance measurement depends only on the charge due to majority carriers, with inversion and charge trapping effects being ignored. Comparison with one-dimensional-related models differs as much as 200% over the given doping range. For shallow gradient profiles satisfying quasiuniformity conditions, the database is used directly to find the doping profile. Converting a 512×512 point image takes less than 2 min.