Towards “atomistic” dopant profiling using SCM measurements

In this article we develop a mathematical algorithm for computing the spatial locations of ionized impurities in semiconductor materials using scanning capacitance microscopy (SCM) measurements. We show that SCM measurements can in principle be used to determine the coordinates of the doping atoms in a layer of a thickness equal to the width of the depletion region if the noise in the SCM measurements is extremely low. The proposed mathematical algorithm is based on computing the doping sensitivity functions (i.e. the Gâtaux derivatives) of the differential capacitance and using a gradient-based iterative method to find the locations of the ionized impurities.