Regression Procedure for Determining the Dopant Profile in Semiconductors from Scanning Capacitance Microscopy Data
Jay F. Marchiando, Joseph Kopanski
To develop a regression procedure to correlate scanning capacitance microscope data with dopant concentration in three dimensions, the inverse problem is treated in two dimensions as an optimization problem that is formulated as a regularized nonlinear least-square problem, wherein Poisson's equation is numerically solved within the quasi-static approximation in each iteration of the regression procedure. For a given type model ion-implanted dopant profile, two cases are considered; the background doping is either the same or opposite type as that ion-implanted. Due to the long range nature of the interactions in the sample, the regression is done using two spatial meshes, a coarse mesh and a dense mesh. The coarse mesh stepsize is of the order of the probe-tip size. The dense mesh stepsize is a fraction of the coarse mesh stepsize. The regression starts and proceeds with the coarse mesh until the spatial wavelength of the error or noise in the estimated dopant number density profile is of the order of the coarse mesh stepsize. The regression then proceeds in like manner with the dense mesh. Regularization and filtering are found to be very important to the convergence of the regression procedure.
and Kopanski, J.
Regression Procedure for Determining the Dopant Profile in Semiconductors from Scanning Capacitance Microscopy Data, Journal of Applied Physics
(Accessed December 5, 2023)