Computational analysis of etched profile evolution for the derivation of 2D dopant density maps in silicon

The numerical simulation of the etched surface evolution is applied to the selective (chemical and electrochemical) etching dopant delineation technique. The analysis of the etched sample section, obtained by means of transmission electron microscopy, is performed using a 3D simulation code based on the level set method for evolving surfaces. The correlation between the etched profile and the total dopant distribution is inferred, assuming that a functional relationship F = F{rho(r)} occurs between the local dopant density rho(r) and the local etch rate F(r). The reliability of the etch rate expression, derived by the theory of the charge transport in the solution-semiconductor interface, has been demonstrated by using the direct electrical simulation of the current flow during the etching process. The calibration of the technique consists in the fit of the parameters in the F = F{rho(r)} relation depending only on the external conditions (bias potential, chemical moisture). The fitting has been performed, using reference profiles, at fixed optimal conditions. The measurement of the 2D dopant density map is based on the cross graphical comparisons, performed automatically by the computational tool, between TEM images of the eroded zone and the simulations of the etched surface, obtained using trial dopant distributions.