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The non-destructive estimation of doping concentrations in semiconductordevices is of paramount importance for many applications ranging from crystalgrowth, the recent redefinition of the 1kg to defect, and inhomogeneitydetection. A number of technologies (such as LBIC, EBIC and LPS) have beendeveloped which allow the detection of doping variations via photovoltaiceffects. The idea is to illuminate the sample at several positions and detectthe resulting voltage drop or current at the contacts. We model a general classof such photovoltaic technologies by ill-posed global and local inverseproblems based on a drift-diffusion system that describes charge transport in aself-consistent electrical field. The doping profile is included as aparametric field. To numerically solve a physically relevant local inverseproblem, we present three different data-driven approaches, based on leastsquares, multilayer perceptrons, and residual neural networks. Our data-drivenmethods reconstruct the doping profile for a given spatially varying voltagesignal induced by a laser scan along the sample's surface. The methods aretrained on synthetic data sets (pairs of discrete doping profiles andcorresponding photovoltage signals at different illumination positions) whichare generated by efficient physics-preserving finite volume solutions of theforward problem. While the linear least square method yields an averageabsolute $\ell^\infty$ error around $10\%$, the nonlinear networks roughlyhalve this error to $5\%$, respectively. Finally, we optimize the relevanthyperparameters and test the robustness of our approach with respect to noise.

Data-driven solutions of ill-posed inverse problems arising from doping reconstruction in semiconductors