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

TL;DR

This paper develops and compares data-driven neural network methods to solve ill-posed inverse problems for estimating doping profiles in semiconductors from photovoltaic measurements, achieving improved accuracy over traditional methods.

Contribution

The paper introduces three neural network-based approaches for reconstructing doping profiles from photovoltaic data, demonstrating their effectiveness on synthetic data and analyzing robustness and hyperparameter effects.

Findings

Neural networks halve the error compared to least squares.

Data-driven methods achieve around 5% error.

Approaches are robust to noise and hyperparameter variations.

Abstract

The non-destructive estimation of doping concentrations in semiconductor devices is of paramount importance for many applications ranging from crystal growth, the recent redefinition of the 1kg to defect, and inhomogeneity detection. A number of technologies (such as LBIC, EBIC and LPS) have been developed which allow the detection of doping variations via photovoltaic effects. The idea is to illuminate the sample at several positions and detect the resulting voltage drop or current at the contacts. We model a general class of such photovoltaic technologies by ill-posed global and local inverse problems based on a drift-diffusion system that describes charge transport in a self-consistent electrical field. The doping profile is included as a parametric field. To numerically solve a physically relevant local inverse problem, we present three different data-driven approaches, based on least squares, multilayer perceptrons, and residual neural networks. Our data-driven methods reconstruct the doping profile for a given spatially varying voltage signal induced by a laser scan along the sample's surface. The methods are trained on synthetic data sets (pairs of discrete doping profiles and corresponding photovoltage signals at different illumination positions) which are generated by efficient physics-preserving finite volume solutions of the forward problem. While the linear least square method yields an average absolute $\ell^\infty$ error around $10\%$, the nonlinear networks roughly halve this error to $5\%$, respectively. Finally, we optimize the relevant hyperparameters and test the robustness of our approach with respect to noise.