A probabilistic approach for approximation of optical and opto-electronic properties of an opto-semiconductor wafer under consideration of measuring inaccuracy and model uncertainty

This paper presents a probabilistic machine learning approach to approximate wavelength values for unmeasured positions on an opto-semiconductor wafer after epitaxy. Insufficient information about optical and opto-electronic properties may lead to undetected specification violations and, consequently, to yield loss or may cause product quality issues. Collection of information is restricted because physical measuring points are expensive and in practice samples are only drawn from 120 specific positions. The purpose of the study is to reduce the risk of uncertainties caused by sampling and measuring inaccuracy and provide reliable approximations. Therefore, a Gaussian process regression is proposed which can determine a point estimation considering measuring inaccuracy and further quantify estimation uncertainty. For evaluation, the proposed method is compared with radial basis function interpolation using wavelength measurement data of 6-inch InGaN wafers. Approximations of these models are evaluated with the root mean square error. Gaussian process regression with radial basis function kernel reaches a root mean square error of 0.814 nm averaged over all wafers. A slight improvement to 0.798 nm could be achieved by using a more complex kernel combination. However, this also leads to a seven times higher computational time. The method further provides probabilistic intervals based on means and dispersions for approximated positions.