A self-consistent hybrid model connects empirical and optical models for fast, non-destructive inline characterization of thin, porous silicon layers

Epitaxially-grown wafers on top of sintered porous silicon are a material-efficient wafer production process, that is now being launched into mass production. This production process makes the material-expensive sawing procedure obsolete since the wafer can be easily detached from its seed substrate. With high-throughput inline production processes, fast and reliable evaluation processes are crucial. The quality of the porous layers plays an important role regarding a successful detachment. Therefore, we present a fast and non-destructive investigation algorithm of thin, porous silicon layers. We predict the layer parameters directly from inline reflectance data by using a convolutional neural network (CNN), which is inspired by a comprehensive optical modelling approach from literature. There, a numerical fitting approach on reflection curves calculated with a physical model is performed. By adding the physical model to the CNN, we create a hybrid model, that not only predicts layer parameters, but also recalculates reflection curves. This allows a consistency check for a self-supervised network optimization. Evaluation on experimental data shows a high similarity with Scanning Electron Microscopy (SEM) measurements. Since parallel computation is possible with the CNN, 30.000 samples can be evaluated in roughly 100 ms.