Evaluating regression-based techniques for modelling fabrication variations in silicon photonic waveguides

For integrated silicon photonics to mature as an industry platform, robust methods for measuring and extracting the geometry of fabricated waveguides are needed. Due to the cost and time needed for SEM or AFM imaging, a method of extracting waveguide variability though optical measurements is often preferred. Here, we present a study of regression-based machine learning (ML) techniques that enable such variability extraction while maintaining compatibility with wafer-scale optical measurements. We first explicitly investigate the issue of non-unique effective and group index pairs that can affect the accuracy of regression-based techniques. Training data is then generated by simulating several geometries of wire waveguides in Lumerical's MODE solver to simulate defects due to process variances. Finally, a representative set of ML regression techniques are tested for their ability to accurately estimate the geometries of said simulated waveguides. To the best of the authors' knowledge, this work represents the first attempt in the literature to i.) explicitly study the effects of non-uniqueness in optical measurement-based metrology and ii) present a model that potentially overcomes said non-uniqueness. This work represents an important step towards the maturing models for process variations in silicon photonic platforms.