Quantifying Variability in Silicon Photonics: A Stochastic Study of Sidewall Roughness and Its Impact on Waveguide Performance

This work presents a comprehensive simulationbased study of surface roughness-induced loss and phase variation in silicon photonic waveguides extended to centimeterscale lengths. Our results indicate that subtle changes in the surface roughness profile can yield measurable variations in overall device performance, despite maintaining the same root-mean-square (RMS) roughness amplitude and correlation length. We compare waveguides' performance as a function of different roughness parameters and use a variational finitedifference time-domain framework to handle large-scale computations. The data reveal that even modest increases in roughness (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma_{\text {RMS }}$</tex>) or correlation length can lead to significant scattering loss and phase uncertainties when segments are stitched together randomly. These findings underscore the need for precise control over the sidewall fabrication process and highlight the value of statistical modeling techniques in designing robust photonic devices.