Differentiable Interference Modeling for Cost-Effective Growth Estimation of Thin Films

Accurate $\textit{in situ}$ monitoring of thin-film growth typically requires complex and expensive techniques such as ellipsometry or X-ray reflectivity. We introduce $\texttt{reflax}$, an open-source library to infer growth dynamics from simple, low-cost single-wavelength reflectance time series. $\texttt{reflax}$ employs a differentiable physics-based simulator in which the film's growth behavior is parameterized by a neural network, minimizing the discrepancy between simulated and experimental reflectance while incorporating physical priors such as growth monotonicity and smoothness for model robustness. To reduce the computional burden introduced by optimizing physical parameters in the simulator, we propose $\textit{neural operator initialized optimization}$, where a neural operator provides a strong initial estimate of the growth function, which can be fine-tuned efficiently. First experimental tests show promising agreement with ellipsometry in the predicted final thickness, suggesting that accurate thickness monitoring can be achieved at much lower cost.