Multiscale Physics-Informed Neural Network Framework to Capture Stochastic Thin-Film Deposition

Abstract

This work outlines the development of a multiscale Physics-Informed Neural Network (PINN) approach to capture the full multiscale thin-film growth process within a stagnation point flow vapor deposition chamber. These PINNs were trained using a multiscale model consisting of a macroscale mass transport partial differential equation (PDE) that captures the gaseous precursor species movement coupled with a microscale stochastic PDE (SPDE) to capture the film surface growth. Both the macroscale and microscale differential expressions were embedded directly within the loss function so that all intercommunication between the two scales could be directly accounted for within the PINN. Furthermore, the SPDE was subjected to series expansions and diagonally orthogonal decomposition to embed it within the PINNs despite the stochasticity. The fully trained multiscale PINNs were validated via comparison to the standard kMC-based multiscale model used to capture thin-film deposition processes. Overall, this work demonstrates the potential of PINNs to capture the entire stochastic behavior of an intercommunicating multiscale system in the presence of molecular-level stochastic variability, which has not been explicitly addressed previously in the literature. Furthermore, they illustrate the significant computational efficiency of the multiscale PINNs, which were orders of magnitude faster than the kMC-based and SPDE-based multiscale models.