Solving the dopant diffusion dynamics with physics-informed neural networks

Simulation plays a crucial role in the semiconductor chip manufacturing. In particular, process simulation is primarily used to solve the dopant diffusion dynamics, which describes the temporal evolution of doping profiles during the thermal annealing process. The diffusion dynamics constitutes a multiscale problem, formulated as a set of coupled partial differential equations (PDEs) with respect to the concentration of dopants and point defects. In this paper, we demonstrate that Physics-Informed Neural Networks (PINNs) can accurately predict not only the evolution of the doping profile, but also the unknown physical parameters, specifically the diffusivities appearing as PDE coefficients. Furthermore, we propose a physics-informed calibration method, which performs PDE-constrained optimization by leveraging a pre-trained PINN model. We experimentally verify that this post-processing significantly improves the accuracy of coefficients fine-tuning. To the best of our knowledge, this is the first demonstration of an annealing simulation for the semiconductor diffusion process using a physics-informed machine learning approach. This framework is expected to enable more efficient calibration of simulation parameters based on measurement data.