Machine Learning for Fast Prediction of Ion Velocity Distribution Functions in Capacitively Coupled Plasmas and for Acceleration of Particle-In-Cell Simulations

Machine learning techniques offer a powerful approach to assimilate previously collected data to improve engineering design and even accelerate high-fidelity numerical simulations. In this work we apply a deep neural-network (DNN) to model the kinetic properties of ion velocity distribution functions (IVDF) in capacitively coupled plasma (CCP) discharges over a wide range of gas pressures and driving frequencies. Using data collected from 250 1D-3V parallel and GPU accelerated particle-in-cell (PIC) simulations of an Argon CCP discharge, a robust DNN is trained to map these inputs to the IVDF within the discharge and at the wafer surface. This model can then be directly applied to predict IVDFs without running new and expensive PIC simulations.

Additionally, when higher accuracy is required, these new predictions of the plasma profiles can be applied to accelerate full fidelity PIC simulations. The plasma profiles generated from the DNN are used as initial conditions for new simulations, which converge, on average, 18 times faster than those initialized with uniform plasma profiles provided by a global model . A workflow is demonstrated whereby a DNN modeling the ion kinetics can be used to accelerate simulations, which in turn improve the model in a virtuous cycle. The eventual target of such a cycle being the development of a digital twin for ion kinetics within CCP discharges.