A Physics-Informed Neural Network for Accurate Prediction of Sheath Plasma within Wall-Bounded Devices

The sheath is ubiquitous in wall-bounded plasmas. Accurate prediction of the performance and control of sheaths is critical for wide-ranging applications in many plasma devices. Slight deviations in the angle or flux of matter and energy due to anisotropic processes within the sheath can strongly impact surface erosion in fusion devices and electric thrusters, limit nanofeature yield in microelectronic fabrication, etc. Active measurement and control of sheath is difficult due to a poor understanding of variable plasma surface interactions (PSI), the effects of in-situ measurements on results, and high temperatures. Predetermined conditions through simulation are necessary for design and failure mitigation. However, the distance in scales of sheath kinetic-fluid hybrid models can become computationally expensive for even a slightly informative simulation and are used primarily to validate reduced fluid models. SurfPlasma, Inc., and subcontractors at the University of Florida in the Department of Material Science and Engineering will produce a novel sheath plasma physics-informed neural network (SPPINN), a machine learning software using physical constraints and data loss functions to predict sheath structure and its properties. This product will address the knowledge gaps in sheath research and commercial applications using a methodology known to learn the entire parameter space all at once. It is also an inherently mesh-free space, requires far less training data than conventional neural networks while removing unphysical solutions, and can make predictions within a few milliseconds once trained. This Small Business Innovation Research Phase I project will provide proof of concept simulation of a practical, canonical benchmark problem using SPPINN. This problem will focus on the edge of the wafer within a microelectronic etching reactor, where changes in the bounding surface material cause warping in the sheath and reduce the yield of high aspect ratio structures. Specifically, the simulation will explore interpretable data of the sheath within a two-dimensional space using a relevant three-fluid simple plasma species using a non-reacting working gas. Interpretable properties across the sheath include potential drop distribution, which determines ion acceleration into the material, ion angular distribution (IADF), and species densities. Verification of the algorithm will be made upon successful training in the microelectronic reactor geometry, and validation made using the reported and industry results. If successful, SPPINN will demonstrate feasibility as a computationally effective means of predicting the sheath structure within a 2D space, applicable to various industries which utilize sheath for PSI processes. SurfPlasma can achieve financial sustainability while enabling cost, time, and waste saving practices for the wider plasma community and industry partners, such as Micron Technology who brought forward the sheath warping problem. Phase II efforts and beyond will consolidate SPPINN into a usable platform with extended fluid/kinetic physical constraints for use in commercial and academic settings. Overall, this study can strengthen the understanding and productivity of plasma reactor environments.