AVS 72 Session PS1-WeA: Machine Learning for Plasma Processes

Advanced packaging is becoming an increasingly important part of AI-era semiconductor scaling alongside continued transistor scaling, as modern computing systems increasingly rely on heterogeneous integration, larger-format packaging, high interconnect density, and package-level thermomechanical reliability to achieve higher bandwidth, lower latency, improved power efficiency, and greater compute density. In both wafer and panel-level packaging, plasma-based etching must operate across increasingly diverse material systems including organic build-up films, dielectrics, polymers, metals, and deep silicon structures, while maintaining tight requirements in uniformity and reliability over larger substrates. In these systems, plasma nonuniformity and substrate warpage become major challenges that impact process stability and yield. To help address these challenges, we explore the use of machine learning techniques such as transfer learning, artificial neural networks, and Hidden Markov models alongside conventional plasma simulations, diagnostics, and process development tools. Target applications include correlating wafer-scale (often axisymmetric) plasma simulation behavior with panel-scale experimental results; improving endpoint detection and plasma process monitoring for the etching of organic materials and deep silicon structures; bridging experimental and prediction gaps in electron temperature and electron density estimation from optical emission spectroscopy; and accelerating plasma process and tool optimization.

The inherent complexity of plasma reaction fields has long hindered precise control of process outcomes. The lack of reaction databases often results in discrepancies between simulations and experiments and delays the implementation of new gas chemistries. The direct application of previously proposed methods for calculating reaction rates or cross sections, such as the transition state theory, remains challenging due to the vast number of reactions and nonequilibrium plasma fields where reactive species often deviate from the Maxwell-Boltzmann distribution. Consequently, data-driven approaches have recently attracted increasing attention as alternative analysis tools for process development [1]. In addition, previous studies have demonstrated that neural networks can virtually reproduce conventional liquid-phase chemical reactions [2].

In this study, we propose a plasma reaction neural network (PRNN) as a framework for the simultaneous analysis of plasma reactions. The neural network, designed based on plasma physics, consists of a single hidden layer with an exponential activation function and is capable of simulating the entire reaction network, where each node represents an elementary reaction. Given densities and temperatures of electrons, ions and neutral species at a certain time, the PRNN predicts the temporal evolution of each reactive species. This plasma-physics-informed machine learning architecture incorporates several physically meaningful parameters, particularly reaction rate coefficients. To validate the proposed model, time-resolved quadrupole mass spectrometry and Langmuir probe measurements were performed under various conditions with varied gas mixtures, pressures, and RF powers to train the PRNN. After fitting the model to the experimental dataset, the stoichiometric coefficients and reaction rate coefficients were extracted from the edge weights and node biases, respectively. The proposed methodology enables direct experimental acquisition of reaction rates with significantly reduced time and resources, regardless of the energy distributions of reactive species. Furthermore, the PRNN is applicable to other complex plasma systems, paving the way for efficient data acquisition for new gas chemistries and the realization of digital twins for plasma processes.

[1] Y. Ando et al., Diam. Relat. Mater. 151, 111687 (2025) [2] W. Ji, S. Deng, J. Phys. Chem. A 125, 1082 (2021)

For plasma processing, there is a need to simulate large plasma devices via kinetic means, since the Electron Velocity Distribution Function in these devices is non-Maxwellian and therefore fluid treatment is insufficient to accurately capture the physics. Even on modern GPU accelerated high-performance computing systems, such simulations can take days or even weeks to deliver engineering relevant insights. Machine Learning (ML) offers many possibilities for accelerating kinetic plasma simulation or developing reduced order models which can provide insights at speeds that could enable rapid computer aided engineering of plasma reactors. We will discuss three recent approaches, including (1) using convolutional neural networks to provide improved initial conditions for PIC simulations which can reduce runtime by nearly 20x [1], (2) development of a hierarchical-embedding autoencoder with predictor (HEAP) architecture which can accurately model the multiscale nature of plasma dynamics [2], and (3) generalizable and interpretable symbolic regression models for ion flux within a capacitively coupled plasma discharge [3]. Together, these methods demonstrate how ML can bridge the gap between high-fidelity kinetic simulation and the fast, predictive modeling needed for practical plasma reactor design.

[1] A. T. Powis, D. Corona Rivera, A. Khrabry, and I. D. Kaganovich, Phys. Plasmas 33, 013902 (2026).

[2] A. I. Khrabry, E. A. Startsev, A. T. Powis, and I. D. Kaganovich, Phys. Fluids 38, 045138 (2026).

[3] M. T. Huynh et al., submitted to Mach. Learn.: Sci. Technol. (2026).