Neural Network Model of Radio-Frequency Plasmas

Low to moderate pressure plasma modeling is playing significant role in chamber design, process development and control for semiconductor manufacturing. Radio-frequency (RF) parallel plate capacitively coupled plasmas (CCP) as well as hollow cathode discharges (HCDs) are extensively used for various plasma materials processing. Investigation of plasma behavior using physics-based plasma models can be computationally expensive due to model complexity. To overcome this challenge, we developed a deep learning based non-linear model order reduction method for low temperature plasma applications.

Hollow cathode discharges form in cylindrical cavities in the cathode. In the RF HCD, RF sheath heating as well as secondary electron acceleration play important roles. For modeling low-pressure RF HCDs, where kinetic effects are important, particle-in-cell Monte Carlo collision (PIC-MCC) modeling scheme is used. To generate data for neural network, a space-filling design of computational experiments utilizing RF voltage at the fundamental frequency, RF voltage at the second harmonic, and their phase difference is used for the PIC-MCC model. We consider time sequence of the applied voltage as input and the corresponding cathode current as output for training the neural network model. A surrogate modeling framework is developed using LSTM (Long Short-Term Memory) based closure. The predictions of the electrode current using the trained neural network model compare well with the results of the PIC/MCC simulations at a significantly lower computational cost.

As the pressure increases, the collisionality of the plasma species increases imposing stringent requirements for time-steps, hence PIC-MCC simulation becomes computationally prohibitive. Additionally with increase in pressure the kinetic effect becomes less significant. Therefore, moderate pressure CCPs have been studied using fluid model for both 1D parallel plate and 2D axi-symmetric discharges. The spatio-temporal profiles of plasma density and electron temperature are captured well in the neural network model for moderate pressure CCPs. The predictive neural network-based machine learning model can potentially be used to understand plasma behavior in a rapid manner as well as to control processes that are used in semiconductor manufacturing.