Recurrent Neural-Network-Based Model Predictive Control of a Plasma Etch Process

In this article, we propose the development of a recurrent neural network (RNN)-based model predictive controller (MPC) for a plasma etch process on a three-dimensional substrate using inductive coupled plasma (ICP) analysis. Specifically, the plasma etch process is simulated by a multiscale model: (1) A macroscopic fluid model is applied to simulate the gas flows and chemical reactions of plasma. (2) A kinetic Monte Carlo (kMC) model is applied to simulate the etching process on the substrate. Subsequently, proper orthogonal decomposition (POD) is used to derive the empirical eigenfunctions of the plasma model. Then the empirical eigenfunctions are utilized as basis functions within a Galerkin's model reduction framework to compute a low-order system capturing dominant dynamics of the plasma model. Additionally, RNN is introduced to approximate dynamics of both the reduced-order plasma system and the microscopic etch process. The training data for the RNN models are generated from discrete sampling of open-loop simulations. A probability distribution function is also involved to present the stochastic characteristic of the kMC model. The trained RNN models are then implemented as the prediction model in the development of MPC to achieve desired control objectives. Closed-loop simulation results are presented to compare the performance of the model predictive controller and a proportional-integral (PI) controller, which show that the proposed MPC framework is effective and exhibits better performance than does a PI controller.