Multiscale modeling and neural network model based control of a plasma etch process

Abstract

In this paper, we present a multiscale model with application to the plasma etch process on a three dimensions substrate lattice with uniform thickness using the inductive coupled plasma (ICP). Specifically, we focus on a etch process on silicon with patterned resistive mask. And a multiscale model is developed to simulate both the gas-phase reactions and transportation phenomena in Cl2/Ar plasma chamber as well as the complex interactions that occurs on the silicon substrate. A macroscopic continuous fluid model, which based on partial differential equations (PDEs), is applied to simulate the plasma reactions as well as the transportation phenomena. The fluid model is constructed in COMSOL MultiphysicsTM. Subsequently, the microscopic interactions that taken place on the substrate are simulated by a kinetic Monte Carlo (kMC) model. A spatial-temporal discrete method is applied to address the issue in computing the fluid model and the kMC model concurrently, in which kMC models are parrallelly computed in discrete locations and data exchange between the fluid model as well as the kMC models are implemented in discrete time. Additionally, neural network (NN) is implemented to approximate the kMC model in order to reduce the computational complexity for model-based feedback control. The NN model is then used in a predictive real-time optimizer that optimize the setpoints of a set of critical proportion integral (PI) loops to achieve desired control objectives. Simulation results shows that the model is accurate and the controllers are effective.