PARAMETER IDENTIFICATION FOR NONLINEAR STOCHASTIC PDE MODEL OF A SPUTTERING PROCESS

Abstract

This work focuses on identification of the parameters of the nonlinear stochastic Kuramoto-Sivashinsky equation (KSE), a fourth order nonlinear stochastic partial differential equation (PDE), that describes the fluctuation of surface height of a sputtering process including two surface micro-processes, diffusion and erosion. To perform the system identification, we initially formulate the nonlinear stochastic KSE into a system of infinite nonlinear stochastic ordinary differential equations (ODEs) by using Galerkin's method. A finite-dimensional approximation of the stochastic KSE is then constructed that captures the dominant mode contribution to the state and the evolution of the state covariance of the stochastic ODE system is derived. Then, a kinetic Monte-Carlo (kMC) simulator is used to generate surface snapshots during process evolution to obtain values of the state vector of the stochastic ODE system. Subsequently, the state covariance of the stochastic ODE system that corresponds to the sputtering process is computed based on the kMC simulation results. Finally, the model parameters of the nonlinear stochastic KSE are obtained by using least-squares fitting so that the state covariance computed from the stochastic KSE process model matches that computed from kMC simulations. Simulations are performed to demonstrate the effectiveness of the proposed parameter identification approach.