Feedback control of surface roughness in sputtering processes using the stochastic Kuramoto-Sivashinsky equation

This work focuses on control of surface roughness in sputtering processes including two surface micro-processes, diffusion and erosion. The fluctuation of surface height of such sputtering processes can be described by the stochastic Kuramoto–Sivashinsky equation (KSE), a fourth-order stochastic partial differential equation (PDE). Specifically, we consider sputtering processes, including surface diffusion and erosion, on a one-dimensional lattice and design feedback controllers based on stochastic PDEs to regulate the surface roughness at desired levels. We initially reformulate the stochastic KSE into a system of infinite stochastic ordinary differential equations (ODEs) by using m t s a u t s C a t F d ©