Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models

Abstract

In this work, we present an approach to estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo (MC) models. We use the process of thin film growth in a stagnation flow geometry and consider atom adsorption, desorption and surface migration as the three processes that shape film micro-structure. A multiscale model that involves coupled partial differential equations (PDEs) for the modeling of the gas phase and a kinetic MC simulator, based on a high-order lattice, for the modeling of the film micro-structure, is used to simulate the process. A roughness estimator is constructed that allows computing estimates of the surface roughness at a time-scale comparable to the real-time evolution of the process using discrete on-line roughness measurements. The estimator involves a kinetic MC simulator based on a reduced-order lattice, an adaptive filter used to reduce roughness stochastic fluctuations and an error compensator used to reduce the error between the roughness estimates and the discrete roughness measurements. The roughness estimates are fed to a proportional-integral (PI) controller. Application of the proposed estimator/controller structure to the multiscale process model demonstrates successful regulation of the surface roughness at the desired value. The proposed approach is shown to be superior to PI control with direct use of the discrete roughness measurements. The reason is that the available measurement techniques do not provide measurements at a frequency that is comparable to the time-scale of evolution of the dominant film growth dynamics.