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

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 modelling of the gas phase and a kinetic MC model, based on a high-order lattice, for the modelling 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. The estimator involves a kinetic MC model 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 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 set-point value. The proposed approach is shown to be superior to PI control with direct use of the roughness measurements. The reason is that the available measurement techniques do not provide measurements at a time-scale comparable to the evolution of the dominant film growth dynamics.