Optimization, estimation, and control for kinetic Monte Carlo simulations of thin film deposition

The deposition of a thin film is a dynamic process that is complex and subject to unknown disturbances. When the dynamics and final material properties are dominated by atomic scale phenomena, it is difficult to apply existing optimization and control tools to improve process repeatability and to optimize the resulting material properties. Currently, feedback loops are used to control sensed quantities, and optimization has been applied to macroscopic reactor conditions like fluid flow. Ultimately, one would like to directly control the material properties that determine the performance of an integrated circuit or MEMS device, even when the property of interest is not directly measured. In this paper an integrated control strategy is applied to an atomic scale kinetic Monte Carlo simulation of thin film deposition. A model reduction approach developed previously for Monte Carlo simulations is used in the design of the control strategy. An input temperature profile that minimizes interface roughness is computed with a gradient optimization, and estimators are designed to infer surface roughness from a measurement of the density of steps. A proportional-integral feedback controller is then sufficient to control surface roughness in the presence of input noise, input offset, and uncertainty in the initial surface configuration.