Feedback control of growth rate and surface roughness in thin film growth

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Abstract
A method for multivariable feedback control of surface roughness and growth rate in thin film growth using kinetic Monte‐Carlo (MC) models is proposed. The method is applied to the process of thin film growth in a stagnation flow geometry including atom adsorption, desorption, and surface migration as the three processes that shape film microstructure and determine film growth rate. A multiscale model involving coupled partial differential equations to model the gas phase and a kinetic MC simulator, based on a large lattice, for the modeling of film growth, is used to simulate the process. A roughness and growth rate estimator constructed allowed computing estimates of the surface roughness and growth rate at a time‐scale comparable to the real‐time evolution of the process. The estimator involves kinetic MC simulators based on small lattice models, adaptive filters used to reduce stochastic fluctuations of the outputs of the small lattice MC simulator outputs, and measurement error compensators used to reduce the errors between the estimates and measurements. The interactions between the inputs (substrate temperature and inlet precursor mole fraction) and outputs (growth rate and surface roughness) in the closed‐loop system are studied and found to be significant. A multivariable feedback controller, which uses the state estimator and explicitly compensates for the effect of input/output interactions, is designed to simultaneously regulate the growth rate and surface roughness by manipulating substrate temperature and inlet precursor mole fraction. Application of the estimator/controller structure to the multiscale process model demonstrates successful regulation of the surface roughness and growth rate to the desired set point values. This approach is shown to be superior to control of the growth rate and surface roughness using two independent feedback control loops.

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