# Modeling and Control of Epitaxial Thin Film Growth

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Martha A. Gallivan

Caltech Mechanical Engineering

Thin ﬁlm deposition is a manufacturing process in which tolerances may approach the size of individual atoms. The ﬁnal film is highly sensitive to the processing conditions, which can be intentionally manipulated to control film properties. A lattice model of surface evolution during thin film growth captures many important features, including the nucleation and growth of clusters of atoms and the propagation of atomic-height steps. The dimension of this probabilistic master equation is too large to directly simulate for any physically realistic domain, and instead stochastic realizations of the lattice model are obtained with kinetic Monte Carlo simulations.

In this thesis simpler representations of the master equation are developed for use in analysis and control. The static map between macroscopic process conditions and microscopic transition rates is ﬁrst analyzed. In the limit of fast periodic process parameters, the surface responds only to the mean transition rates, and, since the map between process parameters and transition rates is nonlinear, new effective combinations of transition rates may be generated. These effective rates are the convex hull of the set of instantaneous rates.

The map between transition rates and expected film properties is also studied. The dimension of a master equation can be reduced by eliminating or grouping conﬁgurations, yielding a reduced-order master equation that approximates the original one. A linear method for identifying the coefficients in a master equation is then developed, using only simulation data. These concepts are extended to generate low-order master equations that approximate the dynamic behavior seen in large Monte Carlo simulations. The models are then used to compute optimal time-varying process parameters.

The thesis concludes with an experimental and modeling study of germanium film growth, using molecular beam epitaxy and reflection high-energy electron diffraction. Growth under continuous and pulsed flux is compared in experiment, and physical parameters for the lattice model are extracted. The pulsing accessible in the experiment does not trigger a change in growth mode, which is consistent with the Monte Carlo simulations. The simulations are then used to suggest other growth strategies to produce rougher or smoother surfaces.