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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.

Ph.D. Dissertation
(PDF, 3070K)

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