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)
Downloading and printing FAQ