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Epitaxial growth dynamics in gallium arsenide Ballestad, Anders

Abstract

The problem of a complete theory describing the far-from-equilibrium statistical mechanics of epitaxial crystal growth remains unsolved. Besides its academic importance, this problem is also interesting from the point of view of device manufacturing. In order to improve on the quality and performance of lateral nanostructures at the lengthscales required by today's technology, a better understanding of the physical mechanisms at play during epitaxial growth and their influence on the evolution of the large-scale morphology is required. In this thesis, we present a study of the morphological evolution of GaAs (001) during molecular beam epitaxy by experimental investigation, theoretical considerations and computational modeling. Experimental observations show that initially rough substrates smooth during growth and annealing towards a steady-state interface roughness, as dictated by kinetic roughening theory. This smoothing indicates that there is no need for a destabilizing step-edge barrier in this material system. In fact, generic surface growth models display a much better agreement with experiments when a weak, negative barrier is used. We also observe that surface features grow laterally, as well as vertically during epitaxy. A growth equation that models smoothing combined with lateral growth is the nonlinear, stochastic Kardar-Parisi-Zhang (KPZ) equation. Simulation fits match the experimentally observed surface morphologies quite well, but we argue that this agreement is coincidental and possibly a result of limited dynamic range in our experimental measurements. In light of these findings, we proceed by developing a coupled growth equations (CGE) model that describes the full morphological evolution of both flat and patterned starting surfaces. The resulting fundamental model consists of two coupled, spatially dependent rate equations that describe the interaction between diffusing adatoms and the surface through physical processes such as adatom diffusion, deposition, and incorporation and detachment at step edges. In the low slope, small amplitude limit, the CGE model reduces to a nonlinear growth equation similar to the KPZ equation. From this, the apparent applicability of the KPZ equation to surface shape evolution is explained. The CGE model is based on fundamental physical processes, and can therefore explain the un derlying physics, as well as describe macroscopic pattern evolution during growth.

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