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Modeling, Analysis, And Simulation Of Discrete-Continuum Models Of Step-Flow Epitaxy: Bunching Instabilities And Continuum Limits, Nicholas O. Kirby

University of Kentucky Doctoral Dissertations

Vicinal surfaces consist of terraces separated by atomic steps. In the step-flow regime, deposited atoms (adatoms) diffuse on terraces, eventually reaching steps where they attach to the crystal, thereby causing the steps to move. There are two main objectives of this work. First, we analyze rigorously the differences in qualitative behavior between vicinal surfaces consisting of infinitely many steps and nanowires whose top surface consists of a small number of steps bounded by a reflecting wall. Second, we derive the continuum model that describes the macroscopic behavior of vicinal surfaces from detailed microscopic models of step dynamics.

We use the …