Instabilities During Step-Flow Epitaxy: A Unified Approach

University Of Kentucky Research Foundation, Lexington KY

Investigators

Abstract

Jabbour DMS-1009562 The main thrust of this project is the study of instabilities that occur during step-flow epitaxial growth. It comprises three parts. The first part concerns the discrepancy between the stability predictions of the standard Burton-Cabrera-Frank model and recent experiments that have established the coexistence of step meandering and bunching. This discrepancy is traced back to the incomplete information that the classical Gibbs-Thomson relation delivers about the step chemical potential. An alternative theory, informed by thermodynamics, yields a framework for resolving the aforementioned discrepancy. The second part focuses on the roles of electromigration and elasticity in the onset and evolution of step instabilities. In both cases, appropriate generalizations of the Gibbs-Thomson relation are embedded in thermodynamically compatible formulations of the resulting free boundary problems. As regards electromigration, the goal is to determine if the interplay between the drift velocity and the jump in the adatom grand canonical potential along steps can explain the observed reversals in the current direction needed to trigger bunching upon transition from low- to medium- to high-temperature regimes. With respect to elasticity, the effect of stress on the stability of an isolated step against meandering and that of a periodic train of steps against bunching is studied. In the third part, the growth of nanowires by molecular beam epitaxy and electrodeposition is considered. Because of its small radius, which implies few steps, the growth of a nanowire is an ideal setting to examine boundary effects on step instabilities and compare the standard Burton-Cabrera-Frank formulation to its proposed thermodynamically consistent alternative. The role of the jump in the adatom grand canonical potential during electrodeposition is probed, especially whether bunching provides a dissipative mechanism for the minimization of the nanowire total free energy. This project develops a unified approach to a central problem at the junction of materials science, solid-state physics, and applied mathematics, namely, the investigation of the onset and evolution of instabilities during step-flow epitaxy. Through a blend of modeling, analysis, and computation, the investigator and his collaborators develop novel mathematical theories that resolve discrepancies between experimental observations and existing models. Instabilities play a critical role in the self-assembly of various nanostructures, which in turn strongly affect the macroscopic performance of devices that span a wide range of technologies, from optoelectronics and data-storage devices to biosensors and energy-conversion systems. A fundamental understanding of the physical mechanisms underlying these instabilities and their interplay can therefore contribute significantly to the design and manufacture of increasingly smaller and more reliable devices with tailored properties for specific applications.