Instabilities During Step-Flow Epitaxy: A Unified Approach

  • Jabbour, Michel (PI)

Grants and Contracts Details


This proposed project comprises three parts. The rst concerns the discrepancy between the stability predictions of the standard Burton{Cabrera{Frank model and recent experi- ments establishing, for vicinal surfaces with minimal kinetic pathways, the coexistence of step meandering and bunching. This discrepancy is traced back to the incomplete informa- tion that the classical Gibbs{Thomson relation gives about the step chemical potential. An alternative theory, informed by thermodynamics, when coupled with an energy-rate calcu- lation that yields the appropriate generalization of the Gibbs{Thomson relation, provides a framework for resolving the aforementioned discrepancy. Specically, the linear stability analysis of the resulting two-dimensional free boundary problem should demonstrate that meandering acts as a precursor to bunching during step ow. Beyond the linear regime, the numerical implementation of a phase-eld version of this theory will deliver information about the nonlinear dynamics of steps. The second part focuses on the roles of adatom electromigration and step and bulk elasticity in the onset and evolution of step instabilities. In both cases, appropriate extensions of the Gibbs{Thomson relation for the step chemi- cal potential will be embedded in thermodynamically compatible formulations of the free boundary problem for step- ow growth. As regards electromigration, the goal is to deter- mine if the interplay between the drift velocity and the jump in the adatom grand canonical potential along steps can explain, in light of the dependence of the latter on the equilibrium adatom coverage, the observed reversals in the current direction needed to trigger bunching upon transition from low- to medium- to high-temperature regimes. With respect to elas- ticity, linear stability and perturbation analysis tools will be used to examine the eects of stress on the stability of an isolated step against meandering and that of a periodic train of steps against both bunching and meandering. In the third part, the growth of nanowires by molecular beam epitaxy and electrodeposition will be considered. Because of its small radius, which implies few steps, the growth of a nanowire is an ideal setting to (i) examine boundary eects on step instabilities, and (ii) compare the standard BCF formulation to its proposed thermodynamically consistent alternative, in particular the dependence of the stability region on the attachment asymmetry. The role of the jump in the adatom grand canonical potential during electrodeposition will be probed, especially whether bunching provides a mechanism for the minimization of the nanowire total free energy. Intellectual merits: The proposed research attempts a unied approach to step instabili- ties. It also aims at resolving discrepancies between experimental observations and existing BCF-type theories. Given the role of instabilities in the self-assembly of various nanostruc- tures, the results obtained herein should benet the crystal growth community.The P.I. and his collaborators will use a judicious blend of modeling, analysis, and computation to bring light to the issues at hand. Broader impacts: Theoretical knowledge of the mechanisms underlying the self-assembly of nanostructures should impact on technological applications ranging from optoelectronics and data-storage devices to biosensors and energy-conversion systems. On the educational front, the P.I. will continue to incorporate some of his research results into graduate-level applied mathematics courses for doctoral students in engineering, science, and mathematics. The P.I. will also continue the dissemination of results through conference participation and organization. One Ph.D. student, Ms. Megan Dailey, will participate in this project.
Effective start/end date10/1/109/30/14


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