Instabilities During Step-Flow Epitaxy: A Unified Approach

JABBURE DMS-1009562该项目的主要目的是研究阶跃流动外延生长过程中的不稳定性。它包括三个部分。第一部分涉及标准Burton-Cabrera-Frank模型的稳定性预测与最近建立了阶跃曲折和聚束共存的实验之间的差异。这种差异可以追溯到经典的Gibbs-Thomson关系所提供的有关阶跃化学势的不完全信息。在热力学的指导下，另一种理论为解决上述差异提供了一个框架。第二部分主要讨论电迁移和弹性在阶跃不稳定性的发生和演化中的作用。在这两种情况下，Gibbs-Thomson关系的适当推广被嵌入到所产生的自由边界问题的热力学相容公式中。关于电迁移，目标是确定漂移速度和沿台阶的ADATOM大正则势跃升之间的相互作用是否可以解释在从低到中到高温区域转变时在电流方向上观察到的触发聚束所需的反转。在弹性方面，研究了应力对抗曲折孤立台阶稳定性和周期性抗聚束台阶稳定性的影响。第三部分研究了分子束外延和电沉积生长纳米线的方法。由于纳米线的半径很小，这意味着步骤很少，所以纳米线的生长是检查步骤不稳定性的边界效应并将标准Burton-Cabrera-Frank公式与其提出的热力学一致性替代方案进行比较的理想环境。探讨了电沉积过程中吸附原子巨正则势跃迁的作用，特别是聚束是否为纳米线总自由能最小化提供了耗散机制。这个项目开发了一种统一的方法来解决材料科学、固体物理和应用数学交界处的一个中心问题，即研究阶跃漂浮过程中不稳定性的开始和演化。通过混合建模、分析和计算，这位研究人员和他的合作者开发了新的数学理论，解决了实验观察和现有模型之间的差异。不稳定性在各种纳米结构的自组装中起着关键作用，这些结构反过来又强烈地影响到跨越从光电子学和数据存储设备到生物传感器和能量转换系统等广泛技术的设备的宏观性能。因此，对这些不稳定性及其相互作用背后的物理机制的基本了解，可以为设计和制造越来越小、更可靠的设备做出重大贡献，这些设备具有特定应用的定制特性。

JabbourDMS-1009562 The main thrust of this project is the study ofinstabilities that occur during step-flow epitaxial growth. Itcomprises three parts. The first part concerns the discrepancybetween the stability predictions of the standardBurton-Cabrera-Frank model and recent experiments that haveestablished the coexistence of step meandering and bunching. This discrepancy is traced back to the incomplete informationthat the classical Gibbs-Thomson relation delivers about the stepchemical potential. An alternative theory, informed bythermodynamics, yields a framework for resolving theaforementioned discrepancy. The second part focuses on the rolesof electromigration and elasticity in the onset and evolution ofstep instabilities. In both cases, appropriate generalizationsof the Gibbs-Thomson relation are embedded in thermodynamicallycompatible formulations of the resulting free boundary problems. As regards electromigration, the goal is to determine if theinterplay between the drift velocity and the jump in the adatomgrand canonical potential along steps can explain the observedreversals in the current direction needed to trigger bunchingupon transition from low- to medium- to high-temperature regimes. With respect to elasticity, the effect of stress on the stabilityof an isolated step against meandering and that of a periodictrain of steps against bunching is studied. In the third part,the growth of nanowires by molecular beam epitaxy andelectrodeposition is considered. Because of its small radius,which implies few steps, the growth of a nanowire is an idealsetting to examine boundary effects on step instabilities andcompare the standard Burton-Cabrera-Frank formulation to itsproposed thermodynamically consistent alternative. The role ofthe jump in the adatom grand canonical potential duringelectrodeposition is probed, especially whether bunching providesa dissipative mechanism for the minimization of the nanowiretotal free energy. This project develops a unified approach to a centralproblem at the junction of materials science, solid-statephysics, and applied mathematics, namely, the investigation ofthe onset and evolution of instabilities during step-flowepitaxy. Through a blend of modeling, analysis, and computation,the investigator and his collaborators develop novel mathematicaltheories that resolve discrepancies between experimentalobservations and existing models. Instabilities play a criticalrole in the self-assembly of various nanostructures, which inturn strongly affect the macroscopic performance of devices thatspan a wide range of technologies, from optoelectronics anddata-storage devices to biosensors and energy-conversion systems. A fundamental understanding of the physical mechanisms underlyingthese instabilities and their interplay can therefore contributesignificantly to the design and manufacture of increasinglysmaller and more reliable devices with tailored properties forspecific applications.