Instabilities During Step-Flow Epitaxy: A Unified Approach

这个项目的主要目的是研究在阶梯流外延生长过程中发生的不稳定性。它包括三个部分。第一部分涉及标准波顿-卡布雷拉-弗兰克模型的稳定性预测与最近建立了阶梯弯曲和聚束共存的实验之间的差异。这种差异可以追溯到经典吉布斯-汤姆森关系提供的关于步化学势的不完整信息。另一种基于热力学的理论为解决上述差异提供了一个框架。第二部分重点讨论了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，吉布斯-汤姆逊关系的适当推广被嵌入到由此产生的自由边界问题的热力学相容公式中。至于电迁移，目标是确定漂移速度和原子经典势跳跃之间的相互作用是否可以解释在当前方向上观察到的反转，从而触发从低到中到高温的转变。在弹性方面，研究了应力对孤立台阶抗弯曲稳定性和周期性台阶抗聚束稳定性的影响。第三部分研究了分子束外延和电沉积制备纳米线的方法。由于其半径小，这意味着很少的步骤，纳米线的生长是一个理想的设置来检查台阶不稳定性的边界效应，并比较标准的伯顿-卡布雷拉-弗兰克公式与其提出的热力学一致的替代方案。探讨了电沉积过程中跳跃对原子大规范势的影响，特别是聚束是否为最小化纳米线总自由能提供了耗散机制。该项目开发了一种统一的方法来解决材料科学，固体物理学和应用数学的中心问题，即研究阶梯流动过程中不稳定性的开始和演变。通过建模、分析和计算的混合，研究者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至关重要的作用，而这反过来又强烈地影响着从光电子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器件的宏观性能。因此，对这些不稳定性及其相互作用的物理机制的基本理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，这些设备具有针对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.