Instabilities During Step-Flow Epitaxy: A Unified Approach

JabbourDMS-1009562 本计画的主要目的是研究阶梯流磊晶成长过程中所发生的不稳定性。 它包括三个部分。 第一部分涉及的standardBurton-Cabrera-Frank模型的稳定性预测和最近的实验，已经建立了一步蜿蜒和聚束共存之间的差异。这种差异可以追溯到经典的吉布斯-汤姆逊关系提供的关于阶跃化学势的不完整信息。 另一种理论，由热力学，产生了解决上述矛盾的框架。 第二部分着重于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，适当的generalizationsof吉布斯-汤姆森关系嵌入在philicallycompatible配方所产生的自由边界问题。至于电迁移，我们的目标是要确定之间的相互作用的漂移速度和跳跃的adatomgrandcanonical势沿着步骤可以解释在电流方向上触发聚束从低到中到高的温度制度过渡所需的browvedreversals。在弹性力学方面，研究了应力对孤立台阶抗弯曲稳定性和一列台阶抗聚束稳定性的影响。 第三部分研究了分子束外延法和电沉积法生长纳米线。 由于纳米线的半径很小，这意味着步骤很少，因此纳米线的生长是检查边界对步骤不稳定性的影响并将标准Burton-Cabrera-Frank公式与其提出的物理上一致的替代方案进行比较的理想设置。 本文探讨了电沉积过程中吸附原子巨正则势的跃变所起的作用，特别是聚束是否提供了一种耗散机制，使吸附原子的总自由能最小化。 这个项目发展了一个统一的方法来解决材料科学、固体物理学和应用数学结合处的一个中心问题，即在步进流外延过程中不稳定性的发生和演化的研究。 通过混合建模，分析和计算，研究者和他的合作者开发了新的理论，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，而这些纳米结构反过来又强烈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设备的宏观性能。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和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.