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A macroscale perspective of near-equilibrium relaxation of stepped crystal surfaces.

机译：阶梯状晶体表面接近平衡松弛的宏观透视图。

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摘要

Crystal surfaces serve a crucial function as building blocks in small electronic devices, especially for mobile communications technology and photovoltaics. In the history of computing, for example, a crucial innovation that hastened the demise of vacuum tube computers was the etching of patterns on surfaces of semiconductor materials, which led to the integrated circuit. These early procedures typically worked with the materials at very high temperatures, where the thermally rough surface could be modeled from the perspective of continuum thermodynamics. More recently, with the drive towards smaller devices and the accompanying reduction of the lifetime of surface features, manufacturing conditions for the shaping of crystal surfaces have shifted to lower temperatures. At these lower temperatures the surface is no longer rough. In order to describe an evolving surface under typical experimental conditions today, we need to consider the processes that take place at the nanoscale.;Nanoscale descriptions of surface evolution start with the motion of adsorbed atoms (adatoms). Because of their large numbers, the concentration of adatoms is a meaningful object to study. Restricted to certain bounded regions of the surface, the adatom concentration satisfies a diffusion equation. At the boundaries between these regions, the hopping of adatoms is governed by kinetic laws. Real-time observation of these nanoscale processes is difficult to achieve, and experimentalists have had to devise creative methods for inferring the relevant energy barriers and kinetic rates. In contrast, the real-time observation of macroscale surface evolution can be achieved with simpler imaging techniques. Motivated by the possibility of experimental validation, we derive an equation for the macroscale surface height, which is consistent with the motion of adatoms. We hope to inspire future comparison with experiments by reporting the novel results of simulating the evolution of the macroscale surface height.;Many competing models have been proposed for the diffusion and kinetics of adatoms. Due to the difficulty of observing adatom motion at the nanoscale, few of the competing models can be dismissed outright for failure to capture the observed behavior. This dissertation takes a few of the nanoscale models and systematically derives the corresponding macroscopic evolution laws, of which some are implemented numerically to provide data sets for connection with experiments. For the modeling component of this thesis, I study the effect of anisotropic adatom diffusion at the nanoscale, the inclusion of an applied electric field, the desorption of adatoms, and the extension of linear kinetics in the presence of step permeability. Analytical conjectures based on the macroscale evolution equation are presented. For the numerical component of this thesis, I select a few representative simulations using the finite element method to illustrate the most salient features of the surface evolution.
机译：晶体表面在小型电子设备中，尤其是移动通信技术和光伏设备中，起着至关重要的作用，作为构建模块。例如，在计算历史上，促使真空管计算机消亡的一项关键创新是在半导体材料表面上蚀刻图案，从而形成了集成电路。这些早期过程通常在很高的温度下与材料一起使用，可以从连续热力学的角度对热粗糙表面进行建模。最近，随着向更小设备的追求以及随之而来的表面特征寿命的减少，用于晶体表面成形的制造条件已经转移到较低的温度。在这些较低的温度下，表面不再粗糙。为了描述当今典型实验条件下不断演化的表面，我们需要考虑在纳米尺度上发生的过程。表面演化的纳米尺度描述始于吸附原子（原子）的运动。由于其数量众多，因此吸附原子的浓度是一个有意义的研究对象。局限在表面的某些有限区域内，原子浓度满足扩散方程。在这些区域之间的边界处，原子的跳跃受动力学定律的控制。对这些纳米级过程的实时观察是很难实现的，实验者不得不设计出新颖的方法来推断相关的能垒和动力学速率。相比之下，可以使用更简单的成像技术来实现宏观表面演化的实时观察。由于实验验证的可能性，我们得出了宏观表面高度的方程，该方程与吸附原子的运动一致。我们希望通过报告模拟宏观尺度表面高度演化的新颖结果来激发与实验的未来比较。；已经提出了许多竞争模型来描述原子的扩散和动力学。由于难以观察纳米级吸附原子的运动，几乎没有任何竞争模型可以因为无法捕获所观察到的行为而被直接排除。本文采用了几个纳米尺度模型，系统地推导了相应的宏观演化规律，其中的一些数值实现了数值化，以提供与实验相关的数据集。对于本文的建模部分，我研究了各向异性吸附原子在纳米尺度上的扩散，所施加电场的包含，吸附原子的解吸以及在阶跃磁导率存在下线性动力学的扩展的影响。提出了基于宏观演化方程的解析猜想。对于本文的数值部分，我选择了一些使用有限元方法的代表性模拟，以说明表面演化的最显着特征。

著录项

  • 作者

    Quah, John.;

  • 作者单位

    University of Maryland, College Park.;

  • 授予单位 University of Maryland, College Park.;
  • 学科 Mathematics.;Physics Condensed Matter.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 248 p.
  • 总页数 248
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;
  • 关键词

  • 入库时间 2022-08-17 11:38:29

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