A Variational Approach to Stimulating Evolving Small Structures

9820713苏现代电子设备是具有亚微米特征的固体结构。它们不仅具有电子功能，而且在制造和使用过程中必须保持结构完整性。小结构是一个相对较新的领域，固体力学研究人员可以对此做出重大贡献。这项提议为该领域的许多问题提出了一个统一的主题：结构演变。在固体结构中，扩散过程可以重新定位质量，因此结构的构型可能会随着时间的推移而改变。例如，胶片可能会分裂成岛屿，而互连可能会产生空洞。虽然对其中一些现象的研究可以追溯到很多年前，但最近的技术发展需要更复杂的能力。现代通用有限元程序可以分析复杂结构的应力场。然而，没有这样的代码来模拟具有多种能量力和动力学过程的不断演变的结构。最近开发的一种变式方法提供了一个令人兴奋的前景。它扩展了连续介质力学中已有的方法，除了变形之外，还包括质量位移作为独立的运动学变量。该方法可以包括从机械应力到电子风的能量力，以及从晶界迁移到表面扩散的动力学过程。过去的注意力集中在特定的现象上，如外延膜的不稳定性和互连空洞。这项建议解决了在实现通用代码时将出现的几个基本问题。重点放在与表面能和弹性能有关的方面，因为这两种能量学在小型固体结构中普遍存在，而且它们的实现问题是通用的。具体地说，我们将研究以下几个方面：*表面能量各向异性*弹性引起的广义力*依赖应变的表面能量我们将为有限元方法发展它们的分析基础，在我们的计算机代码中实现它们，并使用该代码模拟几个突出它们影响的现象。对小尺度和大时间尺度现象的研究将把固体力学学科的范围推向一个具有重大科学技术意义的领域。

9820713SuoModern electronic devices are solid structures of submicron featuresizes. Not only do they serve electronic functions, but also they mustmaintain structural integrity during fabrication and use. The field ofsmall structures is a relatively new one, to which solid mechanicsresearchers can make substantial contributions. This proposal addresses aunifying theme for many problems in this field: structural evolution. Ina solid structure, diffusive processes can relocate mass, so that theconfiguration of the structure may change over time. For example, a filmmay break into islands, and an interconnect may grow cavities. Whilestudies of some of such phenomena go back many years, recent technologicaldevelopments demand much more sophisticated capabilities. Todaygeneral-purpose finite element codes can analyze stress fields in complexstructures. However, no such a code exists to simulate evolving structureswith multiple energetic forces and kinetic processes. A variationalapproach developed recently offers an exiting prospect. It extends theestablished approach in continuum mechanics by including mass relocation asan independent kinematic variable, in addition to deformation. Theapproach can include energetic forces ranging from mechanical stress toelectron wind, and kinetic processes ranging from grain boundary migrationto surface diffusion. Attention in the past has been focused on specificphenomena, such as epitaxial film instability and interconnect voiding.This proposal addresses several basic issues that will arise inimplementing a general-purpose code. Emphasis is placed on aspects relatedto surface energy and elastic energy, because both energetics areubiquitous in small solid structures, and because their implementationissues are generic. Specifically, we will examine the following aspects: * Surface energy anisotropy * Generalized forces due to elasticity * Strain-dependent surface energyWe will develop their analytic basis for the finite element method,implement them in our computer code, and use the code to simulate severalphenomena that highlight their effects. The study of the phenomena atsmall length and long time scales will push the envelope of the SolidMechanics discipline into a field of great scientific and technologicalimportance.