A Variational Approach to Stimulating Evolving Small Structures

现代电子器件是亚微米尺寸的固体结构。 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。 小型结构是一个相对较新的领域，固体力学研究人员可以在这一领域做出实质性的贡献。 这一建议涉及到一个统一的主题，在这一领域的许多问题：结构演变。 在固体结构中，扩散过程可以重新定位质量，因此结构的配置可能会随着时间的推移而改变。 例如，薄膜可能会破裂成岛状，而互连可能会产生空腔。 虽然对这些现象的研究可以追溯到许多年前，但最近的技术发展需要更复杂的能力。 目前通用的有限元程序可以分析复杂结构的应力场。 然而，没有这样一个代码存在来模拟不断变化的结构与多个精力充沛的力量和动力学过程。 近年来发展起来的变分方法提供了一个令人振奋的前景。 它扩展了连续介质力学中的既定方法，除了变形之外，还将质量迁移作为一个独立的运动学变量。 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。 在过去的注意力一直集中在特定的现象，如外延膜的不稳定性和互连voiding.This建议解决了几个基本问题，将出现在实现一个通用的代码。 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无处不在，而且它们的实现问题是通用的。 具体而言，我们会研究以下几个方面： * 表面能各向异性 * 广义弹性力 * 应变相关的表面能我们将发展他们的有限元法的分析基础，在我们的计算机代码中实现它们，并使用代码来模拟突出其效果的几种现象。 在小长度和长时间尺度上对这些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和技术意义的领域。

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.