A Variational Approach to Stimulating Evolving Small Structures

9820713现代电子器件是具有亚微米特征尺寸的固体结构。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。小结构领域是一个相对较新的领域，固体力学研究人员可以做出实质性的贡献。这一建议解决了这一领域许多问题的统一主题：结构演变。在固体结构中，扩散过程可以重新安置质量，因此结构的形态可能会随着时间的推移而改变。例如，薄膜可能会破裂成岛屿，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许多年前，但最近的技术发展需要更复杂的能力。目前，通用有限元程序可以分析复杂结构的应力场。然而，没有这样的代码存在来模拟具有多重能量力和动力学过程的进化结构。最近开发的一种变异方法提供了一个令人振奋的前景。它扩展了在连续介质力学中建立的方法，包括质量重定位和独立的运动学变量，除了变形。该方法可以包括从机械应力到电子风的高能力，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，如外延膜不稳定和互连空洞。该建议解决了在实现通用代码时可能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，因为这两种能量在小型固体结构中无处不在，而且因为它们的实现问题是通用的。具体来说，我们将研究以下几个方面：*表面能各向异性*由于弹性引起的广义力*应变依赖的表面能。我们将为有限元方法开发它们的分析基础，在我们的计算机代码中实现它们，并使用代码模拟几种突出其影响的现象。对小长度和长时间尺度现象的研究将推动固体力学学科的极限进入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.