A Variational Approach to Stimulating Evolving Small Structures

刺激进化小结构的变分方法

• 批准号: 9820713
• 负责人: Zhigang Suo
• 金额: $ 20万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9820713&HistoricalAwards=false
• 关键词: Variational; Approach; Stimulating; Evolving; Small

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.

9820713Suo现代电子设备是亚微米特征尺寸的固体结构。 它们不仅具有电子功能，而且还必须在制造和使用过程中保持结构完整性。 小型结构领域是一个相对较新的领域，固体力学研究人员可以为此做出重大贡献。 该提案解决了该领域许多问题的统一主题：结构演化。 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，薄膜可能会分裂成岛，而互连可能会形成空腔。 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。 如今，通用有限元代码可以分析复杂结构中的应力场。 然而，不存在这样的代码来模拟具有多种能量力和动力学过程的演化结构。 最近开发的一种变分方法提供了令人兴奋的前景。 除了变形之外，它还通过将质量重新定位作为独立的运动学变量来扩展连续介质力学中的既定方法。 该方法可以包括从机械应力到电子风的能量，以及从晶界迁移到表面扩散的动力学过程。 过去的注意力一直集中在特定现象上，例如外延膜不稳定和互连空洞。该提案解决了在实现通用代码时会出现的几个基本问​​题。 重点放在与表面能和弹性能相关的方面，因为这两种能量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。 具体来说，我们将研究以下几个方面： * 表面能各向异性 * 由于弹性而产生的广义力 * 应变相关的表面能 我们将开发有限元方法的分析基础，在我们的计算机代码中实现它们，并使用代码来模拟几个突出其效果的现象。 对小长度和长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和技术重要性的领域。