Modern electronic devices are solid structures of submicron feature sizes. Not only do they serve electronic functions, but also they must maintain structural integrity during fabrication and use. The field of small structures is a relatively new one, to which solid mechanics researchers can make substantial contributions. This proposal addresses a unifying theme for many problems in this field: structural evolution. In a solid structure, diffusive processes can relocate mass, so that the configuration of the structure may change over time. For example, a film may break into islands, and an interconnect may grow cavities. While studies of some of such phenomena go back many years, recent technological developments demand much more sophisticated capabilities. Today general-purpose finite element codes can analyze stress fields in complex structures. However, no such a code exists to simulate evolving structures with multiple energetic forces and kinetic processes. A variational approach developed recently offers an exiting prospect. It extends the established approach in continuum mechanics by including mass relocation as an independent kinematic variable, in addition to deformation. The approach can include energetic forces ranging from mechanical stress to electron wind, and kinetic processes ranging from grain boundary migration to surface diffusion. Attention in the past has been focused on specific phenomena, such as epitaxial film instability and interconnect voiding. This proposal addresses several basic issues that will arise in implementing a general-purpose code. Emphasis is placed on aspects related to surface energy and elastic energy, because both energetics are ubiquitous in small solid structures, and because their implementation issues are generic. Specifically, we will examine the following aspects: * Surface energy anisotropy * Generalized forces due to elasticity * Strain-dependent surface energy We will develop their analytic basis for the finite element method, implement them in our computer code, and use the code to simulate several phenomena that highlight their effects. The study of the phenomena at small length and long time scales will push the envelope of the Solid Mechanics discipline into a field of great scientific and technological importance.
