| Thin film structures of integrated circuits contain many polycrystalline materials. As circuit device dimensions are reduced to increase performance, typical feature sizes of associated polyerystalline structures are also reduced. The dimensions of those structures are approaching the size of grains, and the properties of polycrystalline materials at the level of grains and grain boundaries increasingly are determining circuit performing. In modeling these materials grain boundaries must therefore be modeled explicitly.; For many problems of technological interest, such as hillock formation and electromigration in metal films, the consideration of several coupled physical phenomena (diffusion, stress, electric fields, thermal effects) is required. Efforts thus far to model coupled, physical phenomena in polycrystalline materials typically have been limited to simple grain geometries and analytically determined stresses. The motivation for this work is to create a general field formulation that will enable the treatment of arbitrary boundary value problems on polycrystalline domains. This is accomplished with the development of a detailed thermodynamic basis which reflects lattice-based mechanisms. Continuum level constitutive relations for vacancy flux and stress follow from the thermodynamics in a consistent manner.; The system of equations which results from this treatment requires specialized numerical methods which are developed in this work. Several numerical examples provide test cases for the formulation and begin to address technologically relevant problems. |
