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This Technical Note is motivated by the need to develop efficient and accurate computer modeling of the electro-deposition process commonly used in the fabrication of chip interconnections. A main difficulty owes to the fact that the deposition process is controlled at the bulk (wafer) scale, while the chip features to be produced are microscopic by comparison. Therefore, to accurately model the process computationally, the discretization must be done in such a way that the microstructural behavior is captured. A brute force approach to this would result in extremely large computational problems. Instead we propose an approach based on a combination of multiscale asymptotics and computations. The asymptotics allows us to first compute the solution in the bulk, having averaged out the microstructures. Secondly, the bulk solution, whose computation does not require a very fine discretization, is corrected by adding terms which may be calculated at the microstructural cell level (independently of the bulk solution). Inherent in the approach is the assumption that the microstructure is locally periodic. We demonstrate the proposed computational approach for a simple 2-D example in order to assess its accuracy. A rigorous mathematical justification of the approach, which can be accomplished using homogenization theory, is deferred .

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Michael Vogelius