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More services...Grain Boundary Migration Model in Copper Interconnects
Tim Cale, Daniel Bentz, and Max Bloomfield, RPI
We discuss the use of 3D grain continuum modeling to study grain boundary migration driven by differences in strain energy density. COMSOL Multiphysics is used to compute stresses and strain energy densities in polycrystalline structures caused by temperature changes.
We treat each grain as a single crystal, with the anisotropic elastic properties of single crystal Cu appropriately rotated to match grain orientation in space. The grain boundary speeds are computed using a simple model that relates them to grain boundary mobility and differences in strain energy density on either side of grain boundaries.
The grain boundaries are moved using a multiple-material interface tracking program, PLENTE. We demonstrate the modeling procedure using a structure consisting of a <100> grain in a <111> fiber textured film with hexagonal grains. Velocities computed in response to thermally induced stresses are imported into PLENTE where the structure is moved. The <100> grain is seen to grow, as is seen in experiments. In our second example, PLENTE is used to form a short section of a Cu line. A body fitted mesh is imported into CM where speeds are computed and sent to PLENTE, where the grain structure is evolved. Significant grain boundary evolution is seen after a few tens of minutes.
