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Frost H, Hayashi Y, Thompson C, Walton D. The Effect of Variability Among Grain Boundary Energies on Grain Growth in Thin Film Strips. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-338-295] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTGrain growth in thin-film strips is important to interconnect reliability because grain boundary structures strongly effect the rate and mechanism of electromigration-induced failure. Previous simulations of this process have indicated that the transformation to the fully bamboo structure proceeds at a rate which decreases exponentially with time, and which is inversely proportional to the square of the strip width. We have also reported that grain boundary pinning due to surface grooving implies that there exists a maximum strip width to thickness ratio beyond which the transformation to the bamboo structure does not proceed to completion. In this work we have extended our simulation of grain growth in thin films and thin film strips to consider the effects of variations in grain boundary energy. Boundary energy is taken to depend on the misorientation between the two neighboring grain and the resulting variations in grain boundary energy mean that dihedral angles at triple junctions deviate from 120°. The proportionality between boundary velocities and local curvatures, and the critical curvature for boundary pinning due to surface grooving also both depend on boundary energy. In the case of thin-film strips, the effect of boundary energy variability is to impede the transformation to the bamboo structure, and reduce the width above which the complete bamboo structure is never reached. Those boundaries which do remain upon stagnation tend to be of low energy (low misorientation angle) and are therefore probably of low diffusivity, so that their impact on reliability is probably reduced.
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Frost H, Hayashi Y, Thompson C, Walton D. The Effect of Solute Drag on Grain Growth in Thin Films. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-317-431] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTWe have modelled the microstructural evolution of polycrystalline thin films during grain growth under the situation in which grain boundary migration becomes impeded by solute drag. For this we use a two-dimensional simulation of capillarity-driven grain growth in which grain boundaries migrate at velocities proportional to local curvature. At high driving forces, corresponding to high curvatures, the boundaries are given a mobility corresponding to drag-free motion. At low driving forces, corresponding to curvatures less than some critical value, the boundaries are given a lower mobility which models the effect of solute drag. During grain growth the average curvature of boundary segments decreases. When the boundary curvatures begin to fall below the critical curvature, the grain size distribution evolves to a lognormal distribution, which is maintained as significant further grain growth occurs. This is in accordance with many experimental grain size distributions which are commonly observed to be lognormal.
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