The Effect of Variability Among Grain Boundary Energies on Grain Growth in Thin Film Strips

Abstract

Grain 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 1200. 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. INTRODUCTIONGrain growth in thin film strips has recently become an important concern for reliability because of the reduced width of aluminum interconnect lines and the associated increase in electric current densities. The resistance to electromigration-induced damage is largely determined by the grain boundary microstructure present. In previous work [1-3] we simulated the evolution of the grain structure in thin film strips using the approximation that all boundaries had identical mobilities and energies. The first condition considered was the case in which there is no boundary pinning due to surface grooving. If the initial grain size is sufficiently small compared to the line width there may be a period of normal grain growth. As grain growth proceeds, a few grains will eventually span the width of the line, creating bamboo segments separated by non-bamboo segments or polycrystalline clusters. The grain structure evolution proceeds by the shrinkage of the polycrystalline segments. At any given time the distribution of cluster lengths is approximately exponential. Each cluster shrinks in length at a rate which is approximately constant, and this behavior results in an exponential decay of the fraction of the line which is not bamboo. The time required for a line to become completely bamboo is determined by the length of the longest cluster. It is therefore a statistically variable quantity which depends on line length. Furt...

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