A method for quantification of the effects of size and geometry on the microstructure of miniature interconnects

Because the heterogeneity of microstructure has significant effects on the material properties of ultrafine interconnects, it should be quantified, to facilitate high-fidelity prediction of reliability. To address this challenge, a method based on autocorrelation and singular value decomposition is proposed for quantitative characterization of microstructure. The method was validated by developing a quantitative relationship between reported microstructure and tensile strength for SnAgCuRE solders reported in the literature. The method was used to study the effects of size and geometry in ultrafine Sn37Pb interconnects on microstructure and von Mises stress, which were obtained simultaneously by coupling a phase-field model with an elastic mechanical model. By use of this method the degree of heterogeneity of the microstructure in relation to preferred growth directions of the phases was quantified by use of a scalar microstructure index. It was found that microstructure heterogeneity increases with decreasing standoff height, and is higher for hourglass-shaped solder joints. The average von Mises stress was found to be positively related to the microstructure index. The strong correlation between microstructure index and average von Mises stress was confirmed by nonlinear regression analysis using an artificial neural network. This indicates that the mechanical behavior of ultrafine interconnects can be predicted more accurately on the basis of the microstructure index.