A wavelet analysis on digital microstructure in microbumps

Heterogeneous three-dimensional system integration is the ultimate goal for packaging and integration, where materials are pushed to their physical limits. In this context, the microstructure of packaging materials, which exhibits a multi-scale nature, will be carefully designed and tightly controlled in both manufacturing and in-service conditions to ensure long-term reliability of the electronic products. A multi-level discrete wavelet transform using the haar wavelet is conducted on the dendritic structures, simulated with a phase field model, during solidification in microbumps with different sizes and geometries. The statistical data, e.g. the mean, standard deviation and energy, of the detail coefficients from the wavelet analysis reveal a wealthy of information on the features of the dendritic structure and its evolution during solidification at multiple resolutions. The size and geometry effects on the microstructure formed in the microbumps can thus be quantified by such data. Further studies using techniques such as principle component analysis and Radon transform can be conducted to evaluate the consistence of the result.