Multiresolution sparse decomposition for ultrasonic fault diagnosis in advanced packaging

Abstract

Quantitative defect evaluation using high-frequency scanning acoustic microscopy remains challenging when echoes from multilayer structures are strongly overlapped. A multiresolution matching pursuit (MRMP) method is proposed for echo separation and defect quantification. The method integrates a physically motivated band-limited echo-atom model and a hierarchical sparse decomposition scheme that combines coarse localization, recursive segmentation, and local dictionary refinement. This strategy improves echo-atom alignment while avoiding the computational cost of a globally dense dictionary. Finite-element simulations and experiments on bonded wafers and flip-chip (FC) package are used to validate the method. The MRMP separates adjacent echo components with a demonstrated axial spacing of 16.86 μm in silicon under the present 1 GSa s−1 sampling condition, corresponding to sub-wavelength spacing. For bonded-wafer signals, the MRMP achieves a signal-to-noise ratio of 18.7 dB and a normalized reconstruction error of 11.52%. For FC solder-bump void evaluation, the estimated void ratio decreases from 35.22% using conventional C-scan and 30.02% using fixed-dictionary orthogonal matching pursuit to 18.75%, close to the x-ray reference of 15.35%. The results show that the MRMP improves echo separability and quantitative reliability for ultrasonic inspection of advanced packaging.