Expectation–maximization machine learning model for micromechanical evaluation of thermally-cycled solder joints in a semiconductor

Abstract

This paper aims to study the microstructural and micromechanical variations of solder joints in a semiconductor under the evolution of thermal-cycling loading. For this purpose, a model was developed on the basis of expectation–maximization machine learning (ML) and nanoindentation mapping. Using this model, it is possible to predict and interpret the microstructural features of solder joints through the micromechanical variations (i.e. elastic modulus) of interconnection. According to the results, the classification of Sn-based matrix, intermetallic compounds (IMCs) and the grain boundaries with specified elastic-modulus ranges was successfully performed through the ML model. However, it was detected some overestimations in regression process when the interfacial regions got thickened in the microstructure. The ML outcomes also revealed that the thermal-cycling evolution was accompanied with stiffening and growth of IMCs; while the spatial portion of Sn-based matrix decreased in the microstructure. It was also figured out that the stiffness gradient becomes intensified in the treated samples, which is consistent with this fact that the thermal cycling increases the mechanical mismatch between the matrix and the IMCs.