Integration of machine learning with phase field method to model the electromigration induced Cu6Sn5 IMC growth at anode side Cu/Sn interface

Abstract

Currently, in the era of big data and 5G communication technology, electromigration has become a serious reliability issue for the miniaturized solder joints used in microelectronic devices. Since the effective charge number (Z*) is considered as the driving force for electromigration, the lack of accurate experimental values for Z* poses severe challenges for the simulation-aided design of electronic materials. In this work, a data-driven framework is developed to predict the Z* values of Cu and Sn species at the anode based LIQUID, Cu6Sn5 intermetallic compound (IMC) and FCC phases for the binary Cu-Sn system undergoing electromigration at 523.15 K. The growth rate constants (kem) of the anode IMC at several magnitudes of applied low current density (j = 1 × 106 to 10 × 106 A/m2) are extracted from simulations based on a 1D multi-phase field model. A neural network employing Z* and j as input features, whereas utilizing these computed kem data as the expected output is trained. The results of the neural network analysis are optimized with experimental growth rate constants to estimate the effective charge numbers. For a negligible increase in temperature at low j values, effective charge numbers of all phases are found to increase with current density and the increase is much more pronounced for the IMC phase. The predicted values of effective charge numbers Z* are then utilized in a 2D simulation to observe the anode IMC grain growth and electrical resistance changes in the multi-phase system. As the work consists of the aspects of experiments, theory, computation, and machine learning, it can be called the four paradigms approach for the study of electromigration in Pb-free solder. Such a combination of multiple paradigms of materials design can be problem-solving for any future research scenario that is marked by uncertainties regarding the determination of material properties.