Integration of data-driven approach with theory,computation and experiment.• Free energy density function introduced for thermomigration.• Heat of transport for Cu in Cu 6 Sn 5 phase determined using neural network analysis.• Cold side IMC grain growth modeled using multi-phase field method.
Multicomponent alloys show intricate microstructure evolution, providing materials engineers with a nearly inexhaustible variety of solutions to enhance material properties. Multicomponent microstructure evolution simulations are indispensable to exploit these opportunities. These simulations, however, require the handling of high-dimensional and prohibitively large data sets of thermodynamic quantities, of which the size grows exponentially with the number of elements in the alloy, making it virtually impossible to handle the effects of four or more elements. In this paper, we introduce the use of tensor completion for highdimensional data sets in materials science as a general and elegant solution to this problem. We show that we can obtain an accurate representation of the composition dependence of high-dimensional thermodynamic quantities, and that the decomposed tensor representation can be evaluated very efficiently in microstructure simulations. This realization enables true multicomponent thermodynamic and microstructure modeling for alloy design.npj Computational Materials (2020) 6:2 ; https://doi.
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* pose severe challenges for 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× 10 6 to 10 × 10 6 A/m 2 ) 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 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 the aspects of experiments, theory, computation and machine learning, it can be called the four paradigms approach for 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 determination of material properties.
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