Integration of machine learning with phase field method to model the electromigration induced Cu_(6)Sn_(5) IMC growth at anode side Cu/Sn interface

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,Cu_(6)Sn_(5) 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 10×10^6A/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 kemdata 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.

Combining thermodynamics with tensor completion techniques to enable multicomponent microstructure prediction

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.