Monte Carlo-Based Stochastic Finite Element Model for Electromigration in the Interfaces of SAC Solder and Cu Conductors with Uncertainties in Boundary Conditions

The time-dependent progress of electromigration (EM) in the interfaces of Sn-Ag-Cu solder and Cu conductors is sensitive to the uncertainties in boundary conditions. A Monte Carlo-based stochastic finite element model (MC-SFEM) by the combination of finite element computation with stochastic sampling is proposed in this paper. According to the comparison of different periods and time step scales, the accuracy and convergence of the computational results are recorded. Furthermore, based on the huge database of MC-SFEM, statistical results are compared and analyzed. The correlations of the initial temperature and electrical current with the concentration and gradient of concentration in the interfaces are discussed. The proposed MC-SFEM provides an effective method to perform uncertainty propagation in EM and predict matter concentration in the interfaces with satisfying accuracy and computational robustness. Graphical Abstract