RVE Hybrid Slim Sector Model for Efficient Analysis of Solder Joint Reliability

Abstract

With the relentless trend in ever-increasing number of I/Os on packages and the decreasing pitch of interconnects on packages, the task of modeling the fatigue life of the interconnects is becoming evermore challenging. This paper presents a RVE hybrid slim sector model which could be employed to meet the challenge. In this model, almost all the interconnects between chip and substrate are replaced by an equivalent layer except for a few including and around the critical interconnect. The effective mechanical properties of the equivalent continuum layer are evaluated using a 3-D representative volume element (RVE) based on continuum mechanics and a numerical homogenization method. Formulae to extract the effective material constants are derived using elasticity theory. With finite element analysis of four cases of loading to the RVE, a transversely isotropic plasticity model is developed. Characteristic parameters for Hill's formulation are extracted from the numerical experiments. Temperature dependent mechanical properties are taken into account. A thermomechanical analysis of a 6/spl times/6mm/sup 2/ flip chip package was carried out the RVE hybrid slim sector model and compared with the detailed one-eight model. The results show that the differences in displacements computed is about 3/spl sim/5%. Consequently, the error percentage in the maximum inelastic shear strain and fatigue life prediction is about 5% and 9%, respectively. The improvement in efficiency in terms of preprocessing and computational time is enormous.