Inverse derivation of constants for the constitutive equation and fatigue model of PB-free solder joints based on experiment results, finite element simulation and virtual optimization methodology

Weidong Xie, Mudasir Ahmad (CISCO Systems)

CHALLENGE - Solder joint reliability of Pb-free ball grid array (BGA) components, one of the most commonly used microelectronic devices, is a major concern in product development and qualification. Accelerated Thermal Cycling (ATC) testing, very time consuming and costly, is the primary means to evaluate reliability. A fine-tuned modeling methodology is important in producing quick-turn judgments and risk assessments to expedite product development. The two most critical elements in simulating solder joint reliability are 1) the solder constitutive equations, which describe the solder creep behavior under different working conditions, and 2) the fatigue model which ties the damage index from finite element modeling together with the experimental results. In this study, a novel approach has been explored in which the constants of the constitutive equation and fatigue model for Sn-based Pb-free solder joints were derived inversely based on ATC results of a ceramic BGA test vehicle. 

SOLUTION - In order to cover the typical end-use conditions of the targeted products, the test vehicle was assembled onto PCBs with two different thicknesses and then thermal cycled under three different temperature profiles. The basic idea was that all of the constants, both for the constitutive equation and the fatigue life prediction model, were initially given as a range. Then by utilizing the modeFRONTIER, the FE model was coupled with the virtual optimization algorithm to derive simultaneously all the constants that yielded the best fatigue life predictions compared to the test results. To simplify the problem without compromising the generality, a hyperbolic sine creep constitutive equation and Coffin-Manson fatigue model were selected in the analysis. There were a total of 6 constants to be determined; the initial ranges of the constants were defined by fitting the creep experimental data for a variety of Sn-based solder materials. Available in other publications, the selected solder materials cover a wide range of both Ag and Cu content which therefore represent the typical behavior of the most commonly adopted solder materials by the industry. To reduce the computational cost and enable fast convergence of multiple generation iterations required by the multiple objective optimization algorithms, a very-well benchmarked submodel has been employed. 

BENEFITS - Furthermore, by utilizing ANSYS® high performance computing (HPC) capability, cloud computing, and modeFRONTIER, the computational time was reduced significantly. An overall good correlation was achieved between the fatigue life prediction using the constants derived by this approach and the test characteristic life. Shown in Figure 15 was the predicted life versus test life. It is noted that the goodness of fitting, the coefficient of determination, R2 is 0.85.