Reliability-based design optimization for land grid array solder joints under thermo-mechanical load

Abstract

This paper presents a reliability-based design optimization methodology for second level electronic package solder joints. Due to the inherent variances in physical processes, the product performance is usually a random quanitity of certain probability distribution. The reliability-based design optimization aims to find the most robust as well as effective design in the possible design space. In this paper, the reliability-based design optimization is defined as a multi-objective design optimization problem: one design objective is to maximize the system performance; another is to minimize the performance variance. Differential Evolution optimization algorithm has been modified to handle the multi-objective constrained problems. The response surface is generated with finite element simulations to model the output of the system in the given design space. The probability analysis of the system output is performed on the response surface using Quasi-Monte Carlo simulation method. As a test vehicle, a generic Land Ball Array package interconnect reliability design optimization is analyzed. The Young's modulus, coefficient of thermal expansion, and thickness of the printed wiring board are considered as the controllable design parameters. Meanwhile, the material properties and thickness of the substrate of the package are specified at the their nominal design with the given tolerances as uncontrollable noise parameters. Pareto-optimal solutions of the plastic work and its variance are used to present the possible optimum designs under the temperature cycling load conditions. By applying the reliability-based design optimization procedure the best design for the most effective and robust system performance is abtained.