A novel response surface method for design optimization of electronic packages

Abstract

The response surface method has been widely used in practical engineering design optimization problems, where the optimal searches are based on the response surfaces mimicking the physical processes or models. Sometimes the response surface method is the only practical option to be able to perform design optimization, such as simulation-based design optimization when the simulations are usually computationally expensive. In conventional approaches, the response surfaces are usually built up using a group of sampling points based on certain design of experiment schemes. The accuracy of the response surface depends largely on the number of sampling points and their distributions in the design space, as well as the approximation functions for the response surface. Currently there is no general method that could achieve the necessary accuracy of a response surface with the minimal expensive (or the number of sampling points). In this paper, a novel sequential response surface updating approach is proposed to improve the efficiency and the accuracy of simulation-based optimizations for electronic packages. It is a dynamic and adaptive approach, which starts with a small number of initial sampling points based on Halton sequence (also called quasi Monte Carlo method), and then refines the response surface by adding more sampling points during the optimization process. This method is demonstrated with a design optimization problem of the thermo-mechanical analyses of a ceramic chip carrier assembly. A simplified thermo-mechanical model is used to perform the interfacial stress analysis of the solder bounding. The objective of is to minimize the interfacial stress by changing the bonding compliance in the specified design space. The case study indicates that, comparing with the conventional direct methods, this approach could greatly improve the computational efficiency of optimization processes with the needed accuracy for simulation-based design optimization.