Pan Pacific Symposium Conference Proceedings


Authors: Ichiro Hirata, Ph. D.
Company: System Jisso Research Laboratories, NEC Corporation
Date Published: 1/24/2008   Conference: Pan Pacific Symposium

Abstract: Intensive downsizing and high performance require packages which are used in mobile devices, such as cell phones, PDAs and notebook PCs. However, these thin packages increase warpages during solder reflow or other assembling processes, then the warpages of these packages cause the solder joints failures between PWB and electronic parts. To prevent the failures, we have been trying to estimate the warpages and optimize the design in early design stages. In these stages, we had usually used FEM (Finite Element Method) elastic simulation, moreover, because packages are made from various kind of resins, we have recently started FEM inelastic simulation, visco-elastic simulation. This simulation technique can predict the warpages with high accuracy, for example, this method can calculate the time history of the changing warpage at the constant temperature stage, even though elastic simulation can't calculate the changing warpage at the constant temperature stage. However, the procedure was very difficult and complicate, so structural-design engineers couldn't use the simulation easily and timely. Therefore, we needed a calculation tool for package warpage without using FEM.

From now, multi-layered beam theory has been published, and the theory can estimate a warpage of a multi-beam very easily, however, it can use in a elastic region only, meanwhile classical visco-elastic theory can calculate a deformation of one beam considered with its visco-elastic property. Then I developed the new algorithm which could couple elastic multi-layered beam theory and visco-elastic theory under the assumption that the relaxation modulii would be constant in each calculation time step. So, the coupled theories were programmed by macro language and installed into the spreadsheet. Also, the warpage of three layered benchmark model was calculated by the spreadsheet with the coupled program and FEM visco-elastic simulation. The calculated result of the spreadsheet was good agreement with that of FEM simulation. Then the designers have easily become to estimate the warpages using this spreadsheet (visco-elastic warpage calculation tool).

Key words: multi-layered beam theory, visco-elastic theory, FEM

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