Implementation of the Homogenization Method in the Numerical Estimation of Wafer Warpage

Abstract

Given the growing global demand for high-performance microcomponents, while keeping the size of the microcomponents as small as possible, several manufacturers have chosen to increase the number of thin layers to increase the integration density. These thinner layers cause warping-type deformations during processing. In this study, warping during the development of a stacking composed of a silicon substrate coated with two thin layers, one dielectric in undoped silicate glass (USG) and the other metallic in platinum, was numerically analyzed and validated by comparison with experimental measurements. The numerical study presented in this paper has several components that make it simple and reliable. Indeed, simplifications of the loading conditions were introduced and validated by comparison with experimental results. Another part of the simplification is to integrate a homogenization approach to reduce the number of calculations. The efficiency and precision of the homogenization approach were validated for the mechanical and thermomechanical models by comparing the heterogeneous and homogenized models.