Thermo-mechanical optimization of ceramic substrate with through ceramic vias by Taguchi-Grey method

Through ceramic via (TCV) interconnection technology has emerged as a promising technology applied to high-density three-dimensional (3D) packaging. However, due to the large coefficient of thermal expansion (CTE) difference between the copper-filled TCV and the ceramic substrate, the reliability of TCV is always a problem of ceramic substrate cracks under thermal cycling. In this paper, finite element simulations combined with Taguchi-Grey method are used to optimize the thermo-mechanical behaviors of the ceramic substrate with in-line copper-filled TCVs. An L27 (36) orthogonal array integrated with Grey relational analysis (GRA) are employed to assess the influences of TCV diameter, TCV height, pitch, substrate material, metal layer thickness and substrate cross-sectional area on the thermal deformation, thermal stress and plastic strain. The results indicate that the substrate material and the metal layer thickness are the most important parameters that affect thermal deformation, with the contribution ratios of 40.82% and 31.44%, respectively. For thermal stress, the effects of substrate material, TCV diameter and pitch are account for 46.7%, 26.49%, and 9.38%, respectively. For plastic strain, the TCV diameter has the largest effect, reaching 69.43%. The optimal design parameters are also derived by using GRA and weighting method to compromise each response.