An Anisotropic Equivalent Thermal Model for Shield Differential Through-Silicon Vias

Abstract

An accurate equivalent thermal model is proposed to calculate the equivalent thermal conductivity (ETC) of shield differential through-silicon via (SDTSV). The mathematical expressions of ETC in both horizontal and vertical directions are deduced by considering the anisotropy of SDTSV. The accuracy of the proposed model is verified by the finite element method (FEM), and the average errors of temperature along the X-axis, Y-axis, diagonal line, and vertical directions are 1.37%, 3.42%, 1.76%, and 0.40%, respectively. Compared with COMSOL, the proposed model greatly improves the computational efficiency. Moreover, the effects of different parameters on the thermal distribution of SDTSV are also investigated. The thermal conductivity is decreased with the increase in thickness of SiO2. With the increase in pitch, the maximum temperature of SDTSV increases very slowly when β = 0° , and decreases very slowly when β = 90°. The proposed model can be used to accurately and quickly describe the thermal distribution of SDTSV, which has a great prospect in the design of 3D IC.