Analytical model of the coupling capacitance between cylindrical through silicon via and horizontal interconnect in 3D IC

Abstract

An accurate yet fast approach is developed to calculate the 2D coupling capacitance between the through silicon via (TSV) and horizontal interconnect wire in 3D IC. We consider the realistic cylinder shape of TSV, and derive the analytical formulas utilizing the idea of field-based analysis. To improve the accuracy, theoretical and numerical results are used to calibrate the formulas. The proposed approach is compared with the commercial field solver Raphael using advanced finite difference method. For the TSV with diameter between 5μm and 10μm and wire with length within 20μm, the error of proposed approach is within 8%. While comparing the computational time, the latter is over 5000X faster than the former.