Modeling of Crosstalk in Through Silicon Vias

Abstract—This paper presents analytical formulas to extract an equivalent circuit model for coupled through silicon via (TSV) structures in a 3-D integrated circuit. We make use of a multicon-ductor transmission line approach to model coupled TSV struc-tures. TSVs are embedded in a lossy silicon medium, hence they be-have as metal–insulator–semiconductor (MIS) transmission lines. The models we present can accurately capture the transition be-tween slow-wave and dielectric quasi-TEM modes, which are char-acteristic for MIS transmission lines, as well as the metal–oxide– semiconductor (MOS) varactor capacitance. The results agree well with 2-D quasi-static simulations and 3-D full-wave electromag-netic simulations. The derived equivalent circuit models can easily be applied in circuit simulators to analyze crosstalk behavior of TSVs in a 3-D integrated system. Index Terms—3D IC, crosstalk, metal–insular–semiconductor (MIS) transmission line, through silicon via (TSV)