Modeling of coupled TSVs in 3D ICs

This paper presents analytical formulas to extract an equivalent circuit model for coupled through silicon via (TSV) structures in a 3D integrated circuit. We make use of a multiconductor transmission line approach to model coupled TSV structures. TSVs are embedded in a lossy silicon medium, hence they behave as metal-insulator-semiconductor (MIS) transmission lines. The models we present can accurately capture the transition between slow-wave and dielectric quasi-TEM modes, which are characteristic for MIS transmission lines, as well as the metal-oxide-semiconductor (MOS) varactor capacitance. The results are validated against 2D quasi-static simulations and 3D full-wave electromagnetic simulations. The derived equivalent circuit models can easily be applied in circuit simulators to analyze crosstalk behavior of TSVs in a 3D integrated system.