Modeling and Analysis of Multiple Coupled Through-Silicon Vias (TSVs) for 2.5-D/3-D ICs

In this paper, we, for the first time, modeled and analyzed through-silicon vias (TSVs) in the multi-conductor transmission. TSV is one of the essential technology for 2.5-D/3-D ICs, Definitely, a significant number of TSV must be integrated for the direct vertical interconnections. In this point of view, it is important to propose the accurate modeling and analysis for the multiple coupled-TSVs. Firstly, we utilized the loop inductance matrix to model the self- and mutual-inductance respectively. With the assumption of the quasi-TEM propagation, the capacitance and conductance matrix were subsequently calculated to model the self- and mutual- components. The proposed multiconductor TSVs model was compared with an electromagnetic (EM) solver. The analysis of TSVs was performed based on the insertion loss at frequencies ranging from 0.01 GHz to 20 GHz. From the proposed modeling methodology, the evaluation of an electrical performance for the multiple numbers of TSVs becomes possible. In addition, signal coupling paths were discussed based on the proposed equivalent circuit model and it was observed that the equivalent conductance path is dominant in the signal couplings.