Equivalent lumped element models for various n-port Through Silicon Vias networks

This paper proposes an equivalent lumped element model for various multi-TSV arrangements and introduces closed form expressions for the capacitive, resistive, and inductive coupling between those arrangements. The closed form expressions are in terms of physical dimensions and material properties and are driven based on the dimensional analysis method. The model´s compactness and compatibility with SPICE simulators allows the electrical modeling of various TSV arrangements without the need for computationally expensive field-solvers and the fast investigation of a TSV impact on a 3-D circuit performance. The proposed model accuracy is tested versus a detailed electromagnetic simulation and showed less than 6% difference. Finally, the proposed model can be a possible solution to the industrial need for broadband electrical modeling of TSVs interconnections arising in 3-D integration. Also, our presented work provides valuable insight into creating guidelines for TSV macro-modeling.