Frequency response and transient analysis of through glass packaging vias using matrix-rational approximation (MRA) technique for three-dimensional ICs

Abstract

In this paper, a computationally efficient matrix rational approximation (MRA) technique is developed to analyze the electrical behaviour of through packaging vias in glass interposer (TGVs). Using MRA technique, the electrical behaviour of TGVs utilizing differential multi-bit configuration, filled with composite copper-mixed carbon nanotube bundle (Cu-mCNTB), is investigated. A temperature-dependent π-type equivalent circuit of such differential multi-bit (DM) composite TGVs is developed using partial-element equivalent-circuit technique. The effective complex conductivity of Cu-mCNTB is also derived by appropriately considering the effects of temperature-dependent mean free path in CNTs. The frequency dependent differential- and common-mode impedances are obtained up to 100 GHz through PEEC technique. It is analyzed that composite DM-TGVs outperform silicon via counterparts in terms of reduced insertion loss using proposed MRA technique and verified through high-frequency structure simulator (HFSS). The transient analysis including crosstalk-induced propagation delay, peak crosstalk, and peak timing of coupled Cu-mCNTB/composite DM-TGVs is determined through the proposed MRA model, which exhibits error within 1% compared to the SPICE. The robustness of proposed model is examined under a wide variety of test cases including the proposed 5-Cu-mCNTB composite TGV array. For the transient analysis, the CPU runtime using the MRA model is 18.57 × faster than the SPICE. To the best of the authors’ knowledge, it is for the first time that temperature-dependent modeling and crosstalk analysis of coupled TGV structures is reported using MRA technique.