An ADI–SBTD Technique Free of CFL Stability Condition for Transient Analysis of Coaxial–TGVs in 3D Integration

This paper presents an alternating direction implicit – sampling-biorthogonal time-domain (ADI–SBTD) based formulation, free of the Courant-Friedrichs-Lewy stability condition, for accurate and efficient characterization of the transient analysis of coaxial through-glass vias (C-TGVs). Unlike traditional finite-difference time-domain (FDTD) algorithm, multi-resolution time-domain (MRTD), and sampling biorthogonal time-domain (SBTD) methods, the ADI–SBTD technique retains unconditional stability, thus enabling reliable transient simulations at significantly larger time steps. This leads to a substantial reduction in computational effort without compromising accuracy. The method is exhaustively validated against both the SPICE simulations and the SBTD approach, demonstrating excellent agreement with an average error of less than 1% in the several key performance parameters for examining the transient crosstalk effects in C-TGVs. Comparative studies demonstrate that the ADI-SBTD computational framework achieves accuracy at par with both the SBTD and SPICE-based results, thus confirming its reliability and effectiveness for high-fidelity signal analysis in three-dimensional (3D) integrated systems. Moreover, this approach exhibits superior computational efficiency than the SBTD, thus making it a practical solution for addressing the issues of electromagnetic interference and electromagnetic compatibility in 3D integration.