Transient Analysis of Through Package Coaxial Vias in Glass Interposers Based on SBTD Method

Coaxial through-glass vias (C-TGVs) are crucial components in 3D integration systems due to their potential to enhance signal integrity. To derive closed-form formulas for the calculation of per-unit-height ($p.u.h$) resistance ($R$), inductance ($L$), capacitance ($C$) and conductance ($G$) of C- TGV, an equivalent transmission line model incorporating Bessel and Neumann functions are utilized. A novel sampling- biorthogonal time-domain (SBTD) method using positive sampling basis and biorthogonal dual testing functions to precisely model the crosstalk effects in C-TGVs is developed. The SBTD model exhibits superior accuracy and efficiency in estimating crosstalk-induced delays while reducing computational effort, over SPICE and the conventional finite- difference time-domain (FDTD) method. These attributes highlight the importance of SBTD in addressing EM interference and compatibility issues in the advanced 3D integration systems.