Sampling-Biorthogonal Time-Domain Technique for Temperature-Dependent Transient Analysis of Coaxial-TGVs in 3-D Integration

A novel sampling-biorthogonal time-domain (SBTD) technique by considering the positive sampling basis and biorthogonal dual testing functions is developed to accurately model temperature-dependent crosstalk effects in circular and square coaxial-through glass vias (C-TGVs). An equivalent transmission-line model employing EM theory-based Bessel and Neumann functions to establish closed-form formulae for the frequency- and temperature-dependent resistance, inductance, capacitance, and conductance (per-unit-height) of both C-TGV configurations is presented. The efficacy of proposed SBTD technique is verified with SPICE results and conventional finite-difference time-domain (FDTD) technique. The SBTD technique proves more efficient with respect to FDTD, exhibiting less than 0.7% average error in estimating dynamic crosstalk-induced delay with lesser computational effort. Therefore, it is very useful for addressing the issues of electromagnetic interference and electromagnetic compatibility in 3-D integration.