Signal Integrity Analysis of Tapered Through Packaging Multibit Glass Vias Using Exponential Matrix–Rational Approximation Technique

In this article, we develop a wideband scalable analytical model of tapered through packaging differential multibit vias (TP-DMVs) with pads in glass interposer by developing an exponential matrix-rational approximation (EM-RA) technique. An electrical RLGC model, which also includes the skin effect, is proposed as a function of geometric parameters of tapered through glass vias. The scalability of RLGC equivalent circuit is verified in terms of S-parameters against the 3-D electromagnetic (EM) high-frequency structure simulator (HFSS) up to 100 GHz, for a wide variety of tapered TP-DMV dimensions, including the effects of slope angle and aspect ratio. The maximum reduction in capacitance and conductance values of tapered TP-DMVs with a slope angle is ~75%, while the maximum increase in resistance and inductance value is ~93%. The signal integrity parameters, such as crosstalk, time to reach peak crosstalk, and propagation delay under the influence of surface roughness (SR) and temperature variations, are computed using the EM-RA technique and industry-level simulator SPICE. The variations include temperature and glass SR ranges from (300–500 K) and (150– $1.5~\mu $ m). The comparison shows excellent conformity with less than 1% error. Through the proposed EM-RA technique and Nyquist stability criterion, it is shown that, by increasing the slope angle and pitch, the tapered TP-DMVs become relatively more stable.