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...

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Bibliographic Details
Published in:IEEE transactions on components, packaging, and manufacturing technology (2011) Vol. 15; no. 5; pp. 1014 - 1024
Main Authors: Kumar, Ajay, Dhiman, Rohit
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.05.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Analytical models
Approximation
Aspect ratio
Crosstalk
Equivalent circuits
exponential matrix-rational approximation (EM-RA)
Glass
Inductance
Integrated circuit modeling
Optical scattering
Packaging
Parameters
Phonons
Signal integrity
signal integrity performance
Skin effect
Solid modeling
Stability criteria
Surface roughness
taper effect
Three-dimensional displays
through package vias (TPVs)
ISSN:2156-3950, 2156-3985
Online Access:Get full text
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Summary: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-<inline-formula> <tex-math notation="LaTeX">1.5~\mu </tex-math></inline-formula>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.
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ISSN:2156-3950
2156-3985
DOI:10.1109/TCPMT.2025.3553362