Exponential Matrix–Rational Approximation (EM-RA) Model for SWCNT Bundle and Hybrid Cu-CNT Interconnects

This article presents a variation-aware exponential matrix–rational approximation (EM-RA) model for the signal integrity analysis in single-walled carbon nanotube (SWCNT) bundle and hybrid copper-CNT (Cu-CNT) on-chip interconnects. The variations include temperature (300–500 K) only, and temperature (300–500 K) and dielectric surface roughness (10–180 pm) both. The transient analysis is carried out for the signal integrity parameters, crosstalk and propagation delay, estimation using the proposed EM-RA model. The results obtained using the proposed model are compared with the industry-level simulation program with an integrated circuit emphasis (SPICE) simulator. The comparison shows excellent agreement for the results with less than 1% error. The proposed model is also compared for the computational time complexity. It is observed that a speed-up factor of 74.24 and 48.35 is attained using the proposed temperature-parameterized model during the analysis of coupled-two and coupled-three interconnect lines, respectively. The speed-up further increases to 485.41 and 378.35 for coupled-two and coupled-three lines, respectively, when the temperature and dielectric surface roughness parametrized EM-RA model is used. This computational CPU time expense efficiency and the accuracy of the proposed model in comparison to the HSPICE simulator ensures immense possibility regarding its implementation in computer-aided design (CAD) tools for carrying out the transient analysis of SWCNT bundle and Cu-CNT interconnect lines. Encouraging results for the eye-diagram analysis reports 95.54% and 99.37% of the eye height and eye width for the SWCNT network, and 99.77% and 99.96% of the eye height and eye width for the Cu-CNT.