Transient analysis of graphene-based on-chip interconnects using closed-form MRA model

Abstract

Abstract As interconnects in very-large-scale-integration technology shrinks into the sub-22 nm regime, carbon nanotubes, graphene nanoribbons (GNRs), and Cu-GNRs are emerging as potential replacements for conventional copper on-chip interconnects. This paper presents an matrix-rational-approximation (MRA) model for the fast transient analysis of graphene-based on-chip interconnects. The proposed model’s key feature is that it allows the mathematical representation of the transfer function matrix of on-chip graphene-based interconnect networks in the frequency-domain using closed-form rational functions. The network’s rational functions coefficients are derived from per-unit-length parameters and predetermined coefficients of the Padé approximation. The graphene-based network’s time-domain model is directly obtained from the rational function frequency-domain model without any numerical integration techniques. This makes the proposed MRA model more numerically efficient than conventional simulation program with integrated circuit emphasis (SPICE) models. The results obtained using the proposed model show less than 1% error when compared with HSPICE simulations, ensuring the proposed model’s excellent accuracy. A wide eye-height of 0.8137 V and eye-width of 219.87 ps are obtained for the eye-diagram analysis of multilayer graphene nanoribbon lines at 4 Gbps.