Signal integrity analysis in mixed CNT bundle interconnects using EM-RA

Abstract

This paper presents the exponential matrix-rational approximation (EM-RA) technique for signal integrity analysis in on-chip mixed-carbon-nanotube (CNT) bundle (MCB) interconnects incorporating the temperature (T) and dielectric surface roughness (DSR). The variations considered are temperature, ranging from 300 to 500 K, and dielectric surface roughness (DSR), spanning from 10 to 180 pm. The impact on the area and delay of the MCB interconnect is observed by varying the shells of multi-walled CNTs (MWCNTs) and the number of single-walled CNTs (SWCNTs). Using the proposed EM-RA technique for MCBs, the delay in three-line coupled interconnects is obtained by simplifying its multi-conductor transmission line representation to an equivalent single-conductor model. The transient response has been obtained through SPICE simulation across different numbers of conducting channels in MWCNTs compared to SWCNTs and is validated using EM-RA. The in-phase and out-of-phase delays are computed in this paper considering varying temperatures and dielectric surface roughness for different conducting channels of MWCNTs in relation to SWCNTs. From SPICE simulations, it is observed that with fewer shells in MWCNTs, the MCB on average requires 40.42% smaller area in comparison to the bundled SWCNTs for the same crosstalk delay. Subsequently, for the equivalent MCB area, the delay improves by 47.18% for MWCNTs with fewer shells than for bundled SWCNTs.