Performance Analysis of MLGNR as VLSI Interconnects

Abstract

Due to rapid scaling of interconnect dimensions and increased operational frequencies of integrated Circuits (ICs) in the deep submicron (DSM) regime, the lateral and vertical dimensions of on-chip interconnects are reduced and approached the mean-free path of electron, which is about 40 nm for copper (Cu) at room temperature. Therefore, the on-chip interconnect delay dominates over the device delay due to its excessive values of equivalent electrical parameters (e.g. R, L and C) in highperformance very large-scale integrated (VLSI) circuits. The increasing resistivity of Cu (due to size effects) together with its low current density (~106 A/cm2) have resulted in its degraded interconnect performance in terms of delay, power dissipation and crosstalk. Hence, the semiconductor industries are looking for an alternative to Cu in the DSM regime. Additionally, it has become essential to find a material that is appropriate for potential on-chip interconnect applications to design a high-performance ICs.Multilayer graphene nanoribbon (MLGNR) viz. a graphene-based carbon nanomaterial has emerged as a potential interconnect material. Graphene that recently drawn considerable attention as a possible alternative for interconnects in the developments of next-generation ICs, which exhibits outstanding physical, mechanical, thermal and electrical properties. Therefore, MLGNR based interconnects have been proposed as the most promising alternative to Cu interconnects at DSM technology nodes. The present work studied the impact of temperature on the performance analysis of capacitively coupled MLGNR interconnects in terms of propagation-delay, power dissipation, power-delay-product (PDP), dynamic crosstalk, functional crosstalk and frequency-spectrum of crosstalk-induced noise at a technology node of 14 nm. For this analysis, undoped (neutral) MLGNR (U-MLGNR) as well as intercalation-doped MLGNR (ID-MLGNR) doped with acceptor type intercalate, for instance, stage-II arsenic pentafluoride (AsF5) and ferrous chloride (FeCl3), are considered. A driver-interconnect-load (DIL) configuration is employed, in which interconnect is modeled with a temperature-dependent equivalent single conductor (ESC) model. In DIL configuration, for an interconnect line the driver is actuated by a CMOS inverter and load is actuated by a lumped capacitive load (CL).A similar studies of aforementioned performance matrices are carried out for capacitively coupled interconnects of mixed carbon-nanotube bundle (MCB) and Cu. Based on these performance matrices, the performance of ID-MLGNR interconnects is further compared with their MCBs and Cu counterparts at 14 nm technology node. Four different structures of MCB viz. MCBs (1-4) with and without tunneling effects are considered. The SPICE simulation results reveal that for about 1mm long global interconnect, in single-interconnect configuration, stage-II AsF5 ID-MLGNR with nearly specular edges have lower delay, power dissipation and PDP (power-delay-product) in comparison to MCBs (1-4) with tunneling effects and conventional Cu, over a temperature range from 300 K-500 K. Among the MCBs (1-4) structures, MCB-1 consistently gives better performance in terms of propagation delay within a temperature range from 300 K-500 K. Moreover, for a varied temperature range from 300 K to 500 K, a significant average relative delay improvement is observed for ID-MLGNR interconnects in comparison to the best delay structure of MCBs i.e. MCB-1 and Cu interconnects. Also, the influence of temperature is examined on the crosstalk performance of the adjacent interconnects of AsF5 ID-MLGNR. Both functional crosstalk-induced noise and dynamic crosstalkinduced delay in two-coupled interconnects configuration of ID-MLGNR are analyzed. For the specified temperature range of 300 K to 500 K, in case of crosstalk-induced noise, the AsF5 ID-MLGNR based long interconnects demonstrates superior performance to its MCBs and Cu counterparts. Moreover, the temperature-dependent crosstalk-induced delay is observed less with ID-MLGNR in comparison with both MCB and Cu interconnects. Using the temperature-dependent (TD) and temperature-independent (TI) circuit models, the variation of the time duration of crosstalk-induced overshoot at victim’s output is also studied at different interconnect lengths (from 200 µm to 1000 µm) of ID-MLGNR. It is noted that the width of the noise pulse obtained using TD circuit models is always less as compared to that obtained using TI circuit models for the entire length of interconnect. Additionally, the present work investigates the impact of GNR’s edge shape in an armchair (AC) and zigzag (ZZ) structures on crosstalk performance of U-MLGNR and ID-MLGNR (both AsF5 and FeCl3 intercalated) interconnects. A capacitively-coupled DIL configuration is employed to analyse both the functional crosstalk and dynamic crosstalk. It is observed that over a temperature range from 300 K to 500 K, crosstalk-induced low noise peaks in ID-MLGNRs are obtained with ZZ-edges as compared to U-MLGNR. Whereas, the time duration of crosstalk-induced noise is small for IDMLGNRs with AC-edges. The smaller values of propagation delay and crosstalk-induced delay are obtained with ID-MLGNR (in particular with AC-edges) as compared to U-MLGNR and MCB. It is also observed that AsF5-intercalated ID-MLGNR outperforms FeCl3-intercalated ID-MLGNR in terms of crosstalk-induced noise and delay Furthermore, an analytical frequency-domain model for the capacitively coupled interconnects of MLGNR and MCB is developed. The proposed model provides physical insight into the transient behaviour of coupled interconnects i.e., the input-output transfer function (derived using the fourthorder pade’s approximations) of coupled interconnects under dynamic switching conditions is used to analyze its 3-dB bandwidth (BW), delay and stability performance. From the obtained results, it is noted that among the U-MLGNR, ID-MLGNR (viz. AsF5-intercalated and FeCl3- intercalated), MCB and Cu interconnects, AsF5- intercalated ID-MLGNR exhibits best 3-dB BW performance. Based on the Nyquist stability criterion for relative stability, interconnects of ID-MLGNR are found to be more stable than their U-MLGNR and MCB counterparts, but less stable than Cu. Also, a frequency-domain model for complementary metal oxide semiconductor (CMOS) gate driven single MLGNR interconnect is derived. It is noted that using the proposed CMOS-gate based model, a 3-dB BW improvement of 12.25× is obtained with global length (≈1000 µm) AsF5-doped-MLGNR with respect to linear resistive model. Further, the investigations on temperature-dependent frequency-domain behavior of the capacitively-coupled interconnects under functional switching conditions reveal that the coupled interconnects of AsF5-intercalated ID-MLGNR with armchair edges are highly capable of filtering out the noise frequency components with rise in temperature. The prime objective of this study is to explore the potential of ID-MLGNR as an eminent interconnect material for the technology node defined in the DSM regime (e.g. 14 nm). Under the ITRS projection, the performance of the single and coupled ID-MLGNR interconnects is predicted and the results are compared with its Cu and MCB counterparts. The results offer valuable insights into the advantages of ID-MLGNR interconnects in the DSM regime.