Multilayer Graphene Nanoribbon Research Articles

Performance investigation of doped multi-layer graphene nanoribbon as interconnects in modern technology nodes

In this paper, the performance of intercalation doped multilayer graphene nanoribbons (MLGNR) with modern technology nodes is meticulously investigated. An unconditionally stable FDTD method is used to analyze the transient output of the circuit. Several cases of MLGNR interconnects under different doping materials, stacking directions and contact modes have been discussed. With multiple experiments carried out, it is shown that the Li-doped MLGNR interconnect with vertical stacking orientation has the most outstanding performance, which has the least delay compared with the traditional Cu interconnect and other counterparts in 3-nm and 5-nm nodes. In summary, the Li-doped vertically stacked MLGNR is very promising for carbon nano interconnects in the next generation of integrated circuits.

Crosstalk optimization and gate oxide reliability analysis in intercalation doped MLGNR with reduced vertical thickness

In this paper, the performance of intercalation doped multilayer graphene nanoribbons (MLGNR) with reduced vertical thickness is investigated, and the impact of crosstalk on latency and gate oxide reliability is analyzed. An unconditionally stable FDTD method is used to analyze the transient output of the circuit. Several cases of MLGNR with reduced vertical thickness under different doping materials, stacking directions and contact modes have been discussed. The experimental data show that the Li-doped MLGNR interconnect with horizontal stacking and side contact (SC) has the most outstanding performance, and the delay fluctuation caused by crosstalk is improved by 17.8 % ∼ 68.1 % compared with the Cu interconnect. When specularity p = 0.2, the PDCP (power delay crosstalk product) is found 44.2 % ∼ 61.5 % lower than the Cu interconnect. In addition, the AFR (average failure rate) has also been investigated, and the data showed that the AFR of Li-doped SC-MLGNR remained lowest among all interconnects discussed, for comparison the Cu interconnect is 4.2–5 times larger than the former. In summary, the vertical thickness reduced Li-doped horizontally stacked SC-MLGNR is very promising as carbon nano interconnects in the next generation of integrated circuits.

High-frequency characteristics of multilayer graphene nanoribbon interconnects: Exploring the implications OF SKIN effect

A study is undertaken to explore the frequency-dependent traits of crosstalk delay (X-D), crosstalk noise area (X-NA), and the mean time to failure induced by electromigration (EM-MTF) in interconnects constructed from lithium-doped multilayer graphene nanoribbon (Li-MLGNR) and their optimized counterparts, known as optimized Li-MLGNR (O-LiMLGNR) interconnects. The analysis is based on the skin depth and impedance model incorporating scatterers and the finite thickness of the interconnect. The obtained high-frequency impedance and performance characteristics reveals that O-LiMLGNR outperforms Li-MLGNR, rough copper, and mixed carbon nanotube bundle in terms of X-D, X-NA, and EM-MTF. Subsequently, the performance of O-LiMLGNR, limited by process and temperature variations, is analyzed at high frequencies under the influence of skin-effect. As a result of variations in process parameters and temperature, the O-LiMLGNR exhibits an increase in variations of X-D and X-NA, accompanied by a reduction in variation of EM-MTF as the frequency increases.

Variable Length and Temperature-Dependent Analysis of MLGNR at Nano-Scale Regime

In this paper, a thermally aware equivalent single conductor is proposed, along with analytical modeling to evaluate the parasitic parameters of multilayer graphene nanoribbon (MLGNR) as interconnect, and its performance is analyzed in terms of delay and power delay product (PDP) for 32[Formula: see text]nm, 22[Formula: see text]nm and 16[Formula: see text]nm technology nodes at variable global interconnect lengths (500–2000[Formula: see text]m). It was examined that with rising temperature, there is a strident decrease in the mean free path (MFP) of GNR interconnect, which further influences its own resistance at global length (2000[Formula: see text][Formula: see text]m) for all three technology nodes. The simulation tool Simulation Program with Integrated Circuit Emphasis (SPICE) is used to estimate and compare MLGNR performance in terms of signal delay and PDP for three different technology nodes. It is revealed from the outcomes that the propagation delay and PDP increase at long interconnects (500–2000[Formula: see text][Formula: see text]m) over a temperature range of 200–500[Formula: see text]K for deep submicron technology nodes (16[Formula: see text]nm, 22[Formula: see text]nm and 32[Formula: see text]nm). A similar investigation was performed on the copper interconnect, and it was discovered that the MLGNR performs better in terms of delay and PDP at global levels with a temperature range of 200–500[Formula: see text]K for nano-scaled technology nodes (32[Formula: see text]nm, 22[Formula: see text]nm and 16[Formula: see text]nm).

Scattering-induced circuit modelling and performance analysis of coupled hybrid Interconnections: Sub-threshold performance evaluation

This paper presents the scattering induced circuit modelling and performance analysis in terms of crosstalk and frequency stability in the newly proposed hybrid interconnects operating in the sub-threshold domain. The electrical performances of hybrid copper carbon-nanotube (HCNT), hybrid copper graphene nanoribbon (HGNR) and hybrid Copper carbon (H Carbon) interconnects are examined and compared with that of copper (Cu), single walled carbon nanotube bundles (SWCNTs) and lithium doped multilayer graphene nanoribbon (MLGNR) interconnects in terms of dynamic and functional crosstalk results by employing the transmission line (TL) analytical model for sub-threshold applications. The impact of the grain-size on the resistivity of Cu and the various scatterings induced mean free path (MFP) on the overall resistance has been analysed in the modelling of HGNR interconnects. The comprehensive analysis of the crosstalk induced delay (dynamic crosstalk), the positive peaks and the time-duration (functional crosstalk) ensures the efficacy of hybrid interconnects, especially H Carbon interconnects in the designing of on-chip interconnects. It has also been observed from the frequency response that the maximum 3-dB bandwidth is obtained in the case of H Carbon hybrid interconnects (approx. 6.7586 × 1010 Hz) at 300 K temperature values. Further, the bandwidth values tend to decrease with the rise in temperature values.

Modeling and performance analysis of coupled multilayer graphene nanoribbon (MLGNR) interconnects with intercalation doping

This paper investigated the temperature‐dependent performance of coupled top contact multilayer graphene nanoribbon interconnects (TC-MLGNRs) with different intercalation doping (viz., AsF5-, FeCl3-, and Li-doped) considering edge roughness and crosstalk effect, compared with SC-MLGNR, MWCNT, and copper (Cu) interconnects for 13.4 nm technology nodes at the global level. Based on the equivalent single conductor (ESC) modeling, a distributed transmission line model for coupled doped TC-MLGNRs is presented to obtain the crosstalk delay, step response, transfer gain, and 3-dB bandwidth, which considers in-phase and out-of-phase crosstalk modes and verified with the Hspice simulation. It is demonstrated that all interconnects at room temperature in the in-phase crosstalk mode outperform those in the out-of-phase crosstalk mode in terms of crosstalk delay, transfer gain, and 3-dB bandwidth, and Li-doped TC-MLGNR significantly reduces crosstalk delay and enhances transfer gain and 3-dB bandwidth compared to other interconnects. Moreover, it is found that the victim line of two-line coupling for doped TC-MLGNRs exhibits less crosstalk delay, greater transfer gain, and 3-dB bandwidth compared to the center line of three-line coupling for doped TC-MLGNRs in the same condition. Furthermore, we analyze the crosstalk delay and 3 dB-bandwidth for two- and three-line doped TC-MLGNRs at varying temperatures and compare them with SC-MLGNR, MWCNT, and Cu interconnects. Simulation results show that crosstalk delay and bandwidth performance are temperature dependent, and they both degrade with increasing temperature. Also, Li-doped TC-MLGNRs still exhibit the best crosstalk delay and bandwidth performance of all interconnects. The numerical calculation results show that decreasing interconnect temperature, increasing line spacing, and reducing edge roughness are efficient methods to reduce crosstalk delay and enhance 3-dB bandwidth for Li-doped TC-MLGNRs. In addition, the results obtained by the proposed model are well matched with the Hspice simulation. Hence, our performance analysis demonstrates that Li-doped TC-MLGNR can be a promising material for global interconnect applications in a thermally variable environment.

Delay characterization of multilayer graphene nanoribbon interconnects in presence of scattering and thermal effects

AbstractScattering source‐based mean free path (MFP) and circuit modeling are proposed for three different configurations of undoped multilayer graphene nanoribbon (U‐MLGNR) (viz. horizontal top‐contact (HTC), horizontal side‐contact (HSC), and vertical top‐contact (VTC)). A similar analysis is carried out for doped HTC‐MLGNR (D‐HTC‐MLGNR) considering dopants viz. Li, FeCl3, and AsF5, for a temperature range of 300–500 K. The optimistic intrinsic‐phonon limited (Λeff,1(T)) and realistic scattering limited (Λeff,2(T)) effective MFP models are considered to derive the equivalent resistance of MLGNR. The performance of MLGNR variants, considering Λeff,1(T) and Λeff,2(T), is compared to copper (Cu) (with smooth and rough surface) in terms of coupled line crosstalk‐induced delay (XT‐D). The results show that the MLGNR variants outperform Cu interconnects in terms of XT‐D, for Λeff,1(T). However, structural edge roughness being the dominant scattering source in Λeff,2(T), severely degrades the performance of MLGNR variants in comparison to Cu counterparts. Moreover, for Λeff,1(T) and Λeff,2(T), Li‐D HTC‐MLGNR outperforms other MLGNR variants. Also, among the MLGNR variants, U‐VTC‐MLGNR exhibits a minimum average relative penalty of 21.58 × 102% in terms of XT‐D, when Λeff,2(T) is considered as against Λeff,1(T). Li‐D HTC‐MLGNR with optimized width exhibits 10.59× lower XT‐D and 8.85× higher XT‐D for Λeff,1(T) and Λeff,2(T), respectively, compared to smooth Cu. The optimized Li‐D HTC‐MLGNR demonstrates a reduction of 85.48% and 74.67% in XT‐D values for Λeff,1 (T) and Λeff,2 (T), respectively, when compared to mixed carbon nanotube (MCNT) bundle interconnects.

High compaction and physical graphitization of CNT bundles and network via extreme-load compression using laser-induced shockwave

The physical properties of carbon nanotube (CNT) networks, which are one-dimensional assemblies of CNTs, are still far short of the theoretical limits of individual CNTs. These lowered physical properties of CNT networks are mainly due to their high porosity and relatively weak inter-tube load/electron/phonon transfer efficiency at van der Waals junctions between CNTs and their bundles. We present a simple post-treatment technique utilizing high-intensity laser-induced shockwaves of up to ∼3 GPa that effectively densify CNT bundles and networks and physically transform CNT bundles into flattened multilayered graphene nanoribbons. CNT assemblies were selectively modified without chemical agents, and the network properties could be tuned by adjusting the laser compression intensity. After laser shockwave compaction, the CNT network structure showed two and three times higher specific strength and modulus than the as-prepared CNT networks. Furthermore, the thermal and electrical conductivities of the CNT networks were also amplified by 400–500% after laser shock compression. These enhancements can be explained by the substantial densification of CNT networks and physically activated graphitization leading to increased load/electron/phonon transfer between flattened CNTs and their bundles.

Simultaneous Switching Noise Effects in Graphene-Based Power Distribution Networks

The simultaneous switching noise (SSN) effects in graphene nanoribbon field effect transistor (GNRFET) based ternary circuits are presented in this study. The performance in terms of SSN induced peak noise and propagation delay on power and ground rails are investigated in multilayer graphene nanoribbon (MLGNR) bundled power interconnects using Hewlett simulation program with integrated circuit emphasis (HSPICE) simulator. Furthermore, these investigations are compared to the copper (Cu) and multiwalled carbon nanotubes (MWCNT) based power interconnects. From the results, it is noticed that the proposed MLGNR interconnects shows performance improvements up to 74.9% and 33.8% over the Cu and MWCNT interconnects. Moreover, the SSN peak noise and delay are investigated for different interconnect lengths from 200 μm to 500 μm. It is observed that the SSN noise on power and ground rail is reduced and propagation delay is increased as interconnect length is increased.

Quantum behaved artificial bee colony based conventional controller for optimum dispatch

<p>Since a multi area system (MAS) is characterized by momentary overshoot, undershoot and intolerable settling time so, neutral copper conductors are replaced by multilayer zigzag graphene nano ribbon (MLGNR) interconnects that are tremendously advantageous to copper interconnects for the future transmission line conductors necessitated for economic and emission dispatch (EED) of electric supply system giving rise to reduced overshoots and settling time and greenhouse effect as well. The recent work includes combinatorial algorithm involving proportional integral and derivative controller and heuristic swarm optimization; we say it as Hybrid- particle swarm optimization (PSO) controller. The modeling of two multi area systems meant for EED is carried out by controlling the conventional proportional integral and derivative (PID) controller regulated and monitored by quantum behaved artificial bee colony (ABC) optimization based PID (QABCOPID) controller in MATLAB/Simulink platform. After the modelling and simulation of QABCOPID controller it is realized that QABCOPID is better as compared to multi span double display (MM), neural network based PID (NNPID), multi objective constriction PSO (MOCPSO) and multi objective PSO (MOPSO). The real power generation fixed by QABCOPID controller is used to estimate the combined cost and emission objectives yielding optimal solution, minimum losses and maximum efficiency of transmission line.</p>

Tailoring carbon nanotubes quickly into graphene nanoribbons along axis-direction via dynamic magnetic flux template

So far, the method of top-down preparing graphene nanoribbons by etching of carbon nanotubes (CNTs) mainly relies on the catalytic reaction of Fe, Co, and Ni nanoparticles. However, etching cannot be guaranteed along the CNT axis only. In this study, Ti3AlC2 is decomposed into liquid aluminum in the dynamic magnetic flux template to catalyze the growth of multiwalled carbon nanotubes (MWCNTs). Successively, the obtained MWCNTs are etched in-situ by rutile TiO2 particles to generate multilayered graphene nanoribbons (MLGNRs). Thus-obtained nanoribbons will create zigzag edges full of short-range order segment, demonstrating a spin glass state. This work has paved a new way for a top-down approach to create MLGNRs by tailoring MWCNTs along axis direction only using dynamic magnetic flux template.

Crosstalk analysis of dielectric inserted side contact multilayer graphene nanoribbon interconnects for ternary logic system using unconditionally stable FDTD model

In the present work, for examining the performance of dielectric inserted side contact multilayer graphene nano ribbon (DSMLGNR), a novel Unconditionally Stable Finite-Difference Time-Domain (USFDTD) technique is proposed. This technique overcomes the constraint of courant stability condition prevailing in FDTD technique. The proposed mathematical model is highly time efficient and accurately analyzes the crosstalk effects induced among the coupled interconnect lines. The robustness of the USFDTD technique is verified by determining various performance metrics and justifying it with FDTD technique and HSPICE simulations. The obtained results are in accordance with HSPICE and the average percentage error is less than 1%. For performing the transient analysis, USFDTD model consumes 25% lesser time compared to FDTD technique. Furthermore, accuracy of the proposed model is validated by using Feature Selective Validation (FSV) tool.

RF and Crosstalk Characterization of Chip Interconnects Using Finite Element Method

This paper presents new finite element method (FEM) based approach for radio frequency (RF) and crosstalk (X talk) characterization of chip interconnects. Being based on scattering parameters (S-parameters), this approach truly and accurately demonstrates the transmission line behavior of chip interconnects over a wideband of frequencies. To demonstrate FEM based method, a single-line and a 3-line interconnect test structures on SiO2-Si substrate have been designed and simulated in High Frequency Structure Simulator (HFSS). The RF and crosstalk characterization of chip interconnect materials Copper (Cu), doped multilayer Graphene Nanoribbon (DMLGNR), and neutral multilayer Graphene Nanoribbon (NMLGNR) have been demonstrated in terms of transmission coefficient (Sij & Smn) from 1 to 1000 GHz. The single-line three-dimensional (3D) structures comprising of Cu, DMLGNR, and NMLGNR have maximum transmission loss values of -15.93 dB, -22.03 dB, and - 13.73 dB at frequencies of 643 GHz, 402 GHz, and 643 GHz, respectively whereas three-line bus structure exhibit maximum victim-line transmission loss values of -15.28 dB, -17.47 dB, and -15.98 dB at frequencies of 247 GHz, 829 GHz, and 377 GHz, respectively. Further, the crosstalk results have demonstrated that as frequency increases significant crosstalk is observed between nearby lines due to electromagnetic interference and coupling (EMI/EMC) issues.

Analysis of read speed latency in 6T‐SRAM cell using multi‐layered graphene nanoribbon and cu based nano‐interconnects for high performance memory circuit design

AbstractIn this study, we designed a 6T‐SRAM cell using 16‐nm CMOS process and analyzed the performance in terms of read‐speed latency. The temperature‐dependent Cu and multilayered graphene nanoribbon (MLGNR)‐based nano‐interconnect materials is used throughout the circuit (primarily bit/bit‐bars [red lines] and word lines [write lines]). Here, the read speed analysis is performed with four different chip operating temperatures (150K, 250K, 350K, and 450K) using both Cu and graphene nanoribbon (GNR) nano‐interconnects with different interconnect lengths (from 10 μm to 100 μm), for reading‐0 and reading‐1 operations. To execute the reading operation, the CMOS technology, that is, the16‐nm PTM‐HPC model, and the16‐nm interconnect technology, that is, ITRS‐13, are used in this application. The complete design is simulated using TSPICE simulation tools (by Mentor Graphics). The read speed latency increases rapidly as interconnect length increases for both Cu and GNR interconnects. However, the Cu interconnect has three to six times more latency than the GNR. In addition, we observe that the reading speed latency for the GNR interconnect is ~10.29 ns for wide temperature variations (150K to 450K), whereas the reading speed latency for the Cu interconnect varies between ~32 ns and 65 ns for the same temperature ranges. The above analysis is useful for the design of next generation, high‐speed memories using different nano‐interconnect materials.

Graphene multilayers nanoribbons with chirality from molecular dynamics

In this study, we performed reverse nonequilibrium molecular dynamics simulations (RNEMD) to deeply explore the structural and thermal properties of nanometer sized N-layered graphene nanoribbons (GNRs) with N = 2, 3, 4 and 5. The effect of stacking-types, edge chirality, system’s width, number of layers, temperature, Stone–Wales defects and dislocations are all investigated. The correlation between the interlayer distances and the cohesive energies of N-layer GNRs shows the smallest cohesive energy values for the systems exhibiting the largest interlayer distance. The stacking-type of the layers, namely the AA- and the AB-stacking, influences the thermal conductivity (κ) in a pair-impair dependence of the number of layers which is in good accordance with the change in interlayer distance. Moreover, the κ of AA-stacked GNRs, which are more symmetrical in their lattice structure, is higher than AB-GNRs where the phonon coupling becomes weaker due to the significant phonon mismatch between layers. This anisotropic behavior of κ also depends on the armchair and zigzag edge shape of the multilayer GNRs. System size results reveal that thermal conductivities follow an increasing trend with length and a decreasing behavior with width as well as temperature. Overall, this work would offer a deep understanding of the stability as well as thermal conductivity of multilayer graphene nanoribbons and widen the scope of their potential applications in future GNRs-based nanoelectronic and thermoelectric devices.

Analysis of Multilayer Graphene Nanoribbon Interconnects Constrained by Structural Edge Roughness and Corrugated Surface Dielectric

The transient response, 3 dB bandwidth, and relative stability of undoped‐ and doped‐multilayer graphene nanoribbon (MLGNR) interconnects are investigated based on the mean free path (MFP) model incorporating scatterings induced by structural roughness of edges and corrugation of dielectric surface (viz., SiC, BN, and SiO2). The impact of scattering phenomenon on undoped‐MLGNRs (viz., horizontal top‐contact (HTC) and vertical top‐contact) and doped HTC‐MLGNR is analyzed, and the obtained results are compared with smooth and rough copper (Cu) interconnects at the 13 nm technology node. An ABCD parameter model for transmission lines considering the decoupling technique is employed to analyze three capacitively coupled interconnect lines. The results show that, while Cu interconnects outperform MLGNR variants in terms of step response and 3 dB bandwidth, MLGNR interconnects are more stable than Cu counterparts. Moreover, Li‐doped HTC‐MLGNR interconnects with edge roughness on SiO2 leads to slow and sluggish step response, particularly demonstrating a 1250.4% increase in rise time (tr) and 92.56% decrease in 3 dB bandwidth compared to smooth Cu. However, Li‐doped HTC‐MLGNR without edge roughness on SiC exhibits a 94.7% improvement in tr compared to smooth Cu. Hence, patterning GNRs with smooth edges and less degree of dielectric corrugation is necessary for MLGNR on SiO2 to outperform Cu counterparts.

Electronic transport in doped and dielectric inserted MLGNR interconnects: Crosstalk induced delay and stability analyses at sub-threshold regime

A simplified equivalent distributed temperature-dependent RLC circuit model of coupled multilayer graphene nanoribbon (MLGNR) interconnects has been discussed by considering the relaxation time induced mean free path (MFP), and its impact on line resistance (R) has been examined in detail. Further, the performance of copper, undoped, doped and dielectric inserted MLGNRs has been compared in terms of crosstalk induced delay and frequency response at sub-threshold operating conditions. It is revealed that the various scattering mechanisms (acoustic scatterings, edge roughness etc.) control the overall MFP in undoped and doped MLGNRs, however, the electron MFP in dielectric inserted MLGNRs depends on surrounding dielectric environment. Out of the five different cases of dielectric inserted MLGNRs, the insertion of hafnium oxide (HfO2) between GNR layers, along with silicon dioxide (SiO2) provides the best performance characteristics. To obtain minimum crosstalk delay at the subthreshold operating mode, copper, undoped, doped, and dielectric inserted MLGNRs have been optimized for thicknesses of 36, 38.25, 41.4, and 43.65 nm.

Comparative Analysis of Crosstalk Effects in Dielectric Inserted Horizontal andVertical Multi-layer GNR Interconnects for Ternary Logic System

In this work, the performance of copper (Cu), dielectric inserted horizontal graphene nanoribbon (Di-HGNR) interconnect and dielectric inserted vertical graphene nanoribbon (Di-VGNR) interconnects are investigated using active shielding and passive shielding techniques. However, the analysis is carried out by adapting driver-interconnect-load system. This analysis considers the interconnect length from 500 to 2000 μm for 10 nm technology node. Further, the crosstalk induced effects on various interconnect structures are examined. It is envisaged that Di-VGNR exhibits lowest propagation delay compared to Cu and Di-HGNR. Further, the in-phase and out-phase crosstalk delay among the coupled interconnect lines is determined. It is investigated that active shielded Di-VGNR has least crosstalk induced delay compared to other interconnect structures considered in this study. Therefore, Di-VGNR interconnects outperforms Cu and Di-HGNR and are best suited for future VLSI interconnects.

Power-delay-product optimal repeater design for horizontal and vertical multilayer graphene nanoribbon interconnects

Power-delay-product optimal repeater design for horizontal and vertical multilayer graphene nanoribbon interconnects

Analytical Delay Model and Stability Analysis for MLGNR Interconnects

This paper analyzes the signal delay and relative stability of multilayer graphene nanoribbon (MLGNR) interconnects dependent on temperature at global lengths. A thermally aware driver interconnect load (DIL) system, constituted by equivalent single conductor (ESC) model along with mathematical equations, is proposed to convert multi-conductor transmission circuit into single transmission line of MLGNR. The temperature-dependent analytical delay model of MLGNR is evaluated and the obtained outcomes are compared with the simulated results. The analytical and simulated results are obtained at global interconnect length (2000-[Formula: see text]m) for 32[Formula: see text]nm, 22[Formula: see text]nm and 16[Formula: see text]nm nodes of technology under 200–500[Formula: see text]K temperature range of MLGNR. The simulation and analytical results reveal that the outcomes of the two models correspond well. The trend of the models shows the increase in delay with the rising temperature levels (200–500[Formula: see text]K) for three different nodes of technology. Further, relative stability analysis of MLGNR as interconnect line at three different technological nodes from 500–2000-[Formula: see text]m lengths is examined.