Multilayer Graphene Nanoribbon Interconnects Research Articles

Analyzing Multilayer Graphene Nanoribbon‐Based Via‐Interconnect Scheme: Prospects and Challenges for Monolithic 3D Integrated Circuits

This article presents a multilayer graphene nanoribbon (MLGNR)‐based single‐tier on‐chip nanoscale via‐interconnect scheme (VIS), which combines the vertical MLGNR via and horizontal MLGNR interconnect, as a prospect for monolithic 3D (M‐3D) integrated circuits (ICs). To go beyond the simplifying assumptions of perfect MLGNR and conventional skin‐effect, this study incorporates the impact of edge‐ and substrate‐induced scatterers in a realistic MLGNR and considers the 1D skin depth formula for MLGNR‐based on‐chip interconnect and via. A combined equivalent circuit model is developed to analyze the challenges induced by scatterers, skin‐effect, and crosstalk effect in perfect MLGNR VIS (P‐VIS) and realistic MLGNR VIS (R‐VIS). The results show that for width in the range of 5–30 nm, P‐VIS outperforms R‐VIS in terms of crosstalk delay. Moreover, at high frequencies ranging from 1 to 104 GHz with a width of 16 nm, R‐VIS demonstrates a performance decline of 243.18% (5.3934 × 103%) for L = 4.8 μm (1 mm), respectively, in comparison with P‐VIS. Hence, in order to leverage the potential of MLGNR‐based VIS for M‐3D ICs at high frequencies, it is imperative to integrate Li‐intercalation doping and mitigate the impact of edge and substrate scatterers in MLGNR.

New Comprehensive Stability and Sensitivity Analysis on Graphene Nanoribbon Interconnects Parameters

Based on the transmission line modeling for multilayer graphene nanoribbon (MGNR) interconnects, system stability was studied on intrinsic parameters. In addition to width,length and height variation, dielectric constant, permeability and Fermi velocity path change in multilayer graphene nanoribbon (MGNR) interconnects are analyzed. In thispaper, the obtained results show with increasing dielectric constant and decreasing permeability, Fermi velocity system becomes more stable. Nyquist diagram and stepresponse method results confirm these and are matched with physical parameter variation like resistance, capacitance and inductance in the following sensitivity analysis results where it shows with increasing width and length, sensitivity will decrease and increase respectively. Impulse response diagram results show with increasing 50% width, sensitivity will be zero but with increasing 50% length, amplitude will decrease and the time of setting will increase. On the other hand, from the step response of the transfer function, both width and length increase cause more stability for a system but the width parameter will be a better choice for manipulating the dimension of MGNR to reach a stable system.

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.

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.

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.

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>

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.

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.

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.

Quality of Signal Improvement in Prominent CNTFET Based Ternary Logic System for Futuristic Dielectric Inserted MLGNRs for Integrated Circuit Designs

Booming VLSI technology has graciously facilitated down-scaling dimensions of on-chip devices and interconnects in integrated circuits (ICs) to nano-miniaturized scale. However, at nano-dimensions where added benefits of scaling are constrained by associated highly-dense on-chip nano-interconnect structures, their electro-migration effects and several limiting signal-integrity issues. These cumulatively affect the quality of signal (QoS) at output. Improving output QoS is essential for attaining faithful system performance. The present paper judiciously attempts to address as well as limit this graving issue and is successfully proven by obtained results. Firstly, different structures and their performance of futuristic graphene based multi-layer graphene nano ribbon (MLGNR) interconnect is investigated. These include basic MLGNR and dielectric inserted side contact MLGNR (DS-MLGNR). Secondly, to improve data rates and performance, efficient and novel carbon nanotube field effect transistors (CNTFETs) based ternary logic system is incorporated for the prominent nano-MLGNR interconnects. Thirdly, QoS enhancement of highly potential DS-MLGNR interconnect is proposed using active shielding technique. Finally, is chase to further enrich QoS, adaptive least mean square (LMS) equalization technique is used at the receiver. The proposed work comprising of futuristic novel graphene interconnects with efficient ternary logic system together with adaption of several QoS improvement techniques are magnificent and panacea solution to limiting nano-interconnects in advanced ICs. Several interesting and seminal analyses such as delay, power, power-delay product, crosstalk, eye-diagram are performed that supports the novelty and effectiveness of the proposed work. The vivid performance analyses have been implemented at nano-size 10 nm technology node.

Crosstalk Delay and Noise Optimization in Nanoscale Multi-line Interconnects Based on Repeater Staggering in Ternary Logic

In this study, the crosstalk effects are minimized in coupled multi-line wires based on repeater staggering in ternary logic. For more accuracy, the impact of the coupling capacitance is also considered in our calculations. Our results indicate that the number of repeaters required for optimizing the delay of the multilayer graphene nanoribbon (MLGNR) interconnect is, on average, 43% lower than multi-walled carbon nanotube (MWCNT) interconnect. Moreover, the optimized delay of the MLGNR interconnect is, on average, 48% lower than MWCNT interconnect. The ternary repeater insertion reduces the delay of the MWCNT and MLGNR interconnects carrying ternary signals by 61% and 51%, respectively. The staggered repeater insertion is applied as a practical approach for eliminating the crosstalk noise in the transmitted ternary signals in a multi-line coupled structure. Our results demonstrate that the delay and energy of the staggered repeater-inserted MLGNR interconnects are, on average, 42% and 37% lower than their MWCNT counterparts. Furthermore, the impacts of the process variations are investigated using comprehensive Monte Carlo simulations and the optimized ternary multi-line MLGNR interconnect functions correctly and considerably robustly compared to their MWCNT counterpart.

Edge scattering limited crosstalk analysis in adjacent multilayer graphene interconnects and its impact on gate oxide reliability

PurposeThis paper aims to present the edge scattering dominant circuit modeling. The effect of crosstalk on gate oxide reliability (GOR), along with the mitigation using shielding technique is further studied.Design/methodology/approachAn equivalent distributed Resistance Inductance Capacitance circuit of capacitively coupled interconnects of multilayer graphene nanoribbon (MLGNR) has been considered for T Simulation Program with Integrated Circuit Emphasis (TSPICE) simulations under functional and dynamic switching conditions. Complementary metal oxide semiconductor driver transistors are modeled by high performance predictive technology model that drive the distributed segment with a capacitive load of 0.001 fF, VDD and clock frequency as 0.7 V and 0.2 GHz, respectively, at 14 nm technology node.FindingsThe results reveal that the crosstalk induced delay and noise area are dominated by the overall mean free path (MFP) (i.e. including the effect of edge roughness induced scattering), in contrary to, acoustic and optical scattering limited MFP with the temperature, width and length variations. Further, GOR, estimated in terms of average failure rate (AFR), shows that the shielding technique is an effective method to minimize the relative GOR failure rate by, 0.93e-7 and 0.7e-7, in comparison to the non-shielded case with variations in interconnect’s length and width, respectively.Originality/valueConsidering realistic circuit modeling for MLGNR interconnects by incorporating the edge roughness induced scattering mechanism, the outcomes exhibit more penalty in terms of crosstalk induced noise area and delay. The shielding technique is found to be an effective mitigating technique for minimizing AFR in coupled MLGNR interconnects.

An Energy-Efficient Crosstalk Reduction Strategy for On-Chip Buses Using Carbon-Based Transistors and Interconnects

This paper presents a novel crosstalk reduction scheme based on quaternary logic that eliminates the harmful transition patterns and protects communication channels of system-on-chips (SoCs) against crosstalk. The proposed architecture is designed based on gate-all-around carbon nanotube field-effect transistor (GAA-CNTFET) codec and converter modules considering multi-walled carbon nanotube (MWCNT), and multilayer graphene nanoribbon (MLGNR) interconnects at 10 nm technology. The simulation results indicate that our proposed approach reduces the delay and power-delay product (PDP) on average by 52% and 36%, respectively, for MWCNT interconnects compared to the basic architecture. These improvements are 50% and 35% for the MLGNR interconnects. Moreover, utilizing the MLGNR interconnects instead of MWCNT interconnects in the proposed coded system leads to a 61% shorter crosstalk delay and 65% lower PDP. In addition, the proposed coding scheme leads to 35% reduction in the occupied area and improves PDP, on average, by 37%, and 26% for the MWCNT and MLGNR buses, respectively, as compared to their binary counterparts.

An ultra-energy-efficient crosstalk-immune interconnect architecture based on multilayer graphene nanoribbons for deep-nanometer technologies

An ultra-energy-efficient interconnect structure based on multilayer graphene nanoribbon (MLGNR) interconnects for deep-nanometer technologies is proposed herein. First, a low-swing interconnect based on MLGNRs and high-performance interface circuits using carbon nanotube field-effect transistors (CNTFETs) is proposed. Then, an ultra-energy-efficient interconnect structure is obtained by actively shielding such low-swing lines. The structures under study are simulated comprehensively at the 7-nm technology node. The results indicate that the MLGNR interconnect is significantly more energy efficient than its multiwall carbon nanotube (MWCNT) counterpart in the low-voltage regime. Moreover, the proposed approach is superior to its MLGNR counterparts. The proposed structure leads to 86%, 75%, and 31% lower energy consumption over a length of 500 µm as compared with the typical, actively shielded, and low-swing MLGNR interconnects, respectively. Moreover, the impact of the ratio of the widths of the signal line to the shield line on the performance of the interconnects is evaluated. The energy consumption reduction achieved by the proposed approach is mostly preserved even when using minimum-width shield lines on wider signal lines to reduce the area overhead. Moreover, the impact of process variations on the performance of the interconnects is assessed using Monte Carlo simulations, demonstrating the robustness of the proposed approach.

Edge and Dielectric Surface Roughness-Aware EM-RA Model for MLGNR Interconnects

This paper presents an edge roughness (ER) and dielectric surface roughness (DSR) - aware exponential matrix-rational approximation (EM-RA) model for the transient analysis of multi-layer graphene nanoribbon (MLGNR) interconnects. The proposed model analyzes the signal integrity in terms of the peak crosstalk and the propagation delay. The results obtained using the proposed ER and DSR - aware EM-RA model for the crosstalk and delay analysis are compared with the industry-standard SPICE simulator. The ER and DSR - aware EM-RA model results have excellent accuracy compared to HSPICE with less than 0.5% error. The proposed model provides a speed-up by a factor of 84.36 and 86.05 for carrying out the signal integrity analysis in coupled-two and coupled-three MLGNR interconnect lines, respectively, in comparison to HSPICE. The speed-up further increases with the more refined 2D ER and DSR grid of variations. The CPU memory efficacy of the proposed model is compared with HSPICE. The proposed model's stability is analyzed for a range of local to global interconnects.