Multilayer Graphene Nanoribbon Research Articles

Study of Crosstalk Effect on the Propagation Characteristics of Coupled MLGNR Interconnects

Multi-layer graphene nanoribbons (MLGNRs) material has been a potential solution to replace conventional Cu for next-generation on-chip interconnects. Based on equivalent single conductor model, this paper extracts the equivalent resistance-inductance-capacitance parameters for MLGNRs with consideration of edge roughness and Fermi level. A distributed circuit model for a pair of coupled MLGNR interconnects is provided, with both capacitive and inductive coupling taken into account, and validated against the Spice results and the predicted experiment results in frequency and time domains. Using the proposed model, the impact of various dimensional and technology parameters on the transfer gain and crosstalk delay is investigated for the global MLGNR interconnects at different phase modes. It is demonstrated that MLGNR interconnects with smooth edge exhibit higher transfer gain and lower crosstalk delay in comparison to its Cu counterpart at same dimension. However, edge roughness in the present fabrication technologies is inevitable that significantly deteriorates the propagation performance and the performance difference due to edge roughness is relatively less in wider MLGNR interconnects. Moreover, it is shown that side contact MLGNR interconnects have better electrical performance than that of top contact MLGNR interconnects at short interconnect length in comparison to that at long interconnects due to the domination of in-layer resistance. The results presented in this paper would be helpful to fully understand the propagation characteristics and provide guidelines for signal integrity analysis of MLGNR interconnects.

Molecular dynamics simulation for interlayer interactions of graphene nanoribbons with multiple layers

A new study is conducted with the aid of molecular dynamics (MD) simulation to investigate the effect of shear modulus value of the interlayer van der Waals (vdWs) interactions on free vibration of cantilever multi-layer graphene nanoribbons (MLGNRs). The corresponding calibrated nonlocal parameters of the nonlocal model are obtained accordingly. The vdWs interactions are treated as the cores between every two adjacent graphene layers and their equivalent shear modulus is calculated using MD simulation. The obtained resonant frequencies via the nonlocal sandwich model are compared to the MD simulation results to calibrate the nonlocal parameter. Results reveal a strong conclusion that the calibrated nonlocal parameter is dependent on the values of interlayer shear modulus.

Modeling of the photodetector based on the multilayer graphene nanoribbons

Graphene nanoribbon (GNR), which has unique properties and advantages, is a crucial component of nanoelectornic devices, especially in the development of photoelectric detectors. In this work, an infrared photodetector based on the structure of stacked multiple-GNRs, which is separated by a little thick barrier layers (made of tungsten disulfide or related materials) to prevent tunneling current, is proposed and modeled. Operation of photoelectric detector is related to the electron cascaded radiative transition in the adjacent GNRs strengthened by the electrons heated due to the incident light. With a developed model, the working principle is analyzed and the relationships for the photocurrent and dark current as functions of the intensity of the incident radiation are derived. The spectral dependence of the responsivity and detectivity for graphene nanoribbons photodetector (GNRs-PT) with different Fermi energy, band gaps and numbers of GNRs layers are analyzed as well. The results demonstrate that the spectral characteristics depend on the GNRs band gap, which shows a potential on GNRs-PT application in the multi-wavelength systems. In addition, GNRs-PT has a better spectrum property and higher responsivity compared to photodetectors based on InxGaxAs in room temperature.

Modeling and analysis of crosstalk induced overshoot/undershoot effects in multilayer graphene nanoribbon interconnects and its impact on gate oxide reliability

Crosstalk induced overshoot/undershoot effects in multilayer graphene nano ribbon interconnects (MLGNRs) are investigated with the help of ABCD parameter matrix approach for intermediate level interconnects at both 11nm and 8nm technology node. The worst case crosstalk induced peak overshoot voltage for perfectly specular, doped multilayer zigzag GNR interconnects is comparable to that of copper interconnects. The performance of neutral GNR interconnects is better than that of its doped counterpart with respect to peak crosstalk overshoot. But from the perspective of overall overshoot width and overshoot area contribution, perfectly specular, doped MLGNR interconnects outperform all other alternatives. As far as the effective electric field across the gate oxide is concerned, the doped MLGNR interconnects outperform neutral ones and copper interconnects for all the cases. It is estimated that the doped perfectly specular multilayer GNR interconnects have gate oxide failure rates (AFR) of ~240× and ~790× lesser than copper interconnects for 11nm and 8nm technology node respectively. So, from the gate oxide reliability perspective, perfectly specular, doped multilayer zigzag GNR interconnects are great advantageous to copper interconnects for the future integrated circuit technology generations.

Study on tensile-compressive and shear effects of van der Waals interactions on free vibration of bilayer graphene nanoribbons

This study comprehensively investigates tensile-compressive and shear effects of van der Waals (vdWs) interactions on free vibration of cantilever bilayer graphene nanoribbons (CBGNRs) to be answered to this question that how and how much the effects of each of these factors are in comparison with the other one when they are considered simultaneously. To this end, the CBGNRs are modeled based on sandwich beam theory in which each nanoribbon plays role of sandwich layer and vdWs interactions are equivalent to the sandwich core. At the first step a geometrical–analytical method is presented to calculate the equivalent tensile-compressive and shear moduli of vdWs interactions. After that, a set of coupled governing equations of motion and boundary conditions are derived and solved numerically by the harmonic differential quadrature method. This study shows that for designing multi-layer GNR based applications, such as resonators, the shear effect of vdWs interactions must be considered.

Mid-infrared plasmonic tuning via nanogap control in periodic multilayer graphene nanoribbons

Plasmonic tuning at mid-infrared wavelength by regulating the nanogap between the adjacent multilayer graphene nanoribbons (GNs) is investigated with Finite-Difference Time-Domain (FDTD) method. The 100-nm-wide multilayer GNs formed on a SiO2/p-Si show that plasmon resonance moves to longer wavelength by decreasing the nanogap from 100nm to 5nm, due to the inter-nanoribbon attractive interaction. Also, the resonance wavelength shifts are 7.0, 4.8 and 3.9–3.3μm in this nanogap range for 1-, 2-, 3- and 4-layer GNs, respectively, at Fermi energy (EF) of 0.2eV, implying enhanced confinement in plasmonic oscillation as the number of graphene layer increases. Meanwhile, by shifting the EF from 0.2eV to 0.4eV, the resonance peaks for each multilayer GN move to shorter wavelengths, and the peak shifts in the same nanogap range are further decreased resulting from the increased charge carriers involved in the localized plasmonic oscillation. These observed results can provide an insight in designing mid-infrared plasmonic devices for advanced nano-photonic systems.

Reduced thickness interconnect model using GNR to avoid crosstalk effects

In this research article, we propose a reduced thickness multilayer graphene nanoribbon (MLGNR) interconnect model to reduce crosstalk effects. The $$10\times $$10 higher current capability of MLGN...

Performance analysis of multilayer graphene nanoribbon (MLGNR) interconnects

This paper addresses the impact of interlayer resistance due to c-axis resistivity and contact resistance on performance in terms of delay, power dissipation and power delay product (PDP) of Multi-layer graphene nanoribbon (MLGNR) interconnect. The impact of model parameter i.e. Fermi energy $$(\hbox {E}_\mathrm{F})$$(EF) on performance of MLGNR is also discussed. A similar analysis is performed for copper interconnect and results are compared with MLGNR at 22 nm technology node. The impact of interlayer resistance on equivalent resistance of MLGNR is critically analyzed. Inductive and capacitive coupling between the adjacent layers are included in this analysis. It is found that the MLGNR with interlayer resistance, compared to copper, gives better performance in terms of delay, power dissipation and PDP with higher value of Fermi energy for semi global to global lengths of interconnect (300---1000 $$\upmu \hbox {m})$$μm) whereas reverse is true for local lengths 100---200 $$(\upmu \hbox {m})$$(μm). In addition, performance gap between MLGNR with and without interlayer resistance decreases with increase in Fermi energy.

Analysis of temperature dependent power supply voltage drop in graphene nanoribbon and Cu based power interconnects

In this paper, we propose a temperature dependent resistive model of multi layered graphene nanoribbon (MLGNR) and Cu based power interconnects. Using the proposed model, power supply voltage drop (IR-drop) analysis for 16 nm technology node is performed. The novelty in our work is that this is the first time a temperature dependent IR-Drop model for MLGNR and Cu interconnects is proposed. For a temperature range from 150 K to 450 K, the variation of resistance of MLGNR interconnect is ~2–5× times lesser than that of traditional copper based power interconnects. Our analysis shows that MLGNR based power interconnects can achieve ~1.5–3.5× reduction in IR-drop and ~1.5–3× reduction in propagation delay as compared with copper based interconnects for local, intermediate and global interconnects.

Investigating the Applicability of Graphene Nanoribbon as Signal and Power Interconnects for Nanometer Designs

In this work, we have investigated the applicability of graphene nanoribbon (GNR) as the interconnects for 16-nm ITRS technology node. GNR is proposed as the possible alternative to the traditional copper (Cu)-based interconnect systems in nanometer regime. In this paper, we have performed important studies on GNR for its applicability as power and signal interconnects. For the application of power interconnects, we have investigated the power supply voltage drop (IR drop) and simultaneous switching noise (SSN) in graphene-based interconnect system. We have performed crosstalk noise and overshoot/undershoot analyses for the application of signal interconnects. The results are compared with that of the traditional Cu-based interconnects. The results show that GNR is better than Cu as far as IR drop, SSN, gate oxide reliability and hot carrier reliability are concerned. Our investigation reveals that GNR can be better than the Cu interconnects from all aspects with a multilayer GNR structure. The present graphene-based interconnect technology needs to be advanced, so that the metal–graphene contact resistance is minimized and multilayer GNR structure with large number of graphene layers is supported.

Graphene with Patterned Fluorination: Morphology Modulation and Implications

Recent years have witnessed a large volume of works on the modification of graphene; however, an understanding of the associated morphology or mechanical properties changes is still lacking, which is vital for its engineering implementation. By taking the C4F fluorination as an example, we find that the morphology of both graphene sheet (GS) and graphene nanoribbon (GNR) can be effectively tailored by fluorination patterning via molecular dynamics simulations. The fluorine atom produces out-of-plane forces which trigger several intriguing morphology changes to monolayer graphene, including zigzag, folded, ruffle, nanoscroll, and chain structures. Notably, for multilayer GNR, the delamination and climbing phenomena of the surface layer are observed. Further studies show that the fluorination pattern can also be utilized to modulate the mechanical properties of graphene, e.g., about 40% increase of the effective yield strain is observed for the examined GNR with fluorination patterns. This study not only de...

Performance Improvement in SC-MLGNRs Interconnects Using Interlayer Dielectric Insertion

Due to their higher resistance, single layer graphene nanoribbons (GNRs) are not suitable for high-speed on-chip interconnect applications. Hence, we use multilayer GNRs (MLGNRs) that offer multiple conduction channels and lower resistance. However, MLGNRs turn into graphite as the number of layers increase, which reduces the mean-free path of each layer. Insertion of a dielectric between GNR layers prevents its conversion into graphite, thereby improving its mean-free path and scattering rate. In this paper, we are proposing an analytical model for the time-domain analysis of side-contact MLGNRs (SC-MLGNRs) with intermediate dielectric insertion. The proposed model computes scattering rate, mean-free path, and carrier mobility in GNRs where dielectric has been inserted between individual layers. Our analytical results for mobility and scattering rate have been verified with the existing experimental data that exhibit excellent accuracy (maximum of error 4% for mobility and 16% for scattering time). Based on our analysis, we have found that the electron mean-free path in GNRs strongly depends on surrounding dielectric environment. In that, the mean-free path increases with interlayer insertion of high- $k$ dielectrics. Equivalent $RLC$ parameters, delay, energy-delay product, and bandwidth density are calculated for our proposed GNR interconnects using our model. We observe that these performance metrics significantly improve due to the presence of dielectric between GNR layers. When compared with Cu interconnects, insertion of HfO2 between GNR layers results in reduction in both propagation delay and energy-delay product by $2\times $ for interconnect lengths of $1400 ~\mu \text{m}$ . In addition, zigzag SC-MLGNR interconnect with $N=10$ and $\varepsilon _{2}=20$ gives nearly 35% higher bandwidth density than that of Cu interconnects for all interconnect lengths. In our analysis, we propose a new performance metric, bandwidth density/energy-delay product to determine the performance limits of our proposed interconnect structure. Finally, we compare the performance of SC-MLGNR interconnect structure with copper and optical interconnects to exhibit its application in local and global interconnects.

Tensile strain-induced magnetism transition in multilayer graphene with excess electrons: Stability of the edge-quantum well

The stability of edge-quantum well-induced strong magnetism of multilayer armchair graphene nanoribbon (AGNR) with excess electrons was investigated under applied tensile strain by density functional theory (DFT) calculations. The results indicated that: (1) The strain along the armchair edge direction led to a transition of the multilayer AGNRs from ferromagnetic state to nonmagnetic state when the strain increased to a critical value; (2) The strain induced bond length changes reduced the stability of the edge-quantum well in terms of the reduction of the electrons capturing capacity; and (3) The spin splitting of the energy bands near the Fermi level reduced with the increase of the strain, resulting in the decrease of the spin moment. This finding suggests that the magnetic properties of graphene have strong dependence on its strain states, which is crucial to the design of graphene-based magnetic devices.

Inside Front Cover: Plasmon resonance in multilayer graphene nanoribbons (Laser Photonics Rev. 9(6)/2015)

Inside Front Cover: Plasmon resonance in multilayer graphene nanoribbons (Laser Photonics Rev. 9(6)/2015)

Plasmon resonance in multilayer graphene nanoribbons

AbstractPlasmon resonances in nanopatterned single‐layer graphene nanoribbons (SL‐GNRs), double‐layer graphene nanoribbons (DL‐GNRs) and triple‐layer graphene nanoribbons (TL‐GNRs) are studied experimentally using ‘realistic’ graphene samples. The existence of electrically tunable plasmons in stacked multilayer graphene nanoribbons was first experimentally verified by infrared microscopy. We find that the strength of the plasmonic resonance increases in DL‐GNRs when compared to SL‐GNRs. However, further increase was not observed in TL‐GNRs when compared to DL‐GNRs. We carried out systematic full‐wave simulations using a finite‐element technique to validate and fit experimental results, and extract the carrier‐scattering rate as a fitting parameter. The numerical simulations show remarkable agreement with experiments for an unpatterned SLG sheet, and a qualitative agreement for a patterned graphene sheet. We conclude with our perspective of the key bottlenecks in both experiments and theoretical models. image

Nonlocal Reddy beam model for free vibration analysis of multilayer nanoribbons incorporating interlayer shear effect

Abstract The aim of this study is to investigate the interlayer shear effect on nonlocal free vibration of multilayer graphene nanoribbons (MLGNRs) based on Reddy beam theory. The major novelty of the study is using the higher order shear deformation theory of Reddy to take the van der Waals’ interaction of the layers into account and calibrating the nonlocal parameter with the aids of molecular dynamics (MD) simulations to match the best results. Furthermore, the shear correction factor of nonlocal Timoshenko theory is calculated for modeling the MLGNRs. MLGNRs have broad applications in mechanical devices, such as resonators, sensors and actuators. Accordingly the present results can be used as a reference for future works in which the interlayer shear effects has substantial influences on the mechanical behavior of MLGNRs. The present study outstands for its modeling simplicity and low computational time and cost as well as excellent accuracy.

Multilayer Graphene Nanoribbon and Carbon Nanotube Based Floating Gate Transistor for Nonvolatile Flash Memory

Floating gate transistor is the fundamental building block of nonvolatile flash memory, which is one of the most widely used memory gadgets in modern micro and nano electronic applications. Recently there has been a surge of interest to introduce a new generation of memory devices using graphene nanotechnology. In this article, we present a new floating gate transistor (FGT) design based on multilayer graphene nanoribbon (MLGNR) and carbon nanotube (CNT). In the proposed FGT, a MLGNR structure would be used as the channel of the field effect transistor (FET) and a layer of CNTs would be used as the floating gate. We have performed an analysis of the programming and erasing mechanism in the floating gate and its dependence on the applied control gate voltages. Based on our analysis we have observed that proposed graphene based floating gate transistor could be operated at a low voltage compared to conventional silicon based floating gate devices. We have presented detail analysis of the operation and the programming and erasing processes of the proposed FGT; the dependency of the programming and erasing current density on different parameters; and the impact of scaling the thicknesses of the control and tunneling oxides. To perform these analyses we have developed equivalent models for device capacitances.

Self‐consistent capacitance model for multilayer graphene nanoribbon interconnects

An analytical model for the computation of equivalent capacitance in top-contact and side-contact multilayer graphene nanoribbon interconnects is presented, taking into consideration the interlayer coupling. On the basis of this model, it is observed that interlayer capacitance is a dominant factor that severely degrades the performance of graphene interconnects. The proposed model is verified with simulation data obtained using Synopsys Raphael that exhibits excellent accuracy. Further, a theoretical framework for improvement in key interconnect performance indices such as delay, energy-delay product and bandwidth density is provided by inserting metal atoms between the graphene layers in top-contact graphene nanoribbon interconnects.

Nonlocal Timoshenko beam model for considering shear effect of van der Waals interactions on free vibration of multilayer graphene nanoribbons

In this study, shear effect of van der Waals (vdWs) interactions on free vibration of cantilever multi-layer graphene nanoribbons (MLGNRs) is investigated by using nonlocal Timoshenko beam model and molecular dynamics (MD) simulations. To this end, it is assumed that GNR layers of MLGNRs are perfectly bonded that no delamination will occur in layers interfaces. To calibrate the small scale parameter of the nonlocal Timoshenko model, the first two frequencies of armchair type cantilever MLGNRs with various layers and lengths are extracted using MD simulations and matched with those of the nonlocal Timoshenko theory. Comparing frequencies obtained by the MD simulation and the Timoshenko model shows that if values of the bending rigidity and the interlayer shear modulus (or equivalent shear modulus of Timoshenko theory) are taken as 1.20eV and 3.01GPa, respectively, then it will be possible to use the Timoshenko model for the free vibration analysis of MLGNRs. Moreover, it is observed that the calibrated nonlocal parameter is dependent on the number of MLGNR layers, and its calibrated value increases by increasing the number of GNR layers. This study helps researchers to analyze the mechanical behavior of MLGNRs in which the interlayer shear has apparent impact.

Crosstalk bandwidth and stability analysis in graphene nanoribbon interconnects

Based on transmission line modeling (TLM), and using the Nichols chart, we present a bandwidth and stability analysis, together with step time responses, for coupled multilayer graphene nanoribbon (MLGNR) interconnects that is inquired for the first time. In this analysis, the dependence of the degree of crosstalk relative stability for coupled MLGNR interconnects comprising of both capacitive and mutual-inductive couplings between adjacent MLGNR has been acquired. The obtained results show that with increasing the length or decreasing the width of the MLGNRs, the stability in near-end output increases. While, any increase in the length or width of MLGNRs, decrease the stability of far-end output. Also, by increasing capacitive coupling or decreasing inductive coupling, the near-end output becomes more stable, and the far-end output becomes less stable. Moreover, any increase in the length or capacitive coupling, decreases the bandwidth, whereas any increase in the width or inductive coupling, increases the bandwidth. Finally, transient simulations with Advanced Design System (ADS) show that the model has an excellent accuracy.