Graphene Nanoribbon Interconnects Research Articles

Analysis of Crosstalk-Induced Effects in Multilayer Graphene Nanoribbon Interconnects

Crosstalk effects in multilayer graphene nanoribbon (GNR) interconnects for the future nanoscale integrated circuits are investigated with the help of ABCD parameter matrix approach for intermediate- and global-level interconnects at 11[Formula: see text]nm and 8[Formula: see text]nm technology nodes. The worst-case crosstalk-induced delay and peak crosstalk noise voltages are derived for both neutral and doped zigzag GNR interconnects and compared to those of conventional copper interconnects. The worst-case crosstalk delays for perfectly specular, doped multilayer GNR interconnects are less than 4% of that of copper interconnects for 1[Formula: see text]mm long intermediate interconnects and less than 7% of that of copper interconnects for 5[Formula: see text]mm long global interconnects at 8[Formula: see text]nm node. As far as the worst-case peak crosstalk noise voltage is concerned, neutral GNR interconnects are slightly better performing than their doped counterparts. But from the perspective of overall noise contribution, doped GNR interconnects outperform neutral ones for all the cases. Finally, our analysis shows that from the signal integrity perspective, perfectly specular, doped multilayer zigzag GNR interconnects are a suitable alternative to copper interconnects for the future-generation integrated circuit technology.

Stability Analysis in Top-Contact and Side-Contact Graphene Nanoribbon Interconnects

ABSTRACT In this paper, we have analysed the relative stability of copper, top-contact (TC) and side-contact (SC) multilayer graphene nanoribbon (MLGNR)-based interconnects for next-generation VLSI interconnect technology. We have analysed the Bode stability by varying the interconnect length (10–100 µm) at 16 nm ITRS technology node. Similar analysis has been performed by varying the interconnect width (11–22 nm) at 10 µm interconnect length. It is observed that by increasing the interconnect length (l) as well as interconnect width (w), the relative stability increases for three different types of interconnects. Our analysis shows that the copper-based interconnect shows more stability due to high gain margin and phase margin for a wide range of interconnect length (10–100 µm) as compared to the TC-GNR and SC-GNR interconnect systems. It is also observed that by increasing the wire width, the gain and phase margin of TC-GNR is higher than copper and SC-GNR interconnect. Our analysis predicts that the TC-GNR is the best candidate for interconnect modelling in terms of stability across different technology nodes considering the other benefits of TC-GNR as compared with copper and SC-GNR.

A Novel Unified Model for Copper and MLGNR Interconnects Using Voltage- and Current-Mode Signaling Schemes

A novel unified model, for conventional copper and futuristic multilayer graphene nanoribbon (MLGNR) interconnects, based on a finite-difference time-domain (FDTD) technique has been proposed in this paper. The performance of quasi-transverse electromagnetic model of interconnects has been exhaustively analyzed for both voltage-mode signaling (VMS) and current-mode signaling (CMS) schemes. The effect of variations in edge roughness and dopant dependent Fermi energy in MLGNR interconnects has been examined. The crosstalk and coupling effects in interconnects have been investigated by incorporating capacitive and inductive interconnect parasitic elements. From the results carried out for 32-nm technology node, it has been observed that for similar dimensions and operating conditions, MLGNR interconnects show a significant performance improvement over the copper interconnects. The results also show that the CMS scheme outperforms VMS scheme at global wire lengths and is very suitable for state-of-the-art chip applications. The proposed model results are in close propinquity with the SPICE results. Furthermore, the FDTD-based model is computationally efficient compared to SPICE.

Stability analysis for coupled multilayer graphene nanoribbon interconnects

Based on equivalent single conductor (ESC) concept for multilayer graphene nano-ribbons (MLGNRs), this paper establishes the distributed transmission line model of coupled MLGNR interconnects and derives the analytical expression of coupled transfer function. Using the proposed model and Nyquist stability criterion at the global level of 14nm technology node, the impact of switching factor and various design parameters on the relative stability and crosstalk delay of the coupled interconnects is investigated. It is shown that crosstalk effect makes the coupled interconnect system more stable than that in a single interconnect case. Moreover, increasing the wire length and edge roughness, the coupled interconnects becomes more stable due to the raise in crosstalk delay. Whereas, the increase of wire width, space and doping density, the crosstalk delay decreases, and the coupled interconnects is less stable. The time response for the step input verifies the analysis mentioned above. The results presented in this paper are useful for the design of reliable MLGNR interconnects with better propagation characteristics.

Lithium-Intercalated Graphene Interconnects: Prospects for On-Chip Applications

This paper establishes the importance of the lithium (Li) intercalation in multilayer graphene nanoribbon (MLGNR) interconnects for obtaining superior performance than conventional copper (Cu) on-chip interconnects. For the first time, we report performance analysis of Li-intercalated MLGNRs for local interconnect applications. In that, interconnect thickness is optimized for obtaining lowest delay and energy-delay-product (EDP). At 12 $\mu \text{m}$ interconnect length, our optimized Li-intercalated MLGNRs exhibit $(\approx 22.9~{\mathrm{ ps}})1.9\times $ and $4.1 \times $ lower delay and EDP, respectively, when compared to Cu. Even in presence of edge roughness, they exhibit $(\approx 31.8~{\mathrm{ ps}})1.37\times $ and $2.5\times $ lower delay and EDP, respectively, when compared to Cu. Our analysis quantitatively proves the potential of Li-intercalated MLGNRs for local interconnect applications.

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.

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.

Temperature Dependent IR-Drop Analysis in Graphene Nanoribbon Based Power Interconnect

The paper proposes a temperature dependent resistive model of graphene nanoribbon (GNR) based power interconnects. Using the proposed model, IR-drop analysis for 16nm technology node latest by ITRS is performed. For a temperature range from 150 K to 450 K, the variation of resistance of GNR interconnect is ~ 2-5  times lesser than that of traditional copper based power interconnects. Our analysis shows that GNR based power interconnects can show ~ 2-3 times reduction in Peak IR-drop as compared with copper based interconnects for local, intermediate and global interconnects.

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.

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.

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.

Line width dependence of transport properties in graphene nanoribbon interconnects with real space edge roughness determined by Monte Carlo method

We developed a novel Monte Carlo simulation model to investigate the line width dependence of the transport properties of multi-layered graphene nanoribbon (GNR) interconnects with edge roughness. We reported that the line width dependence of carrier mobility decreases significantly as the magnitude of the edge roughness gets smaller, which agrees well with experiments. We also discussed the influence of the inelasticity of edge roughness scatterings, inter-layer tunneling, and line width dependent band structures on the line width of the GNR interconnects.

First-principles study of electronic transport properties of graphene nanoribbons with pentagon-heptagon (5-7) line defects

ABSTRACTIn this study, we investigated the influence of line defects consisting of pentagon-heptagon (5-7) pairs on the electronic transport properties of zigzag-edged and armchair-edged graphene nanoribbons (GNRs). Using the first-principles density functional theory, we study their electronic properties. To investigate their current-voltage (I-V) characteristics at low bias voltage (∼ 1 meV), we use the nonequilibrium Green’s function method. As a result, we found that the conductance of the GNRs having a connected line defect between source and drain shows better performance than that of the ideal zigzag-edged GNRs (ZGNRs). A detailed investigation of the transmission spectra and the wave function around the Fermi level reveals that the line defects arranged along the transport direction work similar to an edge state of the ZGNRs and can be an additional conduction channel. Our results suggest that such a line defect can be effective for low-resistance GNR interconnects.

High frequency characterization of graphene nanoribbon interconnects

Interconnects and nanoscale transmission lines are critical components in the design of nanoelectronic systems. In this letter, we study the high frequency characteristics of chemical vapor deposition (CVD) graphene nanoribbon (GNR) interconnects and radio frequency propagation in GNRs embedded in a coplanar waveguide structure up to 20 GHz. An equivalent transmission line model is proposed to characterize the GNRs in high frequency regime. The strong agreement between fitting circuit parameters and measured data suggests that our model can be used in the design of nanoscale circuits in which GNRs are used to interconnect elements in the circuits. The fabricated GNRs show fairly constant characteristic impedance at high frequencies which could be useful for radio frequency interconnect applications. Our study provides an insight into microwave behavior of GNRs for developing high speed graphene devices.

Comparative Study on Multilayer Graphene Nanoribbon (MLGNR) Interconnects

Based on an equivalent single-conductor (ESC) model of multilayer graphene nanoribbon (MLGNR) interconnects with side contacts, comparative study on their distributed parameters and transmission characteristics is performed in this paper. It is found that the number of conducting channels of a metallic MLGNR interconnect is the linear function of its width and Fermi energy, which can be described by an analytical equation. Its equivalent inductance and capacitance in the ESC model can also be characterized by a set of closed-form equations. Furthermore, according to the ITRS projection, transmission performance of the MLGNR interconnects with different contacts are predicted and compared with their Cu and carbon nanotube counterparts at different technology nodes. Also, some numerical results prove that MLGNR interconnects can provide better performance than Cu wires in particular at intermediate level. Even with the maximum crosstalk impacts considered, the advantage of MLGNR interconnects over Cu wires can still be kept.

Delay uncertainty in MLGNR interconnects under process induced variations of width, doping, dielectric thickness and mean free path

This paper analyzes the delay performance of multi-layered graphene nanoribbon (MLGNR) interconnect under process induced variations. An equivalent multi-conductor transmission line (MTL) model driven by CMOS gate is employed for the analysis. The propagation delay is analyzed for different interconnect lengths and widths by taking into account the variations in width, dielectric thickness, dielectric constant, interlayer distance and doping concentration of MLGNR. Encouragingly, it is observed that the average deviation in delay is below 3 % for all process induced parameter variations except for the mean free path.

Voltage-dependent parameter extraction for graphene nanoribbon interconnect model through ab initio approach

This paper presents electrical parameter extraction for metallic graphene nanoribbon (GNR) interconnects utilizing ab initio approach. Unlike the studies taking the kinetic inductance, quantum capacitance and Fermi velocity as constant values, voltage-dependencies of these parameters are obtained for GNR transmission line model. The variations of the kinetic energy and the current by the applied voltage are taken as bases for voltage-dependent kinetic inductance calculation. Quantum capacitance and the Fermi velocity are also computed from the kinetic inductance variation. It is concluded that voltage-dependencies of the kinetic inductance and the quantum capacitance have to be taken into account for accurate GNR modelling in nanoelectronic design.

Analytical Time-Domain Models for Performance Optimization of Multilayer GNR Interconnects

In this paper, we are proposing novel analytical time domain models for side contact and top contact multilayer graphene nanoribbon (MLGNR) interconnects. Our proposed models give physical insights about the transient behavior of these MLGNRs. The proposed models have been verified with existing data as well as exhaustive simulation and exhibit excellent accuracy. Based on our analysis, we identify limiting factors that need to be considered for the design of optimum top contact MLGNRs that exceed the performance of copper and match that of side contact MLGNR interconnects. Finally, we compare the performance of our optimum top contact MLGNRs with optical interconnects to predict the future roadmap for next generation interconnect technology.

Transmission Line Model of Graphene Nanoribbon Interconnects

Transmission Line Model of Graphene Nanoribbon Interconnects

Number of Conducting Channels for Armchair and Zig-Zag Graphene Nanoribbon Interconnects

Nanowire-based circuits are candidates for future high-speed electronics. Signal propagation in nanowires can be studied by combining the semiclassical Boltzmann transport theory to the classical transmission line theory. In this paper, we apply this approach to model the signal propagation in graphene nanoribbon (GNR) interconnects. We express the kinetic inductance and the quantum capacitance in terms of the number of effective conducting channels. We study in detail the behavior of the number of effective conducting channels for both the armchair and zig-zag GNRs as their widths vary. This number is computed rigorously, taking into account the actual distribution of the energy spectrum and of the velocity of the conduction electrons. We found that the expressions for the number of conducting channels proposed in the literature give a significant overestimation of its values.