Multilayer Graphene Nanoribbon Interconnects Research Articles

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.

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.

Time and Frequency Domain Analysis of MLGNR Interconnects

Multilayer graphene nanoribbons (MLGNRs) have potentially provided attractive solutions in an intensely growing researched area of interconnects. However, for MLGNR interconnects, the doping is inevitable since the conductivity of neutral MLGNR is much lower than even Cu. Therefore, a doped MLGNR can potentially exhibits smaller resistance in comparison to Cu wires. This paper analyzes and compares the power, delay, and bandwidth performance of Cu and doped MLGNR using an equivalent single conductor model. For similar dimensions, the overall delay and power dissipation of doped MLGNR is substantially smaller by 86.13% and 43.72%, respectively, in comparison to the Cu interconnects. Moreover, MLGNR demonstrates prominently improved bandwidth and relative stability at global interconnect dimensions. However, a narrow width MLGNR in a realistic scenario exhibits rough edges that significantly reduces the mean free path and, thereby, raises its resistance. Considering these facts, this paper for the first time analyzes and compares the performance of Cu and MLGNR interconnects with different edge roughness conditions.

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.

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.

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.

Crosstalk Stability Analysis in Multilayer Graphene Nanoribbon Interconnects

In this paper a time-domain response and Nyquist stability criterion to acquire dependence of degree of crosstalk relative stability based on transmission lines modeling (TLM) is investigated for coupled multilayer graphene nanoribbon (MLGNR) interconnects. This is the first instance that such an analysis has been presented for coupled MLGNR consisting of both capacitive and mutual-inductive couplings. The near-end and far-end outputs of coupled MLGNR individually are compared in two cases, with considering both couplings and without them (single MLGNR). It is observed that the near-end output of the system together with both couplings is more stable and at its far-end output, an induced voltage is created. By increasing capacitive coupling or decreasing inductive coupling, the near-end output becomes more stable. Also, the results of changes of length and width of each ribbon show that by increasing the length and decreasing the width, the coupled MLGNR interconnects become more stable.

Effect of Varying Aspect Ratio on Relative Stability for Graphene Nanoribbon Interconnects

Achieving dense off-chip interconnection with satisfactory electrical performance is emerging as a major challenge in advanced system engineering. Graphene nanoribbons (GNRs) have been recently proposed as one of the potential candidate materials for both transistors and interconnect. In addition, development is still underway for alternative materials and processes for high aspect ratio (AR) contacts. Studding the effect of varying aspect ratio on relative stability of graphene nanoribbon interconnects is an important viewpoint in performance evaluation of system. In this paper, Nyquist stability analysis based on transmission line modeling (TLM) for GNR interconnects is investigated. In this analysis, the dependence of the degree of relative stability for multilayer GNR (MLGNR) interconnects on the aspect ratio has been acquired. It is shown that, with increasing the aspect ratio of each ribbon, MLGNR interconnects become more unstable.

Effect of Varying Dielectric Constant on Relative Stability for Graphene Nanoribbon Interconnects

The remarkable properties of graphene nanoribbons (GNRs) make them attractive for nano-scale devices applications, especially for transistor and interconnect. Furthermore, for reduction interconnects signal delay, low dielectric constant materials are being introduced to replace conventional dielectrics in next generation IC technologies. With these regards, studding the effect of varying dielectric constant (ɛr) on relative stability of graphene nanoribbons interconnect is an important viewpoint in performance evaluation of system. In this paper, Nyquist stability analysis based on transmission line modeling (TLM) for graphene nanoribbon interconnects is investigated. In this analysis, the dependence of the degree of relative stability for multilayer GNR (MLGNR) interconnects on the dielectric constant has been acquired. It is shown that, increasing the dielectric constant of each ribbon, MLGNR interconnects become more stable.

Performance and Energy-per-Bit Modeling of Multilayer Graphene Nanoribbon Conductors

In this paper, physical models are derived for the effective resistance of multilayer graphene nanoribbon (m-GNR) interconnects. The impact of finite resistive coupling between the layers for top contacted m-GNR interconnects is considered. It is found that the addition of more parallel layers does not necessarily translate into a decrease in the overall resistance of m-GNR interconnects. Rather, the improvement in the effective resistance saturates with an increase in the number of layers. The optimal number of layers to minimize the delay and the energy-delay product of m-GNR interconnects is also evaluated. It is found that the optimal number of layers is a function of the interconnect length, interlayer resistance, and the kind of contact that is used. It is demonstrated that, for short interconnect lengths, m-GNR interconnects with smooth edges perform better compared to copper wires.

Signal Transmission Analysis of Multilayer Graphene Nano-Ribbon (MLGNR) Interconnects

Signal transmission characteristics of some multilayer graphene nano-ribbon (MLGNR) interconnects are studied in this paper, with an equivalent single-conductor (ESC) model implemented for the analysis of their transient responses. In this model, both capacitive and inductive couplings between adjacent GNR layers are treated appropriately. According to the derived transfer function using the fourth-order approximation, the output voltage waveforms are predicted for both 14- and 22-nm technology nodes. In particular, the effects of Fermi level of MLGNR on the time delay of the transmitted rectangular pulse are examined and compared. Based on the decoupled partially differential equations (PDEs) for the common and differential modes of voltage wave propagation in the edge-coupled MLGNR interconnects, their output voltage responses are also predicted for different technology nodes, which are useful for the evaluation of on-chip signal integrity or EMC and EMI issues of MLGNR-built transmission lines for the future ICs.

Stability Analysis in Graphene Nanoribbon Interconnects

We present a Nyquist stability criterion based on transmission line modeling for graphene nanoribbon (GNR) interconnects. This is the first instance that such an analysis has been presented for GNR, so far. In this analysis, the dependence of the degree of relative stability for multilayer GNR (MLGNR) interconnects on the geometry of each ribbon has been acquired. It is shown that, increasing the length and width, MLGNR interconnects become more stable.