Graphene Nanoribbon Interconnects Research Articles

Optimal repeater insertion for horizontal and vertical graphene nanoribbon interconnects

AbstractA comparative study on the repeater insertion designs in horizontal and vertical graphene nanoribbon (GNR) interconnects is presented. The optimal numbers and sizes of repeaters are calculated by using the particle swarm optimization algorithm, and then the results are employed to train back‐propagation neural networks. By virtue of the trained neural networks, the optimal repeater designs can be quickly conducted for the GNR interconnects. The proposed optimal repeater design approach is more flexible and more adaptive than conventional analytical methods. By utilizing the proposed approach, it is found that the vertical GNR interconnects need less repeaters yet result in better performance than their horizontal counterparts.

Analysis of Temperature-Dependent Crosstalk for Graphene Nanoribbon and Copper Interconnects

In this article, we propose a temperature-based crosstalk analysis model for rough edge graphene nanoribbon (GNR) and Cu interconnect. Temperature-dependent crosstalk delay and noise analysis for 16 nm technology node (ITRS-2011) is performed for three different chip-operating temperatures are −40°C (233 K), i.e. low temperature, 27°C (300 K), i.e. room temperature, and 105°C (378 K), i.e. high temperature. Our analysis shows that, first by increasing the temperature from 233 to 378 K and also by increasing interconnect length from 10 to 100 µm, the GNR shows less amount of crosstalk-induced delay compared with Cu interconnect and crosstalk noise increase slightly which indicates the performance degradation and reliability issues, second the GNR-based interconnect produce (%) variation in delay due to crosstalk and crosstalk noise is lesser than Cu interconnect when interconnect length increase from 10 to 100 µm by increasing temperature. Hence, GNR interconnect is much more thermally viable as compared with traditional Cu-based interconnect and it is very much useful for nano-scale interconnect modeling.

Modeling and Analysis of Electro-Thermal Impact of Crosstalk Induced Gate Oxide Reliability in Pristine and Intercalation Doped MLGNR Interconnects

This work presents the electro-thermal analysis of crosstalk effects in pristine (undoped) and intercalation doped multilayer graphene nanoribbon interconnects (MLGNRs). A temperature dependent distributed $T-$ network model of MLGNR interconnects has been developed for analyzing the crosstalk induced effects. Further, a temperature-aware gate oxide reliability model has been proposed to compute the crosstalk induced overshoot/undershoot impact on ultra-thin gate oxide for CMOS devices in terms of failure-in-time (FIT) for side-contact (SC) pristine as well as top-contact (TC) Arsenic pentafluoride ( $AsF_{5}$ ), Ferric chloride ( $FeCl_{3}$ ) and Lithium ( $Li$ ) intercalation doped and undoped MLGNR interconnects. Subsequently, comparisons with $Cu$ -based interconnects are made over a range of chip operating temperature from 233K to 450K.

The Ultra-Low-k Dielectric Materials for Performance Improvement in Coupled Multilayer Graphene Nanoribbon Interconnects

The ultra-low-k dielectric material replacing the conventional SiO2 dielectric medium in coupled multilayer graphene nanoribbon (MLGNR) interconnects is presented. An equivalent distributed transmission line model of coupled MLGNR interconnects is established to derive the analytical expressions of crosstalk delay, transfer gain, and noise output for 7.5 nm technology node at global level, which take the in-phase and out-of-phase crosstalk into account. The results show that by replacing the SiO2 dielectric mediums with the nanoglass, the maximum reduction of delay time and peak noise voltage are 25.202 ns and 0.102 V for an interconnect length of 3000 µm, respectively. It is demonstrated that the ultra-low-k dielectric materials can significantly reduce delay time and crosstalk noise and increase transfer gain compared with the conventional SiO2 dielectric medium. Moreover, it is found that the coupled MLGNR interconnect under out-of-phase mode has a larger crosstalk delay and a lesser transfer gain than that under in-phase mode, and the peak noise voltage increases with the increase of the coupled MLGNR interconnect length. The results presented in this paper would be useful to aid in the enhancement of performance of on-chip interconnects and provide guidelines for signal characteristic analysis of MLGNR interconnects.

Performance and Power Optimization for Intercalation Doped Multilayer Graphene Nanoribbon Interconnects

In this work, thickness of AsF5 intercalation doped, Multilayer Graphene Nanoribbon (MLGNR) interconnects is optimized by minimizing various performance and power metrics (i.e. crosstalk-induced signal transmission delay, noise parameters, Noise-delay product (NDP), Energy-delay product (EDP), Power-delay product (PDP) and Noise bandwidth ratio (NBWR)). For perfectly and nearly specular MLGNRs (i.e. specularity index, P = 1 and P = 0.8 respectively), the optimal thicknesses for minimizing the crosstalk-induced delay are 25 nm and 100 nm for intermediate and global level MLGNR interconnects, respectively. However, it is observed that perfectly and nearly specular MLGNRs are immune to noise for thickness less than 40 nm at intermediate level and 200 nm at global level interconnects. They outperform Cu in terms of signal transmission delay, noise width and noise area at both levels of interconnect. But in terms of peak crosstalk noise, Cu is better than all types of MLGNR interconnects. When we talk about NDP, EDP and NBWR, MLGNR thickness optimizes at 25 nm for intermediate level and 100 nm for global level. As far as power dissipation is concerned, perfectly and nearly specular, intermediate and global level MLGNRs are many times better than copper in the whole range of its thickness which can be optimized by minimizing its PDP at 100 nm irrespective of the level of interconnects. It can be inferred from the simulated results that global level MLGNR interconnects are amenable to scaling, whereas intermediate level interconnects have adverse effects of scaling.

Stability analysis of multilayer vertical graphene nanoribbon interconnects

In this work, stability of lithium intercalation doped Multilayer Vertical Graphene Nanoribbon (ML-VGNR) interconnects is estimated and compared with existing copper and lithium intercalated Multilayer Horizontal Graphene Nanoribbon (ML-HGNR) interconnects. ML-VGNR interconnects have a sharp, well behaved transient response among all the interconnect configurations. An isolated copper interconnect has the highest stability but when crosstalk is considered, ML-VGNR interconnect is the most stable one. This work for the first time analyzes and compares the stability of ML-VGNR, ML-HGNR and copper interconnects on isolated, single interconnect and 3-interconnect configurations.

Comparative Analysis of the Crosstalk Effects in Multilayer Graphene Nanoribbon and MWCNT Interconnects in Sub-10 nm Technologies

In this paper, the crosstalk effects in multilayer graphene nanoribbon (MLGNR) interconnects are evaluated and are compared with those in multiwalled carbon nanotube (MWCNT) interconnects in ternary integrated circuits at the 10 and 7 nm technologies. For a more precise evaluation, the five-line bus architecture is considered. Furthermore, the effects of the top and bottom aggressors are considered for a more accurate analysis in sub-10 nm dimensions. The active and passive shielding techniques are also applied to reduce the crosstalk effects. Our results indicate that the MLGNR interconnects outperform the MWCNTs, especially in the more realistic seven-line case, which also considers the effects of the bottom and top layer aggressors. Also, the advantages of the MLGNR interconnects become more significant when the node shrinks from 10 to 7 nm. The crosstalk delays of normal, passively shielded, and actively shielded five-line MLGNRs at 7 nm are on average 49%, 56%, and 54% lower compared to their MWCNT counterparts, respectively. These improvements are 36%, 36%, and 41% regarding the power. Moreover, the normal and actively shielded MLGNRs have 25% and 72% smaller crosstalk noise area than their MWCNT counterparts, respectively. The smaller crosstalk noise for MLGNR leads to noise-free signals at the end of both actively and passively shielded victim lines in ternary logic at the 10 and 7 nm technologies.

Dielectric Surface Roughness Scattering Limited Performance of MLGNR Interconnects

Based on an equivalent single conductor model incorporating surface roughness scattering, the effect of the surface roughness of an underlying dielectric material on the performance of multilayer graphene nanoribbon (MLGNR) interconnects with side contacts is investigated. The performance of MLGNR interconnects with different doping concentrations on the most common dielectrics [SiO2, boron nitride, and silicon carbide (SiC)] is compared with that of Cu counterpart in terms of the time delay and the bandwidth. Results show that the surface roughness of the dielectric material can severely degrade the performance of MLGNR interconnects; hence, it must be taken into account in design considerations. While MLGNR interconnects with perfect edges on the SiC substrate outperform Cu counterpart both in terms of time delay and bandwidth, for other substrate materials, the performance of MLGNR interconnects with respect to Cu counterpart depends on doping concentration and interconnect length.

Electro-thermal RF modeling and performance analysis of graphene nanoribbon interconnects

This paper presents an electro-thermal radio frequency (RF) model and performance analysis for multilayer graphene nanoribbon (MLGNR) interconnects. The number of conduction channels is calculated as a function of temperature and Fermi energy. A comprehensive model is developed to calculate the temperature dependent effective mean free path (MFP) considering different scattering mechanisms. The RF model of doped and undoped metallic top-contact (TC), as well as side-contact (SC) MLGNR interconnects is demonstrated using ABCD parameter based multi-conductor transmission line formalism. The RF performance of arsenic pentafluoride ( $$\text {AsF}_5$$ ), lithium (Li) and ferric chloride ( $$\text {FeCl}_3$$ ) intercalation doped TC-MLGNR interconnects is investigated and compared with pristine (undoped) TC and SC-MLGNR interconnects for different temperatures. For the first time, our investigation shows that the electro-thermal RF performance of TC-MLGNR can be improved by intercalation doping. It is found that $$\text {AsF}_5$$ , Li and $$\text {FeCl}_3$$ intercalated top-contact MLGNR can operate up to a few GHz for semi-global interconnects ( $$100\,\upmu $$ m) and several MHz for global interconnects ( $$500\,\upmu $$ m). Our analysis also proves that the Li intercalated TC-MLGNR shows the best RF performance as compared to conventional copper, pristine, and other type of intercalation doped TC-MLGNR interconnects over the chip operating temperature range from 233 to 378 K. The performance of Li intercalated TC-MLGNR has been found to be improved further by increasing the specularity during fabrication.

Graphene Nanoribbon as Potential On-Chip Interconnect Material—A Review

In recent years, on-chip interconnects have been considered as one of the most challenging areas in ultra-large scale integration. In ultra-small feature size, the interconnect delay becomes more pronounced than the gate delay. The continuous scaling of interconnects introduces significant parasitic effects. The resistivity of interconnects increases because of the grain boundary scattering and side wall scattering of electrons. An increased Joule heating and the low current carrying capability of interconnects in a nano-scale dimension make it unreliable for future technology. The devices resistivity and reliability have become more and more serious problems for choosing the best interconnect materials, like Cu, W, and others. Because of its remarkable electrical and its other properties, graphene becomes a reliable candidate for next-generation interconnects. Graphene is the lowest resistivity material with a high current density, large mean free path, and high electron mobility. For practical implementation, narrow width graphene sheet or graphene nanoribbon (GNR) is the most suitable interconnect material. However, the geometric structure changes the electrical property of GNR to a small extent compared to the ideal behavior of graphene film. In the current article, the structural and electrical properties of single and multilayer GNRs are discussed in detail. Also, the fabrication techniques are discussed so as to pattern the graphene nanoribbons for interconnect application and measurement. A circuit modeling of the resistive-inductive-capacitive distributed network for multilayer GNR interconnects is incorporated in the article, and the corresponding simulated results are compared with the measured data. The performance of GNR interconnects is discussed from the view of the resistivity, resistive-capacitive delay, energy delay product, crosstalk effect, stability analysis, and so on. The performance of GNR interconnects is well compared with the conventional interconnects, like Cu, and other futuristic potential materials, like carbon nanotube and doped GNRs, for different technology nodes of the International Technology Roadmap for Semiconductors (ITRS).

Modeling and Performance Analysis of MLGNR Interconnects

In this work, we have presented the temperature-dependent analytical time domain model for top-contact multilayer graphene nanoribbon (TC-MLGNR) and side-contact multilayer graphene nanoribbon (SC-MLGNR) interconnects for 16[Formula: see text]nm technology node. Using this analytical model, the effective mean free path (MFP) is calculated for different temperatures and then the resistance of GNR interconnect is calculated. The lower resistance of MLGNR is one of the important factors to reduce interconnect delay. The equivalent capacitance for TC-MLGNR is also calculated. It is observed that the performance of graphene interconnects seriously deteriorates due to the presence of the interlayer capacitance. The presence of this interlayer capacitance increases the equivalent capacitance which is the dominant factor that inhibits the performance of TC-MLGNR interconnects. Further, the delay ratio between copper and TC-MLGNR for different interconnect lengths and for three different temperatures (233[Formula: see text]K, 300[Formula: see text]K, 378[Formula: see text]K) is calculated. It is observed that for longer interconnect lengths, the improvement in delay in TC-MLGNR is less as compared to traditional copper-based interconnect at low temperature. Further, power delay product (PDP) of copper and TC-MLGNR for different interconnect lengths and for three different temperatures is also calculated. It is shown that TC-MLGNR interconnects have better PDP than copper interconnects. The crosstalk analysis is performed to estimate the noise and overshoot/undershoot in TC-MLGNR and SC-MLGNR interconnects. It is shown that SC-MLGNR interconnect has better performance as far as the crosstalk is concerned as compared to that of Cu and TC-MLGNR interconnects.

Multi Layer Graphene Nano-Ribbon Interconnects Based Driver-Interconnect-Load System

Nowadays planar graphene based interconnects known as graphene nano-ribbons (GNR), are used for interconnections in VLSI and ULSI chips. The form of GNR which is widely used is multi layer graphene nano-ribbon (MLGNR). In this paper study of propagation delay of a driver-interconnect-load system (DIL) has been carried out along with MLGNR beyond 16nm and comparison has been made with the DIL systems used at 16 nm. In this work different numbers of devices that are connected in parallel have also been considered for three different operating regions like super threshold region, near threshold region, and sub threshold region.

Discontinuous Galerkin Time-Domain Modeling of Graphene Nanoribbon Incorporating the Spatial Dispersion Effects

It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wavenumber (momentum operator) $\mathbf {q}$ . In this paper, to account for effects of spatial dispersion on transmission of high-speed signals along graphene nanoribbon (GNR) interconnects, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed. The atomically thick GNR is modeled using a nonlocal transparent surface impedance boundary condition (SIBC) incorporated into the DGTD scheme. Since the conductivity is a complicated function of $\mathbf {q}$ (and one cannot find an analytical Fourier transform pair between $\mathbf {q}$ and spatial differential operators), an exact time-domain SIBC model cannot be derived. To overcome this problem, the conductivity is approximated by its Taylor series in spectral domain under low- $\mathbf {q}$ assumption. This approach permits expressing the time-domain SIBC in the form of a second-order partial differential equation (PDE) in current density and electric field intensity. To permit easy incorporation of this PDE with the DGTD algorithm, three auxiliary variables, which degenerate the second-order (temporal and spatial) differential operators to first-order ones, are introduced. Regarding to the temporal dispersion effects, the auxiliary differential equation method is utilized to eliminate the expensive temporal convolutions. To demonstrate the applicability of the proposed scheme, numerical results, which involve characterization of spatial dispersion effects on the transfer-impedance matrix of GNR interconnects, are presented.

Vertical Graphene Nanoribbon Interconnects at the End of the Roadmap

To solve electrical contact problem of horizontal multilayer graphene nanoribbon (GNR), a vertical GNR (VGNR) interconnect scheme is proposed. Performance of the VGNR interconnect is theoretically evaluated and compared with those of conventional interconnect technologies. It is shown that the performance of VGNR is comparable (and even superior) to that of the horizontal GNR (HGNR). Moreover, VGNRs may provide a promising solution to the thermal challenges faced by HGNRs in nanoscale ICs.

Analysis of delay fault in GNR power interconnects

AbstractIn this paper, a delay fault model for multilayer graphene nanoribbon (GNR)‐based power interconnects for 16‐nm International Technology Roadmap for Semiconductors technology node is developed for both top‐contact GNR and side‐contact GNR. The delay fault model is developed for different temperature considering the impact of scattering parameters. It is shown that side‐contact GNR‐based power interconnects can reduce the delay fault significantly in comparison with that of Cu and top‐contact GNR interconnects at local, intermediate, and global lengths for a wide range of chip operating temperatures from 233 K to 378 K.

Modeling and Performance Analysis of Graphene Nanoribbon Interconnects

Attempts have been made to propose a compact resistive model for graphene nanoribbon interconnects. Top-contact (TC-GNR) and side-contact (SC-GNR) GNR interconnects have been modeled. The number of conduction channels, mean free path, and resistance are calculated for different Fermi energies and interconnect widths. Present study showed that the resistance of SC-GNR is ~10× less and delay is ~2–16× less than that of TC-GNR.

Temperature‐dependent modeling and performance analysis of coupled MLGNR interconnects

AbstractThe temperature‐dependent circuit modeling and performance in terms of propagation delay, power dissipation, and crosstalk‐induced voltage waveform at the far end of victim line of multilayer graphene nanoribbon (MLGNR) interconnects have been analyzed at 22 nm technology node. A comparative performance analysis between MLGNR interconnects with resistance estimated using temperature‐dependent model and temperature‐independent model is examined. The results obtained are also compared with capacitively coupled interconnects of copper (Cu). The results show that as the temperature is varied from 300 K to 500 K, MLGNR has lower propagation delay and power dissipation as compared to Cu for 1 mm long interconnects. It is also observed that because of the dominance of both low resistance and ground capacitance compared to Cu, MLGNR has better crosstalk‐induced delay and voltage waveforms with rise in temperature at the far end of aggressor and victim line, respectively. Further, simulated results show an average relative improvement in propagation delay of 37.24% and corresponding improvement in power dissipation of approximately 19.59% by using a temperature‐dependent model in comparison to a temperature‐independent model of MLGNR resistance with interconnect lengths varying from 200 to 1000 μm. The reduction in the time duration of victim output pulse over these interconnect lengths also shows a significant improvement of approximately 35% by using temperature‐dependent model as against temperature‐independent model of MLGNR resistance.

Transfer matrix model of multilayer graphene nanoribbon interconnects

A general, algorithmic and exact transfer matrix model is presented for multilayer graphene nanoribbon (MLGNR) interconnects that is based on multi transmission line method (MTLM). In the proposed transfer matrix formulation the effect of Fermi level shift in GNR layers is considered. Also the capacitive and inductive coupling between the GNR layers is regarded in this matrix model. Moreover, in order to get the precise results, the block number parameter for distributed property of the interconnects is proposed for the first time. The straightforward, general and algorithmic format of the proposed matrix model causes it to be used for different technology nodes and length of the interconnects. Moreover any variation in the physical parameters can be involved simply in this formulation. Using this matrix model, one can examine different analytical prospects such as Nyquist, Bode, and Nichols stability criteria, zero and poles and step time responses for on-chip MLGNR interconnects, implemented for integrated circuit applications. Also this matrix model can be used in circuit simulators such as HSPICE in order to simulate the VLSI-ULSI circuits. As the couple of examples, we have extracted Nyquist diagrams and step time responses for 10nm, 14nm, and 22nm technology nodes. The results show that relative stability of MLGNR interconnects increases with increasing technology node and interconnect length. The results demonstrate a considerable difference between the responses obtained using traditional MLGNR interconnect formulation and the exact proposed matrix model.

Performance Analysis of Emerging Interconnects Driven by Devices beyond CMOS

Objective: This paper analyses the performances of Multi Walled Carbon Nanotube (MWCNT), Mixed CNT Bundle (MCB), and Multilayer Graphene Nanoribbon (MLGNR) interconnects incorporated with Carbon Nanotube Field-Effect Transistor (CNFET) and Tunnel Field-Effect Transistor (TFET) technologies. Methods/Statistical Analysis: The performances of the circuits are evaluated at the 32-nm node. HSPICE is used for the simulation of the driver interconnect load framework. The performance parameters, viz. power dissipation, propagation delay, and power delay product (PDP), are assessed, and it is found that a CNFET driver can reduce the propagation delay in MLGNR interconnects by 96%, 38%, and 30%, for local, intermediate, and global interconnect lengths, respectively, in comparison with the TFET driver. Findings: By using a TFET driver, the power dissipation in MLGNR is reduced by 99%, 45%, and 63%, for local, intermediate, and global levels, respectively, compared to the CNFET driver. The PDP of MLGNR is reduced by 99%, 37%, and 47% for local, intermediate, and global levels, respectively, by using a TFET driver instead of a CNFET driver. Applications/Improvements: MLGNR shows lesser propagation delay, power dissipation, and PDP than the MWCNT and MCB interconnects; hence, it is considered the best candidate to replace Cu interconnects in Very-Large-Scale Integration (VLSI) chips.

Modelling and performance analysis of dielectric inserted side contact multilayer graphene nanoribbon interconnects

In this work, performance of dielectric inserted side contact multilayer graphene nanoribbon (Di-side-GNR) coupled interconnects using unconditionally stable finite-difference time-domain (USFDTD) technique has been investigated. The model developed for the same, overcomes the limitation of Courant stability criterion prevalent in the conventional finite-difference time-domain (FDTD) technique. The proposed model accurately analyses the crosstalk effect in copper (Cu), side contact multilayer graphene nanoribbon and Di-side-GNR interconnects. It is found that the crosstalk effect is least in Di-side-GNR amongst the three types of interconnect considered in this study. The proposed model and HSPICE simulation results match closely. Further, for transient analysis USFDTD technique based proposed model takes nearly 1.5 times lesser CPU runtime compared to the conventional FDTD technique.