Graphene Nanoribbon Interconnects Research Articles

Analysis of Crosstalk Noise Using Graphene Nanoribbon Interconnects by Changing Wire Spacing and Electron Mean Free Path

Analysis of Crosstalk Noise Using Graphene Nanoribbon Interconnects by Changing Wire Spacing and Electron Mean Free Path

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.

A survey on pristine and intercalation doped graphene nanoribbon interconnect for future VLSI circuits

The paper presents a review of recent works on pristine and intercalation doped graphene nanoribbon interconnects. Since the last decade, there have been tremendous research interests on graphene-based nanoelectronics. Graphene nanoribbon (GNR) has been projected as an interconnect material to replace the traditional copper interconnects. Since graphene is a planar material, CMOS compatible processes for patterning and making contacts to it, can be developed. Though, fabricating side-contacts in multilayered GNR (MLGNR) is a challenging task, fabrication of top-contact MLGNR is technologically viable. In addition, intercalation doping in top-contact MLGNR improves effective conductivity further. A number of models have been developed to optimize emerging on-chip interconnect technologies and benchmark them against conventional technologies. In this review, physical and electrical models of pristine and intercalation doped MLGNRs have been discussed in brief. A chronological survey towards analytical and spice compatible modeling of pristine and intercalation doped top-contact (TC) and side-contact (SC) MLGNR interconnect, has been presented in this article. A brief review of experimental work on pristine and intercalated GNRs as on-chip interconnect has also been incorporated in this survey. The stability, signal integrity (SI), and power integrity (PI) analysis of pristine and intercalation doped MLGNR interconnect with the presented models have been depicted further. The performance assessments have been compared with conventional copper, and CNT-based interconnects as well. It has been concluded that the side-contact and intercalation doped top-contact MLGNRs can outperform conventional copper-based interconnects.

Edge-Roughness Aware EM-RA Model for Signal Integrity Analysis in MLGNR Interconnects

This article presents a fast and accurate edge-roughness aware exponential matrix-rational approximation (EM-RA) model to capture the signal integrity effects, namely, crosstalk noise and the propagation delay, in coupled-multilayer graphene nanoribbon (MLGNR) interconnects. The proposed model provides a speed-up factor of 75 for coupled-two MLGNR line and a speed-up factor of 51 for coupled-three MLGNR line in comparison with the industry-level simulation program with integrated circuit emphasis (SPICE) simulator. The proposed model results always lie within a 1% error band compared with the HSPICE simulations, thereby ensuring the proposed model’s excellent accuracy. The robustness of the proposed edge-roughness aware EM-RA is confirmed by its application to a range of test cases in coupled-three MLGNR interconnects network. It is observed that the edge-roughness variations modeling plays a critical role in narrow (≤ 45 nm) MLGNRs. To ensure the signal integrity further, the eye-diagram analysis for the worst case scenario considering fully rough-edged MLGNR lines is carried out that provides the eye-height of 864.53 mV and the eye-width of 220.17 ps. The results obtained using the proposed closed-form parameterized EM-RA model ensures its immense possibility of incorporation in VLSI design automation tools for efficient capturing of the signal integrity effects in MLGNR interconnect networks.

Modeling and performance analysis of folded graphene nanoribbon interconnect

AbstractIn this paper, we have modeled the folded graphene nanoribbon (FGNR) interconnect and analyzed the performance for nanometer technology nodes. The mean free path is modeled as a function of GNR width and Fermi energy. The RLC equivalent circuit is modeled further for analyzing delay and RF response. The performance of FGNR is compared to that of multi‐layer horizontal graphene nanoribbon (ML‐HGNR) and multi‐layer vertical graphene nanoribbon (ML‐VGNR) interconnects. Our analysis shows that proposed FGNR interconnect with fully diffusive edges can outperform both the ML‐HGNR and ML‐VGNR interconnects as well as the traditional Cu interconnects.

Crosstalk noise analysis in ternary logic multilayer graphene nanoribbon interconnects using shielding techniques

SummaryThis paper presents an accurate structure for multilayer graphene nanoribbon (MLGNR) bundled interconnects to reduce the effects of crosstalk in ternary logic circuits. In the proposed structures, the signal line is surrounded by the shielding lines to reduce the crosstalk effects. The crosstalk effects such as noise peak, noise area, delay, and power consumptions are compared to effects produced by conventional methods. The impacts of process variation in the proposed structures are also presented. Additionally, the proposed MLGNR interconnect results are compared with the carbon nanotube interconnections. All the proposed circuits are implemented and simulated using HSPICE tool. The simulation results indicated that the passively shielded MLGNR interconnects provide lower crosstalk effects up to 47.7% and 69.4%, respectively, over the active and without shielded interconnects.

New Sensitivity Analysis on Graphene Nanoribbon Interconnects to Determine Importance of Parameters

In this paper sensitivity of a multilayer graphene nanoribbon (MGNR) interconnects parameters investigated. System sensitivity was studied on parameters like length and width in stable condition. The obtained results show 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 step response of transfer function, both width and length increase cause more stability for a system but the width parameter will be better choices for manipulating the dimension of MLGNR to reach the stable system.

Analysis of top- and side-contact MLGNR interconnects: impact on crosstalk, stability, and electromigration

In a recent nanoregime, the cross-coupling capacitance plays an important role due to the high packing density of integrated circuits. It can significantly affect the overall interconnect performance of an IC that can reduce the reliability, durability, and stability of silicon technology. In order to alleviate these problems, this work demonstrates shielded side-contact (SC) and top-contact (TC) multilayered graphene nanoribbon (MLGNR) interconnect to demonstrate stability and cross talk reliability issues. At 32 nm technology, an equivalent single-conductor Pi-type network is proposed for shielded SC- and TC-MLGNR for different spacing and interconnect lengths. Besides, the impact of temperature and higher current density is demonstrated. It is observed that the conventional interconnect material such as Cu exhibits 52.31% faster electromigration breakdown as compared to graphene at 1000 K. Further, the cross talk-induced delay is analyzed for shielded TC-and SC-MLGNR using driver–interconnect–load arrangement. An improved crosstalk-induced delay of 59.36% and 95.97% is observed for SC-MLGNR as compared to a TC-MLGNR with active shielding for an average spacing range of 5–20 nm at local and global lengths, respectively. Furthermore, the power delay product and peak noise of active-shielded SC-MLGNR exhibit on an average 96.82% and 38.20% improvement in comparison with active-shielded TC-MLGNR for the spacing of 5 nm at global length. Moreover, the Nyquist plot is used to demonstrate higher stability of SC-MLGNR than TC-MLGNR at 32 nm technology. Therefore, the overall system performance demonstrates that the active-shielded SC-MLGNR can be treated as a suitable choice for future VLSI technology.

All-2D-Materials-Based Interconnects

Boron nitride (BN) multi-layers are proposed as dielectric material for both horizontal and vertical graphene nanoribbon interconnects. The layer number dependence of the out-of-plane dielectric constant of BN multi-layers is utilized to simultaneously reduce the interlayer dielectric thickness and the crosstalk delay at 7 nm CMOS technology node. Since crosstalk effects are manifested more strongly in denser interconnects, the proposed all-two-dimensional-materials-based interconnection schemes are compared with Cu/low-k technology in terms of crosstalk delay. Results show that by reducing the interlayer dielectric thickness from 20 nm to 2 nm, the crosstalk delay ratio of the horizontal and vertical graphene nanoribbon interconnects to the Cu/pSiCOH counterparts decreases by 27.06% and 12.86%, respectively. It is also shown that as the interconnect length increases, both horizontal and vertical graphene nanoribbon interconnects with the BN dielectric prove more advantageous than the Cu/low-k counterparts.

Relative stability of shielded top- and side-contact MLGNR interconnects

ABSTRACT In a recent nano and deep-submicron regime, the electromagnetic interference primarily plays an important role in determining the overall interconnect performance of an integrated circuit (IC). For instance, it can cause lower reliability, and stability in silicon technology. In order to mitigate these challenges, this work introduces a new technique of active shielding by introducing a jacketed side- (SC) and top-contact (TC) multi-layered graphene nanoribbon (MLGNR) interconnect to demonstrate the relative stability. Depending on the physical configuration, an accurate Pi-type electrical network is proposed for the shielded TC-and SC-MLGNR at 32 nm technology. Using the equivalent circuit model, a fifth-order transfer function is employed to demonstrate the relative stability of SC- and TC-MLGNR at global interconnect lengths.

RF analysis of intercalated graphene nanoribbon-based global-level interconnects

Intercalation doping is emerging as a prospective solution to enhance the performance of graphene nanoribbon interconnects. In this paper, the radio frequency (RF) analysis of stage-2 arsenic pentafluoride- and lithium-doped multilayer graphene nanoribbons (MLGNRs) has been carried out for global-level interconnects in terms of skin depth, surface impedance, critical ratio (CR), transfer gain, and 3-dB bandwidth. The skin-depth results demonstrate that doped MLGNRs exhibit minimum performance degradation primarily due to their higher conductivity, mean free path, and momentum relaxation time as compared to neutral MLGNR. An equivalent second-order accurate RLC model of an intercalation-doped MLGNR has been used to extract the transfer gain and 3-dB bandwidth results at 14-nm technology node for global-level interconnects. The results are further evaluated by implementing an advanced π-type equivalent single conductor derived from multi-conductor transmission line model. The doped MLGNR interconnects demonstrate 11-fold enhancement of 3-dB bandwidth as compared to copper (Cu). Also, the delay and energy-delay-product (EDP) computations in time domain for doped MLGNR interconnects exhibit nearly 10 times lesser delay and significant reduction in EDP than Cu counterparts. It is also observed that optimum values for 3-dB bandwidth and EDP parameters for intercalated MLGNRs could be achieved through width optimization. The RF and transient results validate intercalated MLGNRs as a potential candidate to replace Cu for next-generation global-level interconnects.

Temperature‐dependent analysis of crosstalk and delay uncertainty in multilayer graphene nanoribbon interconnects

SummaryIn this article, we have analyzed delay uncertainty due to crosstalk in multilayer graphene nanoribbon (MLGNR) interconnects. Crosstalk is a challenging problem in deep‐sub‐micron and nanometer designs. In this work, we have analyzed the crosstalk delay with a wide variation in chip operating temperature. The mean free path is modeled as a function of temperature. Furthermore, the resistance of MLGNR interconnect system is modeled. Crosstalk delay analysis is performed for both top‐contact MLGNR and side‐contact MLGNR (SC‐MLGNR) interconnects and compared the results with that of the traditional Cu interconnects. The analysis has been carried out for different interconnect widths 11, 16, and 22 nm and lengths 10, 50, and 100 μm for three different chip operating temperatures 233, 300, and 398K. The decrease in rise/fall delay (speed up) and increase in rise/fall time delay (slow down) are modeled. Finally, the delay uncertainty is modeled for different interconnect systems. The percentage change in delay values for speed up and slow down cases are −23.4%, −29.8% and 114.4%, 161.9%, respectively, for 10μm SC‐MLGNR interconnect. It is shown that the delay uncertainty is significantly less in SC‐MLGNR interconnects and with the advancement of technology the performance is improved as compared with copper interconnects.

The analytical model of frequency response and bandwidth for coupled multilayer graphene nanoribbon interconnects

This paper applies the multilayer graphene nanoribbons (MLGNR) as a prospective candidate material to replace the conventional copper (Cu) for next generation on-chip interconnects. Based on the equivalent single conductor (ESC) modeling, a distributed transmission line model for coupled MLGNR interconnects is presented to obtain the transfer gain and 3-dB bandwidth at the global level of 14 ​nm technology node, which take the in-phase and out-of-phase crosstalk modes into consideration, and verified with the Hspice simulation. It is demonstrated that the MLGNR and Cu interconnects under in-phase mode have a larger transfer gain and a wider 3-dB bandwidth than that under out-of-phase mode, and MLGNR interconnects can more effectively improve the transfer gain and 3-dB bandwidth compared with Cu interconnects at the same conditions. The numerical calculation results show that, decreasing interconnect temperature, increasing line space and increasing driver and load sizes are efficient ways to enhance the transfer gain and 3-dB bandwidth for MLGNR and Cu interconnects. Moreover, the top contact MLGNR (TC-MLGNR) also can be used as an emerging material for on-chip interconnects to replace the conventional Cu. In addition, it is found that the results obtained by the proposed model are in good matching with Hspice simulation and the maximum relative deviation for them is less than 4%, meanwhile the efficiency of CPU runtime is improved over 90% by using the proposed model, as compared to Hspice simulation. The results presented in this paper would be useful to design the on-chip interconnects with better bandwidth characteristics.

Novel Approach to Analyze Crosstalk for a Multi-Line Bus System at 32-nm Technology

This research paper presents a novel approach to analyze the crosstalk-induced delay of multi-layered graphene nanoribbon (MLGNR) and multi-walled carbon nanotube (MWCNT) interconnects. A multi-line driver-interconnect-load (DIL) system is employed to analyze the crosstalk-induced delay for different switching transitions. The interconnect lines of the proposed DIL are said to be operated by either a resistive or a CMOS, or a CNFET driver for different switching transitions at 32-nm technology. Using the unique CNFET driver, the victim line of the multi-level MLGNR/MWCNT-based bus system experiences a delay almost 57.25% and 31.62% lesser in comparison to a resistive driver and a CMOS interconnect driver, respectively. Additionally, the overall worst-case delays are reduced by 89.45% and 98.98% for MLGNR in comparison to an equivalent MWCNT at 100[Formula: see text][Formula: see text]m and 1,000[Formula: see text][Formula: see text]m interconnect lengths, respectively.

Performance and signal integrity analysis of intercalation‐doped MLVGNR interconnects

In this work, signal integrity, power consumption and stability of multilayer vertical graphene nanoribbon (MLVGNR) interconnects are determined and compared with multilayer horizontal GNR (MLHGNR) and conventional copper interconnects for different intercalation dopants and specularity indices. Lithium-intercalated MLVGNR outperforms these conventional interconnects in terms of delay. However, it is not very much immune to noise and also consumes more power but overall noise delay product and power delay product are least among all. As far as stability is concerned, MLVGNR interconnects have a comparable gain and phase margin and a steep transient response without an undershoot as compared with other interconnect configurations, which experience undershoot. It is worth to point out that MLVGNR interconnects are more amenable to scaling compared with other alternatives. This study for the first time analyses and compares the performance, signal integrity and stability of MLVGNR, MLHGNR and copper interconnects.

Temperature-dependent crosstalk between adjacent MLGNR interconnects of different dimensions and its impact on gate oxide reliability

A comprehensive analysis is carried out herein on the impact of the interconnect geometry with nanoscale dimensions on the crosstalk-induced gate oxide reliability in coupled multilayer graphene nanoribbon (MLGNR) interconnects. Simplified circuit models are used to capture the temperature-dependent phonon scattering at temperatures from 300 to 500 K. Three different cases (case-1, case-2, and case-3) of coupled interconnects with fixed sum of width and spacing (interconnect pitch) but varying width/spacing (w/s) ratio are analyzed, revealing that the coupled interconnect geometry controls the impedance parameters. Functional crosstalk analysis shows that the highest positive noise peak of the victim output over the temperature range from 300 to 500 K is obtained in case-3, where the w/s ratio is maximum. On the other hand, the reverse is true for the time duration of the noise pulse at the far end of the victim line in case-2. Analysis of the dynamic crosstalk then reveals that an average percentage delay of approximately 13.45% is obtained in case-3 with respect to (w.r.t.) case-1, while a marginal difference is found in case-2. In comparison with temperature-independent circuit models, the results obtained using the temperature-dependent circuit models of the coupled MLGNR interconnects show an average relative improvement in the time duration of the noise pulse at the victim output by approximately 39%, 35.6%, and 46.6% in case-1, case-2 and case-3, respectively, for the different lengths. The gate oxide reliability in terms of the average failure rate (AFR) for coupled MLGNR interconnects with different widths and lengths is further investigated. The results show an infinitesimal increment of the AFR with the increase in the width and length of the MLGNR interconnects. Moreover, they reveal that the interconnect geometry in case-3 is more prone to gate oxide failure compared with the other cases.

Collaborative Applying the Ultra-low-k Dielectric and the High-k Dielectric Materials for Performance Enhancement in Coupled Multilayer Graphene Nanoribbon Interconnects

Based on transmission line modeling, a new technology of collaborative applying the ultralow-k dielectric and the high-k dielectric materials in coupled multilayer graphene nanoribbon (MLGNR) interconnects (i.e., case 4) to reduce propagation delay and to expand 3-dB bandwidth of the conventional pristine (undoped) MLGNR interconnects is proposed in this paper. By using the decoupling technique and ABCD parameter matrix approach, the transfer function of the equivalent circuit model for coupled MLGNR interconnects is derived to obtain step response, propagation delay, transfer gain and 3-dB bandwidth under in-phase and out-of-phase crosstalk modes at global level of 7.5 nm technology node, which is based on the defined four cases. The results show that the maximum reduction of propagation delay between the proposed new technology (case 4) and the conventional MLGNR interconnects (case 1) can reach 15.911 ns at out-of-phase crosstalk mode for an interconnect length of 4000 μm. The corresponding 3-dB bandwidth for them can be expanded over 2.978 times in the same length as the former. It is demonstrated that the proposed case 4 can obviously reduce the propagation delay and enhance the transfer gain and 3-dB bandwidth compared with the conventional case 1. Moreover, it is found that the coupled MLGNR interconnect under in-phase mode outperform that under out-of-phase mode in terms of propagation delay, transfer gain and 3-dB bandwidth at the same condition. In addition, it is manifested that the victim line of two-line coupled MLGNR interconnects have lesser propagation delay, higher transfer gain and larger 3-dB bandwidth, as compared to three-line coupled MLGNR interconnects at the same case. The proposed new technology in this paper would be beneficial to improve the performance of MLGNR interconnects and to provide the guidelines for the design of next generation on-chip MLGNR interconnect system.

The insertion of high-k dielectric materials in multilayer graphene nanoribbon interconnects for reducing propagation delay and expanding bandwidth

Abstract The multilayer graphene nanoribbons (MLGNR) by inserting the high-k dielectric material between adjacent graphene nanoribbons (GNR) layers to reduce propagation delay and to expand bandwidth of the conventional pristine (undoped) MLGNR interconnects is presented in this paper. An equivalent distributed circuit model of the proposed MLGNR interconnect with high-k dielectric materials is established to derive the analytical expressions of propagation delay, step response, transfer gain and 3-dB bandwidth for 7.5 nm technology node at global level. The numerical simulation results show that the maximum reduction of propagation delay between the proposed MLGNR by inserting SrTiO3 dielectric material and the pristine MLGNR can reach 12.746 ns for an interconnect length of 4000 μm. The corresponding 3-dB bandwidth for them can be expanded over 4 times for the interconnect length. It is demonstrated that the proposed MLGNR by inserting the high-k dielectric material can greatly reduce propagation delay and enhance transfer gain and 3-dB bandwidth compared with the conventional pristine MLGNR interconnects. Moreover, it is found that the results obtained by the proposed model have close agreement with Synopsys HSPICE simulation and the maximum relative error for them is less than 5%, and the average efficiency of CPU runtime is improved 95% by using the proposed model, as compared to HSPICE simulation. The proposed design method has many potential applications in improving performance of MLGNR interconnect and providing guidelines for the next generation on-chip interconnect system.

Thermal Stability Analysis of Graphene Nano-ribbon Interconnect and Applicability for Terahertz Frequency

In this paper, we have studied the thermal stability of GNR and Cu interconnects for terahertz frequency range. The top-contact (TC) and side-contact (SC) GNR interconnects are analyzed for stability, RC-delay, and power consumption at different interconnect lengths ($$10\,{\upmu }\hbox {m}$$, $$50\,{\upmu }\hbox {m}$$ and $$100\,{\upmu }\hbox {m}$$) and different chip operating temperatures (233 K, 300 K and 378 K). The RC-delay and power consumption are analyzed with the help of transmission line model (TLM) using 16nm PTM-HP standard CMOS model. In our analysis, we have shown that the RC-time constant for SC-GNR is $$\sim (3{-}7)\times $$ and $$\sim (2{-}6)\times $$ less than that of TC-GNR and Cu interconnects. Similarly, we have shown that the power consumption for SC-GNR is $$\sim (4{-}7)\times $$ and $$\sim (2{-}5)\times $$ less than that of TC-GNR and Cu. In terms of stability, SC-GNR interconnect is more stable at higher frequency range ($$>10^{12}$$ Hz) compared with TC-GNR and Cu for $$10\,{\upmu }\hbox {m}$$ interconnect length and three different chip operating temperatures.

Impacts of Process and Temperature Variations on the Crosstalk Effects in Sub-10 nm Multilayer Graphene Nanoribbon Interconnects

In this study, a comprehensive analysis of the crosstalk in multilayer graphene nanoribbon (MLGNR) interconnects in the presence of process and temperature variations is performed. The variations of the crosstalk delay, crosstalk noise area, and power are investigated in the presence of process and temperature variations for passively shielded five-line MLGNRs carrying ternary signals in 10nm and 7nm technology nodes. Analyses are conducted considering all of the important sources of process variations using comprehensive Monte Carlo simulations. The results indicate that the impacts of the process and temperature variations on the crosstalk effects become more evident with the technology scaling from 10 to 7nm, mainly due to the reduction of the width and spacing of the interconnects. According to the results, the maximum deviation of the crosstalk delay, power consumption, and noise area are 160ps, $0.9{\mu }\text{W}$ and 16V.ps, respectively for 10nm passively shielded MLGNR interconnect in the presence of all sources of process variations. These values are in turn 335ps, $1.3{\mu }\text{W}$ , and 27V.ps in 7nm node. Moreover, the crosstalk effects are evaluated at various temperatures ranging from 200°K to 450°K. The maximum variations for the crosstalk delay and noise area for 10nm MLGNR interconnects are 57ps and 6V.ps at temperatures higher than room temperature and 6ps and 0.5V.ps for temperatures lower than the room temperature. These variations are in turn 118ps, 9V.ps, 12ps and 1V.ps for 7nm MLGNR interconnects. It is also observed that the variations of the resistance of the $500{\mu }\text{m}$ length MLGNR in the presence of temperature variations are on average 3.9 $\text{K}\Omega $ and 8.2 $\text{K}\Omega $ in 10nm and 7nm technologies, respectively.