Multi-walled Carbon Nanotube Interconnects Research Articles

Modified Knowledge-Based Neural Networks Using Control Variates for the Fast Uncertainty Quantification of On-Chip MWCNT Interconnects

In this article, a modified knowledge-based artificial neural network (KBANN) metamodel is developed for the efficient uncertainty quantification of on-chip multiwalled carbon nanotube (MWCNT) interconnects. The proposed KBANN metamodel utilizes the notion of control variates to enable much faster training than what is possible with standard KBANNs. Importantly, techniques to calculate the optimal value of the control variates in an a priori manner without augmenting the training dataset have been developed in this article. Furthermore, techniques to exploit the control variates depending on whether one or multiple low-fidelity models of the MWCNT interconnects are available have also been developed in this article. The benefits of the proposed KBANN metamodel using control variates over standard KBANN metamodels have been validated using multiple MWCNT interconnect examples spanning multiple technology nodes.

Simultaneous Switching Noise Effects in Graphene-Based Power Distribution Networks

The simultaneous switching noise (SSN) effects in graphene nanoribbon field effect transistor (GNRFET) based ternary circuits are presented in this study. The performance in terms of SSN induced peak noise and propagation delay on power and ground rails are investigated in multilayer graphene nanoribbon (MLGNR) bundled power interconnects using Hewlett simulation program with integrated circuit emphasis (HSPICE) simulator. Furthermore, these investigations are compared to the copper (Cu) and multiwalled carbon nanotubes (MWCNT) based power interconnects. From the results, it is noticed that the proposed MLGNR interconnects shows performance improvements up to 74.9% and 33.8% over the Cu and MWCNT interconnects. Moreover, the SSN peak noise and delay are investigated for different interconnect lengths from 200 μm to 500 μm. It is observed that the SSN noise on power and ground rail is reduced and propagation delay is increased as interconnect length is increased.

Signal Integrity Assessment of GNRFET-Based Ternary Logic for Multi Layered GNR Interconnects with Dielectric Insertion

In this paper, signal integrity assessment is carried out for graphene nanoribbon field effect transistor (GNRFET) based ternary logic with dielectric inserted multi-layered GNR (MLGNR) interconnects. The analyses are carried out for crosstalk effects and eye diagrams with and without shielding lines. In this paper firstly, it is observed that the dielectric inserted MLGNR interconnects show better than copper (Cu) and multiwall carbon nanotube (MWCNT) interconnects. Secondly, active shield technique is adopted, and observed that it exhibits better performance than without shield and passive shield techniques. Also, the power-delay product performance parameter is evaluated and envisaged that active shield technique outperforms passive technique. Further, the eye diagram analysis is carried out for different bit rates. The different performance analyses in the paper have been carried out for 10 nm technology node.

Crosstalk Peak Overshoot Analysis of VLSI Interconnects

As technology extended from deep sub-micron technology to nanometer regimes, the conventional copper (Cu) wire will not be able to continue. Now a substitute approaches such as Carbon Nano Tube (CNT) interconnects have been suggested to ignore the problems associated with global interconnects. Hence in this work, crosstalk analysis of Complementary metal oxide semiconductor (CMOS) buffer-driven of different interconnects have been analyzed for peak overshoot and overshoot width of Cu and CNTs for 16nm technology. For analyzing peak overshoot, the interconnect lengths are varied from 100um to 500um in 16 technology node for Cu, single walled carbon nanotube (SWCNT) and multi-walled carbon nanotube (MWCNT). The values of the peak overshoot and overshoot width changes, as the interconnect length increases, the peak overshoot and width is going to be increases. As Compared to Cu, SWCNT and MWCNT, the peak overshoot and width for SWCNT is lesser than copper and MWCNT. The MWCNT interconnect is less than that of conventional Copper interconnects.

A Bilevel Multi-Fidelity Polynomial Chaos Approach for the Uncertainty Quantification of MWCNT Interconnect Networks With Variable Imperfect Contact Resistances

With on-chip copper interconnects reaching their performance limits at 22 nanometer technology nodes, multi-walled carbon nanotube (MWCNT) interconnects are projected to replace them below this point. A major aspect of MWCNT interconnect design is to perform uncertainty quantification (UQ) in an efficient yet accurate manner. In this paper, a polynomial chaos (PC) based approach is developed for the UQ of MWCNT interconnect networks under the condition that some shells of each conductor of the network are perfectly contacted while others are imperfectly contacted. The key feature of the proposed approach is the development of a bilevel multi-fidelity algorithm where two different low-fidelity models are combined together. The main outcome of using this bilevel approach is to further reduce the computational time cost of state-of-the-art single level multi-fidelity algorithms, especially in the presence of variable imperfect contact resistances where single level multi-fidelity algorithms fail to provide much speedup over conventional PC approaches. The proposed approach adopts a SPICE hybrid model that combines the features of the equivalent single conductor (ESC) model and the rigorous multiconductor circuit (MCC) model of the MWCNT conductors. Then the low-fidelity ESC model, the intermediate-fidelity hybrid model, and the high-fidelity MCC model are exploited in a bilevel multi-fidelity algorithm for the recovery of the PC metamodel of the interconnect network. This proposed bilevel multi-fidelity algorithm is demonstrably 3-5x more numerically efficient than state-of-the-art single level multi-fidelity algorithms while being even more accurate. Once recovered, the PC metamodel is used to derive all statistical information of the network transient responses.

Crosstalk Delay and Noise Optimization in Nanoscale Multi-line Interconnects Based on Repeater Staggering in Ternary Logic

In this study, the crosstalk effects are minimized in coupled multi-line wires based on repeater staggering in ternary logic. For more accuracy, the impact of the coupling capacitance is also considered in our calculations. Our results indicate that the number of repeaters required for optimizing the delay of the multilayer graphene nanoribbon (MLGNR) interconnect is, on average, 43% lower than multi-walled carbon nanotube (MWCNT) interconnect. Moreover, the optimized delay of the MLGNR interconnect is, on average, 48% lower than MWCNT interconnect. The ternary repeater insertion reduces the delay of the MWCNT and MLGNR interconnects carrying ternary signals by 61% and 51%, respectively. The staggered repeater insertion is applied as a practical approach for eliminating the crosstalk noise in the transmitted ternary signals in a multi-line coupled structure. Our results demonstrate that the delay and energy of the staggered repeater-inserted MLGNR interconnects are, on average, 42% and 37% lower than their MWCNT counterparts. Furthermore, the impacts of the process variations are investigated using comprehensive Monte Carlo simulations and the optimized ternary multi-line MLGNR interconnect functions correctly and considerably robustly compared to their MWCNT counterpart.

Evaluation and Reduction of Signal Integrity Issues in Multiwalled Carbon Nanotube On-Chip VLSI Interconnects

Due to advancements in device scaling in very-large-scale integration (VLSI) technology, signal integrity (SI) issues play a major role to determining the performance of on-chip interconnects in high-speed digital circuits. The main SI issues are delays, peak voltage noise effects, crosstalk, and timing uncertainties. Here, the SI issues of the coupled multi-walled carbon nanotube (MWCNT) on-chip interconnects are evaluated with and without the effect of shielding technique and compared to the copper interconnects. The MWCNT exhibits an average of 47.9% smaller propagation delays than Cu in dynamic crosstalk conditions. Further, for crosstalk reduction, the active shielding (AS) and passive shielding (PS) techniques are proposed. With the AS and PS techniques, the MWCNT interconnects experience a decreased delay by 46.8% and 30.15% compared to without shielding technique, respectively. Moreover, the AS exhibits smaller crosstalk effects than the PS technique due to its input switching activities on shielded lines. In addition, the quality of the signal (QoS) and Intersymbol interference (ISI) noise effects of coupled MWCNT interconnect with and without shielding is evaluated. Finally, to improve the QoS and reduce the ISI effects, the decision feedback equalizer with the least mean square adaptive algorithm is implemented at the receiver end.

An Energy-Efficient Crosstalk Reduction Strategy for On-Chip Buses Using Carbon-Based Transistors and Interconnects

This paper presents a novel crosstalk reduction scheme based on quaternary logic that eliminates the harmful transition patterns and protects communication channels of system-on-chips (SoCs) against crosstalk. The proposed architecture is designed based on gate-all-around carbon nanotube field-effect transistor (GAA-CNTFET) codec and converter modules considering multi-walled carbon nanotube (MWCNT), and multilayer graphene nanoribbon (MLGNR) interconnects at 10 nm technology. The simulation results indicate that our proposed approach reduces the delay and power-delay product (PDP) on average by 52% and 36%, respectively, for MWCNT interconnects compared to the basic architecture. These improvements are 50% and 35% for the MLGNR interconnects. Moreover, utilizing the MLGNR interconnects instead of MWCNT interconnects in the proposed coded system leads to a 61% shorter crosstalk delay and 65% lower PDP. In addition, the proposed coding scheme leads to 35% reduction in the occupied area and improves PDP, on average, by 37%, and 26% for the MWCNT and MLGNR buses, respectively, as compared to their binary counterparts.

Vertical Noise Reduction in 3-D Mixed-Signal Integrated Circuits With Graphene Nanoribbon and Carbon Nanotube Interconnects

This study presents the analysis and reduction of vertical crosstalk in mixed-signal 3-D integrated circuits (3-D ICs) with multilayer graphene nanoribbon (MLGNR) and multiwall carbon nanotube (MWCNT) interconnects. The 14-nm technology node is considered for both digital and analog tiers. The assessments are conducted regarding the scattering parameters (S-parameters) for the equivalent circuit model of the transmission lines using the Advanced Design System (ADS) tool. Our studies demonstrate that the MLGNR transmission lines lead to lower mismatch, insertion loss, and vertical crosstalk than their MWCNT counterparts. The results show that using MLGNR improves the area overhead by more than 67% for analog and digital wires. Moreover, our model shows that the vertical noise between the analog and digital tiers is reduced by 1 and 1.62 dB when the intermediate substrate thickness increases from 20 to 30 and 40 μm. The results demonstrate that the perpendicular routing of the MLGNR interconnects reduces the vertical noise by 6.1 dB. Moreover, a 9.21-dB reduction in the vertical coupling is achieved using vertical MLGNRs in the analog IC. Our results also show that using graphene as a shield between the analog and digital chips significantly suppresses the vertical noise between the tiers, and it becomes more effective by increasing the number of graphene layers. According to our results, using one-, two-, and three-layer graphene-shield layers reduces the vertical crosstalk by 10.1, 14.9, and 19.2 dB, respectively. Moreover, the HSPICE simulations demonstrate that the MLGNR interconnects have a lower delay, power, and energy consumption than their MWCNT counterparts in the 3-D mixed-signal architecture.

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.

A Predictor–Corrector Algorithm for Fast Polynomial Chaos-Based Uncertainty Quantification of Multi-Walled Carbon Nanotube Interconnects

In this article, a predictor–corrector algorithm for the fast polynomial chaos (PC)-based uncertainty quantification (UQ) of multi-walled carbon nanotube (MWCNT) interconnect networks is presented. The proposed algorithm intelligently combines the numerical efficiency of the approximate equivalent single conductor (ESC) model of the MWCNT interconnect network with the rigor and accuracy of a multi-conductor circuit (MCC) model. Consequently, this algorithm significantly accelerates the generation of the PC surrogate models (or metamodels) of the network responses for minimal loss in accuracy. These metamodels can be probed efficiently and repeatedly to quantify the impact of manufacturing and fabrication process uncertainty on the MWCNT network responses.

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.

Comparative Analysis of Mixed CNTs and MWCNTs as VLSI Interconnects for Deep Sub-micron Technology Nodes

This research paper presents a performance analysis of the mixed carbon nanotube (CNT) as an interconnect for very large-scale integration (VLSI) circuits at deep sub-micron (DSM) technology nodes. The mixed CNT interconnect is a combination of multiwall CNTs (MWCNTs) and single-walled CNTs (SWCNTs). Using hierarchical modeling, a multiconductor circuit model is proposed for the mixed CNT bundle at global-level interconnect lengths. Due to the insertion of SWCNTs in a MWCNT interconnect, the overall density of the conducting tubes in the proposed mixed CNT interconnect structure increases, thereby decreasing the overall resistance and inductance of the mixed CNTs. The performance of the proposed mixed CNT interconnect is estimated in terms of delay and power delay product (PDP) for different technology nodes (32 nm, 22 nm, and 16 nm) at different interconnect lengths. For comparative analysis, a similar analysis is performed using MWCNT bundle interconnects. The comparative results show that there is reduction in the overall propagation delay and PDP for the proposed mixed CNTs compared to MWCNTs as the interconnect material for DSM technology nodes at global-level interconnect lengths.

Analytical Study of Bundled MWCNT and Edged MLGNR Interconnects: Impact on Propagation Delay and Area

This research letter presents an accurate and efficient model for rough-edged multi-layered graphene nanoribbon (MLGNR) and multi-walled carbon nanotube (MWCNT) bundled interconnects. To address the impact of delay and area, an analytical finite-difference time-domain and real-time simulation based approach are considered. In order to obtain the propagation delay, an equivalent single conductor (ESC) model is accurately presented by simplifying a multi-conductor transmission line (MTL) of bundled MWCNT and MLGNR interconnects. The proposed equivalent ESC model is in good agreement to the MTL with an average deviation of 4.6% only. In order to validate the proposed model, the equivalent resistance, inductance, and capacitance values are compared with standard experimental results. It is observed that the model expression possesses a good agreement with experimental data with an average error of below 9.93%. Using the ESC-based driver-interconnect-load setup, an approximate number of MWCNTs in a densely packed bundle is obtained for a rough-edged MLGNR at 22 nm technology to obtain an equivalent delay. In order to acquire the equivalent propagation delay, a fewer number of MWCNTs in a bundle can provide similar performance as of MLGNR for below 200 μm interconnect length. Furthermore, the number of MWCNTs significantly increases for longer interconnects. Therefore, on an average, an edged MLGNR requires 97.98% lesser area compared to the bundled MWCNT for global interconnects. Hence, a rough-edged MLGNR can be treated as a most desired interconnect material as compared to MWCNT bundle for the future interconnect technology.

An Efficient Crosstalk Model For Coupled Multiwalled Carbon Nanotube Interconnects

In this paper, the crosstalk effects in coupled multiwalled carbon nanotube (MWCNT) interconnects have been analyzed. An unconditionally stable finite-difference time-domain (USFDTD) technique has been used for the crosstalk model. The in_phase delay, out_phase delay, and crosstalk noise for coupled interconnect lines have been determined. It is observed that crosstalk effect is less severe in MWCNT interconnects compared to the conventional copper interconnects. The results of the proposed model have been verified with the conventional FDTD technique, hailey simulation program with integrated circuit emphasis (HSPICE), and feature selective validation. For transient analysis, the proposed model on an average consumes 46% lesser CPU runtime as compared to the conventional FDTD technique. Further, stress and electro-migration effects have been analyzed for copper and MWCNT interconnects. The mean time to failure of MWCNT interconnects is found to be superior than that of copper interconnects.

Repeater Insertion for Multi-Walled Carbon Nanotube Interconnects

Closed-form expressions for the optimized number and size of repeaters in multi-walled carbon nanotube (MWCNT) interconnects are presented. The contact resistance and inductive effects are taken into account. It is found that the propagation delay of MWCNT interconnects can be reduced effectively by inserting repeaters. However, the contact resistance has a significant influence on the optimized number and size of repeaters. Moreover, it is found that both the optimal number of repeaters and the minimum propagation delay are kept almost unchanged with the variation of carbon nanotube (CNT) kinetic inductance. The optimal number of repeaters in the MWCNT interconnect is much smaller than that in its Cu counterpart, thus saving chip area and power consumption.

Variability Study of MWCNT Local Interconnects Considering Defects and Contact Resistances--Part I: Pristine MWCNT

In this paper, an enhanced compact model of multiwalled carbon nanotube (MWCNT) interconnects while considering defects and contact resistance is proposed. Based on the atomistic-level simulations, we have found that defect densities impact MWCNT resistance and ultimately their electrical performance. Furthermore, we have computed by atomistic-level simulations, the end-contact resistance between single-wall carbon nanotube and palladium (Pd) electrode to mimic the Pd–CNT end-contact resistance of each CNT shell in MWCNT. We have developed an advanced shell-by-shell model to include various parameters, such as shell diameter, shell chirality, defects on each shell, and connectivity of each shell to end contacts. We run Monte Carlo simulations to perform variability studies on each of these parameters to understand the electrical performance variation on MWCNT interconnects. We present the simulation results to convey the critical impact of variations. The impact of doping on MWCNT variability in the form of Fermi level shift will be addressed in Part II of this paper.

Variability Study of MWCNT Local Interconnects Considering Defects and Contact Resistances--Part II: Impact of Charge Transfer Doping

In this paper, the impact of charge transfer doping on the variability of multiwalled carbon nanotube (MWCNT) local interconnects is studied by experiments and simulations. We calculate the number of conducting channels of both metallic and semiconducting carbon nanotubes as a function of Fermi level shift due to doping based on the calculation of transmission coefficients. By using the MWCNT compact model proposed in Part I of this paper, we study the charge transfer doping of MWCNTs employing Fermi level shift to reduce the performance variability due to changes in diameter, chirality, defects, and contact resistance. Simulation results show that charge transfer doping can significantly improve MWCNT interconnect performance and variability by increasing the number of conducting channels of shells and degenerating semiconducting shells to metallic shells. As a case study on an MWCNT of 11 nm outer diameter, when the Fermi level shifts to 0.1 eV, up to ~80% of performance and standard deviation improvements are observed. Furthermore, a good match between experimental data and simulation results is observed, demonstrating the effectiveness of doping, the validity of the MWCNT compact model and proposed simulation methodology.

ESD Behavior of MWCNT Interconnects—Part I: Observations and Insights

Multiwall carbon nanotube (MWCNT)-based interconnects have been shown to outperform conventional metal interconnects. For reliable operation of such interconnects, it is imperative to evaluate their reliability at possible fatal events. Here, we report the ESD reliability of MWCNT-based interconnects. High failure current of ~10 mA and unique failure behavior involving discrete and gradual breakdown of individual shells is reported. It was found that MWCNT interconnects change resistance in steps of fundamental quantum resistance ( ${h/2e^{2}}$ ) after individual shell burning. The role of individual shells, diameter, and resistance of the tube in deciding the ESD behavior is investigated, while monitoring the response on a shell-by-shell basis. Contrary to widespread notion of immunity of MWCNT interconnects to electromigration, the ESD-induced melting of contacts is also observed.

Modeling of Joule Heating Induced Effects in Multiwall Carbon Nanotube Interconnects

Electrothermal performance of multiwall carbon nanotubes (MWCNT)-based interconnects has been studied under the influence of self-heating. The interlayer insulator is a low-k ( $\varepsilon _{r}\sim 2$ ) dielectric. Various geometries have been studied for the normal operation and breakdown conditions. Electrothermal coupled equations have been solved iteratively by solving Fourier heat diffusion equation with a finite-element method. Within the relaxation time approximation, mean free path of the electron has been calculated under different scattering mechanisms. Landauer–Buttiker formalism resistance has been used for calculating electrical resistance. Breakdown voltages for varying MWCNT lengths have been calculated and found to be higher in MWCNT with a shorter length. Breakdown voltage varies from 8.2 to 12 V for inner diameters 10–40 nm of 5- $\mu \text{m}$ interconnect length and 50-nm outer diameter. Breakdown voltage decreases with the increase in the length of interconnect. For a 5- $\mu \text{m}$ long interconnect, the breakdown voltage is nearly 8 V whereas for the same diameter $1~\mu \text{m}$ long interconnect it is nearly 22 V. Breakdown current density depends on the geometry $\vphantom {_{\int }} $ of the MWCNT and is estimated on the order of $10^{8}$ A $\cdot $ cm−2.