Mixed Carbon Nanotube Bundle Research Articles

Analysis of Delay and Dynamic Crosstalk in Bundled Carbon Nanotube Interconnects

Mixed carbon nanotube bundles (MCBs) are considered to be highly potential interconnect solutions in the current nanoscale regime. Different MCBs with random and spatial arrangements are proposed based on the placements of single- and multiwalled carbon nanotubes (CNTs) (SWNTs and MWNTs) in a bundle. Propagation delay and dynamic crosstalk performances are analyzed using the modified equivalent single conductor model of proposed MCB topologies. Encouragingly, a significant reduction in propagation delay and crosstalk delay is observed for a spatial arrangement of an MCB wherein MWNTs are placed peripherally to the centrally located SWNTs. Typically, the average delay with and without crosstalk is improved by 82.8% and 80%, respectively, compared to the MCB having randomly distributed SWNTs and MWNTs.

Performance analysis for randomly distributed mixed carbon nanotube bundle interconnects

During the recent past, carbon nanotubes (CNTs) have rapidly gained importance in an intensely growing researched area of interconnects. For various reasons, bundled CNTs are often preferred over single-walled CNTs (SWCNTs) or multi-walled CNTs (MWCNTs). However, during fabrication, it is difficult to control the growth of a densely packed bundle having SWCNTs with uniform diameters or MWCNTs with an identical number of shells. Therefore, a realistic CNT bundle is in fact a mixed CNT bundle (MCB) that consists of SWCNTs and MWCNTs. In light of these facts, an analytical model of a MCB that follows the random distribution of CNTs in a bundle is introduced. Depending on the probability of distribution of CNTs having different diameters, a compact multi-conductor transmission line (MTL) and a simplified equivalent single conductor (ESC) model are presented. Encouragingly, the simplified ESC model exhibits an average error of only 2.44% at different interconnect lengths compared with the delay obtained through the MTL approach. Mean diameter and tube density of the MCB are mapped to the ESC model to analyse the propagation delay, power dissipation and crosstalk. Irrespective of interconnect lengths, it is observed that the performances are significantly improved for higher tube density in a MCB.

Delay and crosstalk reliability issues in mixed MWCNT bundle interconnects

Multi-walled carbon nanotube (MWCNT) bundles have potentially provided attractive solution in nanoscale VLSI interconnects. In current fabrication process, it is not trivial to grow a densely packed bundle having MWCNTs with similar number of shells. A realistic nanotube bundle, in fact, is a mixed CNT bundle consisting of MWCNTs of different diameters. This research paper presents an analytical model of mixed CNT bundle wherein MWCNTs having different number of shells are densely packed. Two different types of MWCNT bundles are presented: (1) MB that contains MWCNTs with similar number of shells (i.e., uniform diameters) and (2) MMB wherein MWCNTs having different number of shells (i.e., non-uniform diameters) are mixed. Multi-conductor transmission line theory is used to present an equivalent single-conductor (ESC) model of different MB and MMB configurations. Using the ESC model, performance is analyzed to address the effect of propagation delay, crosstalk and power dissipation that explores the reliability of an interconnect wire. It is observed that using an MMB arrangement, the overall reduction in delay and crosstalk are 15.33% and 29.59%, respectively, compared to the MB for almost similar power dissipation.

Performance Optimization and Comparison of CNT Interconnect with Copper at VDSM Technology

As the CMOS process technology continues to scale, standard copper (Cu) interconnect will become a major hurdle for the best performance at very deep submicron (VDSM) technology node. The carbon nanotube (CNT) bundles have potential to provide an attractive solution for the higher resistivity and electromigration problems faced by traditional copper interconnects in VDSM technology node. This paper presents important guidelines to minimize the resistance, capacitance and inductance of a mixed CNT bundle interconnect for achieving best performance. The performance of mixed CNT bundle and copper is then compared at local and global interconnects level at 22nm technology node. HSPICE simulations carried out using Berkeley predictive technology model (BPTM) at an operating frequency of 1GHz, shows that for interconnect length of 1000um, the mixed CNT and optimized CNT (CNT_Opt) bundles are 1.98X and 2.20X faster, 74% and 84% more energy efficient respectively than the Copper interconnects.

Interconnect optimization to enhance the performance of subthreshold circuits

Subthreshold circuits are shown to be the best candidate for satisfying the ultra-low power demand of battery-operated systems having moderate throughput. However, exponential increase in driver resistance in subthreshold region and increased global interconnect capacitance will become a major hurdle in improving the speed of subthreshold interconnects. Improving the speed of such low power circuits is a major design challenge in ultra low power domain. This paper presents a comprehensive analysis of Cu and mixed CNT bundle interconnects and investigates their performance in terms of delay and energy delay product (EDP) for future subthreshold circuits. This paper mainly contributes towards optimizing the geometrical (aspect ratio scaling) and process parameters of interconnects especially for subthreshold circuits to increase their speed. Crosstalk analysis has also been carried out with the proposed interconnect geometrical parameters. It has been found that aspect ratio scaling significantly reduces the interconnect delay and switching energy and at minimum aspect ratio, Cu wire performs better than even an optimized mixed CNT bundle for global interconnect length under subthreshold conditions.

A New Spatially Rearranged Bundle of Mixed Carbon Nanotubes as VLSI Interconnection

Scaling of device dimensions down to nanometer range helps achieve unprecedented switching speed and multifunctional processing capabilities of nanoelectronic circuits and systems. However, interconnect constraints in the existing and emerging applications are expected to become the primary bottlenecks unless radical change is introduced in the design and technology of on-chip signal communication medium. In response to this demand, various novel and innovative interconnect solutions like carbon nanotube (CNT) are currently being explored as alternatives to metal wires. This paper proposes a unique structure of mixed CNT bundle with a specific arrangement of single-wall and multi-wall CNTs in the bundle. A comprehensive modeling and analysis of the conductance, inductance, and capacitance of the proposed mixed CNT bundle reveals that there will be no significant decrease in the overall conductance of the bundle, but the structural arrangement clearly reduces capacitive crosstalk between neighboring signal lines. Inductive crosstalk is seen to remain unchanged.

Inter-CNT capacitance in mixed CNT bundle interconnects for VLSI circuits

This article presents a realistic inter-carbon nanotube (CNT) electrostatic coupling capacitance and tunnelling conductance model for a mixed CNT bundle. The change of potential across such a bundle necessitates the need to consider the inter-CNT capacitance in the equivalent circuit of CNT interconnects for very large scale integration circuits. The equivalent transmission line circuit model of a unit bundle containing one single-walled CNT (SWCNT) and one multi-walled CNT (MWCNT) has been shown. This new model is then used to calculate the delay induced by the inter-CNT capacitance and tunnelling conductance, which predicts the relative positioning of MW/SWCNTs in mixed CNT bundle.

Interconnect Design for Subthreshold Circuits

Designing ultralow-power (ULP) efficient very large scale integration digital circuits have received widespread attention due to the rapid growth of portable applications. Device operating in subthreshold region has a strong potential toward satisfying the ULP conditions of portable systems. This paper mainly investigated and compared the performance of single-wall carbon nanotube (SWCNT), Cu, and mixed CNT bundle interconnects for different interconnect lengths and biasing levels under subthreshold conditions. It proposes that individual SWCNT can be used for short and intermediate length interconnects at different bias points in the subthreshold region due to less critical interconnect resistance contrary to superthreshold region. Furthermore, performance analysis of global interconnect shows that in moderate subthreshold region, scaled Cu interconnect performs better than individual SWCNT and mixed CNT bundle, whereas in deep subthreshold region individual SWCNT is still better.

Dynamic crosstalk effect in mixed CNT bundle interconnects

An accurate modelling hierarchy for mixed carbon nanotube (CNT) bundle interconnects is presented. Based on hierarchical modelling, different bundled structures are proposed for different arrangements of single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs). An equivalent model of mixed CNT bundles has been developed by combination of an equivalent single conductor (ESC) model of bundled SWCNTs and MWCNTs. Propagation delay under the effect of dynamic crosstalk has been compared for these proposed structures of mixed CNT bundles. It has been observed that crosstalk-induced time delay improves significantly for the structure where MWCNTs are at the periphery and SWCNTs are at the centre in the bundle.

Transient analysis of mixed carbon nanotube bundle interconnects

Presented for the first time is an accurate modelling hierarchy for mixed CNT bundle interconnects. Single-walled CNTs and multi-walled CNTs have been modelled as equivalent single conductor transmission lines and then combined to form a mixed CNT bundle interconnect, which is basically a multiple equivalent single conductor model. Two multiple equivalent single conductor interconnects have been taken to form the multiconductor transmission line model. The delays from transient analysis for both models for a unit bundle have been compared with the corresponding ones for SWCNT bundles and MWCNTs that exist in the literature. It is found that mixed CNT bundle interconnects are superior to both SWCNT bundle and MWCNT interconnects in terms of delay.

Mixed carbon nanotube bundles for interconnect applications

The increasing resistivity of copper with scaling and demands for higher current density are the driving forces behind the ongoing investigation for new wiring solutions for deep nanometer scale VLSI technologies. Metallic carbon nanotubes (CNTs) are promising candidates that can potentially address the challenges faced by copper, and thereby extend the lifetime of electrical interconnects. This article examines the state of the art in CNT applications with focus on CNT interconnect research. It is observed that individually, single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) exhibit characteristics that can be better exploited when a combination of the two is used – in the form of a CNT bundle that plays a vital role in interconnect applications. The focus here is that the usage of a combination of SWCNT (at the centre area of the bundle) and MWCNT (on the outside) provides great performance boost with lower interaction and crosstalk between neighbouring CNT bundles. Simulation results show that the resistance, capacitance, and inductance of a CNT depend on the probability of metallic CNTs present in the bundle and the length of the nanotube. Because Cu is metallic, it indicates that using a higher number of metallic nanotubes in the bundle would aid the CNT bundle performance. In addition, using MWCNT on the outer periphery of the bundle and SWCNT in the centre of the bundle would be the ideal way to maximise the performance of the bundle. Based on the observations we provide an analysis of why a mixed CNT bundle would be highly suitable as interconnections.

Analysis of CNT Bundle and Its Comparison with Copper Interconnect for CMOS and CNFET Drivers

In nanoscale regime as the CMOS process technology continues to scale, the standard copper (Cu) interconnect will become a major hurdle for onchip communication due to high resistivity and electromigration. This paper presents the comprehensive evaluation of mixed CNT bundle interconnects and investigates their prospects as a low power high‐speed interconnect for future nanoscale‐integrated circuits. The performance of mixed CNT bundle interconnect is examined with carbon nanotube field effect transistor (CNFET) as a driver and compared with the traditional interconnect, that is, CMOS driver on Cu interconnect. All HSPICE simulations are carried out at operating frequency of 1 GHz and it is found that mixed CNT bundle interconnects with CNFET as the driver can potentially provide a substantial delay reduction over traditional interconnects implemented at 32 nm process technology. Similarly, the CNFET driver with mixed CNT bundle as interconnect is more energy efficient than the traditional interconnect at all supply voltages (VDD) from 0.9 V to 0.3 V.

Diameter-dependant thermal conductance models of carbon nanotubes

Carbon nanotube (CNT) bundle is a promising candidate for future electrothermal applications due to its superior thermal properties. A realistic CNT bundle is a mixture of single-wall/multi-wall CNTs due to the nature of bottom-up fabrication process. In order to utilise CNT bundle, its thermal performance analysis needs to be carried out considering both types of CNTs. In this paper, accurate thermal conductance models are introduced for CNTs and mixed CNT bundles considering the influence of diameter and other structure factors. The thermal performance estimation based on these models match the recent measurement results. Considering realistic CNT densities and geometries, the mixed bundle shows two to three times improvement over the copper wire counterpart in terms of thermal conductance.

Analyzing Conductance of Mixed Carbon-Nanotube Bundles for Interconnect Applications

The carbon-nanotube (CNT) bundle is a potential candidate for deep-nanometer-interconnect applications due to its superior conductivity and current-carrying capabilities. A CNT bundle is generally a mixture of single-wall and multiwall CNTs (SWCNTs and MWCNTs) and has not been fully explored in previous studies. This letter introduces a diameter-dependent model to analyze the conductance of both SWCNTs and MWCNTs. Using this model, the conductance performance of the mixed CNT bundles is analyzed, and the estimation is consistent with the corresponding experimental result. This letter also demonstrates that the mixed CNT bundles can provide two to five times conductance improvement over copper by selecting the suitable parameters such as bundle width, tube density, and metallic tube ratio.

Inductance of mixed carbon nanotube bundles

The carbon nanotube (CNT) bundle is a promising candidate for next-generation interconnect/via applications. A realistic CNT bundle is a mixture of single-wall and multi-wall CNTs and its performance analysis needs to consider both kinds of CNTs. The inductances of the mixed CNT bundles are estimated, which are in agreement with the recent experimental results. Impacts of different parameters such as tube density, tube distribution, metallic tube ratio and bundle dimensions are discussed, providing an important guideline to design and fabricate a CNT bundle with a desirable inductance performance.