Low-temperature heat capacity of modified multiwalled carbon nanotubes with diameter 9.4 nm

The crosstalk effects in single walled carbon nanotube (SWCNT) bundle and multi-walled carbon-nanotube (MWCNT) interconnect architectures are investigated for global interconnect lengths under sub threshold conditions. The crosstalk induced time delay and the peak crosstalk voltage on victim wire of multi wire SWCNT bundle and MWCNT interconnect configurations are derived and compared to those of the copper (Cu) wire counterparts for the global interconnects for three different technologies (32-, 22- and 16nm). It is observed that, compared with the Cu, and SWCNT bundle the MWCNT interconnect can lead to a reduction of crosstalk-induced time delay and it becomes more significant with increasing interconnect length, while the peak voltage of the crosstalk-induced glitch in MWCNT interconnects is slightly greater than SWCNT bundle and that of Cu wires. Because of considerable improvement in time delay, MWCNT interconnect will be more suitable for the next generation of interconnect technology as compared with the SWCNT bundle and Cu counterpart.

Multi-wall carbon nanotubes (MWNTs) have potentially provided an attractive solution over single-wall carbon nanotube (SWNT) bundles at deep sub-micron level very large scale integration (VLSI) technologies. This paper presents a comprehensive analysis of propagation delay for both MWNT and SWNT bundles at different interconnect lengths (global) and shows a comparison of area for equivalent number of SWNTs in bundle and shells in MWNTs. It has been observed that irrespective of the type of CNTs, propagation delay increases with interconnect lengths. For same propagation delay performance, the area occupied by SWNT bundle is more than the MWNTs for a specified interconnect length.

ABSTRACTIn nanoscale regime, the performance of traditional copper interconnects degrades substantially in terms of latency, power dissipation and induced crosstalk noise. This is due to miniaturization of electronic devices and many-fold enhancement of interconnect lengths in very large-scale integrated (VLSI) circuits. However, carbon nanotubes (CNTs) due to their unique physical properties such as high thermal conductivity, current carrying capability and mechanical strength have drawn the attention of researchers in recent times. The present paper provides comprehensive investigations in the various CNT structures for on-chip VLSI interconnect applications. Different configurations of CNT structures are studied namely single-wall CNT (SWCNT), multiwall CNT (MWCNT) and mixed-wall CNT bundle (MCB). The performance of CNT interconnects is analyzed using driver-interconnect-load system. It is investigated that the reduction in propagation delay in MCB interconnect is nearly 69%, 60%, 40% and 22% as compared to copper, SWCNT bundle, MWCNT and MWCNT bundle interconnect structures, respectively. This analysis considers an interconnect length variation from 500 to 2500 µm for 32-nm technology node. For the same dimensions the overall reduction in power dissipation in MCB interconnect is nearly 60%, 49%, 45% and 36% as compared to copper, SWCNT, MWCNT and MWCNT bundle interconnects, respectively. Furthermore, the effect of crosstalk on the interconnect structures has been examined. It is investigated that MCB has least crosstalk induced delay than all the other interconnect structures. Consequently, it is envisaged that MCB outperforms copper, SWCNT, MWCNT and MWCNT bundle interconnects and are best suited for future VLSI interconnects.

We have utilized our Multiwalled Carbon NanoTube (MWCNT) and Single-Walled Carbon NanoTube (SWCNT) bundle interconnects model in a widely used π model to study the performances of MWCNT and SWCNT bundle wire inductors and compared these with copper (Cu) inductors. The calculation results show that the Q-factors of Carbon NanoTube (CNT) wire (SWCNT bundle and MWCNT) inductors are higher than that of the Cu wire inductor. This is mainly due to much lower resistance of CNT and negligible skin effect in carbon nanotubes at higher frequencies. The application of CNT wire inductor in LC VCO is also studied and the Cadence/Spectre simulations show that VCOs with CNT bundle wire inductors have significantly improved performance such as the higher oscillation frequency and lower phase noise due to their smaller resistances and higher Q-factors. It is also noticed that CMOS LC VCO using a SWCNT bundle wire inductor has better performance when compared with the performance of LC VCO using the MWCNT wire inductor due to its lower resistance and higher Q-factor.

Multi-walled carbon nanotubes (MWNT) have provided potentially attractive solution over single-wall carbon nanotube (SWNT) bundles at current very large scale integration (VLSI) technologies. This paper presents a comprehensive analysis of propagation delay for both MWNT and SWNT bundles at different interconnect lengths (global) and shows a comparison of equivalent number of SWNTs in bundle and shells in MWNTs for specified propagation delays and lengths. It has been observed that irrespective of the type of CNTs, propagation delay increases with interconnect lengths. For same propagation delay performance, the number of SWNTs required in a bundle are found to be more than number of shells in MWNT for a given interconnect length.

In this paper, we develop a quantitative design technique for multi-walled carbon nanotube (MWCNT) based interconnect, which we utilize to examine the performance and reliability of future nanotube-based interconnect solutions. Leveraging an analytical RLC model for MWCNTs, we create the first closed-form formulation for the optimal nanotube diameter and nanotube bundle height. The results indicate that the proposed design method decreases delay by 21% and 29% on average compared to non-optimized MWCNTs and single-walled carbon nanotube (SWCNT) bundles. We also find that large diameter MWCNT bundles are significantly more susceptible to process variations than SWCNT bundles, which will have important reliability implications in future nano-scale ICs.

In this paper, we develop comprehensive modeling and design techniques for carbon nanotube (CNT)-based interconnects, which we utilize to examine the performance, reliability, and fabrication requirements for future nanotube-based interconnect solutions. We create a generalized model for CNT-based interconnect systems that achieves a high degree of accuracy compared to experimental CNT measurements. Leveraging the model, we develop the first closed-form formulation for the optimal nanotube diameter and bundle height for multi-walled CNT (MWCNT) and single-walled CNT (SWCNT) bundle interconnects for a general set of geometric and process parameters. The results indicate that the proposed design method decreases delay by 21% and 29% on average compared to nonoptimized MWCNT and SWCNT bundles. We also find that future CNT bundle fabrication processes must achieve a nanotube area coverage of at least 30% for optimized CNT bundles and 40% for nonoptimized CNT bundles to obtain competitive performance results compared to copper interconnects. In terms of reliability, we find that large diameter MWCNT bundles are significantly more susceptible to process variations than SWCNT bundles, which will have important implications for their utilization in future nanoscale integrated circuits.

Summary form given only. As carbon nanotubes (CNTs) are becoming the most promising material for nanoelectronic devices, interests on their high-frequency properties are being further increased. Recently, many active researches characterizing single-wall or multi-wall CNTs have been reported. Here, we fabricate the device with a bundle of single-wall CNT (SWCNT) captured between two signal electrodes of a coplanar waveguide (CPW), and report its radio-frequency (RF) characterization and equivalent circuit modeling. The article shows an SEM image of the SWCNT bundle captured between two signal electrodes of the CPW with the gap of 700 nm. First of all, the CPW for GSG measurement was fabricated on the high resistivity Si wafer by photolithography and lift-off process. Further electron beam lithography made the CPW has sharp signal electrodes to alleviate the drastic impedance mismatching with the SWCNT and to minimize the parasitic capacitance between two signal electrodes. The bundle of SWCNTs was captured between two signal electrodes of the CPW by dielectrophoresis alignment. Then, we made the ohmic contact between the SWCNT and the CPW by using Au electroplating and subsequent thermal annealing. This electroplating process does not require one more step of lithography. The article shows the measured transmission (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> ) and reflection (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> ) characteristics of the CPWs with/without SWCNT at frequencies of 0.1 ~ 40 GHz. The transmission of the CPW with SWCNT is 1 dB larger than that of the CPW without SWCNT at 10 GHz. The difference denotes the amount of the transmission through SWCNT, and it is added to the transmission through the parasitic capacitance between two signal electrodes of the open CPW. The reflection of the CPW with SWCNT is maximum 1.7 dB smaller than that of the CPW without SWCNT at 38 GHz. Figure 3 shows the equivalent circuit model of the CPW combined with SWCNT. The parasitic parameter values of the open CPW were extracted from the measurement data of the CPW without SWCNT by ADS optimization. The parasitic values are follows; L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = 0.006 nH, L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> = 0.005 nH, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , = 8 Omega, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> = 10.7 Omega, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = 0.04 pF, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> = 0.05 pF, and C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> = 0.07 fF. Then, we extracted the other parameter values (due to SWCNT) from the measurement data of the CPW with SWCNT, keeping the parasitic values of the open CPW. The values are follows; R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> = 4.1 kOmega, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">el</sub> = 0.9 fF, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CNT</sub> = 1.04 kOmega, and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = 1.2 nH. We completed the total equivalent circuit model of the CPW with SWCNT by using ADS optimization since the de-embedding of CPW pads may result in overestimation due to contact resistance. The article shows the magnitude and phase of the impedance (Z) obtained from the measurement and from the equivalent circuit of the CPW with SWCNT. The measured data are consistent with the modeled data within a reasonable accuracy. In summary, we have captured SWCNT between two signal electrodes of the CPW and presented its high-frequency characterization. From the de-embedding process using the equivalent circuit, we successfully obtain the resistance (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CNT</sub> = 1 -04 kOmega) and the inductance (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = 1.2 nH) of the SWCNT bundle.

This paper deals with timing and stability analysis of single wall carbon nanotube (SWCNT) bundle and multiwall carbon nanotube (MWCNT) interconnects. The performance of SWCNT and MWCNT interconnects are analyzed using driver-interconnect-load system. It is analyzed that MWCNT interconnects are more stable than SWCNT bundle interconnects. It is illustrated that stability of both SWCNT bundle and MWCNT interconnects increases as the length of interconnects increase. The analytical model for stability and step response using ABCD matrix have been presented. The results are verified using SPICE simulations. The average error between analytical and simulation results is 2.1%.

Summary Recently, much attention has been paid to the single walled carbon nanotube (SWCNT) bundle, which exhibits remarkable mechanical, chemical and electrical properties. Here, we present the pattern transformations of the SWCNT bundle under contraction and expansion. We first report three simple relations governing the geometry of the SWCNT bundle under no pressure. Then, due to the expansion of the bundle, a new hexagonal structure is found by using both the hybrid atom-continuum model and density functional theory. The results show that when the diameter of the nanotubes is larger than certain critical value, the nanotubes in the bundle will undergo three phase transformations. The corresponding critical size and the phase diagram of the bundle are also presented. Finally, the pattern transformations of the SWCNT bundle under hydrostatic pressure are calculated by density functional theory and the corresponding mechanisms of the pattern transformations are also investigated. The studies of the pattern transformations of SWCNT bundle can offer new understandings into the fabrication of novel materials and devices at the nano-scales.

Carbon nanotubes are desirable components of nanoelectromechanical (NEM) devices due to their excellent mechanical and electrical properties. In this study, dielectrophoresis, a potential high-rate nanomanufacturing process, was used to assemble single-walled carbon nanotube (SWCNT) bundles suspended over a trench. The intent was to assemble a single SWCNT bundle between two electrodes. However, it was observed that when two or more SWCNT bundles assembled across the trench, the bundles were attached together in a portion of the suspended section. This study models the separation and re-adhesion processes of two adhered SWCNT bundles as their internal tensions are varied using an atomic force microscope (AFM) tip. Two devices were selected with distinct SWCNT bundles. Observation of the force–distance measurements through applying an AFM tip at the middle of the suspended SWCNT bundles, in conjunction with continuum mechanics modelling, allowed the work of adhesion between the two nanotube bundles to be determined. As the force was applied by the AFM tip, the tension induced in each bundle increases sufficiently to partially overcome the adhesion between the bundles, thereby decreasing the adhesive length. The adhesive length then recovers due to the decrease in the induced tension during the unloading process. The average value of the work of adhesion between two adhered SWCNT bundles was determined to be 0.37 J m−2 according to the experimental data and modelling results.

We have determined “effective” Bethe coefficients and the mean excitation energy of stopping theory (I-value) for multiwalled carbon nanotubes (MWCNTs) and single-walled carbon nanotube (SWCNT) bundles based on a sum-rule constrained optical-data model energy loss function with improved asymptotic properties. Noticeable differences between MWCNTs, SWCNT bundles, and the three allotropes of carbon (diamond, graphite, glassy carbon) are found. By means of Bethe’s asymptotic approximation, the inelastic scattering cross section, the electronic stopping power, and the average energy transfer to target electrons in a single inelastic collision, are calculated analytically for a broad range of electron and proton beam energies using realistic excitation parameters.

Charge-induced electrochemical actuation of armchair carbon nanotube bundles

The crosstalk effects in single- and double-walled carbon nanotube bundle bus architectures are investigated and compared in this paper. New equivalent circuit models are proposed for both the single- and double-walled carbon nanotube bundles. It is found that (a) compared to single-walled carbon nanotube (SWCNT) bundle, a double-walled carbon nanotube (DWCNT) bundle bus can lead to a reduction of the crosstalk induced time delay by about 50%, and a slight reduction of delay uncertainty when the tubes are long; and (b) the peak voltage of the crosstalk induced glitch in the SWCNT bundle is lower than that in the DWCNT bundle, but the glitch duration time of the SWCNT bundle is longer than its DWCNT counterpart. These results confirm that the DWCNT bundle bus is more suitable for the next generation of bus technology and its overall performance will be better than that of SWCNT bundles.

Single-walled carbon nanotube (SWCNT) bundles have the potential to provide an attractive solution for the resistivity and electromigration problems faced by traditional copper interconnects. This paper discusses the modeling of nanotube bundle resistance for on-chip interconnect applications. Based on recent experimental results, the authors model the impact of nanotube diameter on contact and ohmic resistance, which has been largely ignored in previous bundle models. The results indicate that neglecting the diameter-dependent nature of ohmic and contact resistances can produce significant errors. Using the resistance model, it is shown that SWCNT bundles can provide up to one order of magnitude reduction in resistance when compared with traditional copper interconnects depending on bundle geometry and individual nanotube diameter. Furthermore, for local interconnect applications, an optimum nanotube diameter exists to minimize the resistance of the carbon nanotube bundle