Electrical transport properties of small diameter single-walled carbon nanotubes aligned on ST-cut quartz substrates
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A method is introduced to isolate and measure the electrical transport properties of individual single-walled carbon nanotubes (SWNTs) aligned on an ST-cut quartz, from room temperature down to 2 K. The diameter and chirality of the measured SWNTs are accurately defined from Raman spectroscopy and atomic force microscopy (AFM). A significant up-shift in the G-band of the resonance Raman spectra of the SWNTs is observed, which increases with increasing SWNTs diameter, and indicates a strong interaction with the quartz substrate. A semiconducting SWNT, with diameter 0.84 nm, shows Tomonaga-Luttinger liquid and Coulomb blockade behaviors at low temperatures. Another semiconducting SWNT, with a thinner diameter of 0.68 nm, exhibits a transition from the semiconducting state to an insulating state at low temperatures. These results elucidate some of the electrical properties of SWNTs in this unique configuration and help pave the way towards prospective device applications.
KeywordsSingle-walled carbon nanotubes Horizontally aligned ST-cut quartz Tomonaga-Luttinger liquid Coulomb blockade Substrate interaction
Single-walled carbon nanotubes (SWNTs), with their miniature size, low structural defects, and various other superior properties [1, 2, 3, 4], are very attractive nanomaterials as basis for future electronic devices [5, 6, 7]. However, there are still many technical obstacles towards the realization of SWNT-based devices, such as the difficulty of their positioning on a substrate, as well as the lack of control of their chirality, which eventually defines their electronic properties. Furthermore, synthesized SWNTs by chemical vapor deposition (CVD) on a substrate are usually short (around 10 μm) and randomly dispersed, which makes it difficult for device fabrication. Recently, it has been reported that arrays of long (hundreds of microns) and horizontally highly aligned SWNTs could be synthesized on some single crystal substrates, such as ST-cut quartz  and sapphire . This is an important breakthrough, as the length of the synthesized SWNTs, and their high alignment, makes their electrical characterization and device fabrication much more accessible than ever before. Indeed, a field-effect transistor (FET) has been demonstrated using aligned SWNT arrays on an ST-cut quartz substrate . It is also noted that the latest Raman and photoluminescence data suggest that these SWNTs have predominantly semiconducting properties [10, 11]. However, and despite a lot of research work on SWNT array on ST-cut quartz [10, 12, 13], no data has been reported so far on the electrical properties or device fabrication of a single isolated SWNT on these substrates, except after their transfer onto silicon substrates . We believe that this is important in order to understand the underlying physics of the SWNTs in this unique configuration, which is crucial for any prospective device applications. Furthermore, it has been reported recently that the aligned SWNTs on ST-cut quartz substrates are in strong interaction with the substrate [14, 15], and the understanding of this interaction and its effects on the electrical transport properties of the SWNTs is therefore very important.
The lack of published data on an individual SWNT could be attributed to the technical difficulty in applying standard electron-beam lithography method for the fabrication of electrical terminals on an individual SWNT on these substrates, as it is usually inseparable from the other SWNTs in the arrays.
In this letter, we present a method for the fabrication of electrical terminals on individual SWNTs aligned on an ST-quartz substrate and the measurement of their electrical transport properties from room temperature down to 2 K. The method consists of CVD synthesis of an individual SWNT from evaporated metal catalyst pad and shadow mask evaporation of metallic electrical contacts on the SWNT. The thickness and dimensions of the catalyst pad are optimized to yield on average one long and horizontally aligned single SWNT after CVD synthesis. In contrast to standard electron-beam lithography technique, this method has the advantage of not exposing the SWNTs to any electron beam irradiation or chemicals that are reported to damage or/and contaminate the SWNTs [16, 17]. Furthermore, in order to minimize any damage or contamination of the SWNT before electrical properties measurements, scanning electron microscopy (SEM), Raman spectroscopy mapping, and atomic force microscopy (AFM) are performed only after all the electrical transport measurements are achieved. The electrical properties of individual SWNTs are measured using four-terminal method to minimize the effects of the contact resistance from the electrodes [18, 19]. The results are compared with theory and discussed in connection with the strong interaction with the substrate.
Electrodes on the SWNT are also fabricated using shadow mask evaporation technique. The metal masks are prepared by the same method as of that used for catalyst pattern. Palladium (Pd) is selected as the material of the electrodes because of its low contact resistance to SWNTs [20, 21]. The Pd electrodes, with a thickness of 50 nm, are EB evaporated in a four-terminal configuration, with a typical distance of 4.0 μm between adjacent electrodes. The electrical properties of the SWNTs are measured from room temperature down to 2 K, using a physical properties measurement system (PPMS, Quantum Design Inc., San Diego, CA, USA) for the temperature control. Voltages of approximately ±1 V are applied by a voltage source (33220A, Agilent, Santa Clara, MA, USA) through a 10 MΩ resistance connected in series with the sample, and the voltage is measured across the inner electrodes on the sample by a voltmeter (Model 2000 Multimeter, Keithley, Cleveland, OH, USA).
For imaging and analytical characterization of SWNTs under the terminals, Raman spectral mapping (RAMAN-11, Nanophoton Corp., Osaka, Japan), AFM system (Nanocute, SII NanoTechnology Inc.), and SEM system (SMI9800SE, SII NanoTechnology Inc.) are used. Raman spectroscopy is performed with a laser of 532 nm in wavelength and spot size of 0.5 μm. AFM is conducted in cyclic contact AC mode.
Results and discussion
First, the values of the resistance at room temperature are considered. The intrinsic resistance of a SWNT in the diffusive regime (non-ballistic) can be estimated from the formula R = R c + R Q (L/l + 1), where R c , R Q = h/4e2 ~ 6.45 kΩ, L, and l are the contact resistance between SWNT and the electrodes, the quantum resistance of a SWNT, the measured length of the SWNT, and the electron's mean free path, respectively . By comparing the 2 and 4-terminal resistances of our samples, and using L = 4 μm (distance between the inner voltage terminals), R c and l are estimated to be 8 and 19 kΩ, and 148 and 18 nm, for SWNT1 and SWNT2, respectively. The deduced mean free paths for SWNT1 and SWNT2 at 300 K are within the range of reported values for SWNTs [18, 33, 34]. Nevertheless, it is very difficult to compare directly with our samples because most of the published electrical transport properties data either do not define the chirality of the measured SWNTs or it is about SWNTs with larger diameters than ours. In general, the SWNT's resistance at high temperatures is theoretically attributed to inelastic scattering between electrons and acoustic phonons within the SWNT . However, the experimentally measured mean free paths of our SWNTs and others [18, 33, 34] are smaller by an order of magnitude than the theoretical calculations . Recently, this discrepancy has been successfully addressed by introducing the effect of surface polar phonons (SPPs) from the substrate [36, 37]. We speculate here that due to its narrower diameter, SWNT2 might be more susceptible to SPPs from the substrate, which enhance its room temperature resistance (i.e., shorter l) in comparison with SWNT1. It is noted from our results that the mechanisms defining the shift in the G-band and the electron's mean free path l should be uncorrelated; otherwise, we would expect SWNT1 to have a shorter l. This is indeed in support of an extrinsic contribution of SPPs from the substrate than an intrinsic one from the SWNTs' own phonons. Further detailed studies on both contributions are therefore needed in the future.
Since SWNT1 is a semiconductor, the measured decrease of its resistance from room temperature down to about 120 K cannot be attributed to an intrinsic metallic property . Based on the observed strong effect of the substrate on the G-band of SWNT1, we speculate that this metallic-like behavior could be originating from an interaction with the substrate that dominates at high temperature. Indeed, the expected semiconducting behavior of the resistance versus temperature is gradually recovered below around 120 K (Figure 4a). One possible indication for a semiconducting energy gap is a thermal activation dependence of the resistance versus temperature, i.e., in the form R ~ exp(U/kBT), where U and kB are an energy barrier and Boltzmann constant, respectively . In order to explore this behavior, a plot of Ln(R) versus 1/T is shown in Figure 4c, which could be very well fitted to the above activation formula from 60 K down to 5 K, with U ~ 0.6 meV. Assuming a standard semiconductor theory , this leads to a semiconducting energy gap of E g = 2U = 1.2 meV. This value is about 2 orders of magnitude smaller than the expected and directly measured energy gap of 1.11 eV for SWNT1 . This difference is not surprising as the simple activation formula above is used just as a qualitative guide, and the resistance versus temperature dependence of semiconducting SWNTs is very complex and there is no simple explicit formula in relation with E g . A more accurate technique of extracting E g is from voltage-current measurements with a gating voltage . However, this is not possible in our current experimental setup.
The resistance of sample SWNT2 increases with decreasing temperature down to 2 K. In order to explore any thermal activation behavior, Figure 4d shows a plot of Ln(R) versus 1/T. The data from room temperature down to 20 K can be fitted very well with the activation formula, leading to an energy gap of E g = 2U = 22 meV. This is in qualitative agreement with a semiconducting behavior in general but not quantitatively with E g = 1.42 eV for SWNT2 , which is due to the same reasons explained before. It is noted that SWNT2 does not exhibit any decrease of R with decreasing T as observed for SWNT1. This could be due to a weaker effect from the substrate (less up-shift in G-band) than that of SWNT1 because of possibly the larger E g of SWNT2.
Finally, the appearance of completely different properties for SWNT1 (TLL/CB) and SWNT2 (transition to an insulating state) at low temperatures and their relation with the observed strong interaction with the quartz substrate is currently not understood. Further theoretical and experimental efforts are underway to elucidate these effects.
In conclusion, a method is introduced to isolate and measure the electrical properties of individual SWNTs aligned on an ST-cut quartz substrate, from room temperature down to 2 K. The diameter and chirality of the measured SWNTs are accurately defined from resonant Raman spectroscopy and AFM. A significant up-shift in the G-band of the Raman spectra of the SWNTs is observed, which increases with increasing SWNTs diameter and indicates a strong interaction with the quartz substrate. A semiconducting SWNT (diameter 0.84 nm) shows Tomonaga-Luttinger liquid and Coulomb blockade behaviors at low temperatures. Another semiconducting SWNT (diameter of 0.68 nm) exhibits a transition from the semiconducting state to an insulating state at low temperatures. These results elucidate some of the electrical transport properties of SWNTs on ST-cut quartz substrates, which can be useful for prospective device applications.
This study was supported by Nano-Integration Foundry (NIMS) in ‘Nanotechnology Platform Project’ operated by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. ESS would like to acknowledge the support and hospitality of NIMS during his visit as a Guest Researcher.
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