In order to synthesize an individual and long SWNT for electrical characterization, the catalyst's pad dimensions are to be controlled accordingly. Figure 2a shows an SEM image of SWNTs synthesized from a catalyst pad of 100 × 10 μm in area. A lot of SWNTs are obtained in this case, with average lengths of more than 100 μm. On the other hand, as shown in Figure 2b, if a catalyst pad of 10 × 2 μm is used, only one or a few SWNTs are obtained, with typically the emergence of an individual SWNT of more than 100 μm in length. In order to precisely deposit the electrodes on a single SWNT, a specially designed substrate holder is used that keeps a fixed overlapping distance between the catalyst and electrode masks to within few microns resolution. Figure 2c shows deposited electrodes on a SWNT synthesized from the same pad's dimensions of 10 × 2 μm.
Figure 3a shows a typical AFM topography image of a SWNT between electrodes. It is noted that with the 2 nm thickness of the Co catalyst used, the obtained SWNTs have typical diameters of less than 1 nm. Figure 3b displays a Raman mapping image used to locate and confirm the presence of a single SWNT located between the electrodes. Figure 3c,d present the AFM thickness profiles of two nanotubes, denoted as SWNT1 and SWNT2, with estimated diameters of around 0.8 and 0.6 nm, respectively. It is noted that the measurement of SWNTs diameters by AFM is not accurate due to the roughness of the quartz substrate (typically 0.1 nm), as well as the interaction forces between the SWNTs and the substrate . In order to precisely determine the diameter and chirality of our SWNTs, a study of the Raman spectrum of each SWNT is required . Figure 3e shows the Raman spectra of the samples, where the G-band peaks are clearly observed for both SWNT1 and SWNT2. It is noted the absence of the D-band peaks from the spectra, which indicates that the synthesized SWNTs are nearly defect-free. However, the radial breathing mode (RBM) peaks were not observed in the spectra of both SWNTs. This indicates that the observed strong G-band signal from our individual SWNTs is from a resonance with the scattered photon, or Elaser– EG-band = Eii, where Elaser, EG-band (≈0.2 eV), and E
, are the laser's energy, the G-band phonons energy, and a SWNT's optical transition, respectively . Applying the above condition on the Kataura plot (i.e., Eii vs diameter) , with Elaser = 2.33 eV (532 nm wavelength) and a typical resonance window of 50 meV  points to two SWNTs satisfying the resonance condition with their E22 optical transitions as shown in Figure 3f. Combining this result with the AFM data, it is clear that SWNT1 and SWNT2 correspond to the semiconducting nanotubes (8,4) and (6,4), respectively. This correspondence is achieved with a high degree of certitude as only two SWNTs felt within the Raman resonance condition of our experiment, and the theoretically calculated diameters of these SWNTs, namely 0.84 and 0.69 nm, for (8,4) and (6,4), respectively, are very close to the experimentally measured values by AFM.
From Figure 3e, it is observed that the G-band's peaks are located at frequencies 1621 and 1610 cm-1, for SWNT1 and SWNT2, respectively. These values are significantly higher than the reported values of around 1590 cm-1 for SWNTs on thermally grown silicon oxide substrates . Similar up-shifts in the G-band have been observed for arrays of SWNTs aligned on ST-cut quartz and were attributed to the strong interaction between the SWNTs and the substrate [14, 15]. However, our results provide a direct correlation between this up-shift in the G-band and the diameter and chirality of individual SWNTs. Since theoretical  and experimental results  show that the main peak of the G-band (i.e., the G+ peak associated with longitudinal vibration of carbon atoms along the SWNT) is independent of the diameter and chirality for semiconducting SWNTs, it is concluded that the observed difference between SWNT1 and SWNT2 should be mainly due to the effect of the substrate. It is noted that the mechanism leading to the alignment of the SWNTs on ST-quartz substrates is attributed to a stronger and preferential interaction along the crystallographic direction  (x-axis) of the ST-quartz during CVD growth [26, 27]. Based on a simple anisotropic Van der Waals interaction model between the SWNTs and the quartz substrate, Xiao et al.  predict an enhancement in this interaction with decreasing SWNT diameter. However, this is not in agreement with our results, where an increase in interaction (i.e., larger Raman up-shift) is observed with increasing diameter. On the other hand, assuming a shortened C-C bond (i.e., an increase in the force constant) along the SWNT's axis, experimental and theoretical works predict an up-shift in the G-band frequency [28, 29], and that the effect is enhanced with increasing SWNT diameter and decreasing chiral angle [30, 31]. This is indeed in agreement with our data if we assume that the interaction with the substrate causes a compression of the C-C bond along the SWNT's axis. It was stipulated that this interaction arises from a difference in the coefficient of thermal expansion between the SWNTs and quartz substrate when cooling down to room temperature after CVD growth . However, the up-shift in the G-band was still observed even after transferring the SWNTs to another quartz substrate after CVD . Therefore, the exact nature of the responsible mechanism for the G-band up-shift on these substrates is still unclear so far.Figure 4 shows the results of the temperature dependence of the electrical resistance (normalized to its value at 300 K) of the two SWNTs measured with an electrical current of 10 nA. For SWNT1, the resistance decreases with decreasing temperature from room temperature down to about 120 K and then it increases by decreasing temperature down to 2 K. At the lowest temperature of 2 K, the resistance reaches about four times its room temperature value of 181 kΩ. On the other hand, the resistance of SWNT2 shows an increase with decreasing temperature from room temperature all the way down to 2 K. However, at 2 K, the normalized resistance reaches about 280 times its value at room temperature of 1.46 MΩ, which is more than 2 orders of magnitude higher than that in the case of SWNT1.
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
(L/l + 1), where R
= 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
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
= 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
. A more accurate technique of extracting E
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
= 2U = 22 meV. This is in qualitative agreement with a semiconducting behavior in general but not quantitatively with E
= 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
Since SWNTs are considered to be 1D systems, with strong electron–electron interaction, they are predicted to exhibit Tomonaga-Luttinger liquid (TLL) behavior at low temperatures [41–43]. Furthermore, SWNTs can act as a quantum dot between metal electrodes and hence show Coulomb blockade (CB) tunneling characteristics at sufficiently low temperatures [44–47]. Incidentally, both TLL and CB theories predict the same scaling laws: the resistance R is proportional to T-α when eV < < kBT (low-bias regime) and to V-α when eV > > kBT (high-bias regime), where V, α, and e, are the voltage drop across the sample, a single scaling coefficient, and the charge of an electron, respectively . In order to extract the values of R in the two different regimes, current–voltage (IV) curves for both samples are measured at various temperatures as shown in Figure 5a,b. At high-bias voltages and low-bias voltage at high temperatures, the IV curves are basically linear with the current I in both samples. However, at low bias and low temperatures, the IV s are not linear, especially in sample SWNT2. The origin of this curvature is discussed below.
First, for sample SWNT1, the low bias R is extracted from the IV curves at I = 1 nA and plotted in a log-log graph versus temperature as shown in Figure 6a. The data fits well a power law above 30 K, with α ≈ 0.1. Note that k
T = 2.59 meV > > eV = 0.29 meV at 30 K. This is in agreement with the regime of validity of the theory. Furthermore, the value of α ≈ 0.1 is in the same order as the reported values in the literature for SWNTs [41, 46, 47]. Next, R, in the high-bias regime, is extracted from the IV curves at T = 2, 5, and 10 K and plotted in a log-log graph versus voltage as shown in Figure 6b. The low temperatures were chosen in order to be as close as possible to the condition eV > > kBT for this regime. For voltages V higher than about 10 mV, the curve fits well a power law, with α ≈ 0.1. This is in very good agreement with the extracted value from R versus T in the other regime. Furthermore, knowing that kBT ≈ 0.9 meV at T = 10 K, the range of voltages where the power-law fit is found to hold (i.e., above 10 meV), indeed satisfies reasonably well the condition eV > > kBT. The inset of Figure 6b shows that from 20 K and above, the resistance is essentially independent of the applied voltage, i.e., the IV curves are linear, which is exactly what was observed in Figure 5a. Hence, the behavior of SWNT1 is consistent with both LLD and CB theories with a scaling exponent α ≈ 0.1. First, it is noted that the extracted contact resistance, R
= 8 kΩ, is higher than the quantum resistance R
, which satisfies a necessary condition for the occurrence of the CB . Another theoretical condition for achieving CB is to have the charging energy E
of the SWNT higher than the thermal energy kBT, with E
≈ 2.5 meV/L(μm) on SiO2. This yields E
≈ 0.6 meV for SWNT1, which requires a temperature T < 7 K for CB to occur. However, the scaling law is observed up to at least 10 K, which suggests that the observed scaling, at least above 7 K, could be indeed a TLL behavior. It is noted from Figure 6b that for bias voltages less than about 9 mV at 2 and 5 K, there is an increase in the resistance that could be attributed to enhanced CB effect with reducing bias voltages. This change in R versus V at low-bias voltages could be attributed to a crossover between the TLL and CB regimes . Nevertheless, to experimentally confirm the CB effect, a gate voltage is required to modulate the SWNT's energy levels in order to possibly observe single electron tunneling as evidence for CB [37, 40], which is beyond our current experimental setup.
The same TLL and CB scaling analysis is applied to sample SWNT2 as shown in Figure 6c,d. For R vs T plot, a fit to T-α at high temperatures satisfying the low-bias condition eV < < kBT, yields an α ≈ 0.5. On the other hand, R vs V plot at the high-bias regime eV > > kBT leads to a power fit V-α, with α ≈ 2. Since the exponents from the two regimes are different, it is concluded that SWNT2 behavior is not consistent with TLL or CB. Figure 6d shows a dramatic increase in resistance at low bias for temperatures below or equal to 10 K. At higher temperatures, as shown in the inset of Figure 6d, the resistance is basically independent of the applied voltage, which is consistent with the linear IV s measured at higher temperature as shown in Figure 5b. The measured very high values of the resistance at low temperatures and low bias (in the order of GΩs) suggest the presence of an insulating state in this region. To explore this possibility, the current is plotted against voltage at the temperatures 2, 5, and 10 K, and low bias, as shown in Figure 7. Indeed, voltage thresholds separating a zero-resistance state (within the noise level of the measurements) and a conductive state at higher voltages are observed. The extracted values of these energy barriers are 82, 63, and 58 meV, for 2, 5, and 10 K, respectively, which are clearly much higher than the thermal energies kBT at these temperatures. Such insulating state in individual SWNTs have been observed by some other groups [50, 51]. An energy barrier of 600 meV has been observed from an IV curve at 4 K for a semiconducting SWNT and was attributed to the intrinsic gap of the SWNT . This value is less than that of SWNT2 (1.42 eV) but still in the same order of magnitude for a qualitative comparison. In the 2-point measurements of Zhou et al. , the contact resistance is included in their IV s, which might induce a barrier due to metal–semiconductor-metal junction effects. This is excluded or at least minimized in our 4-point measurements, as the contact resistance is subtracted in our configuration. Furthermore, the estimated contact resistance R
of SWNT2 is less than 3R
, which is reasonably too small to be considered as invasive or to induce a significant contact barrier . Interestingly, from measurements on suspended (no substrate effects) and ‘ultraclean’ metallic SWNTs, a Mott insulating state was reported, with energy gaps between 10 and 100 meV . Specifically, for SWNTs with diameters similar to SWNT2, the energy barrier was between 70 and 80 meV, which is in good agreement with the measured barriers for SWNT2. However, to explore the nature of the insulating state in SWNT2, gating experiments are needed, which is again beyond the scope of this letter.
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.