Estimation of Lateral Resolution 118 

The lateral resolution of the TERS measurements was evaluated through near-field mapping of the nanotubes. Figure 5.4a shows the near-field Raman map of a SWCNT that is created by integrating the G band in the collected spectra using the [1400-1684 cm-

1_{] spectral range. An area of 120x120 nm}2_{has been mapped with a step size of 12 nm in} both x and y direction, Acquisition time was set to 10 sec per pixel. Three sample spectra corresponding to three pixels inside the Raman map is presented in Figure 5.4b. The AFM topographic image of the mapped nanotube along with a topographic cross-section curve that indicates the height of the nanotube is presented in Figures 5.4c and Figures 5.4e respectively. Figure 5.4d shows average Raman intensity profile which is generated from the map in Figure 5.4a.

Figure 5.4 (a) Near-field Raman intensity map of SWCNT (b) TERS spectra of three arbitrary points on the TERS map (c) AFM topographic image of the SWCNT (d) averaged Raman cross-section obtained from the Raman map in (a), (d) topographic cross section obtained over the dashed line in (c)

The estimated width in AFM image of Figure 5.4e shows about 50% deviation from the height of the studied nanotube due to a convolution by the tip shape. Nevertheless, comparison of the widths (FWHM) of the SWCNT in AFM image of Figure 5.4c (30 nm) and an average width from the Raman map (40 nm) indicates high lateral resolution far beyond the diffraction limit and consequently the near-field nature of the Raman signals. Despite the fact that the estimated width in AFM image is convoluted by the tip shape41 while the dimensions estimated in Raman map is chemical signature, AFM is showing higher resolution in this measurements. We believe that unfavourable scattering effects at the edges of the SWCNT and nanometer drifting of the sample during the mapping process cause deviation from the results that are estimated by AFM topography. Similar Raman map was acquired after the tip was retracted from the sample, however, it was lacking Raman contrast because same signal intensities was recorded everywhere inside the mapped area. Considering the size of the mapping area and the similar Raman intensity observed at the mapped pixels, the resolution obtained in far-field measurements most definitely exceeds 120 nm (10 pixels, 12 nm each) which indicated the diffraction limit of conventional spectroscopy.

To avoid the potential drifting of our AFM system and more accurately estimate the limit of resolution in TERS measurements, we decreased the measurement duration by limiting the Raman spectroscopy to a single line that crosses the carbon nanotube. Consequently more spots with smaller step sizes can be measured within a shorter time range while the unfavourable scattering from the edges of the nanotubes will be reduced. The resulting Raman spectra collected along the white dashed line in Figure 5.5a were used to generate the Raman cross-section curve in Figure 5.5b. The separation between the consequent spots along the dashed line was as small as 1 nm and the acquisition time for each spot was set to 30 sec. A polynomial fit is used to more accurately estimate the half width at maximum height of the intensity peak in Figure 5.5b.

Figure 5.5 (a) AFM image of an isolated carbon nanotube with 15 nm diameter as shown in the inset topographic cross-section curve (b) Raman intensity profile along the dash line in orthogonal direction to the SWCNT’s main axis while the tip is approached to (TIP-IN) and retracted from (TIP-OUT) the sample. The lateral resolution is estimated to be around 20 nm according to the fitted curve.

The collected spectra and the resulting cross-section curve in Figure 5.5b suggest a lateral resolution of ~20 nm for TIP-IN measurements where the TERS tip has approached the surface of the sample. This is in good agreement with the estimated height by AFM image of Figure 5.5a, therefore, an improvement of the resolution is achieved when compared to the results of Figure 5.4. As it is shown in Figure 5.4b, the Raman contrast along the mapped line was completely lost as soon as the tip was

retracted from the surface of the carbon nanotube (TIP-OUT measurements). However, a constant large far-field distribution is observed with intensities close to the highest intensity that was detected in near-field measurements. This large far-field contribution can be explained by resonant behavior of SWCNT but at the same time can originate from undefined background carbon impurities or neighboring carbon compounds. In addition, the TIP-IN data show a non-symmetric shape on one side of the SWCNT, the exact source of which is not known at the moment. Similar to the previous discussion, the presence of carbon impurities or neighboring carbon compounds is a possible reason for this observation.

A similar experiment was performed on a different carbon nanotube using a different gold coated AFM tip to check the reproducibility of the results. Here the separation between the spots along the mapping line (white dashed line in Figure 5.6a) was set to 1 nm and the Raman spectrum from each point was acquired within 30 sec. The Raman intensity profile obtained from this measurement is presented in Figure 5.6b. Similar to

Figure 5.5, a polynomial fit is used to more accurately estimate the half width at maximum height of the intensity peak in Figure 5.6b.

Figure 5.6 (a) AFM image of a nearly isolated carbon nanotube with 10 nm

diameter as shown in the inset topographic cross-section curve (b) Raman intensity cross-section along the dash line in orthogonal direction to the SWCNT’s main axis while the tip is approached to (TIP-IN) and retracted from (TIP-OUT) the sample. The lateral resolution is estimated to be around 20 nm according to the fitted curve.

As estimated by the AFM image in Figure 5.6a the diameter of the carbon nanotube along the mapped line is around 10 nm. TERS Raman cross-section however estimates the diameter to be around 20 nm and the Raman contrast was lost as soon as the tip was retracted as it has been shown in Figure 5.6b. Despite the fact that the lateral resolution is still well beyond the diffraction limit, the difference between the results of Figure 5.5

and Figure 5.6 demonstrate the influence of the tip quality on the limit of accessible resolution in similar measurements. Low reproducibility of the tip coating process results in TERS tips with variable apex sizes and consequently different performances.

Nevertheless, similar resolutions in both measurements of Figure 5.5 and Figure

5.6along with the SEM image of the coated tip which was presented in Chapter 3 (Figure 3.9) estimates an average20-30 nm diameter for the TERS tips that are utilized in this thesis. Therefore, spatial resolutions higher than 20 nm cannot be expected in TERS measurements conducted using such tips. On the other hand, the diameter of a single walled carbon nanotube is expected to be less than 2 nm, therefore according to the height of the studied carbon nanotubes in Figures5.4, 5.5 and 5.6, the three

measurements should have been performed on a bundle of SWCNT’s. This suggests that the lateral resolution could reach a limit beyond 20 nm if a completely isolated carbon nanotube is present. This however is not easy to achieve when the sample is prepared by drop casting of SWCNT solution on glass and more sophisticated sample preparation methods are needed.