Tailored nanoantennas for directional Raman studies of individual carbon nanotubes

We exploit the near field enhancement of nanoantennas to investigate the Raman spectra of otherwise not optically detectable carbon nanotubes (CNTs). We demonstrate that a top-down fabrication approach is particularly promising when applied to CNTs, owing to the sharp dependence of the scattered intensity on the angle between incident light polarization and CNT axis. In contrast to tip enhancement techniques, our method enables us to control the light polarization in the sample plane, locally amplifying and rotating the incident field and hence optimizing the Raman signal. Such promising features are confirmed by numerical simulations presented here. The relative ease of fabrication and alignment makes this technique suitable for the realization of integrated devices that combine scanning probe, optical, and transport characterization.

Figure 1

(a) Sketch of a Ti/Au nanoantenna array patterned on the $\mathrm{Si}/{\mathrm{SiO}}_2$ substrate. The coupling with surface plasmon polaritons and thus the field enhancement depend on the angle $\alpha$ between the CNT axis $\widehat{\mathbf{z}}$ and the direction $\widehat{\mathbf{s}}$ orthogonal to the strips. (b) In some samples we have patterned three arrays ${\mathsf{A}}_{0^{\circ }},{\mathsf{A}}_{{30}^{\circ }}$, and ${\mathsf{A}}_{{45}^{\circ }}$, whose angle $\alpha$ is $0^{\circ },{30}^{\circ }$, and ${45}^{\circ }$, respectively. Owing to the large aspect ratio of such structures, the incident field ${\mathbf{E}}_{\mathbf{i}}$ and the induced field ${\mathbf{E}}_{\mathbf{ind}}$ are in general not parallel, since the latter is preferentially oriented along $\widehat{\mathbf{s}}$. (c) AFM micrograph of our sample $\mathcal{C}$, acquired after all measurements [31].

Figure 2

(a), (b) Reflectance measurements performed on sample $\mathcal{C}$. The reflectance maps are obtained by scanning the sample while illuminating it with ${\lambda }_L=633$ nm light at normal incidence. The laser spot diameter is $1 \mu \mathrm{m}$. The panels (a) and (b) correspond to the reflected signal acquired for incident light polarization ${\widehat{\mathbf{e}}}_{\mathbf{i}}$ oriented orthogonally and parallel to the topmost antenna array, respectively. Both graphs show that the larger the angle between ${\widehat{\mathbf{e}}}_{\mathbf{i}}$ and $\widehat{\mathbf{s}}$, the smaller the SPP coupling. This implies a reduced absorption and thus a larger reflected signal. (c)–(e) Crossed-polarization reflectance measurements on the same sample, with ${\widehat{\mathbf{e}}}_{\mathbf{i}}$ forming an angle of $0^{\circ }$ (c), ${30}^{\circ }$ (d), and ${45}^{\circ }$ (e) with respect to the vertical direction. In this case the presence of an analyzer oriented orthogonally to ${\widehat{\mathbf{e}}}_{\mathbf{i}}$ allows us to observe only the signal with rotated polarization. The reflectance maps demonstrate that the antennas effectively rotate the light polarization, except when this is nearly parallel to the strips.

Figure 3

Raman spectra measured on samples $\mathcal{A}$ (a), $\mathcal{B}$ (b), $\mathcal{C}$ (c), and $\mathcal{D}$ (d). The red curves correspond to the signal acquired on an antenna array orthogonal to the bundle, while the blue ones refer to the bare CNT portion immediately below the antennas, as sketched in panel (e). For all the curves we subtract a background signal acquired next to the CNT. For clarity, a shift of $+100$ counts has been applied to all the enhanced curves. The integration time is 30 s for all the spectra. Panel (f) shows an AFM scan of sample $\mathcal{D}$. To make the CNT visible, we increase the contrast of the areas indicated by the dashed-white rectangles. For sample $\mathcal{D}$ we scan the laser spot over the antenna area highlighted (dashed-blue rectangle) in the AFM scan in panel (f). Panel (g) shows the corresponding color map for the intensity of the $G$ peak. A large signal is observed for the portion of CNT that crosses the antenna strips. The integration time is 5 s/pixel.

Figure 4

(a) SERS spectra measured on the array ${\mathsf{A}}_{0^{\circ }}$ of sample $\mathcal{C}$ for different angles $\gamma$ between the CNT axis $\widehat{\mathbf{z}}$ and incident polarization direction ${\widehat{\mathbf{e}}}_{\mathbf{i}}$. The small oscillations at lower Raman shifts are due to the signal elastically scattered by the antennas. (b) $G$ peak amplitudes plotted as a function of $\gamma$ (black dots). The same measurement has been repeated for the array ${\mathsf{A}}_{{30}^{\circ }}$ (c) and ${\mathsf{A}}_{{45}^{\circ }}$ (d). The gray curves in panels (b), (c), and (d) correspond to a ${cos}^2(\gamma -\alpha )$ fit, with $\alpha =0^{\circ },{30}^{\circ }$, and ${45}^{\circ }$, respectively. All data have been suitably rescaled to take into account the dependence of the incident power on the $\lambda /2$ plate rotation [31]. Finally, the dark counts have been subtracted from all curves.

Figure 5

(a) Finite-difference frequency-domain calculation for the specific case of $\gamma ={30}^{\circ }$. The color plot shows the local value of $|{\mathbf{E}}_T|/E_i$, where ${\mathbf{E}}_T$ is the total electric field. (b) Zoom-in on the region indicated by the cyan-dotted square in panel (a). The arrow pattern shows the local orientation of the ${\mathbf{E}}_T$ vectors (red arrows). (c) $\left|\gamma \right|$ dependence (blue squares) of the Raman cross section for the array ${\mathsf{A}}_{0^{\circ }}$, calculated by integrating ${(E_z\left(z\right)/E_i)}^2$ over the cyan-dotted segment in panel (a). For comparison, we display (red dots) the experimental points [Fig. 4] together with a ${cos}^2\gamma$ fit (red curve) of the measured data. The graph has been normalized such that the value for $\gamma =0^{\circ }$ equals 1 for both experimental and simulated data. (d) Simulated $E_z\left(z\right)/E_i$ values plotted as a function of the $z$ coordinate along the segment highlighted in the panel (a). The red, green, and blue curves correspond to the $\gamma =0^{\circ },\gamma ={30}^{\circ }$, and $\gamma ={45}^{\circ }$ cases, respectively. (e) Zoom-in on a gap between two strips. The field is mostly concentrated within approximately 5 nm around the strip edge, in the so-called hot spots. (f) Calculated angle $\beta$ between ${\mathbf{E}}_T$ and ${\widehat{\mathbf{e}}}_{\mathbf{i}}$ plotted as a function of $z$ along the same range and for the same $\gamma$ values as in the panels (d), (e).

Figure 6

Atomic force microscopy scans of the samples discussed in the present work. (a) AFM scan of sample $\mathcal{A}$ performed before the Raman measurements. (b) AFM scan of sample $\mathcal{C}$ performed before the Raman measurements. (c) The same sample scanned after all the measurement sessions. The topography reveals the presence of contamination exactly in the areas where the laser spot was focused. (d) AFM scan on sample $\mathcal{B}$. The contrast has been exaggerated in order to show the CNT. (e) The same scan displayed with lower contrast. (f) AFM scan on sample $\mathcal{D}$. The contrast has been exaggerated in order to show the CNT. (g) The same scan displayed with lower contrast.

Figure 7

(a) SEM micrograph of nanoantenna arrays nominally identical to the arrays in sample $\mathcal{C}$. (b) Zoom-in on the central array.

Figure 8

(a) Raman spectrum measured on sample $\mathcal{B}$ using a laser source at ${\lambda }_L=532$ nm. The laser spot was placed on the bare portion of the bundle just below the antenna array. Both the Stokes and anti-Stokes peaks are visible. The RBM frequency is ${\omega }_{RBM}=(107\pm 1) {\mathrm{cm}}^{-1}$. (b) Raman spectrum around the $G$ mode frequency, together with a double-peak Lorentzian fit (red curve) showing the $G^{-}$ and $G^{+}$ components (gray curves). (c) Raman spectrum measured on the bare portion of sample $\mathcal{C}$ using a laser source at ${\lambda }_L=633$ nm. The RBM frequency is ${\omega }_{RBM}=(125\pm 2){\mathrm{cm}}^{-1}$. (d) Raman spectrum around the $G$ mode frequency, measured on the same position, together with a Lorentzian fit (red curve). (e) Raman spectrum measured on the bare portion of sample $\mathcal{C}$ using a laser source at ${\lambda }_L=532$ nm. Both the Stokes and anti-Stokes peaks are visible. The RBM frequency is ${\omega }_{RBM}=(130\pm 2) {\mathrm{cm}}^{-1}$. (f) Raman spectrum around the $G$ mode frequency, together with a double-peak Lorentzian fit (red curve) showing the $G^{-}$ and $G^{+}$ components (gray curves).

Figure 9

(a) Raman spectra measured on the bare portion of sample $\mathcal{C}$ between the antenna array ${\mathsf{A}}_{0^{\circ }}$ and ${\mathsf{A}}_{{30}^{\circ }}$. Each curve refers to a different $\gamma$ angle. (b) $G$ peak amplitudes plotted as a function of $\gamma$ together with the best fit for $A{cos}^2(\gamma +\varphi )+I_0$, where $A,\varphi$ and $I_0$ are fitting parameters (best fit: $A=164,\varphi =1.7^{\circ }$, and $I_0=0.7$).

Figure 10

Raman spectra around the $G$ peak measured on sample $\mathcal{C}$. The blue, red, green, and black curves refer to the signal measured on ${\mathsf{A}}_{0^{\circ }},{\mathsf{A}}_{{30}^{\circ }},{\mathsf{A}}_{{45}^{\circ }}$, and on the bundle portion between ${\mathsf{A}}_{0^{\circ }}$ and ${\mathsf{A}}_{{30}^{\circ }}$, respectively. The curves have been offset and rescaled in order to display the same $G$ peak amplitude.

Figure 11

When the unit vectors $\widehat{\mathbf{s}}$ (array axis), $\widehat{\mathbf{z}}$ (CNT axis), and ${\widehat{\mathbf{e}}}_{\mathbf{i}}$ (incident polarization direction) are noncollinear, the Raman process can be approximately described as the result of a series of field projections: the incident electric field $E_0{\widehat{\mathbf{e}}}_{\mathbf{i}}$ is first amplified and projected to $\widehat{\mathbf{s}}$ by the antenna array. Then it is projected to $\widehat{\mathbf{z}}$ owing to the depolarization effect. At this point, the scattered Raman intensity is then proportional to ${cos}^2\gamma {cos}^2\alpha$. The Raman scattered light is again amplified and projected to $\widehat{\mathbf{s}}$, thus providing a further ${cos}^2\alpha$ factor.