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Abstract
In this work, we investigate the light scattering of a single Au nanoparticle cluster assembled in a nanostructured substrate and study how the substrate geometry influences the scattering spectrum. An explicit model was built with the help of the Green’s tensor theory, showing that there are two distinct types of substrate effects, namely, the interferometric scattering caused by the local corrugation and the spectral modulation caused by the global features (i.e., the layered substrate in this work). The result predicted by the model agrees with the experimental results well, providing a simple yet quantitative tool for the spectral interpretation of plasmonic nanostructures with complex substrates.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Single nanoparticle spectroscopy is one of the most important characterization tools in plasmonics, which has been widely used in different fields, including nanostructure characterization [1–3], chemical analysis and biosensing [4–7]. To obtain the signal from a single plasmonic nanostructure, flat substrate [8] and dark field illumination [9,10] are commonly used to get rid of the undesired background. However, in real life scenarios, nanostructured substrates are often needed, and this will lead to complicated spectroscopic results which consists of the signals from both the substrate and the plasmonic structure [11]. In some cases, the substrate may also be stratified [12,13], and it will cause additional modulation effects, making the spectral interpretation more challenging.
In order to understand the above mentioned substrate effect, in this work, we focus on the scattering spectra of a single Au nanoparticle cluster assembled in a nanotemplate on a layered substrate [14–16]. As one of the most widely used types of plasmonic structures, plasmonic nanoclusters not only have rich optical properties [17–20], but also can be easily constructed with chemically synthesized building blocks using nanostructured template (nanoholes and nanogrooves) [21–24]. However, the presence of the nanostructured template can also give strong scattering, which interferes with the scattered fields from the plasmonic nanoparticles [25]. To address the above substrate issue, we study the scattering spectrum of a single plasmonic nanostructure on a structured substrate using the Green’s tensor method [26], which is a unified framework for scattering problems of any given boundary conditions, and further applied the model to the case of a single Au nanoparticle cluster assembled on a layered nanotemplate substrate. The goal is to provide a simple and practical analysis tool for the single particle spectroscopy of plasmonic nanostructures on a complex substrate.
2. Experimental methods
The clusters of Au nanoparticles were fabricated using the templated-assisted self-assembly method, whose typical process is depicted in Fig. 1(a) [16]. First, a 200-nm-thick layer of copolymer (PMMA/MA) was spun on the surface of an ITO glass. By locally decomposing the copolymer with a thermal scanning probe [27,28] (NanoFrazor Explore, Heidelberg Instruments), a template with cylindrical nanoholes of different sizes were fabricated. Then, a solution droplet of Au nanoparticles (80 ± 10 nm in diameter) was brushed over the template with a moving cover glass. A meniscus was formed at the edge of the cover glass, where the solvent volatilized fast and the nanoparticles were accumulated. When the cover glass was dragged over the nanoholes, the meniscus was fixed and deformed by the nanoparticles. The induced capillary force in the process then pushed the Au nanoparticles into the nanoholes.
Fig. 1. (a) Principle of the template-assisted self-assembly. (b) SEM images of Au nanoparticle (80 ± 10 nm in diameter) clusters assembled in nanotemplates. (c) Schematic drawing of the setup for scattering spectrum measurements. (d) Measured scattering spectrum of a single Au nanoparticle assembled in the nanotemplate (solid line), which is significantly different from the scattering spectrum on a flat substrate (dashed line). The right side of the equal sign illustrates the two major substrate effects, namely (1) the interference between the scattering signals from the nanohole and the Au nanoparticle and (2) the modulation effect of the layered substrate (copolymer/ ITO/SiO2).
To achieve a high assembly yield, the depth of the nanoholes was set at 100 nm which is bigger than the diameter of the Au nanoparticles [16]. By adjusting the concentration of the Au nanoparticle solution and the diameters of the nanoholes, clusters of different geometries were made. Figure 1(b) shows the SEM images of nano-clusters comprised of 1-7 Au nanoparticles, including lines, triangles, square and hexagon. In addition, micrometer sized markers were also fabricated to help locate the clusters in measurements.
The scattering measurements of single nanoparticle clusters were performed on a darkfield microscope, which consists of an inverted microscope (Olympus IX73) and a homebuilt darkfield illumination setup, as shown in Fig. 1(c). In measurements, light from a halogen lamp was focused onto an individual nanocluster after passing through the dark field condenser at a large angle. The scattered light was collected by an objective (40X, NA=0.6), and then was recorded by a spectrometer (Andor, SR-303i-B) with a CCD (Andor, DU420A-BEX2-DD). All the spectra were normalized with the spectrum of the lamp in order to get rid of the influence of the light source.
3. Results and discussion
The left side in Fig. 1(d) is the measured scattering spectrum of a nanocluster containing only one Au nanoparticle (blue, solid line). The profile of the measured spectrum is significantly different from that of an individual Au nanoparticle on a flat ITO glass (red, dashed line), which only has a single resonant peak at approx. 550 nm [29].
As aforementioned, the difference is caused by the substrate effect. As depicted in Fig. 1(d), the light collected by the detector has two sources, (i) the scattered light of the nanohole template (red arrows) and (ii) the scattered light of the Au nanoparticle (green arrows). These scattered light fields interfere with each other and then further experience multiple transmission and reflection (yellow arrows) in the layered substrate (copolymer/ITO/SiO2), forming the signal finally recorded by the spectrometer.
The above pictorial explanation has a rigorous mathematical foundation. It is known that the electric field generated by arbitrary complex nanostructures can be given by the coupled dipole method [26]
Here, the nanohole and the Au nanoparticle are both subwavelength in size, and we can then treat them as two independent dipoles without coupling. That is, ${\bf P}$ is solely excited by the external field:
Since the polarizability of the Au nanoparticle ${\alpha _{NP}}$ is complex and highly dispersive while the polarizability of the dielectric nanohole ${\alpha _{hole}}$ is a constant, interference will occur between ${\alpha _{\textrm{NP}}}{{\bf E}_\textrm{0}}$ and ${\alpha _{\textrm{hole}}}{{\bf E}_\textrm{0}}$. The total scattered field $({\alpha _{\textrm{NP}}}{{\bf E}_\textrm{0}} + {\alpha _{\textrm{hole}}}{{\bf E}_\textrm{0}})$ is then modulated by the Green’s function ${\bf G}\textrm{(}{\bf r}\textrm{,}{{\bf r}_\textrm{0}}\textrm{)}$ associated with the substrate (layered structure). This is exactly the interferometric imaging process shown in Fig. 1(d).
3.1 Interferometric scattering of a single Au nanoparticle
In this section, we apply the above model to the simplest case, a single nanoparticle in a nanohole.
Figure 2(a) shows the calculated spectra of the amplitude and phase of the scattered fields of the Au nanoparticle in the infinitely homogeneous space (air). Since the nanoparticle is small, quasi-static approximation can be used, and the scattered fields are determined by the polarizability of the Au nanoparticle [30]
Fig. 2. Theoretical model of the interferometric scattering of a single Au nanoparticle in a template nanohole. (a) The calculated intensity and phase spectra of the scattered field of an Au nanoparticle in the infinite homogeneous background (air). (b) The calculated intensity and phase spectra of the scattered field of a nanohole in the infinite homogeneous medium (copolymer). The scattered fields by the Au nanoparticle (a) and nanohole (b) interfere with each other and form the intensity spectrum (blue curve) in (c). The orange curve in (c) is the phase difference between (a) and (b). The interferometric signal (d) is further modulated by the layered substrate (e), and finally forms the results collected by the spectrometer (f).
The intensity curve shows that there is a resonant peak at 521 nm, which shares the same spectral profile with the experimental result (the dashed line in Fig. 1(d)) except that the resonant peak is blue-shifted. This is because the size of the Au nanoparticle is 80 nm, which is too large for the quasi-static approximation. Nevertheless, the quasi-static approximation provides an explicit formula for the model with a reasonable precision.
Figure 2(b) shows the calculated spectra of the amplitude and phase of the scattered fields of a nanohole in the infinitely homogeneous medium (copolymer). The nanohole is subwavelength, and for simplicity, we use the scattering of an oblate ellipsoid to describe its scattering. Assuming that the ellipsoid hole is excited along its long axis, then the polarizability is expressed as [30]
Figure 2(c) depicts the result of the vector superposition (interference) of the dipole moments of the nanohole and the Au nanoparticle. The orange curve in Fig. 2(c) is the phase difference between the scattered fields of the the nanohole and the Au nanoparticle, which is around π in the whole spectral range. The blue curve exhibited in Fig. 2(c) is the resulting intensity spectrum.
Next, we will discuss about the modulation effect of the substrate. As mentioned above, this modulation process can be described by the Green’s function associated with the stratified media. In practice, the profile of the Green’s function ${\bf G}$ can be derived directly by the experimental results. The scattering field of an empty nanohole in the layered substrate is given by
Combining Eqs. (7) and (8), we have
Here, ${{\bf E}_{\textrm{hole,str}}}$ can be directly measured by using an empty nanohole without Au nanoparticle, and ${{\bf E}_{\textrm{hole,inf}}}{\bf /}{{\bf G}_\textrm{0}}$ can be calculated easily according to Eq. (8). The profile of ${\bf G}$ on the layered substrate can then be obtained using Eq. (9), whose intensity spectrum is shown in Fig. 2(e). It is worth noting that this method can be applied to substrates of any complex structures and not limited to the stratified media.
By multiplying the interference intensity with the modulation coefficients (Fig. 2(e)), we get the final interferometric scattering spectrum (Fig. 2(f)). The shape of the spectrum in Fig. 2(f) is consistent with that of the experimental result (blue, solid line in Fig. 1(d)). In both spectra, there is a dip near 600 nm except that the dip wavelength in Fig. 2(f) is slightly shorter than that of the experimental result. This is mainly due to the blue-shift of the single nanoparticle’s scattering spectrum calculated by Rayleigh Theory mentioned above (Fig. 2(a)).
3.2 Influence of the size of the template nanohole
From above discussion, it can be found that the value of ${\alpha _{\textrm{hole}}}$ determines the strength of the interference effect, and Au nanoparticles assembled in nanoholes with different sizes may have totally different scattering spectra. To verify this point, we performed experiments with nanoholes of different diameters, which have different scattering strength.
Figures 3(a)–3(c) show the cases of a single Au nanoparticle in a nanohole with a diameter of 120 nm, 150 nm and 180 nm, respectively. The first row (i) are the SEM images and the second row (ii) are the corresponding experimental scattering spectra. The third row (iii) are the simulated spectra calculated by FDTD Solutions. In FDTD simulation, we assume that the incident light is a plane wave and the scattered light filed is solved using the Total-Field Scattered-Field (TFSF) source. The fourth row (iv) is the theoretical results calculated by the method introduced in section 3.1.
Fig. 3. Size effect of the nanohole template in interferometric scattering. (a)-(c) A single Au nanoparticle in a 120 nm, 150 nm and 180 nm nanohole, respectively. (i) SEM images of the different samples. (ii) Experimentally measured scattering spectra. (iii) Simulated spectra using the FDTD method. (iv) Theoretical spectra calculated by the method discussed in section 3.1.
In the case of small nanohole (120 nm), the measured scattered spectrum was almost identical to that of a single Au nanoparticle on a flat substrate (Fig. 2(a)), both of which have a resonant peak at approximately 550 nm. This is because when the size of the template hole is small, the scattering of the nanoholes is too weak to induce significant modulation of scattering spectrum. When the size of the nanohole increases to 150 nm, a dip appears at 600 nm in the scattering spectrum. According to the discussion in section 3.1, this is caused by the interferometric effect between the nanohole and the Au nanoparticle. When the size of the nanohole increases further, the scattering signal of the nanohole becomes even larger, making the spectral dip at 600 nm caused by the interference more prominent. This is exactly what is observed in the third column of Fig. 3. The trend of both the simulation and theoretical results agree well with the experimental results.
3.3 Interferometric scattering of nanoclusters
Above we have discussed the interferometric scattering of single nanoparticles, in the following we will discuss about the case of nanoclusters (multiple nanoparticles). As the number of the particles increases, the strength of ${\alpha _{\textrm{NP}}}$ will be much greater than that of ${\alpha _{\textrm{hole}}}$. It can be expected that the contribution of ${\alpha _{\textrm{hole}}}{{\bf E}_\textrm{0}}$ to the scattering spectrum will decrease and even becomes negligible.
To prove this point, we measured the scattering spectra of single clusters consisting of 2, 3, 4 Au nanoparticles, respectively. The results are shown in Fig. 4. All the scattering spectra of these clusters in the nanohole only have one resonant peak, and this is consistent with the spectra of 2-4 Au nanoparticle clusters on a flat ITO glass measured by Bo Yan et al. [20]. This phenomenon indicates that the effect of the template on the scattering of Au nanoclusters is almost negligible when the nanoparticles could fill the template hole.
Fig. 4. Scattering spectra of nanoclusters containing more than one nanoparticles. (a)-(c) are the cases of 2, 3, 4 Au nanoparticles in the template nanoholes, respectively. The first row is the experimental results. The second row is the simulated spectra using the FDTD method.
The second row of Fig. 4 are the simulation results calculated by FDTD Solutions, where the polarization of the vertically incident plane wave was set along the horizontal direction. The simulated spectra match well with the experimental results.
Finally, the authors would like to mention that the analysis method introduced in section 3.1 can also be applied to other structured substrates, since the Green's function method used (Eq. (9)) is applicable to all type of boundaries. More specifically, the local nanostructure close to the plasmonic structure can be processed by interferometric scattering. For global structures (e.g., the layered structure in this work), their effects can be described by G, which can be directly experimentally determined by the method mentioned in section 3.1.
4. Conclusion
In this work, we investigated the scattering spectrum of a single nanoparticle cluster assembled in a nanostructured template, and found that the presence of template can significantly influence the spectral properties. To understand the substrate effect, an explicit theoretical model was established using the Green’s tensor theory. The model shows that there are two types of substrate effects, namely (1) the interferometric scattering between the plasmonic nanocluster and the local corrugation on the template and (2) the modulation effect caused by global features of the substrate (i.e., the layered structure in this work). Moreover, we applied the analysis model to different cases, including the single particle with different nanohole sizes and clusters with different particle numbers. The theoretical results match well with the experimental results. Our work provides a useful tool for analyzing the scattering spectra of single plasmonic nanostructure on nonplanar substrates.
Funding
National Key Research and Development Program of China (2016YFA0201104).
Disclosures
The authors declare no conflicts of interest.
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