We report on the in-situ controlled tuning of the particle gap in single pairs of gold nanodisks by photochemical metal deposition. The optically induced growth of nanodisk dimers fabricated by electron beam lithography leads to a decrease of the interparticle gap width down to 0 nm. Due to the increasing particle size and stronger plasmonic coupling, a smooth redshift of the localized surface plasmon (LSP) resonances is observed in such particle pairs during the growth process. The interparticle gap width, and hence the LSP resonance, can be tuned to any desired spectral position. The experimental results we obtain with this nanoscale fabrication technique are well described by the so-called plasmon ruler equation. Consequently, both the changes in particle diameter as well as in gap width can be characterized in-situ via far-field read-out of the optical properties of the dimers.
©2008 Optical Society of America
The interaction of conductive nanosized particles with electromagnetic radiation manifests itself in collective electron oscillations on the particles, so-called localized surface plasmons (LSP). For some noble metals, the resonance frequency of this oscillation is located in the visible regime, which has attracted attention for at least hundred years . The spectral position of the dipolar electron oscillation resonance depends on various parameters such as the particle size, material, surrounding medium, or the plasmonic coupling to other particles being in close proximity. The variation of these parameters provides a means for tuning the LSP resonance position, and - vice versa - the possibility for monitoring changes in one of these parameters via reading out the LSP resonance.
These characteristics of metal nanoparticles allow their implementation for several interesting applications such as biochemical sensing or surface-enhanced Raman scattering [2, 3]. It is therefore understandable that considerable effort has been devoted to the design and controlled fabrication of metal particle-based nanostructures. Elaborate fabrication techniques are multifarious and include, for example, top-down approaches such as focused-ion-beam (FIB) milling, electron beam lithography (EBL), purely chemical routes for metal deposition and particle fabrication [4, 5], as well as self-assembly-based bottom-up methods [6, 7]. One of the major advantages of EBL and FIB milling is that they allow for the fabrication of arbitrary structure layouts, which are often unachievable with bottom-up strategies. The latter, however, facilitate control over structure dimensions well below the 10-nm range, a limit still challenging the reproducibility of top-down techniques.
In this article, we report on a method which combines the versatility of EBL with the genuine bottom-up technique of photochemical metal deposition. We make use of the mentioned optical properties of metal nanoparticles to achieve in-situ control of the deposition process and thus highest precision in structure fabrication. The capabilities of the combined technique are demonstrated by photochemically decreasing the gap between two individual gold particles to below 10 nm in a highly reproducible manner.
The nanofabrication process presented here is based on the reduction of a metal salt complex to pure metal, initiated by visible laser light and the presence of a nanoscale seed particle. This principle has been used for more than a century in the field of photographic chemistry . Here we apply this chemical method for tuning the size and hence the gap width between two gold nanoparticles fabricated by EBL. The exposure of a particle pair to a gold salt solution and focused laser light results in gold deposition on the particles, i.e., in an autocatalytic particle growth decreasing the interparticle gap.
For nanoscale gap widths, a coupling of the LSP modes of two illuminated particles occurs and leads to extraordinarily enhanced optical fields inside the gap space [9–17]. Thorough theoretical as well as experimental investigations of the plasmonic modes of such coupled particle pairs have been reported during the last years [18–28]. As a result, there is a good understanding of the LSP coupling process based on a relatively simple dipole-dipole interaction model . It is well known that a decreasing distance between two particles (dipoles) leads to a redshift of the LSP resonance wavelength oscillating in parallel to the center-to-center axis of the dimer. Thus, by monitoring the scattering properties of the structure during the growth process, we are able to fully control the tuning of the gap width, as well as the spectral position of the LSP resonance wavelength in-situ. We observe a smooth shift of the plasmon resonance into the infrared wavelength region until an electric contact is established between the particles.
Using EBL, pairs of gold nanodisks of 50 nm in diameter, 20 nm in height, and 30 nm spacing were fabricated on a cover glass. Details of the fabrication process are described elsewhere . The particle dimers were arranged in a rectangular array with 15 μm spacing between the grid points.
For the photochemical particle growth, the dimer sample was mounted on an inverted optical microscope. The particles were embedded in a droplet of a growth solution produced by dissolving hydrogen tetrachloroaureate (HAuCl4) in a low-viscosity immersion oil with refractive index n=1.52 (#1160, Cargille, USA). Upon illumination, gold complexes from the solution are reduced to gold atoms. Due to the catalytic properties of the particles, this reaction takes place only in their very vicinity. Finally, the neutral gold atoms accumulate at the surface of the illuminated particles, leading to a homogeneous increase of the particle size (Fig. 1). A detailed description of the chemistry underlying the photochemical metal deposition can be found in Ref. .
The optical setup used for both particle growth and in-situ monitoring is shown in Fig. 2. Illumination of the particles was performed using a microscope objective (N.A.=1.45), which produced a diffraction-limited 532-nm laser spot (1 mW input power).
Due to their large lateral separation, single pairs could be addressed optically without interference from neighboring particles. Thus, while the addressed particles grow, neighboring, unexposed pairs are not affected. Every single particle pair was illuminated for a sequence of periods of 1 minute duration. These growth periods were interrupted for quantifying the increase in particle size by monitoring the back-scattering spectrum of the respective pair. To this end, collimated white light from a Xenon arc lamp was focused onto the back focus of the microscope objective and imaged onto the object plane, resulting in a circle of 5 μm radius with a uniformly distributed power of 10 μW and a low divergence angle < 10°. This setup provides essentially plane-polarized incident light when a polarization filter is introduced into the collimated part of the beam, and out-of-plane components of the electric field can be neglected in the object plane.
We measured the back-scattered intensity upon illumination with light polarized either along or perpendicular to the axis connecting the centers of the two disks. Due to the high refractive index of the growth solution, light reflection from the glass-solution interface is suppressed and the particle pairs appear as bright scattering centers. The light back-scattered from an individual particle pair was analyzed using a grating spectrometer and a cooled CCD camera in a confocal detection path.
3. Results and discussion
3.1 Reduction of the gap width
The experiment detailed above differs considerably from other investigations of coupled particle pairs [18–28], as in these investigations the particle size was kept constant for decreasing interparticle distance. In our experiment, however, both the particle separation as well as the particle size change simultaneously during laser exposure of one individual dimer. This effect was accounted for by investigating the evolution of the LSP modes oscillating either perpendicularly or in parallel to the center-to-center axis of the dimer separately. This approach helps to better understand the optical response of the sample by separating the effects of increasing particle size and decreasing gap width.
We investigated the evolution of the plasmonic spectrum of single particle dimers with gap widths decreasing from 30 to 0 nm. Besides measuring the LSP resonance wavelength of the perpendicular (λ ⊥) and the parallel (λ ‖) LSP mode, we determined the respective particle diameters and gap sizes by means of SEM. The spectra and electron micrographs are depicted in Figs. 3(a) –3(e). For increasing exposure time, a redshift of the backscattering peaks is observed for both modes (column I and II in Fig. 3). For the parallel mode, a second, short-wavelength LSP mode emerges during exposure [Figs. 3(d) and 3(e)]. We attribute this peak to a higher-order LSP mode typically observed on larger particles .
The images in column III show clear and reliable gap sizes down to 5 nm, whereas smaller gaps are blurred due to limited resolution in SEM. Sufficiently long exposure finally leads to the formation of an electric contact between the disks [Fig. 3(e)]. Note that the redshift of the scattering peaks during the formation of the metallic contact is smooth, and no jump or splitting of the plasmonic spectrum is observed. All described issues of the spectral behavior have been recorded and verified for a large number of individual particle pairs.
We start a more detailed analysis of the growth process with the results for the perpendicular LSP mode. In Fig. 4, the red triangles show λ ⊥ as a function of the particle diameter. For increasing exposure time, i.e., increasing particle diameter, λ ⊥ redshifts due to stronger retardation of the incident electric field over the particle. For comparison, the evolution of the LSP resonance wavelength during the growth of single disks fabricated in the same way as the particle pairs is shown (black squares). Obviously, λ ⊥ shows the same linear dependence on the particle size as found for the resonance wavelength of the single particles. Thus, the growth of the dimers takes place in a fashion highly comparable to the case of single particles.
For this direction of excitation, the dipolar coupling between two particles is expected to result in a marginal blueshift of λ ⊥ compared to the single particle resonance wavelength . However, for particles of constant size this shift is in the order of only 3 – 5 nm for the relatively short interparticle distance range of 30 nm covered in our experiment [22, 27]. As the redshift of λ ⊥ due to the increase in particle size is much stronger, the weak dipole coupling effect can be neglected here, as Fig. 4 shows. Thus, for the perpendicular LSP mode, the optical response of the sample to the increase in particle size is well separated from dipolar coupling effects in the dimer. As a first conclusion, we find that this response compares extremely well to single-particle behavior.
We now turn to the analysis of the LSP mode oscillating in parallel to the center-to-center dimer axis. The redshift of the resonance wavelength of this mode can also be understood already within the scope of a dipole-dipole model . The near-field of the dipolar LSP oscillation on the particles decays with the third power of the inverse distance . Therefore, the strength of the plasmonic coupling of two particles (dipoles) also exhibits a (1/d)3 dependence. Jain et al. have shown that this dependence can be approximated by an exponential decay, and dubbed the empirical equation describing this behavior “plasmon ruler equation” . The equation connects the ratio of the relative LSP resonance peak shift (Δλ ‖=λ ‖-λ0 ‖) to the initial, uncoupled LSP resonance wavelength (λ0 ‖) with the ratio of the particle distance (d) to the particle diameter (D):
where a and b are fit parameters. It was also shown that this equation holds independently of the particle size, as the coupling strength depends on the same powers of the separation d and the particle diameter D and therefore allows for dimensional scaling. However, this dimensional scaling is only valid if also the free resonance wavelength λ0 ‖ is corrected for the change of the particle dimensions. As the particle diameter changes for every exposure step in our experiment, adjusting λ0 ‖ is extremely important.
We carry out this correction by using the results presented in Fig. 4. Because the resonance wavelength of a single particle and the peak position of the perpendicular mode of a dimer show the same dependence on the particle size, we substitute λ0 ‖ in Eq. (1) by λ ⊥,, which we determine experimentally for each respective growth state. Taking this correction into account and inserting our data into Eq. (1) yields the results depicted in Fig. 5(a) . The fit parameters amount to a=0.33 (±0.01) and b=0.25 (±0.01).
In order to further evaluate the coupling process, we performed electrodynamics simulations of the backscattering properties of the nanodisk dimers by means of the multiple-multipole (MMP) method [34, 35], using dielectric data for gold reported by Johnson and Christy . The model pairs consist of disks with initial parameters of 20, 25, and 30 nm for height, radius and edge-to-edge separation, respectively. Height and radius were increased in steps of 5 nm, thus gradually reducing the gap. We calculated the respective scattering spectra as the response to a plane-wave illumination, and determined λ ⊥ and Δλ‖ as described above. Results are depicted in Fig. 5(b). The fit parameters for these calculated data amount to a=0.16 (±0.01) and b=0.29 (±0.01).
Both our experimental as well as calculated decay constants excellently reproduce the value of 0.27 (±0.03) calculated in Ref.  for particle pairs embedded in a medium with dielectric constant εm=2.25. The same is true for our experimentally determined amplitute a, which is in good agreement with the value of 0.29 (±0.03) from the same reference. Our calculated amplitude is somewhat smaller, but well within the range this parameter covers in  for different particle geometries.
As a conclusion, the good agreement between our measured data, our calculations, and previous reports indicates that the plasmonic properties of the photochemically treated particles do not deviate from those generated by conventional techniques. For example, we observe a homogeneous growth of the particles, i. e., no preferential growth direction of the individual particles. As the particles work as catalysts for the photochemical reduction, the reaction takes place in the vicinity of their surface, and there is no precipitation of gold on the substrate next to the particles. No traces of other chemicals are observed neither on the disks, nor on the cover glass.
Finally, we demonstrate how the modification of Eq. (1) allows for the all-optical in-situ determination of the interparticle separation. As the center-to-center distance of the disks is kept constant, the gap width d naturally is a function of the particle diameter D reading d=l0-D, where l0 is the center-to-center distance of 80 nm. Therefore, the disk diameter D can be substituted in Eq. (1) and the gap width can be directly calculated from
Thus, the separation between the particles can be determined at every growth state by measuring the resonance wavelength of the LSP mode oscillating along the center-to-center axis as well as perpendicular to this axis, calculating Δλ ‖, and finally using the fit parameters a and b from Fig. 5(a). This in-situ procedure is a valuable tool, as it can not only be applied for the characterization of the nanostructure under investigation, but also to evaluate the growth process itself. For example, metal deposition rates and their dependencies on parameters such as laser wavelength or intensity can be determined all-optically.
3.2 Photochemical particle welding
The SEM images in Fig. 3 show a clear separation of the individual particles down to a gap width of 5 nm. The reduction of the interparticle spacing below this value is accompanied by extremely high electric fields inside the gap, which in turn induce a high photoreduction rate of gold atoms. Thus, a thin metal bridge is formed on the cover glass already before the radii of the particles actually overlap, i.e., the particles get “photochemically welded”. Under further exposure, the bridge grows both in thickness and height. The SEM micrograph in Fig. 3(e) supports this finding.
This effect, which is driven by the high electric field in the gap region, limits the smallest particle separation obtainable with the presented method to approximately 5 nm. Therefore, in our experiments we do not observe any splitting of the plasmonic modes as reported by Atay et al. for broken contacts , as well as computed by Romero et al.  for two spherical particles with a singular contact point. The spectra in Figs. 3(a) – 3(e) demonstrate that the transition from the LSP mode of the separated particles to the electrically connected case takes place rather gradually, as the connection between the particles is formed by a metal bridge with increasing conductivity. Due to this smooth creation of the contact nanobridge, the observation of touching modes is not possible, as they only exist in dimers with much smaller separation.
We have demonstrated the optically induced growth of single nanoparticle dimers due to photochemical metal deposition. Using this technique and exploiting the increasing plasmonic coupling between the particles, we are able to smoothly tune the LSP spectrum of the particle pair under full in-situ control. As the plasmon ruler equation naturally holds for the particles under investigation and the initial geometrical parameters of the dimers are known, an in-situ optical read-out of the particle distance is possible.
After sufficiently long growth, the particles finally become photochemically welded. In comparison to previous theoretical investigations, where singular contact points between two particles were considered, we do not observe a splitting of the plasmon modes upon contact formation. The smoothness of the electric contact generated in our experiments leads to a smooth transition from the separated- to the connected-particle LSP spectrum.
The presented results show the capabilities of photochemical metal deposition. As metal is only deposited onto the preformed metal structures, we are able to fabricate nanoscale feature sizes by means of far-field optical illumination. Thus, the method is an extremely valuable extension to existing fabrication techniques.
The authors thank Phillip Olk and René Kullock for stimulating discussions, Ellen Kern for the SEM work and Stefan Grafström for help with the manuscript. This work was partially funded by the Studienstiftung des Deutschen Volkes, the Swedish Research Agency, the European Network “PlasmonNanoDevices”, as well as the Specific Target Research Project PLEAS in European Union Framework Program 6.
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