Local photochemical plasmon mode tuning in metal nanoparticle arrays

Susan Derenko; René Kullock; Zhi Wu; Andrew Sarangan; Christiane Schuster; Lukas M. Eng; Thomas Härtling

doi:10.1364/OME.3.000794

1. Introduction

The optical properties of metal nanoparticles are dominated by collective electron density oscillations, so called localized surface plasmons (LSPs). It is well known that the spectral position of the oscillation resonance strongly depends on the dielectric constant of the particle environment [1]. Accordingly, a manifold of LSP-based sensing schemes for refractive index changes have been reported in the past decade [2–4]. In this context it was shown that LSPs in metal nanoparticle arrays can exhibit a similar sensitivity as propagating plasmons in metal films [5]. One of the potential advantages of nanoparticle arrays over metal-layer based approaches such as the Kretschmann-Raether scheme is that a lateral variation of the plasmon resonance can be exploited. For example, the LSP resonance of different locations within a particle array can be tuned to match different excitation wavelengths. Hence, multispectral applications can be envisaged, which offer the additional advantages of simple alignment of the optical path and high reliability [5].

However, lateral variations of the LSP resonance within a particle array are difficult to engineer. Various techniques are established to alter the particle geometry (size, shape [6–8]), either in colloidal solutions during synthesis or by homogeneous deposition on arrays [9,10]. Versatile methods like e-beam lithography and FIB milling are capable of direct writing desired structures but are non-competitive for large scale production due to their high cost and time consumption. To overcome these obstacles we propose a two-stage method to alter sections of homogeneous particle arrays with uniform geometry parameters fabricated by common large-scale lithographic methods [11]. Here we first fabricate a homogeneous nanoparticle array by interference lithography and then apply a photochemical treatment. During photochemical deposition the individual sections of the array can be addressed by appropriate illumination optics. The gradual metal deposition from solution results in a local shift of the plasmonic resonance properties, which can be monitored in situ and therefore in turn allows controlled adjustment of the spectra.

The photochemical method pursued here was previously applied to manipulate the particle size and material composition of clusters below 10 nm in diameter [12,13] in array structures. Unfortunately, such small particles exhibit extremely low scattering and absorption cross sections, and changes in the optical array properties could therefore not be observed nor applied for optical sensing schemes. Here we exploit larger particles – Au nanodiscs with an initial diameter of 140 nm fabricated by interference lithography – and analyze the influence of the deposited material on their optical properties in detail. We find that the plasmon resonance wavelength can be varied in individual array sections. In particular, a blueshift of the resonance wavelength is observed which is in contrast to previous investigation of single gold nanoparticle growth by photochemical treatment in which a redshift of the SPR wavelength occurred [14]. However, it is known from the literature [7,8], that the changes of the optical behavior of a non-spherical object depend on the geometry of the plasmonic structure and is not as straight forward as for spherical particles.

In order to understand these experimental findings also theoretically one might at first glance choose to employ numerical simulations, e.g. the calculation of the field distributions and scattering cross sections in dependence on the geometrical parameters. However, the long range periodicity combined with the individual geometries of the particles – resulting from the growth process – exceeds common numerical limits since neither applying periodic boundary conditions nor considering a few particles only are particular good approaches. Hence, a high computational effort is expected while considerable spectral mismatches would still appear. Furthermore, to gain a physical understanding from numerical simulation is not straight forward.

Therefore we have chosen to apply an analytical model to obtain deeper insight into the spectral behavior, namely the dipolar interaction model (DIM [15]). In contrast to previous investigations where the particle distance was altered to modify resonance properties [16,17], we keep the interparticle distance constant and increased the size of the particles to reflect the growth. A number of simplifications need to be taken for our DIM to work: The nanoparticles are approximated as oblate spheroids in a quasi-static approach, so retardation effects inside the particles are neglected, and the interactions between the particles are restricted to a dipolar but retarded form. These simplifications will lead to noticeable mismatches of spectral properties between theory and experiment, but the model allows to gain analytical relations and a qualitative explanation of the observed blueshift, which is crucial for future applications in sensor development.

2. Materials and methods

2.1. Fabrication of gold nanoparticle arrays

Interference lithography is used to prepare gold nanoparticle arrays with a DUV laser of 266 nm wavelength and the following procedure: First, photoresist (UVN30, Shipley) is diluted (65% UVN30 & 35% Thinner P, Shipley) and spin coated onto glass substrates, followed by a soft bake for 90 s at 140°C. The height of the resist is 250 nm. Interference lithography is carried out using two beams of the DUV laser with energies of 7.55 mJ and 8.55 mJ for 5 s and completed by a post exposure bake at 130°C for 40 s. Development of the resist is achieved with MF-319 (Shipley) for 15 s and an additional rinse with deionized water is applied. O₂-plasma treatment for 20 s at 350 mT and 200 W supports the removal of the resist in the holes. Chromium (3 nm) and gold (30 nm) are deposited using e-beam evaporation. For final lift-off piranha solution is applied, supported by ultrasound and an additional rinse in DI water. The individual particles show a mean diameter of 140 nm and a center-to-center distance of 266 nm corresponding to the laser wavelength.

2.2. Photochemical metal deposition

HAuCl₄ (99%, ABCR GmbH) is dissolved in ethylene glycol (99.5%, Carl Roth) resulting in a 100 mM solution. A quantity of 50 µl is applied to the entire sample. The sample is then transferred to an inverted optical microscope equipped with a 100x magnifying objective. An additional lens allows the defocusing of the light and leads to a lateral expansion of the irradiated spot to 50 µm in diameter. The exposed array sections are separated by a distance of 2 mm from each other so that a lateral overlap of the exposure (proximity effects) is excluded. Irradiation is carried out with a xenon lamp (intensity of 2.94 W/cm²) for various exposure times (15, 30, 45 and 60 minutes), resulting in differently treated array sections referred to as A, B, C, and D in what follows. According to Gachard et al. [18] the photochemical reduction of HAuCl₄ proceeds upon irradiation as:

(H A u^{3 +} C l_{4}) \overset{h υ}{\to} (H A u^{3 +} C l_{4}) * \overset{}{\to} (H A u^{3 +} C l_{3} \dots C l) \overset{}{\to} H A u^{2 +} C l_{3} + C l

2 H A u^{2 +} C l_{3} \overset{}{\to} H A u^{3 +} C l_{4} + H A u^{+} C l_{2}

H A u^{+} C l_{2} \overset{}{\to} A u^{0} + H C l + C l .

First, the Au(III) complex is reduced to an Au(II) complex by means of free electrons which are generated by photodetachment in solution. Since the Au(II) complex is unstable, a disproportionation reaction into the more stable states of Au(III) and Au(I) occurs immediately after Au(II) is formed (Eq. (2)). The following reaction (Eq. (3)) of the Au(I) complex to Au(0) requires another free electron, which is in competition with the initial reaction (Eq. (1)). As a consequence, an induction period occurs in which a sufficient concentration of Au(I) builds up until gold ions agglomerate to particles in the solution. However, if additional seed particles such as the lithographically prepared arrays are present they act as catalysts for the final reaction (Eq. (3)) [18]. The presence of these seed particles efficiently prevents the agglomeration of ions and the formation of new particles in solution [12]. Hence, in the configuration chosen here, the Au(I) ions are reduced to elemental gold exclusively at the catalytically active seed particle surface where the metal atoms are finally deposited. The application of this process to the nanoparticle substrate of our studies is depicted in Fig. 1.

Fig. 1 Mechanism of photochemical deposition of gold from solution applied to separated sections of lithographically fabricated nanoparticle substrates. The growth of the particles can be potentially monitored while the reaction takes place by evaluating the plasmon resonance wavelength.

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Although this sensing configuration allows online monitoring of the spectral change during nanoparticle growth, the HAuCl₄ solution is replaced by pure ethylene glycol afterwards to avoid further metal deposition during optical analysis of the array sections.

2.3. Analysis of manipulated nanoparticle array sections

The development of the plasmonic properties of the array sections are monitored by analyzing the reflected light with an inverted optical microscope (Zeiss Axio Observer Z1). A highly magnifying objective (100x and NA: 0.75) and white-light illumination from a xenon lamp (75W, L.O.T.-Oriel) are used. Ethylene glycol is placed on top of the array for immersion, to facilitate the excitation of LSPs and to minimize effects from the substrate interface [19]. Backscattered light from the previously exposed array sections is collected in the image plane of the microscope objective with a multimode fiber of 100 µm core diameter. Hence, the collection of light is limited to a spot of 1.6 µm. The fiber is connected to a spectrograph (Hamamatsu) and CCD camera (Andor). The obtained spectra are normalized to a reflected spectrum of the bare sample substrate. AFM measurements are obtained with a 5600LS AFM (Agilent Technologies) on a sample area of 3 x 3 µm² within each illuminated array section. The particle height is determined using a MATLAB routine. Finally, SEM images are acquired with a Zeiss NVision 40 electron microscope and a detailed analysis of the particle diameters is carried out with ImageJ [20].

2.4. Simulations

To simulate the optical properties of the sample sections, (back)scattering spectra of nanoparticle arrays are calculated using a dipolar interaction model (DIM) under normal incidence and with a similar formalism as in [15]. The change in shape of the individual particles during growth and their interaction with neighboring particles by retarded dipolar coupling are taken into account. The method is suitable to gain analytical insight into the relations of the growth regimes and to describe the optical responses occurring in the reported experiments. A brief introduction to the theoretical basis shall be given here:

First we choose to approximate a single gold nanoparticle by an oblate spheroid and neglect interface effects due to the homogeneous dielectric surrounding in our experiments (dielectric constant $ε_{d} ≅ \sqrt{1.483}$ ). In the xy-plane the principal component of the spheroid’s polarizability tensor α can be expressed as introduced by Bohren & Huffman [21]:

α_{x y} = \frac{R^{2} h}{2} \frac{ε_{m} - ε_{d}}{3 ε_{d} + 3 L_{x y} (ε_{m} - ε_{d})} .

Here, R and h describe the radius and the height of the particle, while ε_m and ε_d are the dielectric constants of the metal and the dielectric medium in the vicinity of the particles, respectively. L_xy is the geometry factor (not the depolarization factor; see [21], p. 147), which accounts for the particle shape,

L_{x y} = \frac{g (e)}{2 e^{2}} [\frac{π}{2} - \tan^{- 1} (g (e))] - \frac{g^{2} (e)}{2},

with g (e) = {(\frac{1 - e^{2}}{e^{2}})}^{\frac{1}{2}} and e^{2} = 1 - \frac{h^{2}}{{(2 R)}^{2}},

where the eccentricity e is used, which is based on the aspect ratio of the particle. With k being the propagating wave vector, the scattering cross section σ_sca of an individual particle under normal incidence is then obtained by:

σ_{s c a} = \frac{k^{4}}{6 π} {| α_{x y} |}^{2} .

L_xy is known to have a sizeable impact on the LSP resonance condition which can be derived from Eq. (4):

ε_{m, r e a l} (ω) = (1 - \frac{1}{L_{x y}}) ε_{d} .

Considering the case of gold, where the real part of the dielectric function is negative and monotonously decreasing with increasing wavelength, a redshift is expected when L_xy decreases [15]. Furthermore, the contribution from neighboring particles is considered by their dipolar interaction [16,22]. In general one obtains a dipolar coupling tensor C, but due to symmetry (cf [15]) its xy and z components are decoupled and, hence, C_xy can be written as:

C_{x y} = - \frac{1}{d^{3}} \sum_{j \neq 0} \frac{e^{(\tilde{k} {\tilde{r}}_{j} + {\tilde{ϕ}}_{j})}}{{\tilde{r}}_{j}^{3}} {{\tilde{k}}^{2} [{\tilde{r}}_{j}^{2} - {\tilde{x}}_{j}^{2}] + \frac{1 - i \tilde{k} {\tilde{r}}_{j}}{{\tilde{r}}_{j}^{2}} [3 {\tilde{x}}_{j}^{2} - {\tilde{r}}_{j}^{2}]},

where j is used to summate over all particles and dimensionless variables k̃ = kd (wave vector), r̃_j = r_j/d (distance of particle j from the origin), x̃_j = x_j/d (projection of r_j on the x axis) as well as φ̃_j = kx_j sin β are deployed. C_xy is obtained by adding up a circular area with a radius of 3200 particles, each placed in a quadratic grid with a pitch of 266 nm. Using the coupling term, the polarizability of a particle inside the array can be obtained by:

α_{a r r a y} = \frac{α_{x y}}{1 + C_{x y} α_{x y}} .

Finally, by rewriting this equation in the spirit of Eq. (4), one can get an easy understanding of the coupling by means of the geometrical factor:

α_{a r r a y, x y} = \frac{R^{2} h}{2} \frac{ε_{m} - ε_{d}}{3 ε_{d} + 3 L_{a r r a y, x y} (ε_{m} - ε_{d})}

L_{a r r a y, x y} = L_{x y} + \frac{R^{2} h}{6} \cdot C_{x y} .

While L_xy only accounts for the shape of a single particle on the resonance wavelength, the additional term in L_array,xy now introduces the dipolar coupling of the neighboring particles. Equation (12) is now treated as the effective geometry factor for the array and therefore allows an analytical approach to understand the experimental results obtained during particle growth within arrays.

3. Results and discussion

3.1. Particle geometry parameters

First we discuss the changes of the particle geometry as a consequence of photochemical metal deposition. Respective SEM and AFM images of the four exposed spots (sections A, B, C and D) are depicted in Fig. 2. They reveal a sizeable increase in particle height with increased exposure time, while only a minor increase in particle diameter is observed in the SEM images (see also Fig. 3(a)). These findings are highlighted in more detail in Fig. 3(b), where the particle diameter (2R) is plotted versus the particle height h. The two parameters can be expressed by a linear dependence with the empiric approximation:

2 R = 1.75 \cdot h + 87 [n m] .

Figure 3(c) shows the behavior of the mean aspect ratio h/(2R).These data clearly indicate a change in particle geometry from oblate discoidal particles to a more spherical shape due to a preferential increase in height during gold deposition. This leads to a change in the optical response of the plasmonically active nanoparticles. Before we treat this optical effect in more detail, we will briefly discuss the reason for the observed directionally selective growth. For this we point out again that photochemical metal deposition is a diffusion-driven process. Au(I) complexes are induced by photon absorption in the solvent, which are then reduced to elemental gold at the particle surface. The particle array therefore acts as a sink for the Au(I) species. Consequently, a diffusion gradient arises, which drives the activated gold species towards the particle array. The Au(I) complexes arrive at the top of the particle surface earlier than at the vertical edges of the disk, which is why their availability for the latter is reduced. The effect is further supported by the initial geometry parameters of the particles: they have an edge surface of about 0.0132 µm², while the top surface is approximately 0.0154 µm², i.e., 16.7% larger. Figure 4 shows a schematic of the diffusion process in the solution.Additionally to the analysis of average geometry parameters, one can see from Fig. 2 that individual particle growth is initiated at randomly distributed spots on the particle surface, which can be attributed to the graininess of the gold surface. Sakai et al. showed the gold reduction from HAuCl₄ solution without surfactants on gold particles is also orientation selective depending on the chloride concentration in solution [23]. Residual chloride ions may block the surface partially, while individual facets are preferred for growth, leading to the irregular geometries of individual particles during metal deposition.

Fig. 2 SEM (left column) and AFM (right column) pictures obtained from different spots within the same exposed array sections (increased illumination duration from top to bottom). A substantial increase in height is observed for increasing exposure times, while only a minor increase in diameter is present, leading to an increasingly spherical shape of the particles.

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Fig. 3 Graph (A) shows the obtained increase in height and diameter, while graph (B) depicts the evolution of the diameter dependent on height. Since the growth regime is small it can be fitted using a linear approximation. Graph (C) shows the induced change in aspect ratio h/(2R).

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Fig. 4 Schematics of the precipitation of Au(0) to the seed particles during irradiation. The diffusion of the activated gold species towards the seed particles shows a higher deposition rate at the top surface, which leads to the observed preferential increase in height.

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However, additional experiments with annealed nanoparticle substrates (1h at 520°C) showed a deterioration of the overall particle growth. These experiments showed that only a minor fraction of suitable facets is available, which led to growth of triangular or hexagonal plates on the top surface of the lithographically fabricated nanoparticles during photochemical treatment (data not shown).

3.2. Optical spectra of gold nanoparticle array sections

We now turn the focus of the analysis on the desired modification of the optical properties in the individual array sections. Figure 5(a) shows the normalized experimental spectra which indicate a shift of the resonance with different exposure times to the HAuCl₄ solution. Within array section A the determined resonance wavelength is 757 nm, while it is shifted towards 715 nm in array section D. The respective resonance wavelength is determined by means of a Gaussian fit and shown in Fig. 5(b) for the four different exposed sections.The experimental spectra are in contrast to our initial expectation of red-shifted resonance spectra due to increased particle size, higher retardation, and near-field coupling of the particles. We therefore perform DIM calculations to gain a deeper insight into the spectral behavior and to fully understand the reasons of the blueshift of the resonance wavelength for future applications. First, we simulate single particle spectra with the particle dimensions stated in Fig. 3. This already leads to a blueshift of the resonance wavelength for larger particles (data not shown) and can be traced back to the increasing aspect ratio. Since a higher aspect ratio causes a larger L_xy, a blueshift can be predicted (see Eq. (8)). When dipolar interactions from neighboring particles are included into the model, a further enhancement of the blueshift and also a broadening of the resonance spectra towards a FWHM of 80 nm is found and visualized in Fig. 6.Here, the simulated shift is 43 nm for the given geometry parameters, whereas the experimental blueshift is 42 nm during the deposition within 60 minutes illumination time. Therefore, the simulations reflect the experimental findings very well. As already explained in the introduction, the absolute spectral position of the simulated spectra deviates from the experimental ones due to a number of simplifications.

Fig. 5 (a) Evolution of the surface plasmon resonance wavelength during the illumination of individual particle array sections and growth due to photochemical deposition. The blueshift is 42 nm within 60 minutes of illumination (Position A → Position D). (b) Resonance wavelengths determined from a Gaussian fit of the experimental spectra.

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Fig. 6 Scattering spectra simulated with the dipolar interaction model (DIM) which takes the change of particle geometries and their interaction with neighboring particles into account. The simulations verify the experimentally observed blueshift of the resonance wavelength of 43 nm during photochemical growth over 60 minutes.

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Nevertheless, a qualitative explanation for the evolution of the surface plasmon resonance can be given by the effective geometrical factor L_array,xy (Eq. (12)). With the help of a first order Taylor approximation of L_xy in the region of interest between 140 and 180 nm of the diameter, the effective geometrical factor L_array,xy can be obtained by:

L_{x y} \approx B_{0} + B_{1} \cdot \frac{h}{2 R}

L_{e f f, x y} \approx B_{0} + B_{1} \cdot \frac{h}{2 R} + \frac{R^{2} h}{6} \cdot C_{x y},

where B₀ and B₁ are Taylor coefficients. Keeping the resonance condition (Eq. (8)) in mind, the increase of the effective geometry factor for the array leads to a blueshift of the resonance wavelength. The analytical expression shows that while height h is increased, a blueshift can be generated by both, the single particle and the coupling term in Eq. (15). However, there is a trade-off between the two terms when altering the radius R. Experimentally, this will not occur due to the linear dependence of height h and diameter (2R) during growth (Eq. (13)). In our experiment all terms will lead to an increase in the effective geometry factor L_{eff, xy}.

These analytical considerations allow a qualitative understanding of the experimental findings. The obtained blueshift of the resonance wavelength during nanoparticle growth is in good qualitative agreement with our simulations. It is mainly governed by the increase of the individual particle aspect ratios and can now be extended to further applications.

4. Conclusion

We report on a method to tune the plasmonic properties of individual sections of metal nanoparticle arrays locally. The manipulation of the respective plasmonic resonance wavelength is accomplished by photochemical deposition of gold from solution on lithographically fabricated structures. The modification can be conducted independently on various array sections within one array, and the lateral expansion of each section can be controlled by the illumination optics. Although the particle growth leads to individual geometries of the particles, a general blueshift of the resonance wavelength can be observed upon photochemical treatment within the array sections. Such modifications allow applications in various sensor configurations where adjustments of the resonance wavelengths to environmental conditions are important.

Furthermore, the observed blueshift of the LSP resonance wavelength upon extended deposition time is in good agreement with our DIM simulations. The results show that a change in aspect ratio, supported by the interaction with neighboring particles, leads to this change in optical properties for rectangularly ordered arrays. In sum, we obtain plasmonic structures which offer the capability of multispectral applications. With these, sensing schemes can be developed which exploit different wavelength regimes while integration on one single nanoparticle substrate is achieved.

Acknowledgments

The authors kindly acknowledge the support of Sven Niese, Yvonne Ritz and André Striegler at IZFP-D, who contributed to SEM and AFM analysis of the samples. Furthermore, financial supports from FhG Internal Programs (Grant No. ATTRACT 692271), from Deutsche Forschungsgemeinschaft (Grant No. 587596 and No. 1288/10-1), from Bundesministerium für Bildung und Forschung (Grant No. 16V0034) and the Specific Target Research Project PLAISIR in the European Union (EU) Framework Program 7 are gratefully acknowledged.

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Local photochemical plasmon mode tuning in metal nanoparticle arrays

Abstract

1. Introduction

2. Materials and methods

2.1. Fabrication of gold nanoparticle arrays

2.2. Photochemical metal deposition

2.3. Analysis of manipulated nanoparticle array sections

2.4. Simulations

3. Results and discussion

3.1. Particle geometry parameters

3.2. Optical spectra of gold nanoparticle array sections

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (15)

Optical Materials Express