Self-organized growth and optical properties of silver nanoparticle chains and stripes

S. Camelio, D. Babonneau, D. Lantiat and L. Simonot

Laboratoire de Métallurgie Physique, UMR 6630 CNRS, Université de Poitiers, SP2MI, Téléport 2 Bvd M. et P. Curie, BP 30179, 86962 Futuroscope Cedex, France

Email: sophie.camelio@univ-poitiers.fr

Received 13 December 2006, accepted for publication 27 June 2007
Published 19 July 2007

Introduction

Because of their peculiar optical properties, different from those of bulk material, noble-metal nanoparticles embedded in a dielectric matrix have been extensively studied over the last decades [1, 2]. Until recently, most studies have been focused on a statistically large number of particles randomly distributed within the matrix [3–11]. From these works, it has been shown, for example, that collective electronic oscillations can be excited by light and are responsible for pronounced optical resonances in the visible or UV parts of the spectrum—the so-called surface-plasmon resonances (SPRs)—whose intensities, shapes, and positions strongly depend on the morphology and surroundings of the particles and their spatial organization. Recent developments in material synthesis and physical characterization of nanostructures have enabled the investigation of ordered arrays of noble-metal particles for new optical applications. Indeed, it has been shown that plasmonic systems consisting of linear chains of metal nanoparticles can effectively overcome the diffraction limit and guide light in regions much smaller than the free-space wavelength [12, 13]. Such optical systems, which use the localization of the electromagnetic field near the metal surface to confine light, can therefore bridge the gap in size between conventional micro-scale integrated optical devices and nanoscale electronics. However, the fabrication of ordered arrays of metal nanoparticles is still a challenging work and only a few experimental results are reported. For example, Maier et al. used electron-beam lithography to produce plasmon waveguides consisting of closely spaced Au nanoparticles with large diameter of 50 nm [14–16]. More recently, they formed linear Ag nanoparticle chain arrays in silica glass by ion irradiation, with diameters in the 10 nm range and interparticle spacing as small as several nanometers [17]. An alternative approach to organize metal nanoparticles in periodic arrays is to use linearly patterned substrates as templates. For example, Fort et al. have reported that self-alignment of Ag nanoparticles can be obtained by taking advantages of the preferential nucleation in the grooves of faceted alumina surfaces being positioned normal to the direction of material deposition [18]. In our previous work, however, we found that under normal incidence deposition, such a self-organization tends to disappear with increasing facets width with respect to the particle size, due to the nucleation of a large fraction of particles on flat terraces [19]. Another possible solution to produce self-organized nanosystems from linearly patterned templates is to exploit self-shadowing effects through grazing-angle deposition [20–24]. In this letter, we investigate the linear optical response of Ag nanoparticle arrays prepared by ion-beam sputtering shadow deposition onto faceted alumina substrates. We show that under appropriate grazing incidence conditions, only selected facet types are exposed to the atomic beam, resulting in linear arrays of nanoparticle chains or stripes. The optical transmittance spectroscopy data of the obtained nanostructures show evidence for strong plasmon coupling between the Ag nanoparticles.

Experimental

Single crystalline alumina substrates were cut at α_m = 9° from the (0001) planes towards the [110] direction and 2 sides epi-polished by the provider [25]. They have the advantage to be transparent for optical transmission spectroscopy and to be affected by a morphological instability at high temperature producing step bunching. Accordingly, all the substrates were subjected to a 1 h thermal treatment at 1000 °C in air and characterized by atomic force microscopy (AFM) in the tapping mode. As a typical example, fig. 1 shows the error signal AFM image of a bare substrate, which exhibits one-dimensional surface patterns arranged into a terrace-and-step structure. The error signal is a measure of how well the feedback loop is maintaining the desired tapping amplitude. It can be utilized for achieving a more precise recovery of the relief. Analysis of the corresponding topographic AFM image revealed that the patterns consist of a periodic array of alternating flat (0001) terraces (from 70 nm to 120 nm wide) and step bunches (from 10 nm to 20 nm wide), the global miscut angle α_m being conserved.

A 3 nm-equivalent thickness of silver was deposited onto the faceted alumina substrates by ion-beam sputtering under grazing incidence according to the preparation process depicted in fig. 2, at room temperature and without any rotation. The angle of incidence of the silver beam with respect to the averaged substrate surface was fixed to α_i = 5° (divergence angle of 3°), so that parts of the surface were shaded by the nanostructure depending on the orientation of the Ag flux. In mode 1, the silver nanoparticles were expected to nucleate on the parts of (0001) terraces exposed to the Ag flux, while in mode 2 they were expected to nucleate along the step bunches. To complete the study, the same amount of silver was also deposited on a flat alumina substrate (mode 0) under identical grazing-incidence conditions. Subsequently to the silver deposition, the surface was covered with a 20 nm-thick dielectric layer of Al₂O₃ in normal incidence (capping layer) to prevent diffusion and oxidation of the Ag nanoparticles under ambient conditions.

Results

The surface topography of the flat (mode 0) and the 9°-faceted alumina substrates (modes 1 and 2) covered by the Ag/Al₂O₃ bilayer was examined by AFM in the tapping mode. Figures 3(a)-(c) exhibit the error signal AFM images of the samples obtained in mode 0, mode 1, and mode 2, respectively. A simple inspection of the images clearly shows that the silver nanoparticles grown on the flat substrate (fig. 3(a)) are randomly distributed whereas the surface topography of the faceted substrates has led to an in-plane anisotropic organization of the nanoparticles (figs. 3(b) and (c)). Furthermore, the anisotropy strongly depends on the deposition mode. The elaboration mode 1 leads to the formation of nanoparticles stripes (constituted by 3 or 4 nanoparticles in width) aligned along the (0001) terraces and covering about 90% of the terrace area. Assuming a simple geometry as depicted in fig. 2, it is expected that only 1 − tan(α_m)/tan(α_m + α_i) = 36% of the terrace area should be covered by the Ag nanoparticles. Therefore we suggest that a part of Ag might have escaped from the flux zone due to the silver atom concentration gradient formed at the shadow edge [24, 26]. In that case, Ag surface diffusion may be activated by the high kinetic energy of the deposited atoms (average value of 26 eV and standard deviation of 67 eV as determined from SRIM calculations [27]). As concerns the elaboration mode 2, for the same amount of deposited silver, the majority of silver nanoparticles appear strung together in a pearl-necklace-like structure along the steps: the nanoparticles are organized into two lines along each step bunch. From the results mentioned above, the growth of the Ag-nanoparticle chain arrays obtained in mode 2 is considered to proceed as follows. In the very initial growth stage, small islands are nucleated along the step bunches exposed to the Ag flux. As the amount of Ag increases, the islands grow by simple adsorption of incoming atoms and/or coalescence of the neighboring islands. As the particle size approaches the step width, not only the growth is limited along the cross-step direction [28] but also the step bunches become shaded, leading to the formation of a second nanoparticle chain in front of the first one.

The insets in figs. 3(a)-(c) show the auto-correlation functions of the corresponding topographic AFM images. The auto-correlation function (ACF) is the cross-correlation function of an image f(r) with itself [29]:

giving a visual impression of the degree of ordering within the Ag nanoparticle arrays. The annular form of the ACF obtained in mode 0 (fig. 3(a)) indicates that the organization of the nanoparticles on the plane surface is isotropic without long-range order. From the positions of the two maxima in the radial profile of the ACF (fig. 4(a)), it is possible to determine the mean center-to-center distance between the nanoparticles Λ = 24 nm corresponding to the radius of the ring. Additionally, from a quantitative analysis of ACF profiles taken parallel and perpendicular to the steps for mode 1 (fig. 4(b)) and mode 2 (fig. 4(c)), it is possible to determine the ridge-to-ridge distance L and the mean center-to-center distance between the nanoparticles parallel (Λ_||) and perpendicular (Λ_⊥) to the steps. These values are given in table 1. Here, it is worth noticing that the distance Λ_⊥ = 30 nm in mode 2 is relative to the mean center-to-center distance between the particles within the two lines, each group of two lines being separated by L. In contrast, the one obtained in mode 1 (Λ_⊥ = 37 nm) corresponds to the mean center-to-center distance between the particles on the whole surface, i.e. including the mean perpendicular center-to-center distance inside each stripe and between the stripes themselves. Assuming that the total amount of silver and the shape (i.e., the height-to-diameter ratio) of the nanoparticles are the same whatever the deposition mode (0, 1 or 2) and that the mean diameter D of the nanoparticles is equal to Λ_|| in mode 2 (pearl-necklace-like structure) it is possible to evaluate the mean diameter of the nanoparticles in mode 0 and in mode 1 (table 1). It can be seen that the diameter values for mode 1 and mode 0 are reduced by 20% and 30%, respectively, compared to mode 2. This evolution can be interpreted as an increase of the surface area exposed to the Ag flux during deposition leading to a decrease of the local Ag areal density.

Figures 5(b) and (c) show optical transmittance spectra taken at normal incidence, when the incident light is polarized parallel (E_||) and perpendicular (E_⊥) to the surface steps, for mode 1 and mode 2, respectively. Spectra obtained on the flat alumina substrate (mode 0) for the two polarizations of the incident light are also given for comparison (fig. 5(a)). Despite an isotropic in-plane distribution, measurements made with the sample obtained in mode 0 (flat substrate) show two slightly different absorption bands located at 550 nm (2.25 eV) and 570 nm (2.17 eV). In mode 1, two absorption bands are observed with two distinct maxima, respectively, located at 535 nm (2.31 eV) for E_⊥ and 600 nm (2.06 eV) for E_||. At last, in mode 2, for the perpendicular polarization E_⊥, the particle plasmon excitation is manifest as a Lorentzian-shaped absorption band with maximum located at 490 nm (2.53 eV), while for the parallel polarization E_|| no plasmon resonance is found in this case. To analyze the optical data, we use the model developed by Yamaguchi et al. [30], which takes into account the effects of the elec trostatic dipole interaction between particles and between the particles and their mirror images in the substrate, and we extend it to the case of a collection of randomly distrib uted nanoparticles with ellipsoidal shape (with three semi- axes: a, b and c) oriented along the same direction, and to the case of a rectangular array of oblate nanoparti cles (with two equal semi-axes a = b = D/2, i.e. in-plane circular shape, and a third semi-axis c < a). In this model, each excited metal nanoparticle with a diameter much smaller than the wavelength of the exciting light acts as an electric dipole. When assuming the presence of randomly distributed spherical silver nanoparticles (with a diameter equal to 17.7 nm) on an alumina flat substrate embedded in an alumina capping layer, the SPR is expected to be located at 490 nm. Therefore, the nanoparticles produced in mode 0 have to be considered as oblate with a height- to-diameter ratio 2c/D = 0.54 in order to obtain a SPR located around 560 nm. Furthermore, the slight splitting of the absorption bands (Δλ = 20 nm) observed at normal incidence indicates that the deposition of Ag at grazing incidence on a flat substrate induces a slight in-plane anisotropy of the nanoparticles shape, that is not detected when silver deposition is made at normal incidence with a rotating substrate [10, 11]. In this case, as shown in fig. 6(a), our calculations show that the splitting of the SPRs can be attributed to ellipsoidal nanoparticles (with two in-plane depolarization factors L_a ≠ L_b) [1, 2] with an a/b ratio equal to 0.96 (with ) and oriented along a same direction, i.e. parallel to the Ag flux. In the same way, assuming a random distribution in mode 1, the splitting of the SPR (Δλ = 65 nm) can be assigned to ellipsoidal nanoparticles oriented along the direction parallel to the surface steps with an a/b ratio equal to 0.84 (fig. 6(b)). However, the AFM analysis shows evidence of silver nanoparticles distributed in stripes on the (0001) terraces. With the model of ordered oblate nanoparti cle chain arrays, it is possible to determine the spectral position of the SPR when the incident light is perpen dicular or parallel to the nanoparticles chains with the help of the mean values given in table 1: the chains spac ing is taken equal to Λ_⊥ = 37 nm and the center-to-center distance between the nanoparticles is equal to Λ_|| = 26 nm, the mean diameter is equal to D = 20 nm and the height-to-diameter ratio is fixed to 0.54. From these calculations we obtain two SPRs located at 535 nm for E_⊥ and 580 nm for E_|| (fig. 6(c)), in agreement with the measured SPR positions. However, we observe a damping and a broadening of the measured resonances due to the size, shape, and interparticle dispersions that are not included in the model. Since two SPRs are detected, the nanoparticles can still be considered as individual nanoparticles but with a coupling between neighbors higher when the polarization of the incident light is parallel to the steps compared to a polarization perpendicular to the steps. The observed splitting can therefore be attributed to the collective particle plasmon resonances which result from electromagnetic coupling between neighboring in linear nanoparticle arrays [13–16]. Indeed, these interactions act formally as a shape effect but are not related to any ellipsoidal shape [31], showing evidence of the shadowing effect by the terrace-and-step structure on the nucleation of silver onto the terraces. Our study confirms previous results obtained on ellipsoidal nanoparticles randomly distributed onto plane surfaces [10, 11] and on regularly spaced chains of spherical nanoparticles [14–16] suggesting that the interactions play an important role in the splitting. Nevertheless, further investigations have to be undertaken in order to clearly identify the different contributions (morphology/dipolar interactions) to the plasmon resonance splitting. At last, in mode 2, we assign the spectral blueshift of the SPR for E_⊥ and the lack of SPR for E_|| to the pearl-necklace-like structure of the silver nanoparticles. From an optical point of view, this organization can be seen as regularly-spaced silver nanowires oriented in the direction parallel to the steps [31, 32].

Conclusion

From this study, we have been able to elaborate silver nanoparticle chains and stripes by using the shadowing effect of the terrace-and-step structure of an alumina substrate. The obtained in-plane organization of the silver nanostructures depends on the grazing-incidence conditions (angle and orientation of the atomic beam with respect to the nanostructured surface) and their optical properties exhibit an absorption band whose spectral position depends on the polarization of the incident light (parallel or perpendicular to the steps). The preparation technique presented in this letter is obviously strongly dependent on the surface topography and therefore the techniques to obtain regularly faceted surfaces have to be mastered. In such a case, it is thus expected that different nucleation and growth regimes may be exploited in order to tune the splitting of the two SPR bands obtained in mode 1 by varying the deposition angle and the amount of deposited silver. In addition, many applications might benefit from the orientation-dependent plasmon excitation obtained in mode 2 as changing the polarization direction allows one to "switch" the plasmon on or off [31, 32].

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