1. Introduction

The potential in integrating miniaturized sensors for optical applications has considerably grown for the last decade. Tailoring and incorporating custom-made nanoparticles (NPs) [1], especially also arrays of nanorods, has tremendously fertilized this thinking, offering nowadays a variety of devices with targeted functionality for specific spectral ranges.

Broad-band optical tunability, however, achievable within one and the same device has found its limitations, either inherently dictated by the physical properties of the material(s) in use, or given by the boundary conditions when integrating the sensing chip into the final device setup. Ideas of circumventing these bottle-necks list from spectral stitching using a parallel assembly of low-bandwidth devices [2] over using the angular dependent optical response in single sensor investigations [3] to in-situ phase-change matrix materials [4], to list only a few.

Notably, broad-band optical applications may also be realized by implementing plasmonic devices, making use of the strong field enhancement and coupling of such nanoantennas [5]. An anisotropic antenna shape is preferable, since providing a much larger field enhancement at the nanorod apex (both resonantly and non-resonantly), while covering a broader spectral range through dedicated plasmonic nanorod coupling. Finding flexible ways for integrating 2-dimensional carpet-like nanorod arrays thus stands high up in the wish-list.

We delineate here a novel way for using such 2-dimensional gold-nanorod arrays (2D-GNAs) as tunable sensing devices. Efficient 2D-GNA fabrication dates back to the very first SEM investigations in the 50s [6] using anodized aluminum oxide (AAO) matrices as a dielectric or semi-permeable membrane. Nevertheless, AAO-based nanoparticle/ nanorod assembling [7, 8] and plasmonic investigations thereof [9] were carried out in the 90s only. The spectral position of those plasmon resonances depend on the material and geometry of the 2D-GNAs [10, 11] as well as on the refractive index (RI) of the surrounding medium [12]. All these parameters may generally be used in order to spectrally tune the plasmon peak position of the nanorods’ long-axis resonances for the target application in mind, i.e. in surface-enhanced Raman spectroscopy (SERS) [13], second harmonic generation (SHG) [14] or wavelength-selective light detection devices [15]. Notably, the continuous variation of geometry, material, or environment also allow for generating gradient structures out of such simple nanorod devices [11, 15], suddenly extending the devices application range from single-frequency to tunable (static) broad-band responses [16]. Conversely, when searching for a dynamical tuning of such 2D-GNA immediately reduces the above-mentioned set of parameters to RI variations only, since both material and geometry are quasi fixed in those arrays. Hence, sensing subtle changes of the RI matrix material that surrounds the nanorods or using fluids of variable RIs as the matrix material were explored [17]. Moreover, the dynamical change of the NP size in-situ by electrodeposition [18] or photochemical tuning [19] was reported as well.

A mechanical tuning parameter that has been neglected so far and that is easily accessible, is the interrod distance, i.e. the center-to-center spacing between two neighboring nanorods. Provided the substrate and filling matrix of the 2D-GNA allows for elastic deformation (for instance by using an elastomer), then the plasmonic coupling might be reversibly controlled through elastically straining the device, as schematically illustrated in Fig. 1. Similar investigations exist for resonance tuning using strain on elastic substrates covered with gold coated polystyrene spheres [20, 21], randomly ordered gold nanoparticles [22, 23] or electron beam carved horizontal gold nanoantennas [24], which all exhibit resonance shifts upon changing interparticle distance. No such strain investigations have been reported for 2D-GNAs. The advantages of such GNA structures over these other systems are: the possibility to easily tune the initial resonance position over a wide spectral area by controlling the rod diameter; highly confined and dense packed areas of field enhancement on the sample surface due to the vertically arranged antenna shape and no need for slow or expensive tools, like electron beam lithography. Until now, 2D-GNAs have been shown to preserve their plasmonic resonance peaks [25] when partially embedded in a polymer film [26, 27]. Note, that those samples were still embedded in the AAO matrix, allowing only for device bending with a limited range of optical tunability. In contrast, we demonstrate in this paper how to fabricate fully embedded 2D-GNAs into an elastically stretchable polymer film, while then investigating their optical responses upon applying reversible tensile strains of up to 15 %.

 

Fig. 1 Sketch of the cross section (a) and the top view (b) of a 2-dimensional gold nanorod array (2D-GNA) embedded in an elastic polymer. The stretching is achieved by a tensile force along the x-axis. Subsequent transmission measurements are carried out with p-polarized white light under an incident angle φ in the xz-plane. As seen in (b) the uni-axial strain introduces anisotropy to the hexagonal unit cell, depending on its orientation I or II. Additionally, the nanorods are ordered hexagonally only on a short length scale. Therefore, the two unit cells depicted in (b) can be oriented arbitrarily to each other, which influences the effective interrod distance (see discussion).

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2. Experimental

The necessary steps for preparing our dedicated samples are outlined in Fig. 2(a). Steps 1 to 3 reproduce the well-known procedures of nanorod fabrication using anodized aluminum oxide (AAO) matrices [28–30]: Firstly, a 50 nm thin aluminum layer is sputtered onto a clean glass substrate (microscope slide Microcrown from Schott) serving as the adhesion layer for a 10-nm-thin gold electrode. Then a second aluminum layer of a 600 nm thickness is added by sputter deposition, followed by a complete anodization of that layer at 26 V and 1 °C in 0.3 M H₂SO₄, which forms the pores [31]. Because only a thin layer of aluminium is anodized the pores are not perfectly hexagonal arranged. The quality of the last aluminum layer is crucial, because it will determine the quality of the 2D-GNA. An optimization of the corresponding sputtering step was performed by Patrovsky et al. [32]. After anodization, isotropic etching of the AAO in 0.03 M NaOH follows, widening the pores’ diameter and removing the residual alumina barrier layer to the Au electrode at the bottom of every pore. Subsequent electrodeposition is carried out using an aqueous solution containing 0.05 M HAuCl₄, 0.42 M Na₂S₂O₃ and 0.42 M Na₂SO₄, and standard parameters [33] (−0.45 V applied for 130 s). This results in filling the pores with 300 nm long Au nanorods of around 18 nm to 22 nm diameter (depends on the etching time in step 2) and a center-to-center spacing of 63 nm.

 

Fig. 2 (a) The different steps for sample preparation: 1) anodization, 2) pore etching, 3) electrodeposition of gold, 4) mask removal, 5) polymer casting, 6) removing PET layer, 7) sample separation; (b) SEM cross section of a 2D-GNA embedded in a polymer matrix (epoxy resin) prepared by FIB. The viewing direction is 38 ° vertically tilted. The platinum was deposited prior to FIB slicing for protection purposes. Note, that different colors of the platinum result from different deposition methods (electron beam evaporation, ion beam evaporation).

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After removing the complete AAO matrix in 0.03 M NaOH, a 100 μl droplet of the desired polymer is applied to the free top surface. Finally, a piece of PET foil is placed on the droplet in order to flatten the polymer surface. The polymer used here is an epoxy resin (Epo-Tek 310M-1) with an additive of 400 g/mol polyethylene glycol (PEG400) in a mass ratio of 15:1. The PEG400 prevents the epoxy from complete solidification, keeping the new matrix elastic and flexible even after curing on a hot plate for 3 hours at 65 °C. Finally, the PET foil is peeled off the cured epoxy resin, resulting in a smooth and plain surface. Hence, the 2D-GNA is firmly embedded into the elastomer, though still supported by the glass and thin bottom aluminum/Au film.

In order to obtain a free standing polymer film, the 2D-GNA/polymer-composite is either zipped off mechanically from the substrate, or the thin adhesive aluminum layer is etched off in 3 M NaOH for approximately 24 hours. Mechanically peeling-off works well for composite films exceeding a 500 μm thickness; notably, this mechanical process inevitably induces also lateral strain to the 2D-GNA resulting in a tilt of the nanorods which might be even advantageous for optical applications, similar to blazed gratings. Following these protocols allows us to reproduce free standing, embedded 2D-GNAs of a 20 mm × 5 mm × 0.4 mm size with a smooth and planar polymer surface.

3. Results

To check whether the nanorods are really embedded in the polymer matrix, an 2D-GNA/polymer-compound film, which was separated from the rigid substrate by etching in NaOH, was investigated with a scanning electron microscope (SEM) augmented by a focused ion beam (FIB). A cross section was prepared by cutting into the film with the FIB. Prior to the preparation a platinum film was deposited for protection purposes. Fig. 2(b) shows a SEM image of the respective cross section, confirming that the nanorods are completely embedded. At some areas the rods appear branched, which may occur due to distortions during anodization. Also the rods do not form teepee-like structures (rods, that conglomerate at their tips), which results from longer free-standing rods, as seen in [28, 34]. However, the rods are not perfectly aligned parallel to each other [35], as caused by mechanical influences during polymer casting (step 5) after the complete removal of the aluminiumoxide matrix. This may lead to an additional broadening of the optical features. Additionally, the removal of the AAO itself (step 4) is causing a distortion of the gold electrode layer that can be seen in Fig. 2 (b). The NaOH used in this process can partially disolve the adhesion layer through defects in the gold layer when the AAO is almost removed. This is also the reason for small spots of polymer being on the other side of the electrode after polymer casting. To overcome this problem a different adhesion material underneath the gold electrode could be used, which is inert against NaOH and can be etched with an other chemical.

2D-GNAs embedded into the elastomer were optically inspected using an optical setup as sketched in Fig 1(a) (for detailed information on the setup see [30]). The sample is mounted into a linear mechanical stretching device that can be quasi freely rotated around the y-axis with respect to the incoming light beam, thus varying the incident angle φ. Halogen white light (Xenophot 64610 HLX, Osram) is used for illumination and passes a Glan-Thompson prism before impinging p-polarized onto the sample spot of a 2 mm x 0.5 mm size. We analyze the transmitted light with the help of an optical spectrometer (Maya 2000 Pro, Ocean Optics). Only p-polarized light will be used, since for transmission measurements in s-polarization the desired long axis resonance will vanish [30].

Firstly, the angular response of embedded nanorods when applying no strain to the elastomer is inspected. Two different behaviours are observed: Mechanically peeled-of samples as mentioned above, exhibit an appreciable nanorod tilting, resulting in optical spectra that are not distributed symmetrically with respect to the 0 °-reference incidence angle. Such a measurement is displayed in Fig. 3(a). We observe a distorted symmetry in this plot with the local absorbance minimum being determined by the nanorod tilt angle with respect to the incident plane. The asymmetry of the short axis resonance may be explained by a combination of optical length and field component of the incoming light. Regarding the −30 ° and the 0 ° spectrum of the sample from Fig. 3(a): while the electrical field components that are perpendicular to the nanorods have the same absolute value since the tilt angle is approximately 15 °, the optical length is higher for −30 ° incident angle, which may cause the higher absorption. For the +30 ° spectrum having the same optical length as the −30 ° spectrum, it has a much smaller electrical field component perpendicular to the nanorods instead. In contrast to these mechanically peeled-of samples, no rod tilting is observed for samples separated from the rigid substrate through chemical etching. Here, transmission data exhibit spectra that are symmetrical with respect to the 0 °-reference [Fig. 3(b)].

 

Fig. 3 (a),(b) Angle resolved transmission spectra of unstretched, mechanical (a) and chemical (b) separated 2D-GNA/polymer samples. The symmetry axes are depicted by white dashed lines and represent the respective tilt angles of the nanorods. (c) Four typical transmission spectra of one sample (22.6 nm rod diameter) with increasing tensile strain ∊. Note the peak shift and the peak broadening of the long axis resonance. In (d) the long-axis resonance positions as a function of tensile strain ∊ for samples with different rod diameters (listed above each graph) are depicted. Additionally, resonance peak positions from FEM simulations are shown as blue squares. These data points are corrected for anisotropic distortion of the lattice that results from uniaxial strain (see discussion). Note that all spectra are recorded with p-polarized light.

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Optical inspection while stretching the samples was conducted next in the following way: A fixed incident angle was chosen while applying mechanical strain up to a certain threshold value, and then fully releasing this strain again. We thus record optical transmission spectra for any such chosen angle as a function of mechanical load. This procedure is applied for angles ranging from 32 ° to 41 °. Note that the upper angular limit is solely given by geometrical considerations of the actual stretching setup, with the sample mounting partially blocking off the incoming light beam for larger incident angles.

A typical set of spectra with increasing tensile strain ∊ is shown in Fig. 3(c). These spectra were fitted with two Lorentzian peaks that correspond to the nanorod long- and short-axis plasmon resonances, respectively. Fig. 3(d) displays the long-axis resonance-peak position of four different samples as a function of ∊. These four samples differ in pore etching times, hence resulting in different rod diameters, and thus show a quite different spectral behavior. As displayed, larger rod diameters result in a stronger spectral shift when applying the same amount of tensile strain. Fig. 3 clearly indicates the easy but elaborate way in order to profit from strain-controlled plasmonic devices.

4. Discussion

Our experiments (see Fig. 3) show the linear increase/decrease of plasmon resonances when applying a tensile strain to the 2D-GNA/polymer composite. Clearly, the mechanical load is taken up by the elastic matrix rather than exerting lateral strain onto an individual nanorod directly, hence broadening their distance to each other. The observed long-axis plasmon redshift thus stems from an increase of interrod distances, as also proven through theoretical simulations [10,11].

We investigated this effect here in more detail, since exerting an uniaxial tensile strain onto the elastomer/nanorod sample results in the anisotropic deformation of the quasi hexagonal nanorod unit cell [see Fig. 1(b)]. In our simulations, we apply the finite-element-modelling (FEM) platform COMSOL Multiphysics 5.0 (including the wave optics module) to a hexagonal lattice of standing gold nano-cylinders, having a diameter and initial interrod distance of 22 nm and 63 nm, respectively. The rods are embedded in a host matrix of refractive index n = 1.5 [36], and are supported by a glass substrate that carries a 10 nm thin gold layer [see Fig. 4(a) and [30] for details]. The simulated spectra displayed in Fig. 4(b) clearly shows 4 distinct peaks, whereas only the long- and short-axis resonances are visible in the experimental data. The additional peaks arise from several effects: thin film interferences, the assumed perfect hexagonal lattice, and also from reflection at the bottom gold layer [30]. Since the real lattice is quasi-hexagonal that includes also a distribution of interrod distances, which is almost twice as high as the anisotropic deformation, the model uses isotropic strain with an effective inter-rod distance. Additionally, an anisotropic modelling gives no benefits because of the arbitrary orientation of the unit cells in the real quasi-hexagonal cell, which cannot be accounted for in the simulation directly. Instead, the effective interrod distance takes the anisotropic strain of the lattice into account by assuming that the diverging interrod distances can be averaged out and seen as a reduced isotropic strain μ. The relation between the external tensile strain ∊ and the reduced isotropic strain μ is almost linear and can be described by a factor k for small ∊, which will be discussed next.

 

Fig. 4 (a) Unit cell of the FEM-simulation. The array is built up by PEC/PMC (perfect electric conductor/perfect magnetic conductor) boundary conditions at the surfaces normal to the x-axis and by periodic boundary conditions at the surfaces normal to the y-axis. So this unit cell will be mirrored in the x-direction and translated in the y-direction (see [30] for details). (b) Simulated transmission spectra (p-polarized) for 2D-GNAs with 22 nm rod diameter and different interrod distances a. Long and short axis resonances are the only visible peaks in the experiment and have been marked in the plot. Additional peaks visible in this plot are either simulation artifacts or have their origin in the perfect hexagonal lattice that is used in our simulation (the real array is quasi hexagonal). Note that the values for the corresponding tensile strain are calculated with equation (4).

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As known the nanorod lattice may be viewed, in reality, as being of amorphous order, providing a quasi-hexagonal ordering of nanorods at shorter distances, only. Since evanescent, lateral field coupling decays pretty fast, it is fair to assume that every rod possesses 6 neighbors in average, separated by the average interrod distance a. The amorphous long range lattice allows for this unit cell to be randomly in-plane oriented, finding any such configuration with equal weight distributed over the sample surface, as displayed in Fig. 1(b) for configurations I, II, and every intermediate orientation. It thus is fully enough to consider these two basic orientations I and II, and calculate their behavior upon stretching, since rotating the unit cell between I and II will change the distances continuously and monotonously only.

Upon applying a tensile force, the average interrod distance a for these two cases behaves as:

The corrected resonance positions obtained by simulation are illustrated in Fig. 3(d). Apart from a redshift of the resonance’s spectral position, which comes from a bias in the rod diameter measurement from SEM images, the slope of the simulated data fits the measurements of the nanorods reasonably well keeping in mind that the simulation is based on a perfect hexagonal lattice, which is not the case for the experiment. A redshift of the spectral position of the plasmonic resonance usually leads to a peak broadening. In addition, the lattice anisotropy upon strain application will also contribute to that broadening of the resonance peak. Both impacts are seen in Fig. 3(c) and Fig. 5. The anisotropic broadening is the result from deviations between a′₁ and a′₂ (and b′_1,2, respectively). For ∊ > 0:

 

Fig. 5 Change of the full width half maximum (FWHM) of the GNAs’ plasmonic long-axis resonance peaks over tensile strain ∊ applied to the substrate, along with the resonance wavelength deviations as expected from stretching-induced anisotropy and the plasmonic broadening.

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5. Conclusion

We showed an elegant way to fabricate 2D-GNAs embedded in elastic epoxy polymer films. Due to the self organizing bottom-up nature of the aluminium anodization, the use of thin films and the simple polymer casting technique, this method is very easy and cost-efficient. Besides epoxy resin, also other optically clear polymers are conceivable for fabrication as long as they are chemically stable in NaOH.

Using an optical transmission setup, we examined the redshift of the plasmonic long-axis resonance whilst applying a tensile force to the GNA/polymer compound. This shift behaves linearly with respect to the strain applied to the film and measures 10 nm to 20 nm depending on rod diameter (the maximum strain being applied to the samples ranges from 8 % to 15 %). FEM simulations show the origin of the resonance shift as the change of the interrod distance. Furthermore, anisotropy introduced by uniaxial strain reduces the effective increase of the inter-rod distance by approximately 3 times with respect to the increase of the substrate length. The broadening of the resonance peak is dominated by the plasmonic broadening due to the redshift of the peak during stretching. This leads to the conclusion that the anisotropy-induced broadening is negligible against the already broad distributions of diameters and interrod distances caused by the imperfect lattice of the real 2D-GNA. Additionally, an initial rod tilt angle can be introduced with mechanical forces during fabrication, which can be very useful to reduce the external incident angle for future sensing applications.

However, the thin film anodization comes to a limit in terms of production quality after the optimization of the aluminum layer. For further improvements of this application we consider the change of the adhesion layer to reduce fluctuations of the gold layer after polymer casting. Also the complete removal of the gold electrode after the whole fabrication should increase the overall transmittance and improve the applicability of the 2D-GNA/Polymer-Film.

A. Additional SEM-images

To show the quasi-hexagonal structure of the nanorod lattice a top view of the 2D-GNA in AAO is depicted in Fig. 6(a). It can be seen that the lattice has no long range order but still a short range order in matter of a average interrod distance and 6 neighbors in average. There are also empty pores that will also contribute to the spectral properties of the array. In Fig. 6(b) is a cross-section of the array that can be seen in Fig. 6(a). The rods are good shaped and perpendicular oriented, suitable for further fabrication. The next image in Fig. 7(a) shows an array from top after removing of the AAO. Like mentioned earlier at some points the rods seem to conglomerate at the tips, due to the surface tension of the liquids [34]. After polymer casting, curing and separation of the film a surface can be found as it is depicted in Fig. 7(b). Here we see the top of the 2D-GNA/polymer film with the gold electrode on top and defects that come from the casting and separation process. Evaporating a platinum strip for protection on top of this and slicing with the FIB inside the structure the picture from Fig. 2(b) can be found. However in this picture the embedding of the nanorods were complete and the whole polymer were only visible as a black surface. Instead in Fig. 7(c) an early sample is shown with incomplete embedding. The difference between polymer and void is clearly visible.

 

Fig. 6 (a) SEM top view of 2D-GNA after electrodeposition. The Nanorods are still embedded in the AAO and can be seen as bright dots while empty pores are seen as dark dots. The quasi-hexagonal lattice can be seen here. (b) SEM cross section of nanorods in AAO on a glass substrate, showing that the nanorods are well oriented and in good shape.

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Fig. 7 (a) Free standing nanorods after etching of the AAO, showing some conglomeration at tips. (b) Surface of the 2D-GNA/Polymer film after full fabrication process. (c) Cross section of an early attempt of embedding nanorods in polymer showing incomplete covering of polymer in the array.

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B. Additional simulation data

In Fig. 8 simulated transmission spectra for a wider range of interrod distances and wavelengths are depicted. There is a steady redshift of the long axis resonance. But since the prerequisite of small tensile strain is not given for interrod distances bigger than 68 nm this plot is for qualitative purposes, only.

 

Fig. 8 Simulated transmission spectra (p-polarized) for 2D-GNAs with 22 nm rod diameter and different interrod distances a with. Long and short axis resonances are the only visible peaks in the experiment and have been marked in the plot. Additional peaks visible in this plot are either simulation artifacts or have their origin in the perfect hexagonal lattice that is used in our simulation (the real array is quasi hexagonal). Note that the values for the corresponding tensile strain are only given for the first three curves due to the criteria of small tensile strain for equation (4). The curves with higher interrod distance are shown to see that there will be no additional effects besides the redshift of the long-axis resonance even for very high interrod distances. The dashed line is just a guide to the eye.

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To identify the different resonances, in Fig. 9 the average electric field is plotted for a nanorod inside the array at the three resonant wavelengths from the simulation with 63 nm interrod distance. In the plot with 515 nm the electric field primarily oscillates perpendicular to the rod long axis, so this is identified as the short axis resonance. Instead, in the plot for 670 nm the electric field is especially orientated towards the long axis of the rod. Since several nodes along the rod are visible, it is fair to assume this not to be the fundamental mode but a higher mode of the long axis resonance. Also it shows a much higher coupling between the rods, indicated by the high field in the interspace. This resonance is besides the short axis resonance the only visible peak in the measured spectra, so we called it long axis resonance for simplicity. The last plot at 770 nm wavelength shows also an electric field that is mainly oriented along the rod long axis. But this seems to be a simulation artifact produced by the gold electrode, as seen by the very high confined field at the base of the rod. With this knowledge it is now easy to track the corresponding resonance peaks, when increasing the interrod distance.

 

Fig. 9 Plot of the average electric field inside and around a nanorod for the three resonant wavelengths. These plots are extracted from the simulation with 63 nm interrod distance.

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C. Strain translation

For configuration I:

(7)$$a_1^{\prime }=a(1+∊)$$

is obvious. a′₂ can be calculated from the coordinate position of the rod before stretching, which is (−a/2; $\sqrt{3}a/2$) (with center rod as origin). Now the x-direction will be stretched with the factor 1 + ∊ and the y-direction will be compressed by 1 − μ∊. Then the distance to the origin is a′₂:

(8)$$a_2^{\prime }=\frac{a}{2}{\left[{\left(1+∊\right)}^2+3{\left(1-\nu ∊\right)}^2\right]}^{1/2}.$$

In the unit cell are 6 neighbors in which two have the distance of a′₁ and four the distance of a′₂ which leads to the average distance in this orientation:

(9)$$\overline{a}=\frac{2a_1^{\prime }+4a_2^{\prime }}{6}$$

which is equation (1).

For configuration II an analogous method can be used to obtain:

(10)$$b_1^{\prime }=\frac{a}{2}{\left[3{\left(1+∊\right)}^2+{\left(1-\nu ∊\right)}^2\right]}^{1/2}$$

and

(11)$$b_2^{\prime }=a(1-\nu ∊).$$

Funding

German Ministry of Education and Research (BMBF) (03V0762, 13N13732); Cluster of Excellence “Center for Advancing Electronics Dresden (cfaed)”

Acknowledgements

The support from the Cluster of Excellence “Center for Advancing Electronics Dresden (cfaed)” is gratefully acknowledged.

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