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At higher frequencies (visible and infrared) both the dimensions and the individual metal properties play an important role in determining the resonant response of arrays of SRRs. As a result, a substantial difference between the responses of gold- and Al-based SRR arrays has been observed. Additionally, deposition of gold SRRs onto a substrate typically involves the use of an additional adhesion layer. Titanium (Ti) is the most common adhesive thin-film material used to attach gold onto dielectric/semiconductor substrates. In this paper we investigate the impact of the Ti adhesion layer on the overall response of Au-based nano-scale SRRs. The results quantify the extent to which the overall difference in the resonance frequencies between Au- and Al-based SRRs is due to the presence of the Ti. We show that even a 2-nm-thick Ti layer can red-shift the position of SRR resonance by 20 nm. Finally, we demonstrate that by intentional addition of titanium in the Au-based SRRs, their overall resonant response can be tuned widely in frequency, but at the expense of resonance magnitude.
©2010 Optical Society of America
1. Introduction
At the lower frequencies, up to several terahertz, the magnetic resonance (i.e. the LC resonance) of an SRR scales reciprocally with its characteristic dimensions. However, at higher frequencies (optical and mid-infrared regimes) metals do not behave like perfect conductors and behave according to the (complex) Drude model. Therefore, this model determines the overall response of the single-layer SRR structures [1–3]. Prediction of the SRR response is more complicated when dual-metal layer SRRs are considered. Titanium is one of the most common adhesion layers used to deposit gold-based SRRs onto dielectric or semiconductor substrates [3–7]. However, in most of the previous work on Au-based nano-sized SRRs the effect of the Ti adhesion layer has been ignored [3–7]. It is therefore desirable to observe and quantify the effect of the Ti adhesion layer on the overall response of Au-based SRRs, i.e. to find an optimum thickness of Ti layer. Such an analysis will help in more accurate prediction of resonance positions and magnitudes. It will also provide a better understanding of the experimentally observed shift between the responses of Al- and Au-based SRRs [3], when a Ti adhesion layer is used. Selection of the Ti layer thickness also opens up possibilities for tuning the SRR resonances, as described in later parts of this paper.
2. Fabrication and measurements
In this paper, simulated and experimental responses of SRRs with characteristic planar dimensions as small as 200 nm were considered. The devices were composed of either Al or Au layers, together with a variable amount of Ti adhesion layer - while keeping the overall SRR metallization thickness constant at 50 nm. Medium doped n-type silicon substrates with resistivity ~100 Ωcm were used in all cases. The fabrication was performed using direct writing with electron beam lithography. The multi-component metallic layers were deposited onto the silicon using electron-beam evaporation. The patterns were written over an area of around 300 µm × 300 µm. The reflectance measurements were performed at normal incidence with a × 10 microscope objective (NA = 0.25), using a white light source and monochromator with an InGaAs detector operating in the range from 0.8 µm to 1.6 µm - together with a lock-in amplifier. The measurements were taken for two orthogonal linear polarizations of the incident light (TE and TM polarization) - and were then normalized with respect to the reflectivity of a bare silicon substrate. Examples of the measured responses of closely similar-sized Au- and Al-based SRRs are shown in Fig. 1 . The difference in resonance positions between these two cases, reaching as much as ~200 nm, requires an analysis based on the different material properties and the additional inclusion of the effect of the Ti-layer for Au-based devices.
Fig. 1 SEM micrographs of fabricated SRRs and their corresponding experimental reflectance spectra for TE/TM polarization: (a) 50-nm-thick Al SRRs without Ti adhesion layer; (b) 48-nm-thick Au SRRs with 2 nm of Ti layer.
The values of the plasma frequency (ωp) and the collision frequency (ωτ) for bulk gold are 2175 THz and 6.5 THz, whereas those of aluminium are 3750 THz and 19.4 THz [8,9]. As experimentally shown both in Fig. 1 and in reference [3], the higher plasma frequency of Al-based SRRs results in a shorter wavelength of resonance, as compared to Au-based SRRs. On the other hand, the higher collision frequency of Al results in lower magnitude in, as well as the broadening of, the resonance peak of Al-based SRRs.
3. Numerical simulations
The resonant response of the SRRs was calculated using a fully three-dimensional (3-D) simulation of the fabricated device, after convergence tests were performed. The numerical simulations were performed with a commercial finite-difference time-domain method (FDTD) software package from Lumerical. The transmission and reflection characteristics were calculated from a single unit cell for two different optical polarizations, over a wide range of wavelengths. A Drude model was used to describe the frequency-dependent material properties. An integer number of cells with a small mesh-size of 2 nm was applied within the metallic layers, while non-uniform and coarser meshing was used in the surrounding regions. The bulk values of ωp and ωτ (2175 and 6.5 THz) for gold were adjusted to effective values (2400 and 25 THz), following the approach presented in [10], so that the simulation spectrum was in close agreement with the experimental spectrum for minimal Ti content Au structures. For very thin films, the fraction of the oscillating electric field outside the metallic structure is larger, which results in an additional dynamic inductance contribution [10]. At the same time, the effective collision frequency is higher than the bulk value due to the additional scattering experienced by electrons in such thin metal films. In the absence of direct experimental data for our deposited Ti layers, bulk values were used (383 and 136 THz). As a first approximation, an effective medium for the composite was assumed by taking linear combinations of the respective plasma frequencies and collision frequencies for Au and Ti, in proportion to the volume fractions of metal (corresponding to their relative thicknesses). Such a phenomenological approach was used due to the limitations of the software in accurate modeling of the behavior of very thin layers (i.e. a ~2-nm-thick Ti adhesion layer).
4. Effect of titanium adhesion layer
In order to examine how much the Ti adhesion layer contributes to the overall response of the Au SRRs, two different sets of experiments were performed. In the first set of experiments, the overall thickness of the Au/Ti SRR was kept constant at 50 nm, while the thickness of the Ti adhesion layer was increased at the expense of Au. The effect of increasing Ti content in an array of such mixed Au/Ti SRRs is shown in Fig. 2 . By increasing the fractional amount of Ti in the layer composition, both plasmonic and magnetic peaks move towards longer wavelengths - and diminish in amplitude. This flattening effect can be explained by the very high damping frequency of Ti.
Fig. 2 Reflection spectra of dual-layer SRRs with increased Ti quantity, where the overall Au/Ti thickness is kept constant: (a) experimental spectra at two different polarizations; (b) calculated spectra for the extended wavelength range.
From Ordal et al. [8] the collision frequency (ωτ) and plasma frequency (ωp) are associated with the complex dielectric function according to:
and For ω = 6451.61 cm−1, which is equivalent to a free-space wavelength of 1.55 µm, we obtain the corresponding ε1 and ε2 values for titanium of -ε1 = 6.56 and ε2 = 33.3, based on [8]. Putting the values of ω, ε1 and ε2 into Eqs. (1) and (2), we obtain the collision frequency for titanium, ωτ = 136 THz, and plasma frequency for titanium, ωp = 383 THz. Thus, the calculated plasma frequency for Ti is almost one order of magnitude lower than for the other metals. Additionally, Ti is characterized by a very high damping frequency of 136 THz, which is associated with absorption and losses. As more Ti is added to the system, the reflectance response is both red-shifted and reduced in magnitude (see Fig. 2)In a second set of experiments, the thickness of the Ti adhesion layer was gradually increased, while the thickness of the Au layer was kept constant at 48 nm. In this case, the total thickness of the SRRs also increased progressively. In Fig. 3 , a similar trend is observable to that in Fig. 2, i.e. by increasing the amount of Ti in the system, the overall resonant response degrades. However, by maintaining the Au thickness at a constant value, the reflectance response of the SRRs becomes larger in amplitude - and the flattening of the curves for high Ti content layers is no longer apparent. The increasing thickness of the SRRs apparently increases the effective plasma frequency and gives a blue-shift to the peak positions. In this experiment, a trade-off occurs between the increased Ti thickness - which pushes the response towards longer wavelengths while progressively suppressing the peaks - and the increased total thickness, which causes a blue-shift in the resonance peaks. For both simulation and experiment it can be confirmed, from the results shown in Figs. 2 and 3, that an increase of Ti fraction has reduced the observable response nearly to zero, once it forms more than 40% of the overall SRR thickness. The primary conclusion from these results is that the greater absorption in the Ti dominates the overall behavior, once it is present in sufficiently large amounts - even when the amount of Au is undiminished.
Fig. 3 Reflection spectra of dual-layer SRRs with increased Ti fraction and total system thickness, while the Au thickness is kept constant: (a) experimental spectra at two different polarizations; (b) calculated spectra for the extended wavelength range.
The FDTD simulation results presented in Figs. 2b and 3b substantially reproduce the experimental trend for an increased Ti content in dual-layer arrays at wavelengths up to λ = 1600 nm, while additionally showing decreasing reflectance in the extended wavelength range up to λ = 2440 nm. Good agreement with the experimental behavior shown in Figs. 2a and 3a is observed, especially for the magnetic (LC) resonances (around 1600 nm), whereas some discrepancy is evident between the experimental results and the simulated plasmonic peak positions. This discrepancy may be due to the non-ideal shape of the fabricated SRRs (see Fig. 1), in contrast with ideal shape used for the numerical calculations (see left inset in Figs. 2 and 3). The effect of the Ti-layer induced red-shift of both the plasmonic and the magnetic resonances of the Au/Ti bi-layer SRRs is shown in Fig. 4 . It can be seen that the presence of even a 2-nm-thick Ti layer can shift the SRR response by as much as 20 nm.
Fig. 4 Calculated Ti-induced change in resonance position and amplitude for dual-layer SRR as a function of Ti content. The overall thickness of Au/Ti SRR is kept constant: results for (a) TE and (b) TM polarization.
For a strongly composition-dependent behavior, the movement of the resonance towards longer wavelengths is clearly observed, as well as the strongly diminishing amplitude of these effects, for both light polarizations. For Ti-content > 40%, the reflectance at both the plasmonic and magnetic resonance peaks is reduced to about half of its initial/maximum value. Although the amplitude is reduced, addition of Ti (up to 40%) provides additional tuning possibilities for both the electric and magnetic resonance peaks of SRRs, as shown in Fig. 4.
5. Skin depth
It has been shown previously, that the penetration of the electromagnetic field inside metals, in higher frequency ranges such as the optical to mid-infrared regimes, is predicted by their skin depth [11–13]. To calculate the skin depths of both Au and Ti, the respective values of their conductance at a wavelength of 1.55 µm are taken from references [8,14]. The conductances of Au and Ti at 1.55 µm are calculated to be 4.12 × 106 S/m and 2.35 × 106 S/m, respectively. The skin depth (δ) of Au and Ti at a wavelength of 1.55 µm is calculated to be ~17.8 nm and 23.6 nm, respectively from [14]. For these measurements, the effective Au layer thickness is limited by its skin depth. However, as the Ti content increases, it is able to contribute to the conduction by as much as 1.3 times the skin depth. Qualitative information on the expected dissimilarities in the skin depth and field penetration inside different metals is presented in Fig. 5 . Electric field profiles were numerically calculated using the same FDTD software as mentioned earlier, where SRRs with different metal properties were investigated. Simulated electric field distributions (on logarithmic scales) within a nano-sized SRR element and its air surroundings are presented for a pure Au layer and mixed Au/Ti layers, which show the impact of increasing addition of Ti, up to a 70% Ti content. These results were obtained for TM polarized light at certain wavelengths of plasmonic resonance, for a given Ti inclusion. From the cross-sections shown in Fig. 5, it is seen that the maximum electric field strength is observed outside the metal layer, due to the combined effect of the incident and reflected plane waves, while moderate and low field strength occurs at the edges and within the metal itself, respectively. The increase in the penetration depth of the field inside the SRR (Figs. 5b, 5c and 5d), as compared to the pure Au case, is strongly related to the raised Ti content. Such a tendency is in good agreement with the theoretical skin depth values for Au and Ti, calculated using Eq. (3), and additionally explains the Ti-layer induced behaviour of the plasmonic and magnetic resonances observed in Fig. 4.
Fig. 5 Skin depth effect observed in calculated electric field profiles (log scale) for nano-sized SRR at the plasmonic resonance condition: (a) pure Au layer; (b) layer with 4% of Ti content; (c) layer with 40% of Ti content; (d) layer with 70% of Ti content.
Finally, to understand the impact of the Ti adhesion layer on the observed difference between the responses of 50-nm-thick Al-based SRRs and that of mixed Au/Ti-based SRRs (see Fig. 1), an additional experiment was performed. A Ti adhesion layer of 2 nm was added into the fabrication process, while realizing 48-nm-thick Al SRRs and the response was compared to that of a purely Al-based SRR (50 nm) of Fig. 1. The experimental results are shown in Fig. 6 , where a red-shift of about 20 nm is observed for both TE/TM peaks, when compared to results for pure Al SRRs. This result further corroborates the calculated results presented in Fig. 4, where a similar Ti-induced shift was observed in case of Au-based SRRs.
Fig. 6 Comparison between the experimental reflectance spectra of 50-nm-thick Al with that of 2 nm Ti + 48 nm Al SRRs: (a) results for TE polarization; (b) results for TM polarization.
Hence, the difference in the responses of the Au- and Al-based SRRs (see Fig. 1) is mainly caused by their material properties, i.e. because of the lower value of the Au plasma resonance frequency compared with that of Al, and partially by a Ti-induced red-shift. Therefore, at optical frequencies, apart from the size of the SRRs, the plasma frequency of the particular metal used determines the position of the resonances - with the collision frequency determining the broadening as well as the amplitude of reflectance.
6. Conclusions
The influence of Ti adhesion layers on the responses of Au- and Al-based SRRs has been quantified. The presence of a very thin Ti adhesion film, e.g. 2-nm-thick Ti, can produce a red-shift of resonance position of about 20 nm. Nevertheless, the addition of Ti can be utilized for tuning the response of Au-based SRRs, even if it also reduces the overall magnitude of the resonances, due to the highly absorptive nature of Ti. To obtain stronger resonances at shorter wavelengths it is therefore recommended that the thickness of the Ti adhesion layer should be kept to a minimum (~2 nm). Finally, we conclude that the thickness of the Ti adhesion layer should be an important consideration when performing the numerical simulations, as well as in the fabrication and measurement of Au-based SRRs.
Acknowledgements
The authors wish to acknowledge support from the European Commission through the Metamorphose NoE, ECONAM and the COST action MP0702 and also the staff and facilities of the James Watt Nanofabrication Centre at Glasgow University.
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