Localization of Near-Field Resonances in Bowtie Antennae: Influence of Adhesion Layers

Abstract

The near-field resonances of gold bowtie antennae are numerically modeled. Besides the short-range surface plasmon polariton (SR-SPP) mode along the main axis of the structure, a coupled SPP mode is also found in the gap region (G-SPP). The influence of adhesion layers is considered, which depends on the refractive index and the absorption of the adhesion material and whether it is continuous or etched. A high refractive index causes the peak of the SR-SPP to red-shift. High absorption quenches the intensity of the SR-SPP. The magnitude of influence depends on the overlap of the adhesion layer with the SR-SPP and G-SPP modes. The near-field resonance of the SPP mode on the top surface is also considered. An etched metal adhesion layer changes the near-field localization in the gap and causes the enhancement peaks at different heights within the gap to red-shift from top to bottom. A simple optimization method for the near-field localization by the combination of different top and bottom layers is demonstrated.

Appendix

Dielectric properties of Au

The optical properties of Au used in our simulations were determined from experimental measurements. The Au thin film was prepared using reactive DC sputtering deposition (Denton Discovery 18) using a 75-mm-high-purity (99.99%) Au target. The power was 50 W and the process pressure was 10 mT in an Ar atmosphere. The deposition was performed on a microscope glass slide (Fisher Scientific) at ambient temperature (21 °C). The thickness of the film, approximately 100 nm, was measured using a surface profilometer.

The optical properties of Au were measured using variable angle spectroscopic ellipsometry (J.A. Woollam Co. VB-250) [38]. Data were acquired over the angular range from 70° to 75° in steps of 5° and over the spectral range of 400 to 1,000 nm. The Au film was modeled using the bulk properties for Au as a starting point  [39]. The values of the refractive index n and extinction coefficient k were iteratively changed to fit the measured data (Ψ and Δ). The measured values for n and k are shown in Fig. 9 and Table 1. The data are in good agreement with those found elsewhere [39, 40].

Fig. 9

Measured refractive index and extinction coefficient of Au

Table 1 Measured refractive index and extinction coefficient of Au

Dielectric properties of Cr

The optical properties of Cr are taken from reference [39], and are plotted in Fig. 10.

Fig. 10

Refractive index and extinction coefficient of Cr

Dielectric properties of Ti

The optical properties of Ti are taken from reference [39] and are plotted in Fig. 11.

Fig. 11

Refractive index and extinction coefficient of Ti

Dielectric properties of Cr₂O₃

The optical properties of Cr₂O₃ were determined from experimental measurements. The Cr₂O₃ film was sputtered on a glass substrate using a high-purity (99.95%) Cr target and Ar and O₂ gases. The power was 50 W and the process pressure was 10 mT. The partial pressure of the O₂ was approximately 2%.

The optical properties and the thickness of the Cr₂O₃ film were measured using ellipsometry. Before measuring the Cr₂O₃ film, the glass substrate’s optical properties were measured. By measuring the substrate’s properties, we were able to more accurately model the Cr₂O₃ using the substrate in the Cr₂O₃ model. A spectroscopic scan was performed over the spectral range of 400 to 1,000 nm and over the angular range from 70° to 75° in steps of 5°. The glass substrate was modeled using a Cauchy model,

$$ \label{eq:cauchy} n(\lambda)= A+B / \lambda^2+C / \lambda^4 $$

(1)

where A, B, and C are fit parameters for modeling the measured data. The values of these parameters are shown in Table 2. Since the glass slide is nearly transparent over the wavelength of interest, we assume k = 0.

Table 2 Cauchy fit parameters for glass substrate

To measure the Cr₂O₃ film, spectroscopic and transmission measurements were performed. The spectrocopic scan was performed over the same spectral and angular ranges as the substrate. The transmission measurement was performed at normal incidence. During the spectroscopic scan, a strip of translucent adhesive tape was placed on the backside of the substrate to suppress backside reflections [41]. These measurements provide Ψ, Δ, and transmittance T, allowing us to find the n, k, and thickness of the film. The Cr₂O₃ film was modeled using the glass substrate model and data from [42] as a starting point for the Cr₂O₃ film. We then simultaneously fit the oxide’s n, k, and T to the measured data. The thickness of the film measured approximately 6 nm. The values of n and k are shown in Fig. 12 and Table 3.

Fig. 12

Measured refractive index and extinction coefficient of Cr₂O₃

Table 3 Measured refractive index and extinction coefficient of Cr₂O₃

The measured refractive index is in good agreement with literature [43, 42]. The extinction coefficient, however, is slightly higher than expected, presumably due to the low partial pressure of O₂ during deposition.

Dielectric properties of TiO₂

The optical properties of TiO₂ are taken from reference [46] and are plotted in Fig. 13.

Fig. 13

Refractive index and extinction coefficient of TiO₂

Dielectric properties of ITO

The optical properties of ITO were experimentally determined in a manner similar to the other materials. The ITO film was sputtered on a glass substrate using a high-purity (99.99%) ITO target and the same parameters as the Au deposition.

The optical properties were found using ellipsometry. A spectroscopic scan was performed over the angular range from 60° to 75° by 5° increments. Once again, a translucent strip of adhesive tape was used to suppress backside reflections during measurements. The ITO film was modeled using two Lorentz oscillators of the form  [44],

$$ \label{eq:lorentz} \bar{n}^2=\epsilon(\infty)+\sum_{m}\frac{A_m}{E^2-E_m-\textit{i}\Gamma_m E}, $$

(2)

where $\bar{n}$ is the complex refractive index, ε( ∞ ) is the dielectric constant at infinite energy, A _m is the amplitude, E _m is the center energy, E is the energy corresponding to a particular wavelength, and Γ _m is the broadening of the oscillator. The fit parameters are shown in Table 4. The optical properties of the film are shown in Fig. 14 and Table 5.

Table 4 Lorentz oscillator fit parameters

Fig. 14

Measured refractive index and extinction coefficient of ITO

Table 5 Measured refractive index and extinction coefficient of ITO

In general, the optical properties of ITO films vary considerably with deposition conditions and postdeposition processing. Our measured data are similar to the values found in literature for sputtered films [44]. The extinction coefficient of our film, however, is slightly higher at shorter wavelengths, indicating that the film is more lossy. This loss could be reduced by annealing [45].