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Optical properties of localized surface plasmon resonance (LSPR) in Au/Ag alloy were investigated experimentally and numerically. It was found that LSPR spectra of nanostructures at near-infrared wavelengths changed drastically at the 50% Au/Ag mole fraction. Both the experimental results and the finite-difference time-domain simulations using experimentally obtained n, k values showed a similar tendency. At 50% molar fraction, electromagnetic field enhancement reached almost the same value as in pure Au.
©2012 Optical Society of America
1. Introduction
Noble metal nanoparticles such as Au, Ag, and Pt can interact with light, and this leads to the well-known phenomenon of localized surface plasmon resonance (LSPR). This phenomenon is attractive and promising in the field of opto-electronics and sensing. Optical properties of plasmonic materials have been studied widely in the previous decade, particularly, their structural shape, size, and distance between interacting particles. A control over the plasmonic resonance of a material is required to increase the applications it can be used for, including for a surface plasmon resonance (SPR) sensor [1], surface enhanced Raman scattering (SERS) [2,3], nonlinear optical phenomena [4], and energy harvesting [5]. Obtaining the desired optical properties by controlling the properties of a material is important not only for improving device functionality but also for conserving noble metals.
Recently, alloy nanoparticles have received much attention for next generation materials as a catalyst, hydrogen-storage instead of precious metals [6–8]. Alloy nanoparticles allow the control of their plasmon resonance, chemical stability, and Raman activity of adsorbed molecules, through the control of their composition. Historically, the formation of a metal alloy in bulk has been used for the production of coins, jewelry, and industrial products owing to its physical/chemical properties, although there has been little focus on the optical properties of such alloys. Many fabrication methods, based on chemical (co-reduction of metal halides) and physical (laser ablation in solution) processes have been studied for obtaining alloy nanoparticles with desired compositions [9–20]. However, their optical constants have not been systematically studied in experiments, even though they are important for plasmonics. Optical properties of metal nanostructures depend strongly on the metal/alloy and can be described in terms of the complex refractive index n = n + ik, which is related to the relative permittivity ε = n2 = ε1 + iε2. Here, n is the bulk refractive index and k is the extinction coefficient; ε1 and ε2 are the real and imaginary parts of the permittivity, respectively. The relationship between the refractive index and the relative permittivity is given by ε1 = n2 - k2 and ε2 = 2nk. The arithmetic average of bulk Au and Ag is sometimes used [21–24] for simulations of the optical properties of alloy nanoparticles. However, it is not clear whether this can be applied over the entire spectral range.
In this study, we systematically investigated the optical properties of the Au/Ag alloy. Optical properties of alloy nanostructures were experimentally determined, and the finite difference time domain (FDTD) simulations were used to compare optical extinction spectra. Au and Ag, which are well known plasmonic materials, can form a homogeneously face-centered-cubic (fcc) structure for any composition ratio of the metals (see the phase diagram in Fig. 1(a) , [25]) since they have similar atomic radii, lattice constants, and electronic structures. Nanoparticles of Au and Ag alloyed with different ratios were fabricated and characterized experimentally; their optical properties were modeled. New properties of the Au-Ag 50% mixture at near-IR wavelengths is explained by electronegativity and chemical bonding, which reduce electron scattering and losses in the near-IR region.
Fig. 1 Phase diagram of Au/Ag alloy. (a) Melting point values in the phase diagram are obtained from [25] and inset shows a photograph of bulk alloys with Au concentration ranging from 0% (pure Au), 16.7%, 50%, 70% and to 100%. (b) X-ray crystal diffraction spectroscopy of Au, Ag, and Au/Ag alloy (Au:Ag = 1:1).
2. Experimental details
Au/Ag alloy nanostructures are fabricated by electron-beam lithography (EBL) and lift-off [26–28]. Resist (ZEP520A, Zeon Co.) was spin-coated on to a glass substrate at 3000 rpm for 60 s. After baking at 180°C for 2 min, the surface of the resist was coated with a charge-dissipating agent (ESPACER-300Z, Showa Denko Co. Ltd.) for EBL. Circular patterns were drawn with a 50 kV acceleration voltage using the EBL system (ELS 7500EX, ELIONIX Inc.). After development in ZEP-RD (from Zeon Co.) for 1 min and being rinsed twice with ZMD-B for 15 s, a 2 nm layer of Cr or Ni was deposited as an adhesion layer, followed by a 35 nm layer of the alloy. In both cases, a vacuum evaporation system (VPC-410S, ULVAC Inc.) was used. During the metal deposition, due to the large difference in the boiling points and vapor pressures of Au and Ag, the alloy composition differed from that of bulk evaporation material. Therefore, a multi-step evaporation method was performed to obtain homogeneous alloys. The thickness of the metal evaporated in each process was less than 1 nm, which was determined by a quartz microvalance. (When we deposited a layer with more than 1 nm thickness, the extinction spectra showed unstable behavior) Next, lift-off was performed in the resist remover (ZDMAC, Zeon Co.) at 60°C for 3 min, and the device was then rinsed with acetone and methanol.
The resulting structures were characterized by a scanning electron microscope (SEM; JSM-7500F, JEOL Ltd.) and by energy-dispersive spectroscopy (EDS). The transmission spectrum was measured using a confocal microscope system combined with a standard optical microscope (10 times objective lens, NA = 0.5, the pinhole was 0.1 mm in diameter, Optiphoto2, NIKON Co.) and an optical spectrum analyzer (Q8381A, Advantest Co. Ltd.). The crystal form of alloy films was measured using X-ray crystal diffraction by the 2θ -θ method (RINT2500, Rigaku Co.). The optical constants of the film alloy metals were determined by reflection and transmission measurements. Transmission and reflection spectra for different film thicknesses were fitted by the least-linear-square method according to the Drude model [24,29] in the near-IR spectral range. Determined optical constants were used for the FDTD analysis using commercially available software (FDTD solutions, Lumerical Co. Ltd.) to simulate the extinction spectra and electromagnetic field enhancement.
3. Results and discussions
Figure 1(b) shows the thin film X-ray crystal diffraction measurement result. The fcc crystal structure of Au, Ag, and their alloy was determined by X-ray diffraction (XRD). In the case of the fcc crystal structures, XRD peaks appear at angles where all (hkl) values become even or odd. Here, for the 2θ span from 30° to 90°, we see 5 peaks characteristic of the (111), (200), (222), (311), and (222) planes. The atomic radii of Au and Ag are both 144 pm, while the lattice constants are 4.0788 and 4.0862 Å, respectively. Because of these similar crystal parameters, the diffraction peak position appears at similar angles. For the (111) orientation of the crystal, Au/Ag alloy peaks were linearly shifted by a slight amount with respect to the alloy composition, in accordance with Vegard's law [30].
Figure 2 shows scanning electron microscopy (SEM) and energy dispersion spectroscopy (EDS) images of the Au and Ag alloy nanostructures. From the EDS imaging result, the Au (peaks at 2.17 eV, M-shell) and Ag (peaks at 3.06 eV, L-shell) counts were collected. The results showed that nanostructures homogeneously include both Au and Ag within the EDS spatial resolution.
Figure 3 shows the extinction spectra of pattern of nanodiscs of the Au/Ag alloy. By keeping the size and periodicity of nanostructures the same for all compositions, nanodisc alloy was fabricated with seven different compositions and the corresponding extinction spectra were measured. Both 250 and 350 nm nanodiscs show similar behavior, and the spectrum is governed by a blue-shift as the Au mole fraction decreases from 100% to 75% and a red-shift at exactly 50% value; a blue-shift again governs the spectrum for a larger proportion of Ag (i.e., towards 100% Ag). This tendency was independent of the nanodisc diameter, as shown in Fig. 3(b). The spectral shift of the 250 nm nanodisc pattern was larger than that of the 350 nm nanodisc. This was due to a small change in the permittivity in this wavelength range. In addition, when we deposited a layer with more than 1 nm thickness, spectral behavior changed significantly. For example, the 50% spectrum was blue shifted by the largest extent. However, through annealing at 100°C, extinction spectrum easily shifted to longer wavelengths, similar to the case of the deposited layer with <1 nm thickness. Although this phenomenon required further investigation, during annealing treatment, the atom moved into a stable arrangement, and deposition with <1 nm layer thickness could be concluded to lead to well-mixed alloy formation.
Fig. 3 Extinction spectra of the Au/Ag alloy with various compositions and for 250 (a) and 350 nm (b) diameter nanodisc patterns; period is 450 nm, thickness of metal 35 nm.
In order to verify scattering results from the patterns of nanoparticles, experimental values of n, k were determined. Films were prepared with three controlled-thickness deposition values of 20, 30, 40 nm, and the transmission and reflection spectra were measured from 300 nm to 1600 nm for these films. From these spectral data, n, k, d were determined.
Figure 4 shows the experimentally determined n, k values of pure Au and Ag as well as the 50% Au/Ag alloy. The n, k values of arithmetical average of Au and Ag is also shown. The values for Au and Ag were obtained from the available literature. (In addition, we have checked that using our experimental setup, we obtain the same n, k values for the Au film as in the literature.) From UV to visible wavelengths, the experimentally obtained n, k values for the Au/Ag alloy were similar to those obtained by the averaging method. Optical properties in this wavelength range were caused by inter-band transition. The band-edge wavelength (a sharp transition feature) shifted continuously between Au and Ag according to their composition, and this agrees with previously reported results [9–20]. However, at wavelengths longer than 700 nm in the near-IR region, this behavior changed dramatically. In the experimental results, increase in the n and decrease in the k values, as compared to those of pure Au and Ag, were observed. To get further insights into these experimental results, FDTD simulations were performed using the experimentally determined n, k values. Simulations were performed with the following parameters: 250 nm nanodisc diameter, 35 nm thickness of metal (or alloy), and 450 nm periodicity of the pattern. The structure was excited by a plane- wave from the backside of the glass substrate, and the transmission monitor was positioned 15 nm above the nanodisc surface. Intensity monitors were positioned at the middle of the nanodiscs to observe the enhanced light intensity at the LSPR peak.
Fig. 4 The refractive index, n and k, of pure Au, Ag, and 50% Au/Ag alloy determined experimentally and the arithmetic average of pure Au and Ag reference data.
Figure 5 shows the extinction spectra and field enhancement obtained by FDTD simulations. The extinction spectra behavior from the FDTD simulations matched the experimental result almost perfectly. The experimentally obtained n, k values were compared with the arithmetic average of the Au/Ag alloy (shown as a dotted line in Fig. 5(a)). The results predict a blue-shift for a mole fraction change from Au to Ag. The experimentally observed spectroscopic properties of nanodiscs at near-IR wavelengths, where inter band transitions are negligible, can be explained by the optical properties of the alloy (determined by a separate thin-film measurement). To the best of our knowledge, this is the first observation of such behavior. In addition, electromagnetic field enhancement at the resonance peak was calculated and a strong field enhancement was observed at the edge of the nanodisc for a linearly polarized incident plane wave. Figure 5(b) shows a plot of the maximum intensity in the field enhancement map, which is shown in the inset of Fig. 5(b). For all alloy compositions, the enhancement factor was smaller than the arithmetic average, although at 50% Au composition, it was close to the value observed for pure Au.
Fig. 5 FDTD analysis of Au/Ag alloy with experimentally obtained (solid line) and arithmetical average of gold and silver (dashed line) n, k values: (a) extinction spectra, (b) electromagnetic field enhancement; the inset shows the field mapping of gold at peak wavelength of LSPR.
To understand this characteristic behavior of the 50% Au/Ag alloy, n, k values are analyzed by the Drude model:
where ε∞ is the value of ε1 at a high (infinite) frequency, ωp is the bulk plasma frequency defined as (Ne2/ε0m)1/2, and Γ = vf /l = 1 /τ is the collision frequency with τ being the relaxation constant; N is the density of free electrons, e is the electron charge, m is the effective mass of electron, vf is the Fermi velocity, which is 1.4 × 106 ms−1 in Au and Ag, and l is the mean free pass of electrons. The electronic conductivity σ0 = ωp2τ was determined. Intra-band absorption of Au and Ag determines the spectral properties of the alloy for wavelengths from UV to 500 nm, and therefore, we consider the wavelength region from 600 to 1600 nm, where inter-band transition is negligible and the Drude equation matches the experimental data well.Figure 6 shows the calculated ωp and τ for all alloy compositions. For the above three parameters and 50% alloy composition, ωp has a minimum value and τ is relatively large; further, σ0 shows a tendency similar to the mole fraction dependence of τ. ωp is a function of the electron density; τ and σ0 are related to the mean free path of electrons in the nanostructures of the alloy metal. These results indicate that electron damping in alloy is reduced at 50% composition. The plasmon resonance is the interaction of free electrons with the incident light, and the electron damping is directly connected to electromagnetic field enhancement. Typically, in the case of alloy formation, the electrical resistivity increases due to additional impurities because of an increase in the number of different scattering mechanisms. A resistance increasing caused by all the scattering interactions would be linearly combined, a so-called Matthiessen's rule [31,32]. Accordingly, it would be expected that a 50% Au/Ag alloy would have the smallest conductivity and relaxation time. Therefore, minimum field enhancement is expected for the 50% Au/Ag alloy. However, by FDTD simulations based on the experimentally determined n, k values, a field enhancement equivalent to that of pure Au was observed, and this is explained below.
Fig. 6 The plasma frequency and relaxation time, calculated by Drude model with experimentally determined values of n, k and by arithmetical average of gold and silver constants.
The chemical bonding between Au and Ag needs to be examined. Although Au and Ag have similar atomic radii and electronic structures Au: (5d)10(6s)1, Ag: (4d)10(5s)1. Differences between Au and Ag appear in terms of their electronegativity: 2.54 (Au) and 1.93 (Ag) in the Pauling scale, or 1.92 (Au) and 1.87 (Ag) in the Allred-Rochow scale [33,34]). When a chemical bond is formed between Au and Ag, an electron shift occurs as Auδ−-Agδ+, forming a closed-shell structure. The ordering revealed itself as the smallest plasma frequency (see Fig. 6), which is also related to the high free electron density value. When a chemical bond is formed, some of the free electrons are bound between Au and Ag. In addition, a symmetrical bond formation is implied at the 50% of Au and Ag. Their lattice constants are slightly different, and only at a 50% mole fraction can the atoms be ideally ordered with alternating neighbors and pure Au-Ag bonds are established. At different molar fractions, other Au-Au and Ag-Ag bonds appear, and this facilitates distortion and extra scattering as all the three possible bonds have slightly different bonding lengths. Therefore, the crystal structure would be distorted from the ideal fcc structure. This distortion would increase the scattering of electrons, as discussed above.
For understanding the complicated spectroscopic behaviors seen in Figs. 4 and 5, further FDTD calculations were carried out. Extinction spectra of LSPR can be described by the Mie scattering theory [35,36] and are defined by the permittivity of metals, surrounding media, and volume of nanostructures. For simulations, the permittivity of the metal was defined by the values of ωp and τ; for Au, ωp = 13.8 × 1015 s−1 and τ = 9.3 × 10−15 s. Results of the simulations are shown in Figs. 7(a) and 7(b). When ωp varied at a fixed value of τ, the values of ε1 were significantly reduced for an increasing ωp. At the same time, ε2 slightly increased and was less sensitive to ωp. If τ is altered for a fixed value of ωp, ε1 remains almost constant and ε2 decreases. Using these parameters, the extinction spectra of LSPR, with the same geometry as shown in Fig. 5, were calculated (Fig. 7(c)). An increase in ωp causes a blue-shift of the extinction spectra; however, τ and ε2 are less affected by the spectral shift. The spectral shift also affects the light field enhancement. The calculations show that ωp (or ε1) is a dominant parameter for the experimentally observed LSPR spectral shift shown in Figs. 4 and 5.
Fig. 7 (a) The ε1 and ε2 dependence on the ωp with fixed τ ( = 9.3 × 10−15 s) and ωp = 12.0 ~15.5 × 1015 s−1; (b) with fixed ωp ( = 13.8 × 1015 s−1) and τ = 5.56 ~50.0 × 10−15 s. (c) Extinction spectra obtained by FDTD calculations with permittivity values modeled in (a) and (b).
4. Conclusion
Systematic investigation of the optical constants of the Au/Ag alloy and optical properties of alloy nanostructures was carried out. Optical constants of the Au/Ag alloy differ from the arithmetic average of the refractive indices of Au and Ag, especially in near-IR wavelength region. In contrast to the case of typical alloy formation, when electronic conductivity and relaxation time are reduced by the addition of impurities and electron scattering, which also result in a reduction of light field enhancement, an unexpected and opposite behavior is observed at near-IR wavelengths with 50% mole fraction. It was found that at a 50% Au/Ag mole fraction, scattering is reduced (and light enhancement is increased) at near-IR wavelengths. This is confirmed by experiments and numerical simulations, using experimentally determined optical constants. It was found that ωp strongly affects the LSPR spectra. This can be explained by the electronegativity difference and chemical bond formation of the metals. Metals with extremely different electronegativity values would result in a decrease in the value of ωp. Therefore, such metal alloy is expected to have large wavelength tunability. Electromagnetic field enhancement is very sensitive to the ordering of the crystal. Atomic radii, bond lengths, and crystal morphology can all be contributing factors to the scattering of electrons.
Chemical stability of alloy nanostructures is a promising feature for practical applications. Silver nanostructures are easily oxidized or sulfurized in an atmospheric environment; Ag nanorod structures break after two months of exposure to the atmosphere [37,38]. Alloying with Au drastically increases its stability, where more than 25% of Au concentration prevents oxidation at 100°C for 1 h. Further studies on alloying at the nanoscale level are required to obtain a better understanding of crystallography. The obtained results are helpful in new material design and in the control of plasmon resonance and chemical stability.
Acknowledgments
The authors thank Otsuka Electronics Co., Ltd. for measurements of the alloy optical constants. The authors also thank Prof. T. Baba (Yokohama National University) for the fruitful discussions and supporting facilities. Y. N. thanks Prof. S. Juodkazis (Swinburne University of Technology) for the fruitful discussions, Profs. H. Misawa and K. Ueno (Hokkaido Univ.) for the initial explanation of the fabrication methods. This work was financially supported by the Ministry of Education, Culture, Sports, Science, and Technology: KAKENHI Grant-in-Aid for scientific research, the Yokohama Academic Foundation, and the Research Foundation for Optical Science and Technology, Hamamatsu, Japan.
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