Patterned nanoporous-gold thin layers: Structure control and tailoring of plasmonic properties

Microporous and Mesoporous Materials 163 (2012) 153–159

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Patterned nanoporous-gold thin layers: Structure control and tailoring of plasmonic properties G. Ruffato a,b,c,⇑, D. Garoli b,c, S. Cattarin d, S. Barison d, M. Natali e, P. Canton f, A. Benedetti f, D. De Salvador a, F. Romanato a,b,c a

Department of Physics ‘‘G. Galilei’’, Padova University, via Marzolo 8, 35131 Padova, Italy LaNN Laboratory for Nanofabrication of Nanodevices, VenetoNanotech, Corso Stati Uniti 4, 35127 Padova, Italy Istituto Officina dei Materiali IOM-CNR, Area-Science Park, Basovizza 34012, Trieste, Italy d Institute for Energetics and Interphases (CNR-IENI), Corso Stati Uniti 4, 35127 Padova, Italy e Institute for Inorganic Chemistry and Surfaces (CNR-ICIS), Corso Stati Uniti 4, 35127 Padova, Italy f Department of Molecular Sciences and Nanosystems, Università Ca’ Foscari Venezia, Via Torino 155, 30170 Venice, Italy b c

a r t i c l e

i n f o

Article history: Received 4 May 2012 Received in revised form 28 June 2012 Accepted 10 July 2012 Available online 17 July 2012 Keywords: Nanoporous gold Dealloying Metallic gratings Surface plasmon polaritons (SPPs)

a b s t r a c t Nanoporous gold (NPG) layers have been fabricated by silver leaching of Ag–Au alloys with different dealloying processes and working temperatures. Structural, compositional and optical properties of the different samples have been analyzed with several experimental techniques: scanning and transmission electron microscopy (SEM/TEM), electrochemical impedance spectroscopy (EIS), Rutherford back scattering (RBS), spectroscopic ellipsometry. A periodic pattern has been realized on samples surface with focused ion beam (FIB) lithography in order to exploit NPG metallic behavior for surface plasmon polaritons (SPPs) excitation. The plasmonic response of the several NPG gratings has been analyzed and related to structural properties and fabrication conditions. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Nanoporous gold (NPG) has known a growing interest in last decades due to its potential applications in such areas where the concomitance of a high surface-to-volume ratio and the noblemetal chemistry provides benefits in performance and activity: actuation [1], catalysis [2], supercapacitance [3], sensing [4]. This material exhibits a 3D bicontinuous porous structure from few tens to hundreds of nanometers scale [5] which is originated by a spontaneous pattern formation during the selective leaching of the less noble metal from Au alloys [6,7]. This process results in a sponge-like material with a large surface-to-volume ratio and a lower free-electron density that exhibits a metallic behavior below the near-infrared range and thus can support excitation and propagation of surface plasmon modes. Plasmonic properties of nanoporous gold films have been previously shown in recent papers. For example, Yu et al. [8] demonstrated excitation of both propagating and localized surface plasmon resonances in NPG membranes. Dixon et al. [9] reported surface plasmon resonances in

⇑ Corresponding author at: Department of Physics ‘‘G. Galilei’’, Padova University, via Marzolo 8, 35131 Padova, Italy. E-mail addresses: [email protected], [email protected] (G. Ruffato). 1387-1811/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.micromeso.2012.07.027

ultra-thin films of supported nanoporous Au, and Maaroof et al. [10] showed that the plasmonic behavior of nanoporous gold films can be tuned by controlling the porosity through the initial gold fraction in the selected alloy. In those papers however, surface plasmon polariton (SPP) excitation was performed in the Kretschmann’s configuration where a prism is employed in order to couple illuminating radiation with surface plasmon modes. The cumbersome prism presence and the related alignment problems can be overcome with a periodic patterning of the metallic surface that couples diffracted light and offers a solution which is more suitable to miniaturization and embodiment. The aim of this work consists in the analysis of the plasmonic response of patterned nanoporous gold films which have been fabricated from silver leaching of the same initial Ag–Au alloy with different dealloying techniques and working temperatures. After dealloying process, the surface has been patterned with a periodic grating in order to excite surface plasmon polaritons (SPPs). The plasmonic behavior has been studied in order to highlight its dependency on the nanoscale structure which is strictly related to fabrication conditions. In particular, the working temperature is shown to affect the porosity features and thus to represent a preparation parameter effective in tuning the position of the plasmonic range. In this way, starting from the same composition of the initial alloy, it is possible to obtain nanoporous samples with the same gold fraction but different optical properties: a different geometry of gold ligaments and pores

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affects the free-carrier oscillation inside the metal and thus gives a different metallic response. The optical behavior and the greater effective surface make nanoporous gold a promising material for plasmonic applications, e.g., the realization of label-free, real-time, miniaturized analytical sensors in a large variety of fields: environmental protection, biotechnology, medical diagnostics, drug screening, food safety and security [11]. 2. Materials and methods 2.1. Sample preparation and dealloying Rectangular glass substrates were thoroughly degreased in boiling acetone and dried. A 10 nm Cr layer was deposited on glass as an adhesion promoter. Subsequently a Au layer about 100 nm thick was deposited over Cr. Both these depositions were performed, using a BOC Edwards E306 facility, in high vacuum (1  106 mbar) by means of thermal evaporation at a deposition rate of 0.1 nm/s. Finally, a layer about 240 nm thick of Ag75Au25 alloy was deposited in a DC turbo sputter coater (Emitech K575X, Emitech Ltd., Ashford, Kent, UK), using a silver/gold alloy sputtering target Ag62.3/ Au37.7 wt.%, GoodFellow. The sputtering was performed at room temperature under Ar gas flow at a pressure of 7  103 mbar and a DC sputtering current of 25 mA. The composition of alloy (Ag75Au25) was selected on the basis of literature reports, indicating that: (i) 20 at.% Au content is a practical lower limit to warrant a tough porous material [12], whereas at lower Au content the porous structure generated by dealloying tends to fall apart; (ii) above 26 at.% Au the dissolution of Ag atoms is partial and a substantial amount of Ag remains buried, unaffected by dissolution, in the nanoporous structures [13]; (iii) samples with Au content of 28 at.% or higher undergo anodic dealloying only upon application of high potentials, inducing oxidation of surface Au atoms and formation of a low-quality, brittle gold layer. Hence, for most purposes the range 22–25 at.% Au is optimal, and we selected the upper limit to get the denser final material. The dealloying process was performed with two alternative procedures: (i) chemical, exposing the samples to a concentrated HNO3 solution (65%, Fluka puriss. pro analysis) for 4 h at 20 °C (sample Ca) or 1 h at 65 °C (sample Cb); (ii) electrochemical, performed anodising the electrodes at the constant potential E = 0.980 V vs a saturated calomel electrode (SCE), in 0.1 M HClO4 (made up from 60% HClO4, Fluka puriss. pro analysis), for 2 h at 20 °C (sample Ea) or 30 min at 65 °C (sample Eb), using electrochemical cell, apparatus and procedures already described elsewhere [14,15]. Each sample was then washed in two steps, first in a fresh 0.1 M HClO4 solution (1 h), then in distilled water (2 h), gently dried in a nitrogen stream and stored. 2.2. Scanning electron microscopy Scanning electron microscopy (SEM) micrographs were performed, with a semi-in-lens cold cathode field emission scanning electron microscope source of a dual beam FEI Nova 600i instrument. Micrographs were taken at about 10 kV accelerating voltage, using in-lens detector in pure secondary electron signal mode. 2.3. Transmission electron microscopy High-resolution transmission electron microscopy (HRTEM) measurements have been done on a Jeol JEM3010 instrument operated at 300 kV, LaB6 cathode, resolution at Scherzer defocus 0.17 nm. Digital HRTEM images were recorded with a Gatan Multiscan CCD camera MSC794 (1024  1024 pixels, pixel size 24  24 micron, gain corrected and antiblooming enabled).

Specimens for TEM analysis were prepared using mechanical polishing, dimpling and low-angle Ar-ion milling. 2.4. Rutherford back-scattering Composition measurements were carried out by Rutherford back-scattering spectrometry (RBS) at the CN accelerator at LNLINFN Laboratories (Legnaro, Italy) using 2 MeV 4He+ beam. The backscattering angle was 170 degrees. Analyses were performed by means of a homemade simulation code implementing standard equations for RBS spectra calculation. In order to distinguish between the gold signal coming from the NPG and that coming from the above Au layer, spectra where also collected on the bare Au– Cr–glass substrates. The simulations of these spectra were used as a fixed starting point to simulate the full sample. 2.5. Focused ion beam lithography FIB lithography was performed by means of the ion source of the FEI Nova 600i dual beam system. The instrument allows performing high resolution millings with heavy Ga+ ions under acceleration voltage up to 30 kV and with ion current variable from 1.5 pA up to 21 nA. In our experiment we used a 30 kV accelerating voltage and a beam probe current of 280 pA. Digital grating arrays over an area 640  640 lm large were fabricated with a single exposure. The geometry of the grating (duty cycle, period and thickness of the walls) was fixed in order to obtain a plasmonic resonance in the near infrared (near-IR) spectral range. When a metallic grating is designed in order to support propagating plasmonic modes, the pattern period should be of the same order of the illuminating exciting wavelength: typical grating period is about 500 nm for an evaporated gold surface [16]. Since nanoporous gold exhibits a redshift of metallic behavior (see results section), the pattern must be properly dimensioned. A numerical code implementing the rigorous coupled-wave analysis (RCWA) [17] was written in MATLAB environment and simulations of the reflectivity response have been performed in order to select the proper grating period and amplitude that optimize the coupling of the incident light with SPP modes. Taking into account nanoporous gold optical properties in terms of complex refractive index, gratings about 60 nm thick with a period of 1000 nm (duty cycle 0.5) have been designed and patterned on the fabricated samples. 2.6. Spectroscopic ellipsometry Spectroscopic ellipsometry between 300 and 2400 nm (10 nm step) was recorded with VASE Spectroscopic ellipsometer (J.A. Woollam). The goniometer controlled optical bench was set at three different angles of incidence on the sample (50°, 60°, 70°) and ellipsometric angles w and D were recorded in the rotating-polarizer analysis setup (Rotating analyzer ellipsometry – RAE) [18]. Data were analyzed with W-VASE software (J.A. Woollam). A comparative ellipsometric analysis of bare Au–Cr–glass substrate and nanoporous gold samples allows extrapolating the complex permittivity e1 + ie2 and thus the complex refractive index n + ik of nanoporous gold. Reflectivity spectra were acquired with an angular and wavelength spectroscopic resolution of 0.005° and 0.3 nm respectively, using the ellipsometer monochromatized 75 W Xe lamp. 3. Results and discussion 3.1. Chronoamperometric curves Fig. 1(a) shows examples of the chronoamperometric curves recorded in electrochemical experiments, using a logarithmic time

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function of time in Fig. 1(b), shows for the process performed at higher temperature larger intermediate and final values, indicating more rapid and more exhaustive Ag dissolution: anodization at 65 °C actually involves a total charge somewhat above the theoretical value of 175–180 mC cm2, possibly due to some oxidation of the Au surface. 3.2. Porosity analysis

Fig. 1. Time evolution of (a) current density j and (b) integrated charge Q during anodic treatment of Ag75Au25 alloy in 0.1 M HClO4, at E = 0.98 V vs SCE, T = 20 °C (sample Ea) and T = 65 °C (sample Eb).

scale to better show phenomena occurring soon after closing the circuit. The current evolution suggests an intuitive division of the dissolution process in three main steps: rapid Ag dissolution from the outermost alloy layers; progress of dissolution towards deeper regions of fresh alloy, until reaching the back gold substrate; slow dissolution of residual Ag from the depleted alloy. Comparison of experiments at 20 °C and at 65 °C shows that the latter conditions give larger current in the first minute, and a more rapid decay at longer times. The integrated dissolution charge, reported as a

3.2.1. Electrochemical impedance spectroscopy For each sample the porosity has been evaluated with electrochemical impedance spectroscopy (EIS) by estimating the roughness factor, namely the ratio fr = Ar/Ag between the measured surface area Ar and the corresponding geometric area Ag of an ideally flat sample, assumed equal to the ratio between the respective capacities in the low frequency domain (fr ffi Cr/Cg) [19]. EIS measurements were taken using a Solartron 1254 frequency response analyzer and a Solartron 1286 Electrochemical interface, both controlled by a ZPlot-ZView commercial software. The frequency range 20 kHz to 0.1 Hz was explored with 8 points per decade. The double layer capacitance is estimated as the value of the quantity [2pfZ’’]1 at f = 8.4 Hz, in the frequency range typically extending from 50 to 0.2 Hz in which the imaginary impedance Z’’ shows an almost ideal dependence on frequency (slope close to 1.0 in the log – log plot), and compared with the capacity of a smooth gold surface. 3.2.2. Porosity estimation from SEM inspection SEM analysis has been used to get estimations of average pore size and film thickness (Fig. 2). In samples fabricated at room temperature the diameter of gold ligaments is around 12 nm for chemical (Ca) and 15 nm for electrochemical dealloying (Ea). Samples fabricated at higher temperature present a coarser structure and ligament size rises up to 36 nm and 41 nm for chemical (Cb) and electrochemical (Eb) samples, respectively (Table 1). In fact the high temperature is supposed to increase Au atoms mobility

Fig. 2. SEM micrographs of nanoporous gold surface: Chemical sample Ca(T = 20 °C) and Cb(T = 65 °C). Electrochemical samples Ea(T = 20 °C) and Eb(T = 65 °C).

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Table 1 Properties of NPG samples: average pore size from SEM inspection; roughness factor fr from capacity evaluation by EIS; void fraction vf and residual silver fraction from RBS analysis.

Pore size(nm) fr vf (±0.05) Ag %(±3)

Ca

Cb

Ea

Eb

12 35.9 0.61 11

36 11.6 0.64 7

15 28.5 0.61 16

41 13.3 0.68 2

during the dealloying process and to promote gold ligaments growth. Pore-size values are reported in the 1st row of Table 1 and basically correlate with the roughness factor fr (Table 1, 2nd row): if the size increases, the roughness factor decreases, although other factors may influence the result (compare e.g. samples Cb and Eb). 3.2.3. Density analysis from RBS measurements and TEM inspection The dealloying process entails a significant volume contraction, estimated at about 20% for bulky samples [20] and thin films [21] of composition similar to ours. Using this value, the effective density of the NPG is estimated as 0.25/0.80 ffi 0.31 relative to the density of bulk gold, corresponding to a void fraction of about 0.69. This value may be compared with the values in Table 1, estimated from RBS analysis: the agreement is good (void fraction ca. 0.68) for the sample Eb, showing little residual Ag, whereas for the other samples the decrease of void fraction is qualitatively consistent with the increased fraction of residual silver. Analyses of RBS measurements allow estimating the Au and Ag atomic areal density in the porous layer DAu and DAg. There are two contributions to the total measured dose associated to gold atoms: the gold in the ligaments of the porous structure and the bulk gold beneath in the substrate. Once the contributions are distinguished, from the knowledge of the thickness of the two layers it is possible to evaluate the gold fraction in the nanoporous layer. Assuming a volume density of the bulk fraction of the NPG layer equal to the Au volume density (NAu) and considering the real thickness of the layer as measured by SEM images, tSEM, it is possible to evaluate the fraction of void vf in the NPG according to the relation: vf = 1  (DAu + DAg)/(NAu tSEM). This formula is a good approximation considering the very small difference in atomic density between AuAg alloy and Au. In fact, for an alloy sample with a gold content of 25 at.% the lattice parameter is aAlloy = 4.0763 A, slightly lower than in bulk gold where the lattice parameter is aAu = 4.0784 A [22]. This results in an atomic density variation of the alloy with respect to bulk gold in the order of 0.16 %, which is quite negligible.

The results of the previous analysis are reported in the 3rd row of Table 1. As can be noted the data are about 0.64 in good agreement with what expected on the basis of the above considerations and quite independent on the NPG production procedure. Moreover DAg/(DAu + DAg) quantifies the residual concentration of Ag that is reported in the last row of the table. As can be noted from these data, the high temperature promotes silver dissolution while at room temperature chemical dealloying seems to be more efficient than electrochemical technique in silver etching. TEM analyses (Fig. 3) confirm that each gold ligament presents a solid structure without any air inclusion inside it. The high resolution inspection in Fig. 3(b) shows the polycrystalline nature of gold ligaments after dealloying process. 3.3. Plasmonic response of nanoporous-gold gratings If a metallic grating is illuminated with fixed wavelength k and varying incident polar angle h, a reflectivity dip appears in correspondence of the incidence angle hres for which the momentumconservation law on the grating plane is satisfied [23]: ðinÞ ~ kSPP ¼ ~ kjj  n  ~ G

ð1Þ

where ~ kSPP is the wavevector of the excited SPP, kjj ¼ 2kp sin hres is the on-plane component of the incident light wavevector, G ¼ 2Kp is grating momentum, where K is the grating periodicity. Since grating period K is typically comparable and lower than the incident wavelength, in our cases of interest the resonance order is usually n = 1. For a given grating profile, dip features such as width, depth and position strictly depend on the properties of the supporting material, i.e., optical constants of the nanoporous gold layer. Reflectivity measurements have been collected on the patterned zone (Fig. 4) in a h/2h symmetric configuration, with wavelength k scanned from 1250 to 1530 with step size of 5 nm, at fixed incident angle h = 20° (Fig. 5). In the considered wavelength range, resonance broadening and position seem to be mainly affected by sample porosity. Samples fabricated at higher temperature (Cb , Eb) exhibit a broader resonance with respect to samples fabricated at room temperature (Ca , Ea). Comparing samples at room temperature, sample Ea shows a lower width than sample Ca, possibly because of the greater percentage in residual silver (16% versus 11%). The resonance broadening in samples Cb and Eb, prepared at T = 65 °C, as compared to samples prepared at room temperature, is mainly related to the different structure: coarser ligaments and larger pores result in an increase of dissipation sources and in a consequent decrease of surface plasmons life-time. In samples Ca and Ea resonance wavelength kres is around 1380 nm and it is shorter than in samples Cb and Eb, where it is near 1410 nm. Dip

Fig. 3. TEM analysis of gold ligaments structure of sample Eb.

ðinÞ

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Fig. 4. SEM micrograph of sample Eb patterned area, period 1000 nm, duty-cycle 0.5.

Fig. 6. Dispersion curve E(eV)  kSPP(nm1) for surface plasmons polaritons on nanoporous gold gratings and comparison with bulk gold grating (red solid line). Patterned NPG samples fabricated with different techniques and temperatures T: chemical samples Ca (T = 20 °C, black solid line) and Cb (T = 65 °C, black dashed line), electrochemical samples Ea (T = 20 °C, blue solid line) and Eb (T = 65 °C, blue dashed line). Grating period 1000 nm, duty-cycle 0.5, amplitude 60 nm.

yellow color and plasmonic properties in the visible range. In contrast, nanoporous gold films do not become plasmonic at visible wavelengths but rather in the near IR, depending on void content and structure, i.e., pore size. Results of ellipsometric analysis highlight different optical properties for samples prepared with different dealloying processes and temperatures (Fig. 7). In order to understand how the plasmonic response changes with the preparation technique, we examine the effective frequency-dependent dielectric function e(x). In the range from near-UV to IR, the permittivity is well described with a Lorentz-Drude model: Fig. 5. Reflectivity for wavelength scan in the range 1250–1530 nm with step size 5 nm for fixed incidence angle of 20°. Comparison of the reflectivity response between a non-patterned NPG surface (green solid line) and patterned NPG samples fabricated with different techniques and temperatures T: chemical samples Ca (T = 20 °C, black solid line) and Cb (T = 65 °C, black dashed line), electrochemical samples Ea (T = 20 °C, blue solid line) and Eb (T = 65 °C, blue dashed line) . Grating period 1000 nm, duty-cycle 0.5, amplitude 60 nm.

position seems to mainly depend on fabrication temperature rather than on the dealloying technique. For each sample, reflectivity spectra have been collected with different incident wavelengths k in the range 1350–1650 nm, step size 50 nm, for angle h interrogation from 15° to 40°, step 0.1°. Resonance polar angle hres shifts toward greater values for increasing wavelength and it is possible to reconstruct SPP dispersion curve x  k (energy VS wavevector). For each incident wavelength k, SPP momentum kSPP has been calculated from resonance position hres by applying the equation of momentum conservation for grating coupling Eq. (1). In Fig.6 experimental data points of SPP dispersion curve are plotted for each sample. NPG curves differ from the dispersion relation of bulk gold and curves for samples with the same dealloying temperature overlap. This result implies, as expected, a dependence on pore size and thus on the fabrication temperature, rather than on the dealloying technique. For a given energy, SPP momentum increases with pore size, i.e., the fabrication temperature. 3.4. Analysis of nanoporous-gold optical response Fully dense gold films exhibit a negative dielectric constant in the optical range for wavelengths above 550 nm. The result is the

eðxÞ ¼ e1 þ eUV ðxÞ þ eD ðxÞ þ eIR ðxÞ ¼ e1  x2 x2AUV þixx UV

s;UV

x2

p  x2 þixx

s;D

IR  x2 x2Aþi xx IR

ð2Þ

s;IR

where e1 takes into account the constant contribution to polarization due to d band electrons close to the Fermi surface. eUVx is a Lorentz oscillator of amplitude AUV that describes the 3d energy band-to-Fermi Level interband transition centered at a frequency xUV in the UV range with a band-width xs,UV.. eDx represents the Drude contribution due to free s-electrons, with plasma frequency xp and relaxation time s = 2p/xs,D. The last term eIRx is added in order to describe the behavior of the dielectric response in the near IR range and it is associated to the excitation of localized surface plasmons. This contribution has been modeled with a Lorentz resonance with amplitude AIR, centered at a frequency xIR in the near-IR range with a band-width xs,IR. For each sample, the permittivity values calculated from ellipsometric analysis have been fitted with the oscillator model of eq. 2 in order to get an estimation of the fitting parameters. Results are collected in Table 2 and are compared to bulk gold (data from Palik [24]). In nanoporous gold the intraband absorption term in the UV range is weaker than in bulk gold: inside gold ligaments each Au atom interacts with much fewer atoms than in bulk metal and this results in a discretization of dipole transitions between sp electron eigenstates and so in the weakening or disappearance of the transition of d electrons to the conduction band [9]. The reorganization of gold atoms also affects the relaxation time s of free carriers in the Drude term which is shorter than for bulk gold, since it is related to the scattering processes in the material. The

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free-charge density N is much lower than expected on the basis of the (full) metal fraction in the sponge. In sample Cb for example, fabricated by chemical dealloying at T = 65 °C, the free-electron density is 5% the bulk gold value NAu and it is about half the density for sample Ca, fabricated at room temperature with the same process. The resulting free-charge density is lower than the expected 33% of bulk gold and moreover it results quite different in samples fabricated at different working temperatures. A Maxwell–Garnett (MG) approach can be employed to model the effective dielectric constant of nanoporous layer by assuming the medium as a system of void inclusions into a continuous gold matrix [26–27]. Typically associated with the MG model [27], the geometric effect is taken into account with a corrective parameter L, the effective depolarization factor, that describes the optical response of the inclusions and depends on their shape and structure (e.g., L = 1/3 in the case of spherical inclusions). The resulting relation between the effective free electron density NNPG in nanoporous gold and the free charge density NAu of bulk gold is given by [26]:

mf NNPG ¼l¼1 NAu 1  Lð1  mf Þ

Fig. 7. Dielectric permittivity real part e1 and imaginary part e2 from ellipsometric analysis. Comparison between evaporated gold (data from Palik) and nanoporousgold chemical (Ca and Cb) and electrochemical (Ea and Eb) samples.

Table 2 Estimated parameters of optical models (Eq. 2–4). Parameters defined in Section 3.4.

e1 xp[eV] s [fs] AIR[eV2] xIR[eV] xs,IR[eV] AUV[eV2] xUV[eV] xs,UV[eV] N [1021 cm3]

l

vf L

Ca

Cb

Ea

Eb

Bulk Au

2.04 3.04 6.05 4.63 1.25 1.66 24.95 4.79 4.49 6.73 0.13 0.61 0.75

1.69 1.96 4.32 7.23 1.32 2.09 28.18 5.18 3.51 2.79 0.05 0.64 0.89

2.11 3.59 4.86 1.95 1.50 0.93 45.73 5.01 6.52 9.35 0.18 0.61 0.65

1.63 2.26 3.46 6.73 1.55 2.06 28.50 5.11 3.82 3.70 0.07 0.68 0.85

5.92 8.36 10.05 Abs Abs Abs 86.65 4.71 3.15 50.78 1 0 -

effective density NNPG of free carriers in nanoporous gold can be estimated from plasma frequency [25] xp:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi NNPG e2 xp ¼ me0

ð3Þ

where e and m are electron charge and mass and e0 is the void permittivity. As expected, free-charge density is lower in nanoporous gold samples than in bulk gold obviously because of the lower metal fraction. Although the void fraction vf is almost the same for all samples and around the value 2/3 (see Table 1), the effective

ð4Þ

where vf is the void fraction. By inserting into eq. 4 the values of void fraction from RBS measurements and the free-charge density ratio l calculated from the previous optical analysis, it is possible to get an estimation of the depolarization factor L for each sample (see Table 2). Samples fabricated at the same working temperature, although with different dealloying processes, exhibit similar depolarization values. The average factor is L0.9 for samples fabricated at higher temperature and results greater than the average value L0.7 for the same dealloying processes at room temperature. As expected from eq. 4, the free-charge density ratio l decreases for increasing depolarization L, at fixed void fraction vf. In fact the free-carrier density NNPG, and consequently the plasma frequency xp, is lower for samples fabricated at higher temperature, i.e. with coarser ligaments and larger pore size, while porosity (intended as the void fraction of the porous material) and the average sample density is about the same. Clearly gold ligament size and shape affect the effective free-electron density and this results in different optical response and metallic behaviour.

4. Conclusions Nanoporous gold samples fabricated with chemical and electrochemical dealloying at two different temperatures (20 and 65 °C) show structural and optical properties depending markedly on the processing temperature and little on the dealloying technique: the higher working temperature causes coarsening of the porous structure, producing a material with lower free charge density showing a redshift of plasmonic properties and different optical response. Thus by acting on the temperature of the dealloying procedure it is possible to tune the plasma frequency of nanoporous gold and control the position of the plasmonic range. Patterning of nanoporous gold surfaces with lithographic techniques provides plasmonic platforms with an enhanced surface-to-volume ratio and a working optical range that can be selected by properly acting on the fabrication parameters. The possibility of tuning the position of the plasmonic response may be interesting in applications, e.g. whenever the illuminating source has a fixed emission range to be exploited for SPP excitation. Acknowledgements This work has been supported by a Grant from ‘‘Fondazione Cariparo’’ – Surface PLasmonics for Enhanced Nano Detectors and

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