Spectroscopic ellipsometry modelling of thin AuSn films and nanostructures as plasmonics materials

A considerable interest in nanostructured thin films from intermetallic compounds of noble metals (Ag and Au) and post-transition metals is raised due to their unique plasmonic properties, which makes them potential materials for application in photonics, catalysis and biosensing systems. In this work the possibility for deposition of polycrystalline AuSn thin films was investigated, as thin films with the same composition and different thicknesses (10-100 nm) were obtained by co-depositing of Au and Sn metals. The chemical composition was determined by X-ray microanalysis. The X-ray diffraction patterns indicated formation of the intermetallic compound AuSn in the thin films. The complex permittivity ε = ε′ - i.ε″ of the thin AuSn films as function of the thickness was investigated by spectroscopic ellipsometry. The possibility for application of nanostructures from the AuSn intermetallic compound as suitable substrates for the needs of surface-enhanced Raman and fluorescence spectroscopy in the spectral interval 2.8 - 4.7 eV was analysed.


Introduction
The use of intermetallic alloys of gold and silver with post-transition metals is one of the ways for manipulation of plasmon resonance in such nanostructures to higher photon energies [1,2].The alloys from the Au-Sn system and the nanoparticles prepared from them are characterized by high conductivity [3,4] and variation of the plasma frequency in a wide spectral interval [5].The Au/Sn nanoparticles demonstrate selectivity with respect to some organic compounds [6] and find application in synthesis of semiconducting metal oxide nanostructures [7].The phase diagram of the Au-Sn system shows that gold and tin form several intermetallic compounds (Au 5 Sn, AuSn, AuSn 2 and AuSn 4 ) [8].Their high ordered structures suggest that they may be potential plasmonic materials with good efficiency [1,9].The density functional theory calculations, presented in [10], predict better performance as plasmonic materials in the ultraviolet spectral (UV) region of intermetallic compounds of gold with Al, Cd, Mg, Sn and Zn.Thus, the preparation of such thin films or nanostructures is a challenge.
The main method for obtaining of thin Au-Sn films is deposition of double-layer coatings of gold and tin [7,10].A major disadvantage of using thicker coatings is that due to the large diffusion coefficients of Au and Sn, different intermetallic phases of the two metals may be formed.The formation of particular intermetallic phases in Au/Sn bilayer coatings built by thin layers of gold and tin with thicknesses of ~20 -50 nm depends significantly on the deposition rate and the heating temperature of the coatings [10].The synthesis procedure of nanoparticles with different Au and Sn content is reported in [5] as the addition of tin to the gold nanoparticles leads to a shift of their absorption maximum to shorter wavelengths [11].
The aim of the present work is to obtain thin nano-sized layers of the AuSn intermetallic compound by depositing very thin layers of Au and Sn, to investigate the thickness dependence of their optical properties, and in the case of formation of island microstructure due to small thickness of the coatings, to observe the so-called size effect in the complex permittivity values.The plasmonic properties of thin AuSn films will be evaluated on the basis of calculated spectra of complex permittivity and their applicability as amplifying substrates for surface-enhanced Raman spectroscopy tests will be checked.

Experimental details
In order to obtain thin films with a precise stoichiometry, we deposited a set of multilayered specimens with foreseen solid state synthesis of the hexagonal AuSn compound, by thermal evaporation in vacuum (residual pressure of 10 -3 Pa) using a suitable holder and adjustable screening masks allowing deposition of several samples in one vacuum cycle at the same conditions of the Au and Sn fluxes, which provides thin films with the same composition and different thicknesses.Further information about the deposition method can be found in [12].The foreseen thicknesses were realized by variation of the number of sublayers.During the deposition of each sublayer, the rate of evaporation and the amount of substance deposited per unit surface area for each metal was controlled -8 μg/cm 2 for Au and 6 μg/cm 2 for Sn.Due to the odd number of the sub-layers into the coatings, in order to maintain the stoichiometry, the first and last layers from gold were half of the whole needed substance.
The chemical composition of the samples was determined by energy dispersive X-ray microanalysis using a scanning electron microscope SEM Philips 505 with an EDAX 9100 microanalyzer.The phase analysis of the Au-Sn films was realized from experimental XRD patterns, taken using an X-ray diffractometer Philips 1710 with CuK α irradiation (λ=0.15406nm) in the Bragg angles (2θ) range from 20° to 60° (step of 0.03°), using the JCPDS database as reference.The complex permittivity of the films was examined by a spectroscopic ellipsometric platform UVISEL 2 (Horiba Yvon) in the spectral range of 0.6-6.5 eV at an angle of incidence of 50°, 60° and 70°.Fluorescence measurements of 0.1 wt.% water solution of tryptophan were performed on a USB4000 Ocean Optics spectrometer with an optical waveguide and 254 nm emission line of Hg lamp.Raman spectroscopic measurements were carried out on the same equipment using excitation line at 488 nm of Ar-laser with intensity 60 mW/cm 2 .The analyzed samples were prepared using thin AuSn films as substrate and one drop of approximately 0.5 mL of L-Tryptophan water solutions with different concentrations.

Results and discussion
The X-ray microanalysis results showed good agreement between the theoretically calculated and the experimentally determined composition of the thin films.The thicknesses of the samples are in the interval between 10 -100 nm, as they were determined by ellipsometric measurements, except for the 100 nm coating, where due to the large thickness and the high absorption, a profilometer was also used.These results, as well as the number and thicknesses of the sublayers, are presented in table 1.
The further XRD study showed that a chemical reaction occurred between the Au and Sn elements and the foreseen AuSn compound was successfully synthesized, as its peaks appear on the XRD patterns [JCPDS 08-0463] together with an insignificant amount of Au 2 O 3 [JCPDS 71-0579] was also seen, which logically increases with the decrease of the thickness and some peaks from the silicon substrate appear -table 1.In opposite to the results presented by Yamada et al. [13], no other Au-Sn compounds were found in our samples.This should be because the Au-Sn interdiffusion was realized in much thinner samples.The structural evaluation of the AuSn compound in the samples was realized on the most intensive peaks of the XRD patterns using the common Scherrer equation and a procedure described in [14].The average sizes of the AuSn crystallites decrease logically with the decrease of the overall thickness of the thin films -from 35 nm for the thickest to 8 nm for the thinnest (table 1).The samples show very steady formation of the AuSn compound without any deviations from the reference bulk crystal [JCPDS 08-0463] with interplanar spacing of 2.222 Å and insignificant strain.Two models were applied for fitting the measured spectra of the ellipsometric angles Ψ meas and Δ meas : (i) an isotropic continuous layer with a rough overlayer on an absorbing substrate and (ii) a single porous layer.The validity of the model was determined by minimization of the values of mean square error function (χ 2 ), which accounts the discrepancies between Ψ meas and Δ meas and the theoretically calculated values for Ψ calc and Δ calc .The obtained values of χ 2 showed that the first model gives the best fits of the experimental data for the 50 nm and 100 nm coatings while the second model describes better the experimental results for the thinner films with thicknesses of 13 and 22 nm.The Drude-Lorentz model was applied to parameterize the complex permittivity of the Au-Sn films [15].
The dispersion of the complex permittivity on the photon energy for thin AuSn films with different thicknesses (10 -100 nm) are shown in figure 1.The real part of the complex permittivity, ε' of thin films with thicknesses greater than 50 nm possesses negative values in the entire studied spectral range.The maximum in the spectra of the imaginary part, ε" of these films, located in the infrared spectral region at photon energies ~ 0.8 eV, indicates that the contribution of interband transitions to permittivity is significant [2,9].In the case of thin films with thicknesses less than 30 nm, the ε' changes its sign from negative to positive in the visible spectral region.This effect is related to a change in the microstructure of the thin film from a continuous to an island due to a decrease of the thickness, which leads to a change in their conductivity and a change in the sign of the ε'.The maximum in Im{1/ε} is associated with electron waves propagating in the volume or the so-called volume plasmon.These waves are longitudinal and do not interact with light.For gold, a maximum located at 2.3 eV corresponding to its plasma frequency is visible.In the case of AuSn, this maximum is situated at 5.5 eV.In the thin films with an island microstructure, the individual islands can be considered as nanoparticles dispersed on the substrate.The spectra of the cross-section of absorption, σ abs. of spherical nanoparticles from Au and AuSn with radius, a = 15 nm, embedded in a dielectric medium with refractive index of 1.5 was theoretically modelled using a procedure described in [16] and is shown in figure 2 (b).The values of σ abs .were determined from the complex permittivity data for thick 100 nm film.In metallic structures, the oscillations of the electronic plasma reaching the surface propagate locally over the nanoparticle with the so-called localized surface plasmon frequency.These oscillations are characterized by a transverse component with frequencies lower than that of the volume plasmon, expressed by the appearance of a maximum in the ε".The σ abs.for AuSn has maximum values at photon energy ~2.3 eV, and a good match with the position of the maximum in the ε" spectrum is seen in the case of 13 nm thin film.Using a procedure for calculation described in [17], the ratio between the dipole electric field  This result was tested by fluorescence enhancement of emission of tryptophan at 350 nm, exited by a 254 nm line of Hg lamp and by excitation of Raman scattering of 488 nm line of argon laser.A comparison of the emission on a pure glass and on a substrate covered with gold or AuSn showed that the emission enhancement of the fluorescence of tryptophan from a substrate with a deposited thin film of AuSn is better than this of gold and is 3 times higher compared to that from a clean glass substrate (figure 4).The results of the surface enhancement of the Raman scattering of tryptophan are presented in figure 5.For comparison, the absence of Raman signal in the case when a clean glass substrate was used is shown.The spectra show the Raman bands of L-Tryptophan at 861, 927, 1136, 1434, 1527, and 1625 cm -1 [18,19].A good sensitivity and Raman signal acquisition is seen up to concentrations of about 10 -7 wt.% L-Tryptophan in water, after which the sensitivity drops sharply, although some of the most intensive Raman bands are still observed at concentrations of 10 -9 wt.%.

Conclusions
The present work demonstrates the possibility for deposition of thin films of the intermetallic compound AuSn with thicknesses in the range of 10-100 nm.Appropriate ellipsometric models were established to determine the complex permittivity of thin AuSn films as a function of their thickness.The results demonstrated that the volume plasmon frequency of AuSn falls in the UV region at 5.5 eV and that this material is suitable for preparation of plasmonic nanostructures as effective substrates for surfaceenhanced Raman and fluorescence spectroscopy in the 2.8 -4.enhancement of the fluorescence of tryptophan from a substrate with a predeposited thin film of AuSn is 2 times higher compared to a substrate with gold film.A good sensitivity and Raman signal acquisition is seen up to concentrations of about 10 -7 wt.% L-Tryptophan in water.

Figure 1 .
Figure 1.Effective values dispersion of real (a) and imaginary (b) parts of the complex permittivity of thin AuSn films.

Figure 2 (
Figure2(a) shows a comparison of the spectral dependence of the dielectric loss function, Im{1/ε} of a 100 nm thin AuSn film and data for a thin film of gold with the same thickness and approximately the same crystallites' sizes (30 -35 nm).The maximum in Im{1/ε} is associated with electron waves propagating in the volume or the so-called volume plasmon.These waves are longitudinal and do not interact with light.For gold, a maximum located at 2.3 eV corresponding to its plasma frequency is visible.In the case of AuSn, this maximum is situated at 5.5 eV.In the thin films with an island microstructure, the individual islands can be considered as nanoparticles dispersed on the substrate.The spectra of the cross-section of absorption, σ abs. of spherical nanoparticles from Au and AuSn with radius, a = 15 nm, embedded in a dielectric medium with refractive index of 1.5 was theoretically modelled using a procedure described in[16] and is shown in figure2 (b).The values of σ abs .were determined

Figure 2 .
Photon energy[eV] |E dipole | 2 induced in Au and AuSn nanoparticles with diameter 20 nm and the external electric field |E| 2 = 1.10 8 V/m were outlined.The spectral dependence of maximal values of |E dipole | 2 /|E| 2 ratio is shown in figure 3. The comparison with the calculated values of Au shows that the |E dipole | 2 /|E dipole | 2 ratio reaches higher values at high photon energies in the spectral region between 2.8 -4.7 eV.

23rdFigure 4 .
Figure 4. Emission fluorescent spectra of tryptophan on a clean glass substrate and a substrate with a pre-deposited very thin films of Au and AuSn.

Figure 5 .
Figure 5. Surface enhancement of the Raman scattering of tryptophan with different concentrations in water.

Table 1 .
Composition, sublayer's properties, registered phases and microstructure of AuSn layers with different thicknesses.