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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4126–4138
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Simulation and experimental investigation of optical transparency in gold island films

Alexander Axelevitch, Boris Apter, and Gady Golan  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4126-4138 (2013)
http://dx.doi.org/10.1364/OE.21.004126


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Abstract

Localized surface plasmons-polaritons represent collective behavior of free electrons confined to metal particles. This effect may be used for enhancing efficiency of solar cells and for other opto-electronic applications. Plasmon resonance strongly affects optical properties of ultra-thin, island-like, metal films. In the present work, the Finite Difference Time Domain (FDTD) method is used to model transmittance spectra of thin gold island films grown on a glass substrate. The FDTD calculations were performed for island structure, corresponding to the Volmer-Weber model of thin film growth. The proposed simulation model is based on fitting of experimental data on nanostructure of ultra-thin gold films, reported in several independent studies, to the FDTD simulation setup. The results of FDTD modeling are then compared to the experimentally measured transmittance spectra of prepared thin gold films and found to be in a good agreement with experimental data.

© 2013 OSA

1. Introduction

Thin metal films have attracted large scientific and practical interest due to their specific properties and multiple applications. One of these properties is the rise of collective behavior of free electrons confined to the metal films under electromagnetic field influence. This phenomenon is called as a surface plasmon-polariton (SPP). Surface plasmons (SPs) arise from the interaction of light with free electrons at dielectric/metal interface. Under certain conditions the free electrons on the metal surface oscillate in resonance with the incident light wave, resulting in excitation of SPs, propagating along the interface or confined to the metal particles [1

1. H. Raether, Surface Plasmons On Smooth And Rough Surfaces And On Gratings (Springer, 1988).

, 2

2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

]. It was found that the width of SPP resonance peak and its position are depending on the particle size, shape and environment [3

3. S. Link, C. Burda, Z. L. Wang, and M. A. El-Sayed, “Electron dynamics in gold and gold–silver alloy nanoparticles: The influence of a nonequilibrium electron distribution and the size dependence of the electron–phonon relaxation,” J. Chem. Phys. 111(3), 1255–1264 (1999). [CrossRef]

5

5. K.-S. Lee and M. A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: Sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110(39), 19220–19225 (2006). [CrossRef] [PubMed]

]. SPP-based structures are widely used in science and technology, for example as highly-sensitive chemo- and bio-sensors [6

6. G. Boisde and A. Harmer, Chemical and Biochemical Sensing with Optical Fibers and Waveguides (Arthech House, 1996).

, 7

7. J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003). [CrossRef] [PubMed]

]. The enhancement of the electromagnetic field at the metal/dielectric interface [8

8. V. M. Agranovich and D. L. Mills, eds., Surface Polaritons-Electromagnetic Waves at Surfaces and Interfaces (North Holland/Elsevier Science, 1982).

] is responsible for surface-enhanced non-linear optical phenomena [9

9. H.-E. Ponath and G. I. Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (Modern Problems in Condensed Matter Science) (North-Holland, 1991).

] such as Raman scattering and second harmonic generation [10

10. O. A. Aktsipetrov, E. M. Dubinina, S. S. Elovikov, E. D. Mishina, A. A. Nikulin, N. N. Novikova, and M. S. Strebkov, “The electromagnetic (classical) mechanism of surface enhanced second harmonic generation and Raman scattering in island films,” Solid State Commun. 70(11), 1021–1024 (1989). [CrossRef]

], fluorescence [11

11. J. Kümmerlen, A. Leitner, H. Brunner, F. R. Aussenegg, and A. Wokaun, “Enhanced dye fluorescence over silver island films: analysis of the distance dependence,” Mol. Phys. 80(5), 1031–1046 (1993). [CrossRef]

, 12

12. A. Karabchevsky, C. Khare, B. Rauschenbach, and I. Abdulhalim, “Microspot sensing based on surface-enhanced fluorescence from nanosculptured thin films,” J. Nanophotonics 6, 1–12 (2012).

], and infrared absorption [13

13. M. Osawa, “Surface-Enhanced Infrared Absorption,” in Near-Field Optics and Surface Plasmon Polaritons, S. Kawata, ed. (Springer Berlin Heidelberg, 2001), pp. 163–187.

].

In the present study we used the Finite Difference Time Domain (FDTD) method [23

23. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]

] to simulate transmittance spectra of ultra-thin gold films deposited on glass substrate. In order to build a simulation model of island shape evolution, we collected and processed experimental data from independent sources and got empirical parameters for FDTD calculations.

2. Gold islands on glass substrate: geometrical model

According to the well-known Volmer-Weber model of thin film growth [24

24. J. E. Greene, “Thin film nucleation, growth, and microstructural evolution: an atomic scale view,” in Handbook of Deposition Technologies for Films and Coating, 3rd Ed., Ed. P. M. Martin, ed. (Elsevier, 2010), Chap. 12, pp. 554–620.

], at initial stages of film growth, isolated, 3D metal islands are formed on the substrate surface, instead of continuous metal film. Figure 1
Fig. 1 Continuous metal film and island metal film grown on glass substrates.
represents the continuous and island thin gold films grown on a glass substrate.

This growth mechanism was experimentally proved in numerous studies [14

14. S. Norrman, T. Andersson, C. G. Granqvist, and O. Hunderi, “Optical absorption in discontinuous gold films,” Solid State Commun. 23(4), 261–265 (1977). [CrossRef]

22

22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

]. In these studies the developing of nano-islands during the gold film deposition was demonstrated by electron microscopy (EM) and atomic force microscopy (AFM) imaging. Also, excitation of localized surface plasmons, associated with gold islands, was clearly indicated by corresponding dips/peaks in measured transmittance, absorbance or extinction spectra. In parallel with experimental studies, intensive theoretical analysis and numerical simulations were undertaken [14

14. S. Norrman, T. Andersson, C. G. Granqvist, and O. Hunderi, “Optical absorption in discontinuous gold films,” Solid State Commun. 23(4), 261–265 (1977). [CrossRef]

16

16. S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B 18, 647–695 (1978).

, 25

25. M. M. Wind, J. Vlieger, and D. Bedeaux, “The polarizability of a truncated sphere on a substrate I,” Physica A 141(1), 33–57 (1987). [CrossRef]

29

29. I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61(11), 7722–7733 (2000). [CrossRef]

] in order to characterize the optical properties of nano-scale metal islands deposited on various substrates and to fit theoretical results to experimental data. The optical (spectral) response of metal nano-islands was analyzed using the effective-medium model [14

14. S. Norrman, T. Andersson, C. G. Granqvist, and O. Hunderi, “Optical absorption in discontinuous gold films,” Solid State Commun. 23(4), 261–265 (1977). [CrossRef]

16

16. S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B 18, 647–695 (1978).

] or by calculation of polarizability [25

25. M. M. Wind, J. Vlieger, and D. Bedeaux, “The polarizability of a truncated sphere on a substrate I,” Physica A 141(1), 33–57 (1987). [CrossRef]

29

29. I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61(11), 7722–7733 (2000). [CrossRef]

] of a truncated spheres and oblate spheroids in electrostatic approximation (island size is much smaller than the wavelength of exciting light).

We have carried out a detailed computer simulation of spectral transmittance of ultra-thin, island-like gold films using the 3D FDTD method. Since 1966, when it was first introduced [23

23. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]

], the FDTD method has become a common and very effective tool for analysis of electromagnetic problems including modeling and design of nano-photonic and plasmonic structures. In order to simulate the localized surface plasmon resonance in thin gold film, we have adapted the Volmer-Weber model of film growth to our nanophotonic simulation tools. As can be seen in Fig. 2
Fig. 2 Continuous metal film and spherical metal segments on the flat substrates.
, in our simulation study the shape of isolated, gold nano-island, deposited on flat surface, is modeled by simple spherical cap (segment) with height h, base diameter D and sphere radius R. The center of spherical cap is placed at depth d below the substrate surface. For comparison, a continuous gold film with nominal thickness t is shown in Fig. 2 as well.

The nominal thickness should be calculated according to specifications of deposition technique (see Section 3.2 below). Since our simulation study is aimed on calculation of spectral transmittance of thin, island-like gold films at various nominal thicknesses, we should find suitable empirical fits for geometrical parameters of the gold spherical cap (Fig. 2) as functions of the nominal thickness: D(t), h(t), R(t) and d(t). The data required for these fits were collected from three independent sources [16

16. S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B 18, 647–695 (1978).

], [20

20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

] and [22

22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

]. From the experimental results presented in these sources, the average lateral size D(t), average height h(t) and the density N(t) of gold islands were extracted and summarized in Table 1

Table 1. Average Diameter, Height and Density of Gold Islands Versus Nominal Thickness

table-icon
View This Table
.

The values of average diameter and height presented in Table 1 are based on two different techniques: analysis of AFM images [20

20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

, 22

22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

] and analysis of EM images [16

16. S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B 18, 647–695 (1978).

]. As can be seen from Table 1, combination of data from several sources [16

16. S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B 18, 647–695 (1978).

, 20

20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

, 22

22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

] covers the entire thickness range of interest (1.1 - 15 nm). These data were fitted to suitable functions. The choice of fitting functions for geometrical parameters of gold islands D(t) and h(t) is based on following consideration: As it was reported in experimental studies [16

16. S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B 18, 647–695 (1978).

, 20

20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

22

22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

, 30

30. W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nano design,” Appl. Phys. B 63, 381–384 (1996).

], the plasmon resonance wavelength exhibit red shift with increase of nominal thickness of deposited films. According to theoretical analysis [4

4. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003). [CrossRef]

, 30

30. W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nano design,” Appl. Phys. B 63, 381–384 (1996).

] and computer simulations [4

4. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003). [CrossRef]

] this red shift is attributed to increase of aspect ratio of oblate metal nanoparticles, e. g. the plasmon resonance shifts to the red for more oblate particles. In our case of gold spherical caps the aspect ratio is defined as follows:
a(t)=D(t)/h(t).
(1)
This value should increase with increase of nominal thickness in order to provide the red-shift behavior of plasmon resonance.

In order to find empirical relations between the nominal thickness t and the geometrical parameters of gold islands D(t) and h(t), we have tried different fitting functions (linear, power, second-order polynomial and exponential) and combinations of them. It was found that expected behavior of aspect ratio (1) (increase with nominal thickness) can be obtained with the second-order polynomial fit for D(t) and linear fit for h(t).

Figure 3
Fig. 3 Average diameter of gold islands versus nominal thickness (the data extracted from [16], [20], [22]). The dashed curve represents the second-order polynomial fit by Eq. (2).
and Fig. 4
Fig. 4 Average height of gold islands versus nominal thickness (the data extracted from [20], [22]). The squares represent AFM imaging data [20, 22] and the triangles represent EM imaging data [20]. The dashed lines show the linear fits for AFM and EM data. The solid line represents linear fit by Eq. (3) (average of linear fits for AFM and EM data).
represent the dependences (presented by symbols) D(t) and h(t), plotted using the data from Table 1, and corresponding fitting curves (dashed curves). As shown in Fig. 4, the linear fit for h(t) was calculated as average of the linear fits for AFM [20

20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

, 22

22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

] and EM data [20

20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

]. The found empirical relations between nominal thickness and geometrical parameters of gold spherical caps (islands) are given by
D(t)=0.2407t2+3.7928t+0.1938,nm,
(2)
h(t)=0.9266t+1.731,nm,
(3)
where the nominal thickness t should be substituted in nanometers.

The islands' aspect ratio, corresponding to the empirical relations (2) and (3), is plotted in Fig. 5
Fig. 5 Island's aspect ratio versus the nominal thickness.
. Using the geometry, presented in Fig. 1, we get the radius Rof spherical cap and the depth dof its center below the substrate surface, both versus the nominal thicknesst:

R(t)=D2(t)8h(t)+h(t)2,
(4)
d(t)=D2(t)8h(t)h(t)2.
(5)

Figure 6
Fig. 6 Evolution of cap's shape with increase of nominal thickness.
represents the evolution of cap's shape calculated with (4) and (5) for various nominal thicknesses.

3. Simulation and experimental details

3.1 FDTD simulation setup

To simulate transmittance spectra of gold (Au) nano-caps deposited on glass substrate we used commercially available FDTD Solutions software from Lumerical Solutions, Inc [32]. The simulation was based on the setup shown in Fig. 8
Fig. 8 Simulation setup.
. In this setup, identical spherical gold caps are randomly distributed on the top planar surface of glass (SiO2) substrate. The geometrical parameters of the caps and their surface density were calculated using the empirical expressions (2) - (6).

The optical properties of materials, used for simulation, were taken from [33

33. Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, 1998).

] (SiO2 substrate) and [34

34. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

] (Au thin films). As shown in Fig. 8, the simulation area has square cross-section in x-y plane. The gold nano-caps are illuminated from the top by the normally-incident (along z-axis) plane wave which is linearly-polarized in x-z plane. The transmitted optical field is recorded by planar monitor (virtual 2D detector), placed inside the SiO2 substrate, parallel to its top surface. The simulation area is bounded in x- and y-directions by parallel planes in which periodical boundary conditions are defined. To prevent any reflections, a Perfect Matching Layers (PMLs) are applied as bottom and top boundaries of the simulation area. The transmittance spectra of the simulated structure were obtained by broadband pulse excitation and calculation of Fourier transform of time-dependent, transmitted field, recorded by the monitor.

3.2 Practical implementation

The island gold films were prepared using a laboratory thermal evaporation setup working at residual pressure of (2.5 - 4) × 10−6 Pa. The deposition setup was equipped with the two-stage vacuum system based on the diffusion pump. The films were deposited on the glass substrates cleaned in the ultrasound bath in isopropyl alcohol and drained by a compressed air flux. During the deposition, all substrates were kept at room temperature.

Gold films were evaporated at residual pressure from tungsten baskets. Deposition was provided up to full evaporation of material from the cell. Portions of the material for evaporation were prepared with help of the microbalance ViBRA. Value of this mass was found by calculation from the defined (nominal) film thickness using follows relation written for the point evaporation source [35

35. R. W. Berry, P. M. Hall, and M. T. Harris, Thin Film Technology (Van Nostrand, 1968).

]:
t=M4πρcosθr2.
(7)
Here t is the nominal film thickness, M is the mass of the evaporated material, ρ is the material density, r is the distance between an evaporation source and a substrate, and θ is the deposition angle defined by geometry of the substrate. It should be noted, that this formula can be used only for rough estimation of an average thickness of ultra-thin films. In this case, certain assumptions about the structure of the film, the shape and size of the islands, can be made only on the basis of measurement of electrical and optical properties of this film and topographic surveillance using SEM or AFM. Optical absorption and transmittance of gold films on glass substrates were measured in wavelength range from 200 to 1100 nm using the UV-2800 UV/VIS spectrophotometer of UNICO.

4. Results and discussion

4.1 Simulated and measured transmittance spectra

As can be seen in Fig. 9, the plasmon resonance completely dismisses from the films, thicker than 10 nm. It should be noted that FDTD-simulated transmittance spectra, shown in Fig. 9, are in a good agreement with experimental extinction and transmittance spectra presented in [20

20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

, 22

22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

].

Figure 10
Fig. 10 Plasmon resonance wavelength versus the nominal thickness. The dashed curve represents exponential fit.
shows the dependence of plasmon resonance wavelength on the nominal thickness. The data, presented by squares in Fig. 10, where obtained from FDTD-calculated transmittance spectra, shown in Fig. 9. Slightly non-linear dependence of resonant wavelength on nominal thickness in the range 1-10 nm can be fitted by exponential function.

Figure 11
Fig. 11 Transmittance of thin gold films deposited by thermal evaporation.
represents measured transmittance spectra of thin gold films on the glass substrates, prepared as specified above, in Section 3.1. All these films have a transmittance maximum at λ ≈500 nm, however at longer wavelength they behave differently. One can see that thinner films have a transmittance minimum which depends on the film’s thickness. The position of this minimum shifts toward the longer wavelengths with increase of film thickness and disappears at the transition to a continuous film. Thus, there are two different types of anomalies of transmittance spectra inherent in the gold films. The first is a maximum, observed at fixed wavelength, corresponding to the nature of the metal. The second is a minimum, associated with discontinuous structure of the film, and observed at specific, thickness-dependent wavelengths. Obviously these two phenomena have different explanations.

In the metals having fully filled d-shells, only interband transitions of electrons are enabled. Therefore, the maxima of transmission spectra for such metals are conditioned by existence of bulk absorption modes according to their dispersion equation [2

2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

]
ω=kc/ε(ω)
(8)
where k is the complex wavenumber, c is the light speed in vacuum and ε(ω) is the complex, frequency-dependent dielectric function. So, the maximum at wavelength λ = 500 nm, in the transmittance spectra of Au films, is observed for island as well as for continuous flat films [36

36. N. L. Dmitruk and A. V. Korovin, “Physical nature of anomalous optical transmission of thin absorptive corrugated films,” JETP Lett. 89(2), 68–72 (2009). [CrossRef]

]. This explains the natural yellowish color of the gold.

The nature of the minima, shown in Fig. 11, can be explained by excitation of localized plasmons-polaritons with the intensity and at the frequency depending on the size and shape of the islands forming the film. In accordance with the size of these nano-particles, the plasmon resonance is shifted to longer wavelengths with increase of particles’ size. So, we can see the same red shift of the SPP spectral location, depended on the film thickness, similar to the red shift, in the FDTD-simulated spectra, presented in Fig. 9. Also, it should be noted that the plasmon resonance exists only on very thin island films. In the coalescing films the localized plasmons-polaritons disappear.

The difference between the simulated (see Fig. 9) and the experimental (see Fig. 11) transmittance spectra may be explained by assumption used in our simulation model. We assumed that all the gold islands have identical sizes (see part 3.1). Most likely, the random distribution of real islands sizes around their average value leads to smoothing of experimental transmittance spectra. The transmittance edge at 300 nm, observed in the experimental spectra, is due to absorption in the glass substrate. This transmittance edge is not presented in the simulated spectra because of short distance between the top surface of glass substrate and the 2D monitor, recording the transmitted light.

4.2 FDTD simulation of electrical field intensity distributions

Figure 12
Fig. 12 Two-dimensional distribution of electrical field intensity on the top surface of the glass substrate.
represents the two-dimensional distributions of electrical field intensity on the top surface of glass substrate (z = 0) calculated using FDTD method.

These distributions were recorded at resonant wavelengths, corresponding to squares in Fig. 10, for nominal thicknesses 1 - 10 nm, and at wavelengths, predicted by dashed curve in Fig. 10, for nominal thicknesses 15 and 20 nm. As can be seen from these simulated distributions, at nominal thicknesses 1 - 7 nm, isolated islands are present on the substrate without significant overlapping (coalescence). Strong field enhancement due to excitation of localized surface plasmons is seen around the isolated islands. This image of plasmon-enhanced field correlates with relatively narrow plasmon dips in the transmittance spectra shown in Fig. 9. At nominal thicknesses 8 - 10 nm, significant overlapping of gold islands can be seen in Fig. 11. This corresponds with the broadening of plasmon resonance dips in Fig. 9. In thicker films (nominal thicknesses 15 and 20 nm), the islands fully overlaps forming quasi-continuous gold films in which plasmon resonance is totally suppressed and corresponding resonant dips dismiss from the transmittance spectra.

5. Conclusion

In this work, we developed and experimentally verified a simulation model of thin gold island films growth and their optical properties. The proposed model is based on fitting the experimental data on size, shape and surface density of gold nano-islands to suitable functions of nominal thickness of ultra-thin film. The 3D Finite Difference Time Domain (FDTD) method was used to calculate the transmittance spectra of modeled gold island films. The transmittance spectra, calculated using the proposed model, exhibit the well-known, thickness-dependent red shift of the plasmon resonance associated with discontinuous structure of thin gold films. The model also demonstrates that localized surface plasmons-polaritons are excited only in island gold films. With beginning of coalescence process in the island films, the plasmon-polariton resonance disappears. The proposed method can be applied to the investigation and characterization of other metal islands films, for example silver or copper thin films.

References and links

1.

H. Raether, Surface Plasmons On Smooth And Rough Surfaces And On Gratings (Springer, 1988).

2.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

3.

S. Link, C. Burda, Z. L. Wang, and M. A. El-Sayed, “Electron dynamics in gold and gold–silver alloy nanoparticles: The influence of a nonequilibrium electron distribution and the size dependence of the electron–phonon relaxation,” J. Chem. Phys. 111(3), 1255–1264 (1999). [CrossRef]

4.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003). [CrossRef]

5.

K.-S. Lee and M. A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: Sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110(39), 19220–19225 (2006). [CrossRef] [PubMed]

6.

G. Boisde and A. Harmer, Chemical and Biochemical Sensing with Optical Fibers and Waveguides (Arthech House, 1996).

7.

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 377(3), 528–539 (2003). [CrossRef] [PubMed]

8.

V. M. Agranovich and D. L. Mills, eds., Surface Polaritons-Electromagnetic Waves at Surfaces and Interfaces (North Holland/Elsevier Science, 1982).

9.

H.-E. Ponath and G. I. Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (Modern Problems in Condensed Matter Science) (North-Holland, 1991).

10.

O. A. Aktsipetrov, E. M. Dubinina, S. S. Elovikov, E. D. Mishina, A. A. Nikulin, N. N. Novikova, and M. S. Strebkov, “The electromagnetic (classical) mechanism of surface enhanced second harmonic generation and Raman scattering in island films,” Solid State Commun. 70(11), 1021–1024 (1989). [CrossRef]

11.

J. Kümmerlen, A. Leitner, H. Brunner, F. R. Aussenegg, and A. Wokaun, “Enhanced dye fluorescence over silver island films: analysis of the distance dependence,” Mol. Phys. 80(5), 1031–1046 (1993). [CrossRef]

12.

A. Karabchevsky, C. Khare, B. Rauschenbach, and I. Abdulhalim, “Microspot sensing based on surface-enhanced fluorescence from nanosculptured thin films,” J. Nanophotonics 6, 1–12 (2012).

13.

M. Osawa, “Surface-Enhanced Infrared Absorption,” in Near-Field Optics and Surface Plasmon Polaritons, S. Kawata, ed. (Springer Berlin Heidelberg, 2001), pp. 163–187.

14.

S. Norrman, T. Andersson, C. G. Granqvist, and O. Hunderi, “Optical absorption in discontinuous gold films,” Solid State Commun. 23(4), 261–265 (1977). [CrossRef]

15.

C. G. Granqvist and O. Hunderi, “Optical properties of ultrafine gold particles,” Phys. Rev. B 16(8), 3513–3534 (1977). [CrossRef]

16.

S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B 18, 647–695 (1978).

17.

F. Parmigiani, G. Samoggia, and G. P. Ferraris, “Optical properties of sputtered gold clusters,” J. Appl. Phys. 57(7), 2524–2528 (1985). [CrossRef]

18.

R. Lazari, J. Jupille, and Y. Borensztein, “In situ study of a thin metal film by optical means,” Appl. Surf. Sci. 142(1-4), 451–454 (1999). [CrossRef]

19.

D. Dalacu and L. Martinu, “Optical properties of discontinuous gold films: finite-size effects,” J. Opt. Soc. Am. B 18(1), 85–92 (2001). [CrossRef]

20.

I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater. 16(18), 3476–3483 (2004). [CrossRef]

21.

J. Siegel, O. Lyutakov, V. Rybka, Z. Kolská, and V. Svorčík, “Properties of gold nanostructures sputtered on glass,” Nanoscale Res. Lett. 6(1), 96 (2011). [CrossRef] [PubMed]

22.

A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia 32, 1–13 (2012). [CrossRef]

23.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]

24.

J. E. Greene, “Thin film nucleation, growth, and microstructural evolution: an atomic scale view,” in Handbook of Deposition Technologies for Films and Coating, 3rd Ed., Ed. P. M. Martin, ed. (Elsevier, 2010), Chap. 12, pp. 554–620.

25.

M. M. Wind, J. Vlieger, and D. Bedeaux, “The polarizability of a truncated sphere on a substrate I,” Physica A 141(1), 33–57 (1987). [CrossRef]

26.

M. M. Wind, A. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of a truncated sphere on a substrate II,” Physica A 143(1-2), 164–182 (1987). [CrossRef]

27.

M. M. Wind, P. A. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films 164, 57–62 (1988). [CrossRef]

28.

M. M. Wind, P. A. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A 157(1), 269–278 (1989). [CrossRef]

29.

I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B 61(11), 7722–7733 (2000). [CrossRef]

30.

W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nano design,” Appl. Phys. B 63, 381–384 (1996).

31.

J. Grand, P.-M. Adam, A.-S. Grimault, A. E. Vial, M. L. de la Chapelle, and J.-L. Bijeon JS. Kostcheev and P. Royer, “Optical extinction spectroscopy of oblate, prolate and ellipsoid shaped gold nanoparticles: experiments and theory,” Plasmonics 1, 135–140 (2006).

32.

http://www.lumerical.com/

33.

Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, 1998).

34.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

35.

R. W. Berry, P. M. Hall, and M. T. Harris, Thin Film Technology (Van Nostrand, 1968).

36.

N. L. Dmitruk and A. V. Korovin, “Physical nature of anomalous optical transmission of thin absorptive corrugated films,” JETP Lett. 89(2), 68–72 (2009). [CrossRef]

OCIS Codes
(310.1860) Thin films : Deposition and fabrication
(310.6860) Thin films : Thin films, optical properties
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Thin Films

History
Original Manuscript: December 10, 2012
Revised Manuscript: January 15, 2013
Manuscript Accepted: January 17, 2013
Published: February 11, 2013

Citation
Alexander Axelevitch, Boris Apter, and Gady Golan, "Simulation and experimental investigation of optical transparency in gold island films," Opt. Express 21, 4126-4138 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4126


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References

  1. H. Raether, Surface Plasmons On Smooth And Rough Surfaces And On Gratings (Springer, 1988).
  2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  3. S. Link, C. Burda, Z. L. Wang, and M. A. El-Sayed, “Electron dynamics in gold and gold–silver alloy nanoparticles: The influence of a nonequilibrium electron distribution and the size dependence of the electron–phonon relaxation,” J. Chem. Phys.111(3), 1255–1264 (1999). [CrossRef]
  4. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B107(3), 668–677 (2003). [CrossRef]
  5. K.-S. Lee and M. A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: Sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B110(39), 19220–19225 (2006). [CrossRef] [PubMed]
  6. G. Boisde and A. Harmer, Chemical and Biochemical Sensing with Optical Fibers and Waveguides (Arthech House, 1996).
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  10. O. A. Aktsipetrov, E. M. Dubinina, S. S. Elovikov, E. D. Mishina, A. A. Nikulin, N. N. Novikova, and M. S. Strebkov, “The electromagnetic (classical) mechanism of surface enhanced second harmonic generation and Raman scattering in island films,” Solid State Commun.70(11), 1021–1024 (1989). [CrossRef]
  11. J. Kümmerlen, A. Leitner, H. Brunner, F. R. Aussenegg, and A. Wokaun, “Enhanced dye fluorescence over silver island films: analysis of the distance dependence,” Mol. Phys.80(5), 1031–1046 (1993). [CrossRef]
  12. A. Karabchevsky, C. Khare, B. Rauschenbach, and I. Abdulhalim, “Microspot sensing based on surface-enhanced fluorescence from nanosculptured thin films,” J. Nanophotonics6, 1–12 (2012).
  13. M. Osawa, “Surface-Enhanced Infrared Absorption,” in Near-Field Optics and Surface Plasmon Polaritons, S. Kawata, ed. (Springer Berlin Heidelberg, 2001), pp. 163–187.
  14. S. Norrman, T. Andersson, C. G. Granqvist, and O. Hunderi, “Optical absorption in discontinuous gold films,” Solid State Commun.23(4), 261–265 (1977). [CrossRef]
  15. C. G. Granqvist and O. Hunderi, “Optical properties of ultrafine gold particles,” Phys. Rev. B16(8), 3513–3534 (1977). [CrossRef]
  16. S. Norman, T. Andersson, and C. G. Granqvist, “Optical properties of discontinuous gold films,” Phys. Rev. B18, 647–695 (1978).
  17. F. Parmigiani, G. Samoggia, and G. P. Ferraris, “Optical properties of sputtered gold clusters,” J. Appl. Phys.57(7), 2524–2528 (1985). [CrossRef]
  18. R. Lazari, J. Jupille, and Y. Borensztein, “In situ study of a thin metal film by optical means,” Appl. Surf. Sci.142(1-4), 451–454 (1999). [CrossRef]
  19. D. Dalacu and L. Martinu, “Optical properties of discontinuous gold films: finite-size effects,” J. Opt. Soc. Am. B18(1), 85–92 (2001). [CrossRef]
  20. I. Doron-Mor, Z. Barkay, N. Filip-Granit, A. Vaskevich, and I. Rubinstein, “Ultrathin gold island films on silanized glass. Morphology and optical properties,” Chem. Mater.16(18), 3476–3483 (2004). [CrossRef]
  21. J. Siegel, O. Lyutakov, V. Rybka, Z. Kolská, and V. Svorčík, “Properties of gold nanostructures sputtered on glass,” Nanoscale Res. Lett.6(1), 96 (2011). [CrossRef] [PubMed]
  22. A. Axelevitch, B. Gorenstein, and G. Golan, “Investigation of optical transmission in thin metal films,” Physics Procedia32, 1–13 (2012). [CrossRef]
  23. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966). [CrossRef]
  24. J. E. Greene, “Thin film nucleation, growth, and microstructural evolution: an atomic scale view,” in Handbook of Deposition Technologies for Films and Coating, 3rd Ed., Ed. P. M. Martin, ed. (Elsevier, 2010), Chap. 12, pp. 554–620.
  25. M. M. Wind, J. Vlieger, and D. Bedeaux, “The polarizability of a truncated sphere on a substrate I,” Physica A141(1), 33–57 (1987). [CrossRef]
  26. M. M. Wind, A. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of a truncated sphere on a substrate II,” Physica A143(1-2), 164–182 (1987). [CrossRef]
  27. M. M. Wind, P. A. Bobbert, J. Vlieger, and D. Bedeaux, “The polarizability of truncated spheres and oblate spheroids on a substrate: comparison with experimental results,” Thin Solid Films164, 57–62 (1988). [CrossRef]
  28. M. M. Wind, P. A. Bobbert, J. Vlieger, and D. Bedeaux, “Optical properties of 2D-systems of small particles on a substrate,” Physica A157(1), 269–278 (1989). [CrossRef]
  29. I. Simonsen, R. Lazzari, J. Jupille, and S. Roux, “Numerical modeling of the optical response of supported metallic particles,” Phys. Rev. B61(11), 7722–7733 (2000). [CrossRef]
  30. W. Gotschy, K. Vonmetz, A. Leitner, and F. R. Aussenegg, “Thin films by regular patterns of metal nanoparticles: tailoring the optical properties by nano design,” Appl. Phys. B63, 381–384 (1996).
  31. J. Grand, P.-M. Adam, A.-S. Grimault, A. E. Vial, M. L. de la Chapelle, and J.-L. Bijeon JS. Kostcheev and P. Royer, “Optical extinction spectroscopy of oblate, prolate and ellipsoid shaped gold nanoparticles: experiments and theory,” Plasmonics1, 135–140 (2006).
  32. http://www.lumerical.com/
  33. Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, 1998).
  34. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  35. R. W. Berry, P. M. Hall, and M. T. Harris, Thin Film Technology (Van Nostrand, 1968).
  36. N. L. Dmitruk and A. V. Korovin, “Physical nature of anomalous optical transmission of thin absorptive corrugated films,” JETP Lett.89(2), 68–72 (2009). [CrossRef]

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