# Optical Characterization of Al Island Films: A Round Robin Test

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fabrication and Measurements

#### 2.2. Optical Characterization Approaches

- Non-parametric model: This approach is based on the assumption that the wavelength-dependencies of the real (n) and imaginary (k) part of the MIF effective refractive index are arbitrary smooth functions [14,22,24]. The discrepancy function to be minimized is:$$DF=\sqrt{\frac{1}{M}\sum _{q}\sum _{j}{\left[\frac{{y}_{q}\left({n}_{j},{k}_{j},{d}_{A{l}_{2}{O}_{3}},{d}_{MIF}\right)-{\widehat{y}}_{q,j}}{{\sigma}_{q,j}}\right]}^{2}+{\alpha}_{1}\sum _{j}{\left[{n}_{j}^{{}^{\u2033}}\right]}^{2}+{\alpha}_{2}\sum _{j}{\left[{k}_{j}^{{}^{\u2033}}\right]}^{2}},$$
- Gaussian oscillators: The MIFs’ effective optical constants are modelled with a set of Gaussian oscillators, as described in [9]. The effective dielectric function assuming the contribution of N oscillators reads as:$${\u03f5}_{eff}\left(E\right)={\u03f5}_{\infty}+\sum _{m=1}^{N}\left[{\u03f5}_{GR,m}\left(E\right)+i{\u03f5}_{GI,m}\left(E\right)\right]$$$${\u03f5}_{GI,m}\left(E\right)={A}_{m}\left[{e}^{-{\left(\frac{E-{E}_{c,m}}{{B}_{m}}\right)}^{2}}-{e}^{-{\left(\frac{E+{E}_{c,m}}{{B}_{m}}\right)}^{2}}\right]$$$${\u03f5}_{GR,m}\left(E\right)=\frac{2}{\pi}p.v.{\int}_{0}^{\infty}\frac{\xi {\u03f5}_{GI,m}\left(\xi \right)}{{\xi}^{2}-{E}^{2}}d\xi $$$$DF=\sqrt{\frac{1}{M-p}\sum _{q}\sum _{j}{\left[\frac{{y}_{q}\left(A,B,{E}_{c},{d}_{A{l}_{2}{O}_{3}},{d}_{MIF}\right)-{\widehat{y}}_{q,j}}{{\sigma}_{q,j}}\right]}^{2}},$$
- $\beta $-do model: The $\beta $-do model [18,19] essentially consists of a multiple-oscillator model where each oscillator is replaced by a $\beta $ distribution in order to account for inhomogeneous line broadening. The dielectric function is then expressed as a sum over N oscillators:$${\u03f5}_{eff}\left(E\right)={\u03f5}_{\infty}+\sum _{m=1}^{N}\sum _{s=1}^{P}\frac{{\sum}_{s}{w}_{m,s}{\chi}_{m}\left({E}_{s},E\right)}{{\sum}_{m}{w}_{m,s}}$$$${\chi}_{m}\left({E}_{s},E\right)=\frac{{J}_{m}}{\pi}\left(\frac{1}{{E}_{s}-E-i{\Gamma}_{m}}+\frac{1}{{E}_{s}+E+i{\Gamma}_{m}}\right)$$$${w}_{m,s}=\frac{{\left({E}_{s}-{E}_{m,min}\right)}^{{a}_{m}-1}{\left({E}_{m,max}-{E}_{s}\right)}^{{b}_{m}-1}}{{\left({E}_{m,max}-{E}_{m,min}\right)}^{{a}_{m}+{b}_{m}-2}}$$In this case, the discrepancy function reads as$$DF=\sqrt{\frac{1}{M}\sum _{q}\sum _{j}{\left[\frac{{y}_{q}-{\widehat{y}}_{q,j}}{{\sigma}_{q,j}}\right]}^{2}+{\alpha}_{3}{\left[\frac{2\left({d}_{MIF}-{\widehat{d}}_{MIF}\right)}{{d}_{MIF}+{\widehat{d}}_{MIF}}\right]}^{2}+{\alpha}_{4}{\left[\frac{2\left({d}_{A{l}_{2}{O}_{3}}-{\widehat{d}}_{A{l}_{2}{O}_{3}}\right)}{{d}_{A{l}_{2}{O}_{3}}+{\widehat{d}}_{A{l}_{2}{O}_{3}}}\right]}^{2}},$$

## 3. Results and Discussion

#### 3.1. Structural Characterization

#### 3.2. Optical Characterization

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Kaiser, N. Review of the fundamentals of thin-film growth. Appl. Opt.
**2002**, 41, 3053–3060. [Google Scholar] [CrossRef] [PubMed] - Stenzel, O.; Macleod, A. Metal-dielectric composite optical coatings: Underlying physics, main models, characterization, design and application aspects. Adv. Opt. Technol.
**2012**, 1, 463–481. [Google Scholar] [CrossRef] [Green Version] - Ghobadi, A.; Ghobadi, T.G.U.; Ozbay, E. Lithography-free metamaterial absorbers: Opinion. Opt. Mater. Express
**2022**, 12, 524–532. [Google Scholar] [CrossRef] - Janicki, V.; Amotchkina, T.V.; Sancho-Parramon, J.; Zorc, H.; Trubetskov, M.K.; Tikhonravov, A.V. Design and production of bicolour reflecting coatings with Au metal island films. Opt. Express
**2011**, 19, 25521–25527. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yu, R.; Mazumder, P.; Borrelli, N.F.; Carrilero, A.; Ghosh, D.S.; Maniyara, R.A.; Baker, D.; García de Abajo, F.J.; Pruneri, V. Structural coloring of glass using dewetted nanoparticles and ultrathin films of metals. ACS Photo.
**2016**, 3, 1194–1201. [Google Scholar] [CrossRef] [Green Version] - Nath, J.; Smith, E.; Maukonen, D.; Peale, R.E. Optical Salisbury screen with design-tunable resonant absorption bands. J. Appl. Phys.
**2014**, 115, 193103. [Google Scholar] [CrossRef] [Green Version] - Li, Z.; Butun, S.; Aydin, K. Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films. ACS Photo.
**2015**, 2, 183–188. [Google Scholar] [CrossRef] [Green Version] - Willey, R.R.; Stenzel, O. Designing Optical Coatings with Incorporated Thin Metal Films. Coatings
**2023**, 13, 369. [Google Scholar] [CrossRef] - Sancho-Parramon, J.; Janicki, V.; Zorc, H. On the dielectric function tuning of random metal-dielectric nanocomposites for metamaterial applications. Opt. Express
**2010**, 18, 26915–26928. [Google Scholar] [CrossRef] [Green Version] - Held, M.; Stenzel, O.; Wilbrandt, S.; Kaiser, N.; Tünnermann, A. Manufacture and characterization of optical coatings with incorporated copper island films. Appl. Opt.
**2012**, 51, 4436–4447. [Google Scholar] [CrossRef] - Biegański, P.; Dobierzewska-Mozrzymas, E.; Kępiński, L. Application of effective medium theory with consideration of island shapes to interpret optical properties of discontinuous Pt films. Appl. Opt.
**2012**, 51, 6945–6951. [Google Scholar] [CrossRef] [PubMed] - de Vries, A.J.; Kooij, E.S.; Wormeester, H.; Mewe, A.A.; Poelsema, B. Ellipsometric study of percolation in electroless deposited silver films. J. Appl. Phys.
**2007**, 101, 053703. [Google Scholar] [CrossRef] - Hövel, M.; Gompf, B.; Dressel, M. Dielectric properties of ultrathin metal films around the percolation threshold. Phys. Rev. B
**2010**, 81, 035402. [Google Scholar] [CrossRef] [Green Version] - Amotchkina, T.V.; Janicki, V.; Sancho-Parramon, J.; Tikhonravov, A.V.; Trubetskov, M.K.; Zorc, H. General approach to reliable characterization of thin metal films. Appl. Opt.
**2011**, 50, 1453–1464. [Google Scholar] [CrossRef] [Green Version] - Sancho-Parramon, J.; Janicki, V.; Zorc, H. Tuning the effective dielectric function of thin film metal-dielectric composites by controlling the deposition temperature. J. Nanophoto.
**2011**, 5, 051805. [Google Scholar] [CrossRef] [Green Version] - Lončarić, M.; Sancho-Parramon, J.; Zorc, H. Optical properties of gold island films—A spectroscopic ellipsometry study. Thin Solid Film.
**2011**, 519, 2946–2950. [Google Scholar] [CrossRef] - Brendel, R.; Bormann, D. An infrared dielectric function model for amorphous solids. J. Appl. Phys.
**1992**, 71, 1–6. [Google Scholar] [CrossRef] - Wilbrandt, S.; Stenzel, O. Empirical extension to the multioscillator model: The beta-distributed oscillator model. Appl. Opt.
**2017**, 56, 9892–9899. [Google Scholar] [CrossRef] - Stenzel, O.; Wilbrandt, S. Beta-distributed oscillator model as an empirical extension to the Lorentzian oscillator model: Physical interpretation of the β_do model parameters. Appl. Opt.
**2019**, 58, 9318–9325. [Google Scholar] [CrossRef] - Wilbrandt, S.; Stenzel, O.; Liaf, A.; Munzert, P.; Schwinde, S.; Stempfhuber, S.; Felde, N.; Trost, M.; Seifert, T.; Schröder, S. Spectrophotometric Characterization of Thin Semi-Transparent Aluminum Films Prepared by Electron Beam Evaporation and Magnetron Sputtering. Coatings
**2022**, 12, 1278. [Google Scholar] [CrossRef] - Stenzel, O.; Wilbrandt, S.; He, J.Y.; Stempfhuber, S.; Schröder, S.; Tünnermann, A. A Model Surface for Calculating the Reflectance of Smooth and Rough Aluminum Layers in the Vacuum Ultraviolet Spectral Range. Coatings
**2023**, 13, 122. [Google Scholar] [CrossRef] - Stenzel, O.; Petrich, R. Flexible construction of error functions and their minimization: Application to the calculation of optical constants of absorbing or scattering thin-film materials from spectrophotometric data. J. Phys. Appl. Phys.
**1995**, 28, 978. [Google Scholar] [CrossRef] - Djurišić, A.B.; Chan, Y.; Li, E.H. Progress in the room-temperature optical functions of semiconductors. Mater. Sci. Eng. Rep.
**2002**, 38, 237–293. [Google Scholar] [CrossRef] - Amotchkina, T.V.; Trubetskov, M.K.; Tikhonravov, A.V.; Janicki, V.; Sancho-Parramon, J.; Zorc, H. Comparison of two techniques for reliable characterization of thin metal–dielectric films. Appl. Opt.
**2011**, 50, 6189–6197. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Franklin, D.; He, Z.; Mastranzo Ortega, P.; Safaei, A.; Cencillo-Abad, P.; Wu, S.T.; Chanda, D. Self-assembled plasmonics for angle-independent structural color displays with actively addressed black states. Proc. Natl. Acad. Sci. USA
**2020**, 117, 13350–13358. [Google Scholar] [CrossRef] - McPeak, K.M.; Jayanti, S.V.; Kress, S.J.; Meyer, S.; Iotti, S.; Rossinelli, A.; Norris, D.J. Plasmonic films can easily be better: Rules and recipes. ACS Photo.
**2015**, 2, 326–333. [Google Scholar] [CrossRef] - Nguyen, H.V.; An, I.; Collins, R. Evolution of the optical functions of thin-film aluminum: A real-time spectroscopic ellipsometry study. Phys. Rev. B
**1993**, 47, 3947. [Google Scholar] [CrossRef] - Nguyen, H.V.; An, I.; Collins, R. Evolution of the optical functions of aluminum films during nucleation and growth determined by real-time spectroscopic ellipsometry. Phys. Rev. Lett.
**1992**, 68, 994. [Google Scholar] [CrossRef] - Dobrowolski, J.; Ho, F.; Waldorf, A. Determination of optical constants of thin film coating materials based on inverse synthesis. Appl. Opt.
**1983**, 22, 3191–3200. [Google Scholar] [CrossRef] - Palik, E.D. Handbook of Optical Constants of Solids; Academic Press: Cambridge, MA, USA, 1998; Volume 3. [Google Scholar]
- Trubetskov, M. OTF Studio Software. Available online: https://www.otfstudio.com (accessed on 4 May 2023).
- Arwin, H.; Aspnes, D.E. Unambiguous determination of thickness and dielectric function of thin films by spectroscopic ellipsometry. Thin Solid Film.
**1984**, 113, 101–113. [Google Scholar] [CrossRef] - Hilfiker, J.N.; Singh, N.; Tiwald, T.; Convey, D.; Smith, S.M.; Baker, J.H.; Tompkins, H.G. Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry. Thin Solid Film.
**2008**, 516, 7979–7989. [Google Scholar] [CrossRef]

**Figure 1.**X-ray diffraction scans for Al island films with different mass thicknesses. Green lines correspond to pure fcc-Al phase (JCPDS Card No. 03-065-2869).

**Figure 2.**Scanning electron microscopy picture of bare Al islands (not coated with Al${}_{2}$O${}_{3}$) having a mass thickness equal to 15 (

**a**), 24 (

**b**) and 32 nm (

**c**).

**Figure 3.**EDS measurements of the surface of the sample with Al island film (not coated with Al${}_{2}$O${}_{3}$) having a mass thickness equal 24 nm.

**Figure 4.**Fits of experimental data (black symbols) of the sample with ${d}_{Al}$ = 12 nm obtained by the three modelling approaches employed in the study: non-parametric approach (red lines), Gaussian oscillators (green lines), $\beta $-do model (blue lines). Data corresponds to ellipsometric angles $\Delta $ (

**a**) and $\Psi $ (

**b**), depolarization (

**c**), transmittance measured with the J.A. Woollam V-VASE ellipsometer (

**d**), transmittance (

**e**) and reflectance (

**f**) measured with the Perkin Elmer $\lambda $25 spectrophotometer.

**Figure 5.**Effective refractive index (solid lines) and extinction coefficient (dashed lines) of the metal island film layer for films with different mass thickness.

**Figure 6.**Real (solid lines) and imaginary (dashed lines) parts of the effective dielectric function of the metal island film layer for films with different mass thickness.

**Figure 7.**Effective refractive index (solid lines) and extinction coefficient (dashed lines) of the metal island film layer for the sample with ${d}_{Al}$ = 15 nm using different approaches (red—parameter free dispersion, green—Gaussian oscillators, blue—$\beta $-do model) and only spectrophotometric data in the whole spectral range (

**left**) and in the spectral range 250–1100 nm (

**right**).

**Table 1.**Thickness for Al metal island film (${d}_{MIF}$) and Al${}_{2}$O${}_{3}$ overlayer (${d}_{A{l}_{2}{O}_{3}}$) as determined by the different approaches employed in this study.

${\mathit{d}}_{\mathbf{Al}}$ (nm) | 3 | 10 | 12 | 15 | 24 | 32 | |
---|---|---|---|---|---|---|---|

Non-parametric model | ${d}_{MIF}$ (nm) | 0 | 4.5 | 8.7 | 9.1 | 19.8 | 25.8 |

${d}_{A{l}_{2}{O}_{3}}$ (nm) | 20.0 | 20.2 | 28.2 | 25.8 | 26.1 | 21.4 | |

Gaussian oscillators | ${d}_{MIF}$ (nm) | 0 | 4.6 | 10.8 | 11.4 | 26.4 | 34.5 |

${d}_{A{l}_{2}{O}_{3}}$ (nm) | 19.9 | 15.9 | 25.7 | 23.3 | 16.8 | 10.1 | |

$\beta $-do | ${d}_{MIF}$ (nm) | 3.0 | 9.8 23.3 | 13.9 | 16.8 | 25.9 | 27.2 |

${d}_{A{l}_{2}{O}_{3}}$ (nm) | 15.0 | 14.6 8.0 | 23.4 | 19.0 | 19.2 | 19.6 |

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**MDPI and ACS Style**

Sancho-Parramon, J.; Amochkina, T.; Wilbrandt, S.; Kamble, H.; Janicki, V.; Salamon, K.; Stenzel, O.; Trubetskov, M.
Optical Characterization of Al Island Films: A Round Robin Test. *Coatings* **2023**, *13*, 1073.
https://doi.org/10.3390/coatings13061073

**AMA Style**

Sancho-Parramon J, Amochkina T, Wilbrandt S, Kamble H, Janicki V, Salamon K, Stenzel O, Trubetskov M.
Optical Characterization of Al Island Films: A Round Robin Test. *Coatings*. 2023; 13(6):1073.
https://doi.org/10.3390/coatings13061073

**Chicago/Turabian Style**

Sancho-Parramon, Jordi, Tatiana Amochkina, Steffen Wilbrandt, Hrishikesh Kamble, Vesna Janicki, Krešimir Salamon, Olaf Stenzel, and Michael Trubetskov.
2023. "Optical Characterization of Al Island Films: A Round Robin Test" *Coatings* 13, no. 6: 1073.
https://doi.org/10.3390/coatings13061073