Yttrium fluoride (YF3) thin films with a thickness range of 10.8−1079.0 nm were prepared by electron beam evaporation. Spectroscopic ellipsometry was used to study the thickness-dependent optical properties of YF3 ultrathin films in the 300−820 nm wavelength range. With increasing thicknesses, the refractive indices of the intrinsic YF3 films increase slightly and approach that of bulk YF3 due to the decrease of void fractions. The effective refractive indices of the YF3 films also increase with increasing thicknesses, due to the surface and interface effects besides the contribution of decrease of void fractions.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The rare-earth fluorides are attractive and excellent materials in the optical field because of their refractory nature, chemical stability, and outstanding optical properties . Considerable efforts have been made in studying the optical properties of various rare-earth fluoride films [2–4]. The phonon energy of the fluorides is lower than the phonon energy of the oxides, which leads to increased transparency window, low polarizability, and thus lower refractive index, and lower vibrational energy [5–7]. The low phonon energy of fluorides enables the high-efficiency radiative transition of rare-earth ions or luminescent materials when used as a matrix . Moreover, the fluoride materials provide low refractive indices and optical dispersions over a wide spectral range extending from UV to mid-infrared wavelengths. Therefore, the fluorides can be used as low-phonon-energy host materials for integrated photonic applications. Yttrium fluoride (YF3), as a common and important fluoride compound, has been widely used as substitutes for radioactive ThF4, nanoparticles with efficient multicolor photoluminescence, optical coatings such as high-reflection mirrors, thin-film interference filters, anti-reflective coatings with other optical films ranging from the near-UV to IR [9–15].
However, not much work has been carried out on the optical properties of YF3 thin films, especially for YF3 ultrathin films thinner than 50 nm. Furthermore, the optical properties and dielectric properties of ultrathin films at nanoscale are different from those of bulk materials because of the effects of surface and interface [16,17]. Several works show that the optical properties of YF3 with different thicknesses grown by different coating techniques are different from the bulk’s one and are different from each other [18–21]. Therefore, the thickness-dependent optical properties of YF3 ultrathin films is worth further study. Spectroscopic ellipsometry, as a powerful nondestructive and sensitive technique, is now one of the popular tools for studying thin films, for it can provide extremely high accuracy and sensitivity in measuring the polarizations changes of light reflected from the sample surface [22–24]. In this study, we have prepared YF3 films with various thicknesses by electron beam evaporation (EBE) and presented their thickness-dependent optical properties by variable-angle spectroscopic ellipsometry (VASE). The surface morphology of the samples was viewed by atomic force microscopy (AFM). The cross-section of those samples was inspected by field-emission scanning electron microscopy (FESEM). These results will be helpful to the applications of YF3 ultrathin films in optical thin-film devices, microelectronic devices, and related technologies.
2. Experimental details
The YF3 films with thickness range of 10.8−1079.0 nm were fabricated by the EBE method under the same deposition conditions. The YF3 evaporation source was granular material of 99.99% purity and was heated by an electron beam at a high voltage of 7 kV. Single-side polished, crystalline <100> n-type silicon (99.99% in purity) wafers with diameter of 2 inches, 350 ± 20 μm in thickness, and 2−8 Ω cm in resistivity, were used as substrates. Over ten YF3 samples with various thicknesses have been fabricated at a deposition rate of 0.2−0.3 nm/s. Specific information about our laboratory coating equipment has been reported [25,26].
A home-built rotating-polarizer-analyzer ellipsometer was employed to acquire the ellipsometric parameters (Ψ, Δ) of all YF3 samples every 10 nm in the wavelength range of 300−820 nm at incident angles of 65°, 70°, and 75° [27,28]. The precision of Ψ is 0.005° and the precision of Δ is 0.01°. The surface morphology of the prepared YF3 thin films was viewed with AFM (XEI-100, PSIA Corp., Korea) in the noncontact mode. Thicknesses of the YF3 thin films were measured by FESEM (HITACHI, FESEM-4800-1).
3. Results and discussion
The optical properties of the fabricated YF3 thin films with various thicknesses were characterized by the VASE measurement. Since the ellipsometry is a model-based measurement, the measured ellipsometric data in the whole spectra should be fitted to an appropriate optical model and a suitable dispersion model most physically meaningful fit, to obtain the optical constants and physical thicknesses of the prepared YF3 thin films. A two-film optical model, which is suited to calculate the optical constants of dielectric layers grown on a silicon substrate, was initially used in the fitting process . Since YF3 is transparent in the considered wavelength range, the dispersion function for the YF3 films was expressed using the Sellmeier dispersion model29–31]
However, a simple optical model with the structure of air ambient/YF3 film/Si substrate, as shown in Fig. 1(a), cannot fit the experimental ellipsometric parameters well, especially in the long-wavelength band where the data fitting error for the ultrathin films increases significantly. Therefore, an interface layer with silicon-induced gap states (SIGS) was introduced between the fluoride layer and the Si substrate, as shown in Fig. 1(b). The SIGS expressed the breaking down of the Si-Si bond of the Si substrate, and the decay length of the interface states was about 0.12 nm near the interface . The thickness of the SIGS layer was accordingly assumed to be 0.12 nm. The Lorentz oscillator dispersion model, which is used to describe frequency-dependent polarization due to bound charge, was adopted to describe the dielectric function of the SIGS layer 
As shown in Fig. 2, the fittings of all YF3 thin films agree well with the measured ellipsometric parameters with a typical RMSE value less than 0.30, implying that the optical model and dispersion model used for analysis are reliable and reasonable. With this fitting process, parameter Bn in Eq. (1) could be given by a function of the film thickness Bn = A0 exp (−d0/d), where d is film thickness in nm, A0 = 1.11 ± 0.06, d0 = 5.47 ± 1.27. Hence, by substituting Bn = A0 exp (−d0/d), into Eq. (1), an empirical dispersion formula for the ultrathin YF3 films can be obtained and given by
Figure 3 shows the dispersion curves of refractive indices for the YF3 films with thickness range of 10.8−1079.0 nm obtained from the Sellmeier model, where the film thicknesses were obtained from VASE measurement. The refractive index decreased slightly as the wavelength varied from 300 to 820 nm for all samples. Besides, the refractive indices of the YF3 films increase significantly as the film thickness increased from 10.8 nm to 1079.0 nm. For example, at 550 nm wavelength, n is 1.497 for the 1079.0 nm-thick film and 1.259 for the 10.8 nm-thick film. The variation of the refractive index versus film thickness at 550 nm wavelength is shown in Fig. 4. The refractive indices maintained nearly a constant for YF3 films thicker than 80 nm and reduced sharply for YF3 films thinner than 80 nm. A similar phenomenon can be found at other wavelengths.
A cross-sectional image of a sample viewed by FESEM in Fig. 5 shows a thickness of 76.8 nm, which agrees with the fitted result of 76.7 nm. The slight difference between the two methods is due to that the measurement of FESEM was performed in the micrometer range while the measurement of VASE was performed in the millimeter range.
The variation trend of the refractive index versus the film thickness can be expressed by a simple inverse proportional function, given by1(c). The effective dielectric constant of the system of surficial roughness/YF3 film/interfacial oxide layer can be evaluated from a series capacitor model. The model assumes that the three dielectric layers in the system are represented by three capacitors in series with the dielectric constants of the three layers, respectively [34,35]. The effective dielectric constant of the system (εeff) can be expressed by
The expression of εeff can be simplified by a symbol C, expressed as
By substituting the relationship between the refractive index and the dielectric constant (i.e., n = ε1/2) for transparent materials in the visible band and using Taylor expansion, the effective refractive index of the system (neff) can be obtained as the following form
The expression is the same in form as Eq. (5), which expressed the variation of the refractive index versus film thickness. The interfacial oxide layer is not pure SiO2 but is a complex depth-dependent nonstoichiometric Si−Yx−Fy−Oz. Assuming that the interfacial oxide layer is mainly contributed by the oxidation of the Si substrate, its refractive index and thickness can be measured by the ellipsometry before coating. The ellipsometric measurement results showed that the dielectric constant of the interfacial oxide layer is 6.78, and the thickness is 2.1 nm, which agrees with the results reported by Chaneliere et al. [34,36]. Therefore, the values of the interfacial oxide layer obtained by ellipsometry are appropriate. Besides, the surface roughness is generally considered to be a mixture of media and air. The effective medium approximation (EMA) model, which is conventionally used in the analysis of the optical properties of a mixed media containing two or more components, was used to express the surficial roughness layer and given by [29,37]
The optical constants of the intrinsic YF3 film were further obtained by considering the effect of the interfacial oxide layer and the surficial roughness layer, based on the optical model in Fig. 1(c). The refractive indices (λ = 550 nm) for the intrinsic YF3 films of different thicknesses are shown in Fig. 7. As the film thickness increases, the refractive index of the YF3 film increases slightly and approaches the value of bulk YF3, which could be attributed to the existence of voids in the films [39,40]. Although only the results at 550 nm were given in Fig. 7, similar results were found at other wavelengths. These intrinsic YF3 films may be regarded as composite films composed of voids and YF3 granules, which can be quantitatively analyzed using the EMA model. The void fractions fvoid of the intrinsic YF3 films versus the film thickness were obtained, as shown in Fig. 7. As the film thickness increases, the void fraction reduces monotonically, which agrees with the results reported by McMarr et al. [39,40]. More voids are filled with granules during the film growth, resulting in a more dense film . Therefore, the refractive index of the intrinsic YF3 film increases due to a higher density of a thicker film.
In summary, YF3 thin films with different thicknesses were fabricated on Si substrates by electron beam evaporation and were measured by the VASE technique in the 300−820 nm wavelength range. The fitted results from the Sellmeier dispersion model show that the refractive indices of the YF3 thin films thinner than 80 nm reduce with the decrease of thickness, and those of the YF3 thin films thicker than 80 nm approach the value of bulk YF3. This phenomenon is attributed to the contribution of the interfacial composite layer and the surficial roughness layer of the samples. The surficial roughness layer was confirmed by AFM. The relationship between the refractive index and thickness of YF3 thin films was fitted by an inverse proportional function and was explained by the series capacitance theory. As the film thickness increases, the void fraction reduces monotonically, while the refractive index of the intrinsic YF3 film increases slightly and approaches the value of bulk YF3 due to the higher density of the thicker film. For detailed consideration in designing thin-film devices, the surface and interface effects as well as the void fraction must be considered to obtain high performance of devices. Results from this study will be helpful to design and fabricate optical thin film devices using YF3 thin films in multilayer, microelectronic devices, and related technologies.
National Natural Science Foundation of China (61775042, 11674062); Fudan University-CIOMP Joint Fund (FC2017-003).
The authors declare no conflict of interest.
1. G. Hass, J. B. Ramsey, and R. Thun, “Optical properties of various evaporated rare earth oxides and fluorides,” J. Opt. Soc. Am. 49(2), 116–120 (1959). [CrossRef]
2. F. S. Maddocks and R. E. Thun, “Properties of evaporated film capacitors,” J. Electrochem. Soc. 109(2), 99–103 (1962). [CrossRef]
3. S. F. Pellicori and E. Colton, “Fluoride compounds for IR coatings,” Thin Solid Films 209(1), 109–115 (1992). [CrossRef]
4. K. Iwahori, M. Furuta, Y. Taki, T. Yamamura, and A. J. A. O. Tanaka, “Optical properties of fluoride thin films deposited by RF magnetron sputtering,” Appl. Opt. 45(19), 4598–4602 (2006). [CrossRef]
5. T. Munehiro, F. Shinobu, and K. Toshio, “Sol-gel processing and characterization of alkaline earth and rare-earth fluoride thin films,” J. Mater. Res. 14(4), 1610–1616 (1999). [CrossRef]
6. F. Zhang, J. Li, J. Shan, L. Xu, and D. Zhao, “Shape, size, and phase-controlled rare-earth fluoride nanocrystals with optical up-conversion properties,” Chem. - Eur. J. 15(41), 11010–11019 (2009). [CrossRef]
7. S. D. Jackson, “Power scaling method for 2-µm diode-cladding-pumped Tm3+-doped silica fiber lasers that uses Yb3+ codoping,” Opt. Lett. 28(22), 2192–2194 (2003). [CrossRef]
8. C. Buchal, T. Siegrist, D. C. Jacobson, and J. M. Poate, “1.5 μm photoluminescence of Er3+ in YF3, LuF3, and LaF3 thin films,” Appl. Phys. Lett. 68(4), 438–440 (1996). [CrossRef]
9. G. Chen, H. Qiu, R. Fan, S. Hao, S. Tan, C. Yang, and G. Han, “Lanthanide-doped ultrasmall yttrium fluoride nanoparticles with enhanced multicolor upconversion photoluminescence,” J. Mater. Chem. 22(38), 20190–20196 (2012). [CrossRef]
10. G. G. Condorelli, G. Anastasi, and I. L. Fragalà, “MOCVD of YF3 and Y1-xErxF3 thin films from precursors synthesized in situ,” Chem. Vap. Deposition 11(6-7), 324–329 (2005). [CrossRef]
11. V. Barrioz, S. J. C. Irvine, and D. P. Jones, “In situ and ex situ stress measurements of YF3 single layer optical coatings deposited by electron beam evaporator,” J. Mater. Sci.: Mater. Electron. 14(9), 559–566 (2003). [CrossRef]
12. T. Pilvi, E. Puukilainen, F. Munnik, M. Leskelä, and M. Ritala, “ALD of YF3 thin films from TiF4 and Y(thd)3 precursors,” Chem. Vap. Deposition 15(1-3), 27–32 (2009). [CrossRef]
13. P. Chindaudom and K. Vedam, “Characterization of inhomogeneous transparent thin films on transparent substrates by spectroscopic ellipsometry: refractive indices n(λ) of some fluoride coating materials,” Appl. Opt. 33(13), 2664–2671 (1994). [CrossRef]
14. F. Lemarquis, G. Marchand, and C. Amra, “Design and manufacture of low-absorption ZnS–YF3 antireflection coatings in the 3.5–16-μm spectral range,” Appl. Opt. 37(19), 4239–4244 (1998). [CrossRef]
15. J. DiJon, E. Quesnel, B. Rolland, P. Garrec, C. Pelle, and J. Hue, “High-damage-threshold fluoride UV mirrors made by ion-beam sputtering,” Proc. SPIE 3244, 406–416 (1998). [CrossRef]
16. G. He, L. D. Zhang, M. Liu, J. P. Zhang, X. J. Wang, and C. M. Zhen, “Thickness-modulated optical dielectric constants and band alignments of HfOxNy gate dielectrics,” J. Appl. Phys. 105(1), 014109 (2009). [CrossRef]
17. J. Sheng, J. Karasawa, and T. Fukami, “Thickness dependence of photocatalytic activity of anatase film by magnetron sputtering,” J. Mater. Sci. Lett. 16(21), 1709–1711 (1997). [CrossRef]
18. D. F. Bezuidenhout, K. D. Clarke, and R. Pretorius, “The optical properties of YF3 films,” Thin Solid Films 155(1), 17–30 (1987). [CrossRef]
19. L. Pei, Z. Jiaqi, Z. Yuankun, and H.J.N.I. Jiecai, “Preparation and optical properties of sputtered-deposition yttrium fluoride film,” Nucl. Instrum. Methods Phys. Res., Sect. B 307(jul.15), 429–433 (2013). [CrossRef]
20. J.-Y. Robic, V. Muffato, P. Chaton, M. Ida, and M. Berger, “Optical and structural properties of YF3 thin films prepared by ion-assisted deposition or ion-beam sputtering techniques,” Proc. SPIE 2253, 195–207 (1994). [CrossRef]
21. E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pelle, and F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” Proc. SPIE 2776, 366–371 (1996). [CrossRef]
22. M. Losurdo, “Applications of ellipsometry in nanoscale science: Needs, status, achievements and future challenges,” Thin Solid Films 519(9), 2575–2583 (2011). [CrossRef]
23. M. Losurdo, M. Bergmair, G. Bruno, D. Cattelan, C. Cobet, A. de Martino, K. Fleischer, Z. Dohcevic-Mitrovic, N. Esser, M. Galliet, R. Gajic, D. Hemzal, K. Hingerl, J. Humlicek, R. Ossikovski, Z. V. Popovic, and O. Saxl, “Spectroscopic ellipsometry and polarimetry for materials and systems analysis at the nanometer scale: state-of-the-art, potential, and perspectives,” J. Nanopart. Res. 11(7), 1521–1554 (2009). [CrossRef]
24. J. A. Woollam, P. G. Snyder, and M. C. Rost, “Variable angle spectroscopic ellipsometry: A non-destructive characterization technique for ultrathin and multilayer materials,” Thin Solid Films 166(1-2), 317–323 (1988). [CrossRef]
25. Q. Cai, Y. Zheng, P. Mao, R. Zhang, D. Zhang, M. Liu, and L. Chen, “Evolution of optical constants of silicon dioxide on silicon from ultrathin films to thick films,” J. Phys. D: Appl. Phys. 43(44), 445302 (2010). [CrossRef]
26. L. Yang, Y. Zheng, S. Yang, Z. Liu, J. Zhang, R. Zhang, S. Wang, D. Zhang, and L. Chen, “Ellipsometric study on temperature dependent optical properties of topological bismuth film,” Appl. Surf. Sci. 421(PT.B), 899–904 (2017). [CrossRef]
27. L. Y. Chen and D. W. Lynch, “Scanning ellipsometer by rotating polarizer and analyzer,” Appl. Opt. 26(24), 5221–5228 (1987). [CrossRef]
28. L. Chen, X. Feng, Y. Su, H. Ma, and Y. Qian, “Design of a scanning ellipsometer by synchronous rotation of the polarizer and analyzer,” Appl. Opt. 33(7), 1299–1305 (1994). [CrossRef]
29. S. Yang, Y. Zheng, L. Yang, Z. Liu, W. Zhou, S. Wang, R. Zhang, and L. Chen, “Structural and optical properties of highly (110)-oriented non-polar ZnO evaporated films on Si substrates,” Appl. Surf. Sci. 421(PT.B), 891–898 (2017). [CrossRef]
30. F. Hiroyuki, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).
31. H. Tompkins and E.A. Irene, Handbook of Ellipsometry (William Andrew, 2005).
32. J. Xu, R. Zhang, Z. Chen, Z. Wang, F. Zhang, X. Yu, A. Jiang, Y. Zheng, S. Wang, and L. Chen, “Optical properties of epitaxial BiFeO3 thin film grown on SrRuO3-buffered SrTiO3 substrate,” Nanoscale Res. Lett. 9(1), 188 (2014). [CrossRef]
33. F. Giustino, A. Bongiorno, and A. Pasquarello, “Atomistic models of the Si(100)–SiO2 interface: structural, electronic and dielectric properties,” J. Phys.: Condens. Matter 17(21), S2065–S2074 (2005). [CrossRef]
34. C. Chaneliere, J. L. Autran, R. A. B. Devine, and B. Balland, “Tantalum pentoxide (Ta2O5) thin films for advanced dielectric applications,” Mater. Sci. Eng., R 22(6), 269–322 (1998). [CrossRef]
35. R. A. B. Devine, “Nondestructive measurement of interfacial SiO2 films formed during deposition and annealing of Ta2O5,” Appl. Phys. Lett. 68(14), 1924–1926 (1996). [CrossRef]
36. G. B. Alers, D. J. Werder, Y. Chabal, H. C. Lu, E. P. Gusev, E. Garfunkel, T. Gustafsson, and R. S. Urdahl, “Intermixing at the tantalum oxide/silicon interface in gate dielectric structures,” Appl. Phys. Lett. 73(11), 1517–1519 (1998). [CrossRef]
37. L. W. Barron, J. Neidrich, and S. K. Kurinec, “Optical, electrical, and structural properties of sputtered aluminum alloy thin films with copper, titanium and chromium additions,” Thin Solid Films 515(7-8), 3363–3372 (2007). [CrossRef]
38. Z. Xu, F. Zhang, R. Zhang, X. Yu, D. Zhang, Z. Wang, Y. Zheng, S. Wang, H. Zhao, and L. Chen, “Thickness dependent optical properties of titanium oxide thin films,” Appl. Phys. A: Mater. Sci. Process. 113(3), 557–562 (2013). [CrossRef]
39. P. J. McMarr, J. R. Blanco, K. Vedam, R. Messier, and L. Pilione, “Thickness-dependent void fraction of rf-sputtered amorphous Ge films by spectroscopic ellipsometry,” Appl. Phys. Lett. 49(6), 328–330 (1986). [CrossRef]
40. L. J. Pilione, K. Vedam, J. E. Yehoda, R. Messier, and P. J. McMarr, “Thickness dependence of optical gap and void fraction for sputtered amorphous germanium,” Phys. Rev. B 35(17), 9368–9371 (1987). [CrossRef]
41. I. Petrov, P. B. Barna, L. Hultman, and J. E. Greene, “Microstructural evolution during film growth,” J. Vac. Sci. Technol., A 21(5), S117–S128 (2003). [CrossRef]