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Abstract
In recent years, we have been witnessing the intensive development of optical gas sensors. Thin palladium and platinum films as well as tungsten trioxide films with palladium or platinum catalysts are widely used for hydrogen detection, and the optical constants of these materials are required for sensor development. We report the optical parameters retrieved from a set of ellipsometric and transmission spectra for electron-beam evaporated palladium, platinum, and tungsten trioxide films. The tungsten trioxide films were 81 nm, 162 nm, and 515 nm thick and the metal films were as thin as 5–7 nm. Ultrathin palladium and platinum films were shown to be successfully described by local and isotropic permittivity, which is quite different from known bulk values. However, this permittivity showed a strong dependence on adjacent materials, thus illustrating that the ultrathin metallic films can be considered composites characterized by effective permittivity. With the obtained refractive indices and permittivities, the optical spectra of fabricated WO3/Pd and WO3/Pt nanostructures incorporating 1D grating of Al2O3 were in an excellent agreement with the calculated ones without requiring any additional fitting procedures or inclusion of surface roughness layers in numerical models.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
Daria P. Kulikova, Alina A. Dobronosova, Vladimir V. Kornienko, Igor A. Nechepurenko, Aleksandr S. Baburin, Evgeny V. Sergeev, Evgeniy S. Lotkov, Ilya A. Rodionov, Alexander V. Baryshev, and Alexander V. Dorofeenko, "Optical properties of tungsten trioxide, palladium and platinum thin films for functional nanostructures engineering: erratum," Opt. Express 28, 35413-35414 (2020)https://opg.optica.org/oe/abstract.cfm?uri=oe-28-23-35413
1. Introduction
Current industrial demands pose challenging problems for researchers and engineers engaged in gas sensors development [1]. There is a particular need for sensors with ultrafast response operating in fast flow and in aggressive or contaminated environments, portable sensors, and sensors providing reproducible responses on trace concentrations of a certain gas as well as analyzers of multicomponent gas mixtures.
An essential approach to gas mixture analysis is the integration of sensors based on different physical principles in a single device [2,3]. Therefore, the development of sensors exploiting new physical mechanisms is a crucial task [4]. Widely used sensors are resistive [5–9], electrochemical [10], catalytic [11], photoionization [12], and optical IR sensors [13]. Optical sensors based on changes in the optical absorption and refractive indices of specific gasochromic materials in the presence of analyzed gas have been widely studied in recent years [14–19]. Metal oxides are commonly used for this purpose. In particular, tungsten trioxide (WO3) covered by a palladium or platinum catalyst is applied for the detection of hydrogen and other reducing gases. Palladium is also separately used because the dissolution of hydrogen in it causes its properties to change [20,21].
The sensing function of palladium is due to the formation of palladium hydride, which initiates changes in permittivity and specific volume. Nowadays, palladium-based optical hydrogen sensors are being actively developed; schemes utilizing optical fibers [22] and plasmonics [23–26] have been proposed. Pd-rich alloys [27] and films including Pd layers [28] change their magneto-optical properties upon hydrogen absorption as well. Recently, high-quality ultrathin palladium and platinum films have become available, and study of their optical properties has started. In Ref. [29], permittivity of ALD films found by spectroscopic ellipsometry is reported.
Tungsten trioxide, a commonly known electrochromic material [30], exhibits a distinguished gasochromic response [31], which is attributed to the formation of tungsten bronze, $\textrm{HW}{\textrm{O}_\textrm{3}}$ [32], and/or the oxygen vacancies, $\textrm{W}{\textrm{O}_{3 - x}}$ [33], with absorption in the near-infrared and red parts of visible range [30]. Interest in various optical and plasmonic nanostructures involving $\textrm{W}{\textrm{O}_\textrm{3}}$ has been increasing. Hydrogen detection with single-pass schemes based on optical fibers [34,35], resonance fiber structures [36], the Kretschmann geometry in planar and fiber configurations [32], and plasmonic nanostructures [37] has been demonstrated. However, the potential of optical nanostructures for gas sensing has not yet been realized. Surface waves and Tamm states in photonic crystals [38], magnetooptical systems [39,40], plasmonic nanoparticle arrays [41,42], integrated plasmonic waveguides [43,44], plasmonic lasers [45–48], and 2D materials-based nanostructures [49,50] seem highly perspective if they are functionalized with gasochromic materials. To design such nanostructures, it is necessary to know the optical characteristics of gasochromic material, namely the wavelength-dependent refractive index n and extinction coefficient k. It is equally important to know the optical properties of ultrathin (2–30 nm) Pd and Pt films because they can differ significantly from the table data [51].
The optical properties of $\textrm{W}{\textrm{O}_\textrm{3}}$ films have been studied in numerous papers (see works [30] and [52] and references therein), most of which focus on electrochromic properties. Many studies have examined the properties of the ultraviolet band gap, which are determined from measurements of the spectral absorbance $\alpha $. For different dielectrics, the frequency dependences of $\alpha $ are approximated by the $\alpha (\omega )\propto {({\omega - {\omega_g}} )^\eta }$ law near the interband transition frequency. The value of $\eta $ is associated with the type of transition: $\eta = 1/2$ is for the direct allowed, $\eta = 3/2$ is for the direct inhibited, $\eta = 2$ is for the indirect allowed, and $\eta = 3$ is for the indirect inhibited type [52–54]. The lowest interband transition for $\textrm{W}{\textrm{O}_\textrm{3}}$ is known to be the indirect allowed type, i.e., $\eta = 2$ [30,55–57].
Refractive index and extinction coefficient data for WO3 have previously been published for films formed by magnetron sputtering in different regimes [57,58] and by thermal evaporation [53]. These dependences were calculated from the transmittance and reflectance measured at normal incidence. The most reliable procedure for the retrieval of optical parameters of $\textrm{W}{\textrm{O}_\textrm{3}}$ was performed in Ref. [59], whereby the optical parameters of magnetron sputtered film were restored by simultaneous fitting of the calculated transmission, reflection, and ellipsometry spectra to the experimentally measured ones. More progress for a magnetron sputtered $\textrm{W}{\textrm{O}_\textrm{3}}$ film was made in Ref. [60], whereby the permittivity retrieval produced a good agreement between the calculated and measured data for both transmission spectra and ellipsometry at three angles of incidence. The wavelength-dependent permittivity of $\textrm{W}{\textrm{O}_\textrm{3}}$ was approximated by the Tauc-Lorentz formula [61]. It is worth mentioning that intermediate layers describing surface roughness are often used in the retrieval of permittivity of thin films [60,62–65]. When using such data to calculate new structures, it is also necessary to add corresponding roughness layers, with the properties generally being unknown. In particular, the parameters of the roughness layers nontrivially depend on the neighboring media as well as the geometry of the device.
In the present paper, we publish a permittivity data for $\textrm{W}{\textrm{O}_\textrm{3}}$, Pd, and Pt films formed by electron beam evaporation. Based on the experimental transmission spectra and ellipsometry at three angles, the permittivity data are retrieved both pointwise at each wavelength point and for $\textrm{W}{\textrm{O}_\textrm{3}}$ by parameterization with the Tauc-Lorentz formula. Good agreement between the calculated and experimental results was obtained without the use of additional surface roughness layers. Therefore, the obtained parameters can be directly applied to design devices with integrated electrochromic and gasochromic materials without the addition of auxiliary layers into the model. For ultrathin Pt and Pd films, good agreement was obtained between the calculated and experimental spectra by using local isotropic permittivity, which greatly simplifies calculations of corresponding devices.
2. Technological, experimental and computational techniques
Samples of $\textrm{W}{\textrm{O}_\textrm{3}}$ films were prepared on a UV grade fused silica substrate (hereafter referred to as the substrate), some of which were covered by a catalyst (Pd or Pt) ultrathin film of 5-7 nm thickness measured by quartz crystal microbalance monitor. Reference palladium and platinum films of the same thickness were also deposited directly on the substrate.
Thin films of tungsten oxide are characterized by a wide variation in stoichiometry, as the percentage of oxygen can vary. In turn, the chemical composition determines the layer’s optical properties. For the controlled production of a given stoichiometry, a working gas inlet, deposition rate variation, substrate heating, and ion assisting are used during the formation of the oxide layer. All of this leads to a strong dependence of the film parameters on the deposition regime.
Tungsten trioxide films were deposited by electron beam evaporation. The deposition rate and working pressure (flow of injected gas) were varied during the development of the evaporation process. We found that a minimum optical absorption of the fabricated films was observed for the following conditions: deposition rate of 0.5 nm/s and working pressure of 5×10−3 Pa (without substrate heating or ion assisting). The metals were evaporated from a cassette of an electron beam evaporator at deposition rates of 0.1 and 0.05 nm/s for the palladium and platinum, respectively, at the same base pressure of 8×10−8 Pa.
Similar structures without catalyst were fabricated to retrieve the optical parameters of all the constituents in substrate/WO3/catalyst structures. The latter films were deposited in the same process in all the structures, including WO3 films of the same thickness, the latter films were deposited in the same process. This was necessary in order to ensure perfect matching of the WO3 films parameters for the subsequent correct extraction of the parameters of the catalyst films.
Optical parameters of metal and $\textrm{W}{\textrm{O}_3}$ films ($\varepsilon ^{\prime}$ and $\varepsilon ^{\prime\prime}$ vs $\lambda $) were determined from the transmittance spectra ${T_{\exp }}(\lambda )$ measured at normal incidence and from ellipsometric spectra ${\psi _{\exp }}({\lambda ,\theta } )$, ${\Delta _{\exp }}({\lambda ,\theta } )$ measured at three angles of incidence: $\theta = 45^\circ $, 60° and 75°. The simultaneous fitting of these seven spectra by the variation of two quantities ($\varepsilon ^{\prime}$ and $\varepsilon ^{\prime\prime}$, or alternatively n and ) ensured reliability of the results.
The optical properties of tungsten trioxide films were experimentally studied with V-VASE Woollam ellipsometer (USA) and a UV-3600 Plus double-beam spectrophotometer (Shimadzu, Japan). The visible and near-infrared spectra of ellipsometric parameters ψ and Δ and the transmission spectra were measured.
We used our own program to restore the permittivity spectrum. The spectrum of the refractive index of the substrate was taken from its passport. The correspondence of this data to experimentally measured data was reliably confirmed. Two approaches were used for the permittivity retrieval:
- i) Pointwise retrieval of n and k values at each $\lambda $ with simultaneous optimization of the layer thickness. For this purpose, a residual function$$\begin{array}{l} {\Phi _1}({\{{{\varepsilon_\lambda }} \},d} )= \sum\limits_{\{\lambda \}} {{\chi _1}{{|{T({\lambda ,\theta = 0,{\varepsilon_\lambda },d} )- {T_{\exp }}(\lambda )} |}^2}} \\ + \sum\limits_{\{{\lambda ,\theta } \}} {{\chi _2}{{|{\rho ({\lambda ,\theta ,{\varepsilon_\lambda },d} )- {\rho_{\exp }}({\lambda ,\theta } )} |}^2},} \end{array}$$was minimized over the values of the complex permittivity ${\varepsilon _i}$ at each $\lambda $ and over the thickness d of the film. We also denoted Т calculated transmittance values, $\rho = {r_p}/{r_s}$ ratio of complex reflection coefficients in p- and s-polarizations, whereas a corresponding experimental value is found as ${\rho _{\exp }} = \textrm{tan}({{\psi_{\exp }}} )\exp ({ - i{\Delta _{\exp }}} )$. Weight coefficients ${\chi _{1,2}}$ determine the relative contribution of transmittance and ellipsometry to the residual function; their empirically determined values are ${\chi _1} = 8$ and ${\chi _2} = 1$. This procedure gives complex permittivity values at each wavelength and layer thickness, which provide the fitting of the experiment. The advantage of this method is the “direct determination” of the dispersion curves giving the best fitting result; however, disadvantages are the presence of artifacts in the obtained spectra (see Section 3) and the absence of a guarantee that the obtained permittivity obeys Kramers-Kronig relations.
- ii) To avoid artifacts in the dispersion curves, the permittivity spectrum can be approximated by any suitable function that satisfies Kramers-Kronig relations. Particularly, our analysis confirmed (see Ref. [60]) that the $\textrm{W}{\textrm{O}_\textrm{3}}$ dispersion was excellently fitted by Tauc-Lorentz formula [61] developed for the description of permittivity of semiconductors with allowed indirect interband transition [30,56], in which the imaginary part of permittivity demonstrated a quadratic behaviour at the band edge:$$\varepsilon ^{\prime\prime}(\Lambda )= AC\frac{{{\Lambda _0}{{({\Lambda - {\Lambda _g}} )}^2}}}{{\Lambda [{{{({{\Lambda ^2} - \Lambda _0^2} )}^2} + {C^2}{\Lambda ^2}} ]}}\theta ({\Lambda - {\Lambda _g}} ), $$whereas the real part of permittivity $\varepsilon ^{\prime}(\Lambda )$ was calculated from Eq. (2) with the Kramers-Kronig relation and described by the well-known cumbersome formula [66] (see Eqs. (S1)–(S7) in Supplementary Materials). Here, the inverse wavelength $\Lambda = 1/\lambda $ (in $\textrm{c}{\textrm{m}^{ - 1}}$) was used instead of the frequency.
Optimization of the permittivity parameters ${\varepsilon _\infty }$, A, C, ${\Lambda _0}$, ${\Lambda _g}$ and of the film thickness d (total 6 parameters for the whole spectrum) was carried out by minimizing the function
$$\begin{array}{l} {\Phi _2}({{\varepsilon_\infty },A,{\Lambda _0},{\Lambda _g},d} )= \sum\limits_{\{\lambda \}} {{\chi _1}{{|{T({\lambda ,\theta = 0,{\varepsilon_\infty },A,{\Lambda _0},{\Lambda _g},d} )- {T_{\exp }}(\lambda )} |}^2}} \\ + \sum\limits_{\{{\lambda ,\theta } \}} {{\chi _2}{{|{\rho ({\lambda ,\theta ,{\varepsilon_\infty },A,{\Lambda _0},{\Lambda _g},d} )- {\rho_{\exp }}({\lambda ,\theta } )} |}^2}} . \end{array}$$
The result was a parametrically defined dispersion of the complex dielectric constant and an optimized thickness value. The advantages of the method are the exclusion of artifacts having the form of noise and oscillations, as well as the automatic fulfillment of the Kramers-Kronig relation; however, disadvantages are a worse (compared with the pointwise retrieval) agreement with the experiment and the need for the right choice of dispersion model.
To demonstrate the practical applicability of obtained dispersions, Section 5 describes experimental spectra and results of numerical calculations conducted by using COMSOL Multiphysics. A calculation model of the fabricated 1D nanostructure was a single unit cell with periodic boundary conditions and had the structural parameters specified in Section 5. The periodic ports were applied to launch the incident wave and to calculate transmission spectra.
3. Results: optical properties of tungsten trioxide films
We begin with the results for tungsten trioxide film with the smallest thickness, which is determined to be 81 nm by the retrieval procedure. The results of pointwise refractive index retrieval ($n + ik = \sqrt {\varepsilon ^{\prime} + i\varepsilon ^{\prime\prime}} $) of $\textrm{W}{\textrm{O}_\textrm{3}}$ film have shown an excellent agreement between the calculation and experiment; however, the obtained spectra involve artifacts (circles in Figs. 1(a) and 1(c)) of two kinds: random noise and slow regular oscillations. In particular, noise in the extinction coefficient k leads to non-physical negative values. Slow oscillations of both n and k are also non-physical; more precise, they arise from interference fringes in the experimental spectra. Ideally, oscillations should completely disappear from the resulting n and k spectra. However, inevitable errors associated with imperfections of samples and the measurement errors leave traces of these resonances in n and k.
Fig. 1. The wavelenth-dependent refractive index (a, b) and extinction coefficient (c, d) of $\textrm{W}{\textrm{O}_\textrm{3}}$ films. (a, c) Comparison of the results obtained for 81 nm thick film from the same experimental data using different methods: pointwise retrieval at each spectral point (circles) and approximation by Tauc-Lorentz model (lines). The inset shows a close-up of the extinction coefficient dependence on the wavelength. (b, d) A comparison of the results for 81 nm- (solid curves), 162 nm- (dashed curves) and 515 nm-thick (dotted curves) $\textrm{W}{\textrm{O}_\textrm{3}}$ films obtained from our experimental data using the Tauc-Lorentz fit with the results of previous studies [59,60] (crosses and black solid line).
To eliminate these artifacts, wavelength-dependent permittivity was appximated by the Tauc-Lorentz model (2). The results confirmed a good agreement between this model (solid lines in Figs. 1(a), and 1c) and the pointwise permittivity dispersion. The result of calculating the transmission and ellipsometry spectra from the obtained permittivity fitted the experimental spectra well (see Fig. S1 in Supplementary). For the 81 nm thick sample, the following Tauc-Lorentz dispersion parameters were obtained: ${\varepsilon _\infty } = 2.56,$ $A = 5.97 \times {10^5}$ cm−1, $C = 1.26 \times {10^4}$ cm−1, ${\Lambda _0} = 3.64 \times {10^4}$ cm−1 and ${\Lambda _g} = 2.65 \times {10^4}$ cm−1.
The data obtained for tungsten trioxide films of other thicknesses (Figs. 1(b) and 1(d)) show a slight increase in the refractive index. The refractive index is expected to be between these values at intermediary thicknesses. Furthermore, an increase in the thickness leads to increased optical losses (correspondence between the calculation results and experimental data is demonstrated in Figs. S2 and S3). In addition, the discrepancy between the experimental and calculated data increased. Presumably, this was due to the cracking of thicker films of tungsten trioxide, which resulted in scattering. The obtained results are quite close to previously-published data (Figs. 1(b) and 1(d)); however, a noticeable difference is observed, which is presumably due to different deposition technologies and, as a result, different structures of the films.
4. Results: optical properties of ultrathin palladium and platinum films
For the experimental study of the optical properties of metal (palladium and platinum) films, two types of topologies were fabricated: substrate/metal and substrate/WO3/metal. The same set of measurements was performed as described in Section 3: the transmission spectrum at normal incidence and the spectra of ellipsometric parameters at the three angles. The refractive index spectra of $\textrm{W}{\textrm{O}_\textrm{3}}$ described in Section 3 were used to determine the effective permittivities of the ultrathin metal films. Only the pointwise permittivity retrieval (see Section 2) was carried out, whereas the parametrization of the permittivity dispersion was not conducted.
SEM images of the palladium and platinum ultrathin films surface (Fig. 2, also see a cross-section image in Fig. S10) showed that these films were continuous despite their ultra-small thicknesses (see insets in Figs. 2(b) and 2(d)). Only the Pt film on SiO2 substrate exhibited some signs of discontinuity (Fig. 2(c)). The size of the grains on all the films appeared as small as 10-20 nm, which presumably decreases scattering. Rare defects observed in Fig. 2 come from the substrate. Note that these defects are so clearly marked because metal conformly coats the relief of the substrate. As we show below, these coatings can be well-described by effective parameters.
Fig. 2. SEM images of palladium (a, b) and platinum (c, d) films deposited directly on a quartz substrate (a, c) and on a 81 nm thick WO3 film (b, d). Insets show images of the samples after annealing at 600°C illustrating the continuity of as-fabricated films.
For the palladium and platinum films deposited directly on the substrate, the permittivity was close to zero and positive in the long-wavelength part of the spectrum (red curves in Fig. 3). Such behavior is not typical for metal [51,67,68]. The effective permittivity of similar metal films deposited on a film of tungsten trioxide (blue and green curves in Fig. 3) was significantly different. These data were closer to the values known for bulk samples (compare with solid curves in Fig. 3).
Fig. 3. Real (a,b) and imaginary (c,d) parts of permittivity of Pd (a, c) and Pt (b, d) films deposited directly on the substrate (circles) and on WO3 films of various thicknesses (81 nm – crosses, 162 nm – triangles), and the same quantities for bulk materials published in Ref. [51] (solid lines).
he possibility of describing an ultrathin film by isotropic dielectric constant is nontrivial. Nevertheless, the consistency of our results was confirmed by the following: (i) the spectra measured at different angles of incidence and polarization were simultaneously well-described by the obtained permittivity (Figs. S4-S9); and (ii) the residual function (1) had a rather sharp minimum at the optimal value of the effective film thickness (Fig. 4). One can note that a considerable growth of the residual function, which has a sense of discrepancy of the fitting procedure, is observed at a 1 nm change in the thickness, which can be considered as an accuracy of the retrieved thickness value.
Fig. 4. Discrepancies depending on the thickness of the Pd (a) and Pt (b) ultrathin films assumed in calculation. Vertical lines mark optimum thickness values for each sample.
The Pd and Pt films are definitely composites, as their properties depend on neighboring materials. However, the effective permittivity is not approximated by known mixing formulae (Bruggemann, Garnett, symmetrized Garnett, etc). All of the permittivity data are given in Dataset 1 [69], Dataset 2 [70], Dataset 3 [71] and Dataset 4 [72].
5. Verification of the obtained results
Fig. 5. (a) Optimized structure of a sensing element (the side view of the unit cell is shown) and calculated amplitude of the electric field distribution for λ = 710 nm, (b) measured (solid curve) and calculated (dashed curve) thransmission spectra for the sensing element with the Pd calalyst, (d) the same with Pt catalyst, (c) SEM image of the unit cells of a fabricated sensing element. Light polarization was along the stripes.
The dispersions of tungsten trioxide and ultrathin catalyst films reported above were used to find the structural parameters of a nanostructure elaborated as a sensing element (substrate/Al2O3 grating/WO3/Pd or Pt). The nanostructure was optimized to obtain the largest changes in transmission in the presence of hydrogen (which will be reported elsewere) and was an 1D dielectric grating consisting of $\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}$ stripes coated with the $\textrm{W}{\textrm{O}_\textrm{3}}$ and ultrathin catalyst (Pd and Pt) films. To obtain a higher quality factor of resonances (see plots b and d), the nanostructure had the following characteristics: the grating period was D = 470 nm, $\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}$ stripe thickess was 110 nm and stripe width was 220 nm, $\textrm{W}{\textrm{O}_\textrm{3}}$ thickness was 111 nm and Pd thickness was 1 nm. Figure 5(c) shows a SEM image of the fabricated sensing element. For light polarized along the stripes, the distribution of the electric field amplitude in a unit cell is shown in Fig. 5(a) at the resonance due to coupling light through the diffraction condition λ = neffD = 710 nm, where neff = 1.51 is the effective refractive index of the guided mode of the system. One can see that the measured and calculated spectra were in a good agreement.
Thus, we have demonstrated that high-quality samples enable the avoidance of intermediary surface layers in calculation models. We show that the parameters obtained in such a manner provide a good correspondence when dealing with a nanostructure of complex geometry. This is very advantageous, because the properties of the surface layers depend nontrivially on geometry.
6. Conclusions
It is widely known that metal oxides exhibit significantly different optical properties depending on the fabrication technology. However, the results reported here and in other literature demonstrate that the tungsten trioxide optical properties do not manifest substantial variation, even when using different deposition techniques (Figs. 1(c) and 1(d)). This is likely due to the high level of modern technology, which enables the obtainment of reproducible results.
Describing the optical properties of thin metallic films has always been a challenging task. The problems of homogenization of optical parameters [73,74], boundary conditions, and nonlocality have not yet been fully solved. All of these issues lead to significant difficulties in the prediction of realistic responses of desired nanostructures. Modern technology of metal films fabrication enables the formation of highly homogeneous thin metallic films (Fig. 2, also see Ref. [75]). In this work, we illustrate the applicability of the simplest description of experimentally obtained ultrathin films with effective permittivity. We believe that the demonstrated data can be used for predicting the optical properties of nanostructured sensing elements with any design based on palladium or tungsten trioxide/catalyst gasochromic films.
Funding
Russian Foundation for Basic Research (20-02-00504); Foundation for the Advancement of Theoretical Physics and Mathematics.
Acknowledgments
Samples were fabricated at the BMSTU Nanofabrication Facility (FMN Laboratory, FMNS REC, ID 74300). The authors are thankful to A.V. Andriyash for fruitful discussions. This work was supported by Russian Foundation for Basic Research through research project N 20-02-00504. D.P. Kulikova acknowledges the financial support from the Foundation for the Advancement of Theoretical Physics and Mathematics (BASIS).
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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