Multilevel effective material approximation for modeling ellipsometric measurements on complex porous thin ﬁ lms

: Catalysts are important components in chemical processes because they lower the activation energy and thus determine the rate, efficiency and selectivity of a chemical reaction. This property plays an important role in many of today ’ s processes, including the electrochemical splitting of water. Due to the continuous development of catalyst materials, they are becoming more complex, which makes a reliable evaluation of physicochemical properties challenging even for modern analytical measurement techniques and industrial manufacturing. We present a fast, vacuum-free and non-destructive analytical approach using multi-sample spectroscopic ellipsometry to determine relevant material parameters such as film thickness, porosity and composition of mesoporous IrO x – TiO y ﬁ lms. Mesoporous IrO x – TiO y ﬁ lms were deposited on Si wafers by sol – gel synthesis, varying the composition of the mixed oxide ﬁ lms between 0 and 100 wt% Ir . The ellipsometric modeling is based on an anisotropic Bruggeman effective medium approximation (a-BEMA) to determine the ﬁ lm thickness and volume fraction of the material and pores. The volume fraction of thematerial wasagain modeled using a Bruggeman EMA to determine the chemical composition of the materials. The ellipsometric ﬁ tting results were compared with complementary methods, such as scanning electron microscopy (SEM), electron probe microanalysis as well as environmental ellipsometric porosimetry (EEP).


Introduction
Catalysis plays an important role in technical chemistry for the production of chemicals, novel products or pharmaceuticals. Catalysis also plays a crucial role in energy conversion processes, as catalysts determine the rate, efficiency and selectivity of electrochemical reactions. Electrochemical conversion processes for large-scale hydrogen production can contribute to the efficiency of energy transformation. However, the current state of the art still relies on expensive and rare precious metals such as platinum or iridium. Therefore, a more efficient use of catalyst materials requires a reduction in the current precious metal content.
The introduction of supported nanoparticles or porous coatings are promising approaches to reduce the noble metal content while maintaining the activity. In this context, both nanoparticles and porous coatings have a high surfaceto-volume ratio and thus serve to increase the active surface area. The latter represents a good compromise between surface chemical catalysis and mass transfer.
Iridium oxide-based catalysts are typically used for the oxygen evolution reaction (OER) in the electrochemical water splitting, as they exhibit a good combination of both activity and stability. Yet, iridium and its oxides are scarce and expensive resources and therefore require an efficient use. This can be achieved by increasing the active surface area through the synthesis of nanoparticles or the introduction of porosity. In the case of porous materials, studies show that the introduction of porosity in such materials leads to a significant reduction in the required overpotential [1]. A mesoporous IrO x film thus shows a reduction in overpotential of about 17% compared to the non-porous catalyst film [2].
Another way to reduce cost is to replace the expensive noble metals with less costly materials. Current research is mainly focused on metal oxides such as MnO x , FeO x , CoO x and NiO x due to their good activity in the OER under acidic conditions [3]. In this context, MnO x seems to be a very attractive candidate since it is a very stable material in low pH electrolytes [4]. However, a major drawback of these materials is usually the higher overpotential required, which reduces the efficiency of catalysis.
An alternative approach is to add a second element or material to either increase the activity by changing the structure or to reduce the precious metal content while maintaining the activity. Willinger et al. showed in their work that adding potassium to the iridium oxide catalyst can change the crystal structure, thus leading to an increase in activity [5]. Oakton et al., on the other hand, pursued the approach of dispersing iridium oxide nanoparticles in titanium oxide in their studies and were thus able to achieve a reduction in the noble metal content [6,7]. A similar approach to the latter was also followed by Bernicke et al. in which they synthesized a mesoporous network of iridium oxide and titanium oxide [8,9]. These synthesized mixed oxide films showed high conductivity and high surface area and activity in the acidic OER.
These studies show that the catalyst materials developed today are becoming increasingly complex, making reliable evaluation of physicochemical properties challenging even for modern analytical measurement techniques. Many characterization procedures are performed in high vacuum and are not always completely nondestructive, especially when parameters such as layer thickness or the chemical composition are to be determined. For instance, the reductive electron beam used in electron microscopy (EM) can alter material properties. Also, transmission electron microscopy (TEM) studies have shown that the electron beam is able to reduce IrO x to Ir and thus misinterpretation of the results may occur [10]. Other methods such as X-ray photoelectron spectroscopy (XPS) or secondary ion mass spectrometry (SIMS) to determine the chemical composition of the material at the outer surface and below (in the bulk) also involve the destruction of the material (e.g., by sputtering). As an alternative to these techniques, spectroscopic ellipsometry can serve as a vacuum-free and non-destructive method. It involves determining changes in the polarization state of an electromagnetic wave upon reflection, resulting in a change in amplitude ratio and a phase shift [11,12].
The group around Sanchez showed in their work ellipsometric investigations of the porosity and pore sizes of a bimetallic mesoporous NbVO 5 film [13]. May et al. also showed ellipsometric studies of mixed MoWO x films in their study and determined the band gap energy as a function of Mo content [14]. Here, the authors used for each MoWO x film a separate model. Buiu et al. also focused on ellipsometric studies of mixed metal oxides and showed a dependence of the band gap energy on the composition of hafnium silicate films [15]. Also in this case, the different compositions were modeled with a separate model, which means that no information about the composition of the films can be obtained.
Here we report on the vacuum-free and non-destructive ellipsometric analysis and modeling of bimetallic mesoporous IrO x -TiO y films with different weight percent (0-100 wt% Ir ) Ir in Ir/TiO 2 to determine relevant parameters like film thickness, porosity and chemical composition, using only the models of the pure metal oxides (i.e., IrO x and TiO y ). This approach includes the characterization and modeling of the pure mesoporous IrO x and TiO y films with an anisotropic Bruggeman effective medium approximation (a-BEMA). The variations of the bimetallic mesoporous IrO x -TiO y films were then characterized using the pure metal oxide models in a Bruggeman effective medium approximation (BEMA) with a multi-sample analysis (MSA). The derived material parameters such as film thickness, porosity and their chemical composition were validated by complementary methods such as scanning electron microscopy (SEM), electron probe microanalysis (EPMA) and environmental ellipsometric porosimetry (EEP).

Chemicals
Iridium acetate (Ir[CH 3 COO] n , 99.95% metal base, about 48% Ir) from chemPUR and titanium chloride (TiCl 4 , 99.9%) from Sigma-Aldrich were used to synthesize the mesoporous iridium-titania films. The polymer template (PEO-PB-PEO, containing 18,700 g mol −1 polyethylene oxide [PEO] and 10,000 g mol −1 polybutadiene [PB]) was purchased from Polymer Service Merseburg GmbH [16]. Ethanol (EtOH, >99%) was used as solvent from Sigma-Aldrich. All chemicals were used without further preparation. The films were deposited on unilaterally polished Si wafers with (100)-orientation (Siegert wafers) via dip coating under controlled conditions (see Synthesis). The Si wafers were cleaned with ethanol prior to film deposition. For quantification and validation of Ir mass loading, an iridium foil (0.25 mm thick, 99.8% [metal base], 22.7 g cm −3 ; abcr chemicals GmbH), a TiO 2 reference material, and a Si wafer from Siegert Wafers were used as reference materials for electron probe microanalysis (EPMA).

Synthesis of iridium-titanium oxide films
Iridium titanium oxide films were prepared in a slightly modified synthesis to that described by Bernicke et al. [8] In a typical synthesis for a 30 wt% IrO x -TiO y film (30 wt% Ir in Ir/TiO 2 ), 141 mg of the PEO-PB-PEO polymer template was dissolved in 3.75 ml ethanol at 40°C. After complete dissolution, a second solution containing 751 mg of titanium(IV) chloride in 3.75 ml of ethanol was added and mixed at 40°C for 1 h. Subsequently, 272 mg of iridium(III) acetate was added and mixed at 40°C for another hour. The dark green solution obtained was transferred to a preheated Teflon cuvette (40°C) and immediately coated by immersion under controlled conditions (25°C, 40% relative humidity) at a withdrawal rate of 200 mm min −1 . The films thus prepared were dried under the same conditions for 5 min and then calcined in a preheated muffle furnace in flowing air at 400°C for 10 min. For the variation of wt% Ir within the IrO x -TiO y films was realized by adjusting the amount of iridium(III) acetate during the synthesis.

Physicochemical characterization
Ellipsometry measurements were performed using a variable angle M2000 DI spectroscopic ellipsometer (J.A. Woollam) in a spectral range between 192 and 1697 nm. The spectral resolution of the used ellipsometer is about 5 nm bandwidth in the UV/Vis and about 10 nm in the NIR. The mesoporous IrO x -TiO y films on single polished (100) silicon substrates were measured at angles of incidence (AOI) of 55°, 60°, 65°, 70°, and 75°relative to the normal. The measured Ψ and Δ spectra were modeled using CompleteEASE software (v6.42). The pure IrO x and TiO y films were modeled, respectively, and the IrO x -TiO y mixed oxide films were subsequently analyzed with the models of the pure films in a multi-sample analysis with respect to their film thickness, porosity, and composition.
The porosities of the films were additionally analyzed using environmental ellipsometric porosimetry (EEP) with an ambient cell and a fixed incidence angle of 60°. Pure water served as the solvent. Relative humidity was adjusted by mixing a water-saturated nitrogen gas flow with a dry nitrogen gas flow. The total N 2 flow was 2 l min −1 , controlled by two mass flow controllers, at a constant temperature of 23°C. Relative humidity was measured for the exiting gas flow and for each water partial pressure downstream of the cell.
Scanning electron microscope (SEM) images were acquired on a JEOL 7401F at 10 kV. Images were then analyzed for extracting the film thickness using the ImageJ program (v. 1.51w, www.imagej.nih.gov/ij/). EPMA were performed on a Carl Zeiss Supra 40 equipped with a Schottky field emitter and an energy dispersive X-ray spectrometer (EDS) with a 10 mm 2 silicon drift detector (SDD) having an energy resolution of 123 eV (Bruker XFlash 5010). Here, the measured net peak X-ray intensities of interest were divided by the electron probe current and spectra lifetime to calculate the k EPMA values. EDS spectra were recorded at accelerating voltages of 15, 20, 25, and 30 kV for the Ir L α , Ti K α , O K α , and Si K α lines, respectively. StrataGem thin-film analysis software (v. 6.7 SAMx, Guyancourt, France) was used for quantification of the chemical composition [17].

Ellipsometric modeling
Mesoporous metal oxide films were generally modeled using an anisotropic Bruggeman effective medium approximation (a-BEMA) described by D. Schmidt and M. Schubert, due to the synthesis-related ellipsoidal pore geometries in the z-direction, i.e., perpendicular to the substrate [18].
The (a-BEMA) is expressed as follows: with depolarization factors: ϵ i as dielectric functions and f i as volume fraction of the i th component (i.e., the guest fraction, i = a, b, c), and ϵ eff, j describes the effective major dielectric function (j = x, y, z) [18]. The real depolarization factors L j only depend on the real shape parameters U j of the ellipsoid and the two relationships (U x /U z ) and (U y /U z ) serve to precisely define the shape [18]. In this context, the a-BEMA layer consists of the volume fraction of the metal oxide matrix and void. In the case of the bimetallic mixed oxides, the metal oxide matrix was modeled using a BEMA to model the volume fractions of both metal oxide matrix materials.
The BEMA is defined as: with ϵ EMA as dielectric constant of the mixed phase, ϵ i as dielectric functions and f i as volume fraction of the i th component (i.e., the guest fraction, i = a, b, c) [12,19]. γ represents the factor that describes the shape of the guest volume and can be expressed as follows: where L defined the depolarization factor. In the isotropic case, i.e., for 3-dimensional spheres, L = 1/3 and γ = 2 [19]. The titanium oxide matrix material was modeled by a summation of two coupled Tauc-Lorentz functions to describe the optical properties of amorphous semiconductors near the band edge [20]. The Tauc-Lorentz function described in detail by G. E. Jellison Jr. and F. A. Modine and is expressed as follows [21,22]: where Amp n is the amplitude of the n th oscillator (eV), En n the center energy of n th oscillator (eV), Γ n the width (full width at half-maximum) of the n th oscillator (eV) and E g the band-gap energy (eV). Fit parameters of the Tauc-Lorentz parametrization are the amplitude Amp n , the width Γ n , the center energy En n , and the band-gap energy E g . The iridium oxide matrix material was modeled with a multipeak function model using a Drude function to describe free carrier effects [23,24], due to the electrical conductivity of the IrO x material and three Lorentz functions for the description of different atomic transitions [11,19].
The Drude functions is defined as: with where E is the photon energy (E = hν = ħω), ℏ the reduced Planck constant, ϵ 0 the vacuum dielectric constant, ρ R the resistivity (Ω cm), R. Sachse et al.: Multilevel EMA for SE on complex porous thin films τ the mean scattering time (fs), m * the electron effective mass (9.11 • 10 −31 kg), N the electron concentration (cm −3 ), q the electron charge (1.60 • 10 −19 C) and μ the electron mobility (cm 2 V −1 s −1 ) [25]. Fit parameters for the Drude model are the resistivity ρ R and the mean scattering time τ.
The Lorentz function is defined as: with Amp n as the amplitude of the n th oscillator (unitless), Γ n width (full width at half-maximum) of the n th oscillator (eV) and En n the center energy of n th oscillator (eV) [26]. The fit parameters of the Lorentz parametrization are the amplitude Amp n , the width Γ n and the center energy En n .

Root mean squared deviation
In order to minimize the deviation between theoretical and experimental measured variables, the definition of a figure of merit, the root mean squared deviation (D RMS ), was used. The D RMS can be expressed as follows: with N = cos(2Ψ) (11) C = sin(2Ψ)cos(Δ) (12) S = sin(2Ψ)sin(Δ) (13) where Y is the number of wavelengths and Z the number of fit parameters.

Multi-sample-analysis
Measuring multiple samples of the same material with different properties, such as film thickness, is mostly used to gain additional information about the dielectric function and reduce the correlation between model functions and material parameters. However, multisample analysis can also be used to investigate the properties of several samples simultaneously [27]. However, for this purpose, the following sample properties must be assumed: (1) All samples are of the same type, i.e., they are mesoporous metal oxide films with a comparable porosity, deposited on the same Si substrates with a native oxide layer and calcined at the same temperature.

Results and discussion
Mesoporous IrO x -TiO y films are complex due to their porosity and the mixture of two materials and cannot be analyzed directly ellipsometrically with MSA since parameter couplings may occur. Therefore, in a first step, the individual components of the mixtures, i.e., IrO x and TiO y , are analyzed separately to determine the dielectric functions of the materials. Then, the analysis of the mixed phases, which were varied between 0 and 100 wt% Ircontent (wt% Ir ), is performed using the previously determined dielectric functions of the pure metal oxides to determine the film thickness, porosity and chemical composition. These parameters were determined by the MSA, which were additionally validated by independent methods for the accuracy of the result. Table 1 gives an overview of the spectroscopic ellipsometry results for the pure mesoporous metal oxide films and for the mesoporous mixed metal oxide films. The second section of Table 1 summarizes the results of the complementary methods for film thickness, porosity and Ir-content.

Mesoporous TiO y film
The mesoporous TiO y film was synthesized in a slightly different synthesis than described in the literature [16,[27][28][29], deposited on a Si substrate via dip coating and calcined in a preheated muffle furnace at 400°C under air for 20 min. SEM images in Figure 1a and b show a uniform pore surface and film thickness of the synthesized films.
For the modeling of the ellipsometry spectra, a model consisting of a Si substrate (literature values) [30,31], a native oxide layer (literature values) [32] and a-BEMA [18] layer (Eq. (1)) was used. The a-BEMA layer is composed of the volume of the TiO y material (two E g coupled Tauc-Lorentz [Eqs. (5) and (6)]) and the pore volume (void). By removing the template polymer during calcination, the layer shrinks, and the pores acquire an elliptical shape. This is fitted by the anisotropy factor in z-direction of the a-BEMA layer. Figure 2 shows the measured and modeled Ψ and Δ spectra (AOI: 55-75°, in 5°steps), as well as the dielectric functions.
Both the modeled Ψ and Δ spectra show good agreement with the measured values, whereas some larger deviations between model and measured Δ spectra are observed in the region around 4-5 eV (Figure 2a and b). However, the D RMS value does not exceed 22.408. Figure 2c shows the dielectric function of TiO y material described by two coupled Tauc-Lorentz functions. For comparison, literature values of the ordinary dielectric functions of the rutile [33] and anatase [34] phases of TiO 2 are shown. The dielectric functions of the mesoporous TiO y layer are more similar in shape to the TiO 2 rutile phase than the anatase phase. In both spectra (ε 1 and ε 2 ) the anatase phase shows a kind of shoulder at the main peak, which is not present in Table : Summary of material properties of mesoporous IrO x -TiO y films derived from spectroscopic ellipsometry and material properties of the complementary methods.

Spectroscopic ellipsometric measurements and modeling
Spectroscopic ellipsometry   the modeled spectra similar to the rutile phase. Thus, the mesoporous TiO y layer could be an amorphous or not perfectly stoichiometric rutile TiO 2 layer. From the fit results of the two Tauc-Lorentz functions (see Figure 2c), the band gap energy for the TiO y material is 2.95 eV. Compared to the band gap energies of the rutile phase (E g = 3.04 eV) [33] and the anatase phase (E g = 3.23 eV) [34], the band gap energy of the TiO y material is generally lower but very close to the value of the rutile phase, which reinforces the assumption of an amorphous rutile TiO 2 layer. In addition, a film thickness of 133.1 nm and a porosity value of 46.8% were derived from the fit. The most important results (i.e., film thickness and porosity) are summarized in Table 1 and will be discussed in detail together with the MSA results.

Mesoporous IrO x film
The mesoporous IrO x film was synthesized as described in ref. [35] and calcined at 400°C in a preheated muffle furnace for 5 min in air. The top view SEM image in Figure 3a shows an ordered pore structure at the outer surface area and the cross-sectional image (Figure 3b) reveals a film with a uniform film thickness.
Similar to the modeling of the TiO y layers, a model was used for the mesoporous IrO x layer consisting of a Si substrate (literature values) [30,31], a native oxide layer (literature values) [32], and a-BEMA (Eq. (1)) [18], which in turn consists of the IrO x material (Drude-Lorentz parametrization [Eqs. (7) and (9)]) and a void for the mesopores (Figure 3c). A detailed description of the model can be found in ref. [35].
Modeling of both Ψ and Δ spectra (measured at AOIs between 55 and 75°, in 5°steps) show good agreement in this case as well (Figure 4a and b). Again, slightly higher deviations in the range around 5 eV are observed in the modeled Δ spectra (Figure 4b), but in this case the D RMS value is no more than 8.274.
The dielectric functions were fitted by a Drude-Lorentz parameterization since the IrO x material is a conducting metal oxide (Figure 4c). Besides the Drude function in the low photon energy range (<2 eV), there is also a small absorption band at 1 eV represented by a Lorentz function. In addition, two absorption bands at 4 eV and at 7.  dielectric functions of the IrO x material can be attributed to free electron transitions and interband transitions. A more detailed description of these transitions can be found in refs. [35][36][37]. As a result of the fitting, parameters such as resistivity, film thickness and porosity can be derived. The resistivity value amount to 9.31 • 10 −4 Ω cm, the film thickness is 60.6 nm and a porosity value of 44.3% is obtained. Also in this case, the most important fitting results (film thickness and porosity) are summarized in Table 1 and will be discussed together with the derived results of the MSA.

Multi-sample analysis of IrO x -TiO y films
Finally, with the two TiO y and IrO x models developed previously, the IrO x -TiO y mixed oxide films with different compositions can be studied by spectroscopic ellipsometry. The IrO x -TiO y mixed oxide films were also prepared via dip coating and synthesized in a slightly modified synthetic route as described in ref. [8]. The films were deposited on Si substrates and subsequently calcined in air at 400°C for 10 min in a preheated muffle furnace. Figure 5 shows top view and cross section SEM images of a mesoporous IrO x -TiO y film with 30 wt% Ir content in Ir/TiO 2 , and the model used. The top view SEM image shows an ordered pore structure on the outer surface without any sign of phase separation. In the cross-sectional image, a uniform film thickness is observed.
A model consisting of a Si substrate (literature values) [30,31], a native oxide layer (literature values) [32] and an a-BEMA (Eq. (1)) [18] for the mesoporous layer was used for modeling. The a-BEMA [18] layer contains the volume fractions of the material matrix and the void for the mesopores. The material matrix, in turn, was modeled with a Bruggeman EMA (Eq. (3)) containing the volume fractions of the dielectric functions of TiO y and IrO x material from the previously modeled pure metal oxide layers. Subsequently, IrO x -TiO y films with an Ir-content between 0 wt% Ir (pure TiO y ) and 100 wt% Ir (pure IrO x ) were analyzed by MSA, where for each layer the film thickness, the volume fraction between the TiO y and IrO x material, the volume fraction of the void and the anisotropy in z-direction served as free parameters. Figure 6 shows exemplary measurement raw data and the deviation between the measured and modeled Ψ and Δ spectra of the mesoporous IrO x -TiO y film with 30 wt% Ir content, as well as the changes of the dielectric functions as a function of the Ir-content within the layers.
The modeled values generally show good agreement with the measured Ψ and Δ spectra (AOIs 55-75°, 5°steps), although again there are larger deviations when modeling the Δ spectra (Figure 6a, b). The single D RMS value for the 30 wt% Ir IrO x -TiO y film is 48.161. However, the D RMS value of the MSA is only 44.922.
The dielectric functions show a systematic change with increasing Ir-content (Figure 6c). Thus, the 15 wt% Ir IrO x -TiO y film still shows a quite similar pattern of dielectric functions compared to the pure TiO y film. At 30 wt% Ir , an absorption feature slowly becomes visible in ε 2 in the low photon energy range (about 1 eV), which becomes more obvious with increasing Ir-content. This feature can be attributed to the increasing Ir-content and the resulting increase in free charge carriers (higher electrical conductivity). The typical absorption band of TiO y in the range of 3-4 eV (ε 1 ) and 4-5 eV (ε 2 ) also decreases significantly with increasing Ir-content.
The derived material parameters layer thickness, the volume fraction of void (porosity) and the volume fraction of IrO x (converted to wt% Ir ) are shown in Figure 7.
The derived film thickness ( Figure 7a) shows a film thickness around 140 nm (130-150 nm) for the films from 0 wt% Ir to 45 wt% Ir , which decreases at higher Ir-content (>45 wt% Ir ). All films were deposited on the Si substrates under the same conditions (25°C ambient temperature, coating solution temperature of 40°C, 40% relative humidity) and constant withdrawal rate of 200 mm min −1 .
The differences in film thickness can therefore be attributed to the composition of the dip coating solution. We attribute this effect to changes in the viscosity of the solutions which leads to a variation of the amount of the amount of the solution coated on the substrate at constant withdrawal rate. The derived volume fractions of the voids show a relatively constant value at about 45% over the entire variation of the films (Figure 7b). This is in good agreement with similarly synthesized mesoporous films of the types TiO y , IrO x or their mixtures. It is also in good agreement with the fact that the same amount of template polymer was used for the different film syntheses and thus the porosity should be almost the same for all films.
The IrO x volume fractions converted to wt% Ir (Ir in Ir/TiO 2 ) also show good agreement compared to the nominal Ir fraction used during synthesis (Figure 7c). Thus, the analysis shows a constant increase of the Ir-content with increasing amount of the Ir precursor used.

Validation of MSA fit results
Since spectroscopic ellipsometry (SE) is an indirect method, the results of the material parameters are strongly dependent on the quality of the optical model. In order to get an indication of the accuracy of the derived results, they are validated with complementary analytical methods. For this purpose, environmental ellipsometric porosimetry (EEP) was used to validate the porosity, SEM for the film thickness and EPMA for the Ir-content. Figure 8 shows the parity plots for layer thickness (SE versus SEM), porosity (SE versus EEP) and Ir-content (SE versus EPMA versus nominal). The deviations of the ellipsometric methods (SE and EEP) were obtained by a sensitivity analysis for the respective parameter (i.e., layer thickness, porosity and Ir content), which is described in detail by Rosu et al. in ref. [27]. The deviations of the film thickness obtained by SEM cross-sectional images were determined by the standard deviation of several measurements along the fracture edge. For EPMA, the deviations were also determined by the standard deviations of the measured net peak X-ray intensities of interest. The obtained film thicknesses from SE and SEM provide similar values in a range less than 15 nm and similar trends (Figure 8a). It should be noted that the exact same location could not be measured between the two methods. However, previous homogeneity analyses on IrO x films show that inhomogeneity contributes only negligible amounts to the result uncertainties [35]. Thus, the analysis using the ellipsometric model approach shows a good agreement for the film thickness for all measured samples in the range between 0 wt% Ir and 100 wt% Ir and all values are in the range of a relative deviation of about 10%.
EEP measurements are an accurate method for determining the porosity of thin films [38][39][40]. The porosity values of the EEP adsorption isotherms were determined using the same models as those of the SE analysis. The porosity values of the two methods agree to less than 10% (Figure 8b), which shows a good agreement of the measurement results of the two methods and also in this case the values are in the range of relative deviation of 10%. Comparable results on similar mesoporous layers are also reported in the literature [27,29,35].
The comparison of the Ir-content is performed with EPMA. In this analysis, X-ray intensities of interest are measured at different accelerating voltages using energy dispersive X-ray spectroscopy (EDS), normalized to electron probe current and lifetime and quantified using defined standards of each element. A detailed description of this approach can be found in refs. [17,29,35]. Both methods, SE and EPMA, provide a very good agreement with the material contents nominally used in the synthesis, which show a relative deviation of less than about 10% of the derived values (Figure 8c). It should be also noted that the SE modeling shows a slightly better agreement than EPMA at a higher Ir-content of 75 wt% Ir . However, all values of the two methods are within their deviations.

Conclusion and outlook
In this study, we have shown that parameters like film thickness, porosity, and chemical composition of complex thin mesoporous mixed metal oxide films of the iridium oxide-titanium oxide type are accessible to spectroscopic ellipsometric measurements. The modeling approach provides changes in optical properties as a function of material composition as well as material properties such as film thickness, porosity and Ir-content. The derived results from SE agree well with the values obtained by the complementary techniques SEM, EPMA and EEP.
The analytical approach described here also offers the possibility of correlating electrochemical activity properties with optical material parameters in future analyses. The relationship of the dielectric function to the energy loss function can contribute to a better understanding of the structure-activity relationship. In addition, spectroscopic ellipsometry, through its fast and vacuum-free analysis, offers the possibility to study electrochemical reactions in-situ and/or operando under more realistic conditions, allowing a deeper understanding of catalytic systems.
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: Andreas Hertwig and René Sachse acknowledge generous funding from the project ATMOC (20IND04, Traceable metrology of soft X-ray to IR optical constants and nanofilms for advanced manufacturing). This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme. Ralph Kraehnert acknowledges generous funding of the DFG via SPP2080 (406695057) and of BMBF project ATO-KAT (03EK3052A).

Conflict of interest statement:
The authors declare no conflicts of interest regarding this article.