A Noble Metal High-Entropy Alloy for Mid-Infrared Metasurfaces

Engineering ›› 2025, Vol. 49 ›› Issue (6) :81 -89. DOI: 10.1016/j.eng.2025.01.017

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2025-03-18

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Abstract

High-entropy alloys (HEAs) are promising materials for photonic applications. In such applications, permittivity is essential for numerical studies. In this work, we experimentally determine the complex permittivity of an HEA composed of five noble metals—Au, Ag, Cu, Pd, and Pt. The measurements are conducted across a broad wavelength spectrum, spanning the ultraviolet, visible, and mid-infrared regions. The experiments, numerical simulations of reflection spectra, and analysis of absorption and scattering cross-sections reveal the potential for fabricating perfect absorber and emitter metasurfaces using this noble HEA. In addition, crystallography studies clearly show the formation of a uniform material. The lattice constant and electron work function of the alloy are found to be 0.396 nm and (4.8 ± 0.4) eV, respectively—results indicate that the formed HEA alloy is well mixed.

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High-entropy alloy / Metasurfaces / Plasmonics

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Yoshiaki Nishijima, Teruaki Sudo, Yasutaka Matsuo, Saulius Juodkazis. A Noble Metal High-Entropy Alloy for Mid-Infrared Metasurfaces. Engineering, 2025, 49(6): 81-89 DOI:10.1016/j.eng.2025.01.017

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1. Introduction

An efficient, light-absorbing metasurface can be designed as a two-dimensional (2D) material with a metal–dielectric (insulator)–metal (MIM) structure, comprising a top layer of metallic nanoparticles, a nano-thin spacer, and a metal base layer. The underlying metal base layer suppresses light transmission, while the patterned top layer of metallic nanoparticles minimizes overall light reflection from the MIM structure [[1], [2], [3], [4]]. This type of metamaterial enables highly efficient light absorption at the designed wavelength, making it suitable for applications such as photothermal conversion devices [[5], [6], [7]].

Interestingly, electromagnetic field calculations have revealed that, under antireflective conditions, the optical absorption and scattering coefficients become equivalent when metasurfaces are constructed using common plasmon materials of gold (Au), silver (Ag), and copper (Cu) bands [8]. It has been experimentally determined that the emissivity of an MIM metasurface does not reach 100%, even when the reflection spectrum shows a completely antireflective condition (transmittance = 0, reflectance = 0). This finding suggests that light is not fully absorbed under antireflective conditions, and thermal radiation does not reach 100%. Achieving “true perfect absorption and true perfect radiation” requires precise control of the absorption and scattering cross-sections, σ_abs and σ_sca, respectively, which play a critical role in the behavior of metasurfaces. For conventional MIM metasurfaces made of Au, it has been shown that σ_abs is equal to σ_sca under the minimum anti-reflection condition. Previous studies have demonstrated that, by carefully controlling σ_abs and σ_sca through the use of multilayer Au–silicon (Si) nanodiscs, the response of an MIM structure can be separated into peaks corresponding to σ_abs and σ_sca [8].

In our previous work [8,9], we realized a perfect absorber/emitter using an MIM structure through the intricate tuning of absorption via scattering, achieved by increasing σ_abs relative to σ_sca [8,9]. This was accomplished by increasing the thickness of the chromium (Cr) film serving as an adhesive between the Au and dielectric layers, thereby enhancing the contribution of absorption.

For thermal emitters designed for the infrared (IR) band, the choice of materials for MIM patterns is crucial, as higher emissions can be obtained at elevated temperatures. When Au and Cr are stacked and heated, Cr rapidly diffuses into the Au, compromising the MIM structure’s absorption properties and degrading its optical performance. Furthermore, when Cr is used, absorption in the shorter wavelength range of 1–3 μm becomes more pronounced, and its absorption spectrum broadens. Therefore, we focused on the search for homogeneous metallic materials with strong absorption properties. We propose the use of high-entropy alloys (HEAs), which, by definition, are metallic materials composed of five or more metallic elements alloyed in nearly equal atomic ratios. A schematic illustration of the HEA metasurface is shown in Fig. 1. This composition maximizes the configurational entropy of the metallic materials [10,11].

The configurational entropy S can be expressed as a percentage, as follows:

(1)

S = - R_{g a s} \sum_{i =1}^{N} \frac{1}{N} ln \frac{1}{N} = R_{g a s} ln N

where R_gas is the gas constant, N is the number of possible compositions, and i is the number of mixed elements. In conventional two-component alloys, the configurational entropy is given by R_gasln2, which is approximately equal to 0.69R. However, in a five-component alloy, the configurational entropy increases to approximately 1.61R. An HEA material is defined as having S > 1.5R, whereas 1.0R < S < 1.5R for a middle-entropy alloy, and S < 1.0R for a low-entropy alloy. In the case of conventional two-component alloys, phase separation typically occurs without enthalpically unfavorable alloying due to the low configurational entropy. Phase formation is thermodynamically governed by the Gibbs free energy of mixing, ΔG = ΔH − T_eΔS, where ΔH and ΔS represent the enthalpy and entropy changes at temperature T_e, respectively. In contrast, when the configurational entropy is increased, even under enthalpically unfavorable conditions, entropy acts as a driving force, leading to the formation of a single-phase alloy (similar to the formation of a surfactant-to-oil/water emulsion). This phenomenon is advantageous, as it reduces electron scattering at the plasmon resonance.

It has been reported that HEA conversion increases the mechanical strength of metals [10,11]. Several studies on HEAs using precious metals [[12], [13], [14], [15], [16], [17], [18]] have shown that HEAs exhibit a greater catalytic effect than stand-alone palladium (Pd) or platinum (Pt). However, thus far, HEAs have not been adopted for use in optical devices due to their optical and plasmonic properties. The noble metals and electron-rich elements such as aluminum (Al) or magnesium (Mg) have limited applications in metamaterials, where they could otherwise favorably expand the spectral range of plasmonic resonances.

Recently, alloys have generated significant attention as materials for plasmon resonance. Several studies have been conducted on this topic, with alloys of Au, Ag, and Cu being fabricated [[19], [20], [21], [22], [23], [24]]. For the first time, we have obtained the complex permittivity ε ≡ (n + iκ)² of metallic tri-metal alloys made of Au, Ag, and Cu at different mixing ratios and used these alloys for their plasmonic function (where n is the refractive index and κ is the extinction coefficient). We have also found that the formation of Au and Pd alloys improves the hydrogen response and enables the development of optical hydrogen sensors.

In optical applications based on plasmon resonance, determining the complex refractive indices (n + iκ) of metallic materials is essential for electromagnetic field calculations, including numerical methods such as finite-difference time-domain (FDTD) calculations, which provide exact numerical solutions to Maxwell’s equations. However, when an alloy is formed, the complex permittivity becomes different, and it is not accurate to use the arithmetic mean of the constituent parts to describe the alloy [21,23]. In addition, the permittivity changes because of the size and defects (i.e., grain boundaries, stacking faults, dislocations, and porosity), which are influenced by the conditions under which a film is deposited. Therefore, the permittivity, ε, of a film deposited under the same conditions used for the nanoparticle top layer of an MIM must always be determined experimentally.

In this study, we constructed an MIM metasurface using an HEA composed of Au, Ag, Cu, Pd, and Pt. The reflectance spectra were experimentally measured, and the corresponding cross-sections for reflection, absorption, and scattering contributions were modeled using the FDTD method. These results can be extended to imply high efficiency in photo-thermal energy conversions.

2. Experiment

2.1. Sample preparation and characterization

Metasurface fabrication was performed as described elsewhere in more detail [2,5]. In brief, 5 nm Cr film and 200 nm Au film were thermally deposited onto a silicon substrate. After the deposition of 5 nm Cr film, a set of samples with silicon dioxide (SiO₂) layers with thicknesses ranging from 100 to 500 nm (with 100 nm steps) was deposited via electron-beam (EB) evaporation. Subsequently, the samples were spin-coated with an EB lithography (EBL) resist, and EBL exposure was used to define the metallic nanostructures on the top layer. The size of the nanodiscs was defined by EB drawing, with less than 5% deviation in diameter. A triangular periodic array pattern without structural defects was defined. The Cr 5 nm and various metals were deposited after the resist’s development, followed by lift-off. Five metal alloy targets with the required composition were purchased from Tanaka Precious Metal Co., Ltd. (Japan) to form the HEA and were used for sputtering. The powder metallurgy method with 20 atm% of the five elements was performed to form the HEA target, where the atm% composition was guaranteed by the supply company. Microspectroscopy was used for the spectral characterization of the metasurface MIM structures, which had a footprint with a 300 μm cross-section. A Fourier-transform-IR (FT-IR) spectrometer and microscope unit (FTIR-6000 and IRT-1000, JASCCO, Japan) were used to measure the reflection spectra in the mid-IR (MIR) region. A 350-nm-thick Au film was used as the reflection reference, with 98% reflectance across the entire MIR region.

To confirm the formation of the HEA, we performed X-ray diffraction (XRD; Rigaku, Japan), X-ray photoelectron spectroscopy (XPS; ULVAC-PHI, Japan), and ultraviolet photoelectron spectroscopy (UPS; Riken Keiki, Japan) analyses to determine the crystal lattice constant, the binding energy of each atom, and the work function, respectively. The XPS was conducted in survey mode to obtain the wide-range XPS spectra and identify the region-of-interest peaks for the narrow-band measurements. In addition, scanning transmission electron microscopy (STEM; JEOL, Japan) and energy-dispersive X-ray spectroscopy (EDS) were utilized to characterize the HEA films. This enabled our analysis of the structural changes occurring due to the formation of the HEA.

2.2. Determination of the permittivities of the metals

Spectroscopic ellipsometry was employed to determine the permittivities of the metals. A 200-nm-thick film was deposited on a glass substrate to eliminate reflections from the substrate. To measure the permittivity over a wide bandwidth range, ultraviolet (UV)–visible (VIS) spectroscopic ellipsometry (200–1000 nm) and MIR spectroscopic ellipsometry (1 700–20 000 nm) were used. After determining the optimal permittivity for each measurement result using the Drude–Lorenz model, the results of both the UV–VIS and MIR measurements were concatenated to find the optimal parameters using the single Drude–Lorenz model and the least-squares method. The following equation defines the Drude–Lorenz model used in this study for analysis:

(2)

ε (ω) = ε (\infty) - \frac{ω_{P, D}^{2}}{ω^{2} + Γ_{D}^{2}} + i \frac{ω_{P, D}^{2} Γ_{D}}{ω (ω^{2} + Γ_{D}^{2})} + \sum_{j} (\frac{ω_{P, L, j}^{2} (ω_{0, j}^{2} - ω^{2})}{{(ω_{0, j}^{2} - ω^{2})}^{2} + Γ_{L, j}^{2} ω^{2}} + i \frac{Γ_{L, j} ω_{P, L, j}^{2} ω}{{(ω_{0, j}^{2} - ω^{2})}^{2} + Γ_{L, j}^{2} ω^{2}})

where ε(∞) is the real part permittivity at high frequency, which is the sum of the ε(∞) from both the Drude and Lorenz models; ω is the Angular frequency; ω_P,D is the plasma frequency of the Drude model; Γ_D is the dumping constant of the Drude model; ω_P,L,_j is the plasma frequency of the Lorenz model; ω_0,_j is the central angular frequency in the Lorenz model; Γ_L,_j is the dumping constant of the Lorenz model; and j is the indicator number, which indicates the oscillation number. In this study, values of j = 1 or 2 are used.

2.3. FDTD calculation

FDTD calculations were performed using the Ansys Lumerical FDTD Solutions package. Palik’s parameters were used for the thin gold film in the lower layer of the MIM structure [25]. The calculations were performed using the experimentally obtained permittivity of the upper nanodisc structure. The nanodisc diameter was swept from 500 to 2000 nm in 100 nm increments and recalculated in 10 nm increments, especially in regions of lower reflectivity. The permittivity of Palik was used for SiO₂, and calculations were performed for film thicknesses of 50, 100, 150, 200, 300, and 400 nm. The thickness of the Au nanostructures was set to 50 nm, under the same conditions as those used in the experiment.

3. Results and discussion

This study focused on the optical properties of a noble metal HEA and its application in MIM metasurfaces. Moreover, structural characterization, which is of paramount importance, was conducted as a supplementary analysis to the optical study and is presented in Appendix A. The key findings are summarized below.

3.1. Crystallographic features of the HEA

All the crystallographic characterization data are summarized in Appendix A. Fig. S1 and Table S1 in Appendix A presents the results of the XRD crystallographic analysis of the metal films. Weak signatures from the Si substrate and Cr adhesion layer were identified in certain regions of the XRD curve. The HEA film exhibited a single-phase face-centered-cubic (fcc)-type structure, which was distinct from the individual metal XRD patterns obtained under the same conditions. A small section of the HEA film was cut using a focused ion beam and analyzed by means of STEM. The STEM-EDS mapping results, as shown in Fig. S2 in Appendix A, indicate that the five metals are uniformly distributed within the film at the STEM spatial resolution. The STEM results, shown in Fig. S3 in Appendix A, facilitated the determination of crystal lattices. EB diffraction over a small area revealed multiple diffraction patterns, suggesting that the HEA exhibits a range of lattice distributions and local ordering. This is a well-documented phenomenon in HEAs [26,27].

The spatial averaging of the XRD maps revealed that the crystal lattice constants were in excellent agreement with the average values of the five constituent metals. Furthermore, the crystal lattice structure closely resembled those of Pd and Pt, indicating that the elements were well mixed and formed a single-phase crystal.

The XPS and UPS spectra are presented in Figs. S4–S6 in Appendix A, respectively. Broadband XPS measurements indicated that binding energies corresponding to nearly all orbitals of the constituent atoms were detectable in the HEA (Table S2 in Appendix A). After baseline adjustment, the spectra showed results similar to the average spectra of the five elements (Fig. S4). However, shifts or disappearances of certain peaks were observed. To further investigate the alloy formation, narrow-band analysis was performed. It was found that almost all peaks had shifted to lower energies. This shift is generally attributed to the acceptance of electrons from external sources [[28], [29], [30]]. In other words, the pool of free electrons within the alloy primarily provides electrons that become bound during alloy formation. From the UPS measurements, the work functions were approximately 4.7 eV for the HEA and the constituent metal carriers (Fig. S5). These values are consistent with those of the individual elements. These results suggest that the HEA was successfully formed in the Au, Ag, Cu, Pd, and Pt system using the sputtering method, and that the optical properties of the nanostructures reflect the characteristics of the HEA. In the following sections, we present a summary of the experimental and FDTD simulation results for the resonance properties of actual metasurfaces fabricated from noble HEAs.

3.2. Optical reflection spectra of metasurfaces

An extensive set of detailed experimental and FDTD results is summarized in Appendix A. Fig. 2 shows the experimental and FDTD simulated reflection spectra of MIM metasurfaces with different metallic elements, using a 300 nm SiO₂ dielectric spacer. Figs. S7 and S8 in Appendix A provide a summary of all spectral data for varying SiO₂ thicknesses and for the experimental and simulated results, respectively. The HEAs are characterized by the formation of low reflection conditions across a broad range of wavelengths, coupled with relatively narrow resonance line widths. In contrast, the Au, Ag, and Cu metasurfaces exhibit narrow resonance line widths, but show low reflection over a more limited range of wavelengths. For example, SiO₂ films with thicknesses of 100 and 200 nm exhibit lower reflections over a broader range than those with a thickness of 300 nm, but this range is still narrower than that observed in the HEAs. In contrast, Pt and Pd metasurfaces exhibit a more extensive range of low reflections, although their resonance spectra are broader.

Fig. 3 shows graphical representations of the minimum reflectance, resonance linewidth in wavenumber units, and resonance center wavenumber, all extracted from the experimental spectral data. The 2D plots, projected onto the 2D cross-sections of the three-dimensional (3D) plot—the center wavenumber versus reflection, center wavenumber versus width, and reflection versus width—are summarized in Fig. S9 in Appendix A. In this analysis, the resonance linewidth is defined as the difference between the maxima and minima of the first derivative of the resonance spectrum. The mathematical formula shows that the difference between the maxima and minima of the derivatives is slightly larger than the half-width in a bell-shaped function system, which provides a significant advantage for analysis, as it can be performed with uniform accuracy, including for asymmetric bell-shaped experimental results. The projections of the 3D plot (Fig. 3) show the relationships between the reflectance and resonance linewidth, resonance center wavenumber, resonance linewidth, and reflectance versus resonance center wavenumber. The results show that the relationship between the resonance center wavenumber and the resonance linewidth is narrower for all metals at lower wavenumbers. Additionally, the resonance linewidths of Au, Ag, and Cu decrease with lower reflectivity, while those of HEA, Pt, and Pd increase under low-reflectivity conditions. For SiO₂ films with thicknesses of 100 and 200 nm, the same trend of narrowing resonance linewidth was observed for Au, Ag, and Cu. However, for SiO₂ films thicker than 300 nm, the resonance linewidth exhibited a trend similar to that of Pt and Pd.

The resonance linewidths of Pt and Pd were up to twice as large as those of Au, Ag, and Cu, while those of the HEAs were only 1.5 times larger than those of Au, Ag, and Cu. This difference is expected to reduce the absorption losses in Pd and Pt. To analyze the optical behavior of these metals in greater detail, their permittivities were measured over a broad range of wavelengths, from UV–VIS to MIR, using spectroscopic ellipsometry (Table 1).

3.3. Optical permittivity of the metals

Fig. 4 shows the permittivities of the six metals across the UV–VIS to MIR range. Although data in the 1000–1700 nm range were unavailable, the Drude–Lorenz model was used to generate a smooth and continuous permittivity curve over the entire measurement range of 200 to 2 × 10⁴ nm by fitting the data using the least-squares method. The use of the Lorenz model across this broad spectral window allowed for the determination of permittivities from 200 to 2 × 10⁴ nm. Fig. 4 shows plots of the first three terms (Eq. (2)) of the Drude–Lorenz equation used in the analysis and of the Drude and Lorenz components separated. Notably, ε(∞) is a constant that must be included in both the Drude and Lorenz terms independently. However, due to analytical complexities, separating these terms is challenging. Therefore, they are treated as a single constant. The results show that the permittivity of the HEAs is more similar to those of Pd and Pt than those of Au, Ag, and Cu. However, as shown in the imaginary part of the Lorentz model, the loss-related contributions are smaller than those of Pt and Pd. Table 1 lists the parameters obtained from the analysis using the Drude–Lorentz model for the experimentally measured permittivity extracted through curve fitting. As mentioned earlier, ε(∞) represents the combined contribution of the Drude and Lorenz terms and has a baseline-like contribution to the permittivity. In addition, the values of high-ε(∞) frequencies were extrapolated from a finite range of experimental data, and the resulting estimates were prone to errors. We confirmed that fixing these parameters to the ideal metal permittivity did not significantly affect the analytical results.

In general, the plasma frequency is related to the carrier density. When the effective electron mass is constant, a larger value corresponds to a higher carrier density. The HEAs exhibited the second-highest free electron density after Au, Ag, and Cu, as well as the highest bound electron density among the six metals. A high free electron density is essential to induce significant plasmon resonance, and the results suggest that the HEAs are more “plasmonic” than Pd and Pt. The increased density of bound electrons indicates that some abundant free electrons in Au, Ag, and Cu have been converted into bound electrons. This is consistent with the XPS measurements, which show that nearly all binding energies shifted to lower values, suggesting electron acceptance.

The damping coefficient was the largest for the HEAs among all the metals, making the material less prone to a high-quality factor Q resonance compared with single metals. The damping constant is also closely related to absorption loss and is strongly influenced by the crystalline state of the material. Structural defects, such as grain boundaries, dislocations, and stacking faults, play a significant role in this context. The sharp peak obtained in the X-ray crystal structure analysis indicates that the variation in the grain boundary size was effectively suppressed. Hence, a highly homogeneous structure was formed. However, based on the lattice constants of the crystals, it was difficult to conclusively determine whether a single phase was present in the HEAs. Considering the lattice constants of the crystals and the atomic radius of a single atom of 140 pm, which was inferred from the lattice constant of the HEA, the formation of a single-phase HEA is considered plausible. The lattice constants of the HEAs are larger than those of Cu, Pt, and Pd. This increase is attributed to the repulsion between the nuclei and the elongation of bonds caused by a decrease in the interatomic distance, leading to a distorted geometry. This distortion between the crystal lattice and atomic radii is thought to be responsible for the increased damping of the optical response of the electrons. At the plasmon resonance, a balance is formed between the oscillation of free electrons and the losses and damping caused by various factors. In the present system, the absorption was improved over a wide range of wavelengths, possibly by coincidence. It is important to continue analyzing the permittivity of different HEA systems, develop a methodology to precisely control the Drude and Lorenz parameters, and establish a unified approach for material discovery. The objective is to identify the material with a resonance linewidth comparable to that of Au, Ag, and Cu, but with enhanced absorption properties. After obtaining the complex permittivity of the newly engineered metallic material, its resonance properties were calculated using FDTD simulations. Simultaneously, the scattering (σ_sca) and absorption (σ_abs) cross-sections were quantitatively determined using the proposed method.

3.4. FDTD simulations

Fig. 5 shows the reflectance R, ratios of the cross-sections σ_abs/σ_sca, σ_abs, and σ_sca plots for the data corresponding to the lowest reflectance condition from the comprehensive FDTD simulation results. For Au, Ag, and Cu, the peaks of σ_abs and σ_sca coincide and are equal at the reflectance minimum (σ_abs/σ_sca ≈ 1). In contrast, for the HEA, Pt, and Pd, the σ_abs and σ_sca peaks occur at separate wavenumbers, indicating that σ_abs is much larger than σ_sca at the resonance wavelength corresponding to the low reflectance, where absorption is dominant.

To examine this in more detail, the ratios of σ_abs and σ_sca (σ_abs/σ_sca) at each resonant wavelength were plotted against the reflectance (Fig. 6). For Au, Ag, and Cu, the minimum reflection occurred at σ_abs/σ_sca = 1 in all simulation results for different SiO₂ thicknesses. Therefore, all the data—including those for Au, Ag, Cu, and varying SiO₂ thicknesses—can be plotted as a single Gaussian function, represented by the dotted gray line in the figure. The HEA and Pt also follow this relationship when the SiO₂ thickness ranges from 50 to 150 nm. However, for thicker SiO₂ films, σ_abs/σ_sca > 1 is observed. Under these conditions, absorption becomes dominant and aligns well with the experimental reflection spectra. In the case of Pd, the shift in σ_abs/σ_sca is the largest among all the metals. This indicates that the strong absorption of metals reduces the Q factor of the MIM resonance. The shifted σ_abs/σ_sca value is similar to that of the 50 nm Cr added as an adhesion layer, as shown in our previous work [8]. These results indicate that the HEA with Au, Ag, Cu, Pd, and Pt achieves “true perfect absorption” and “true perfect thermal emission.”

4. Conclusion

This study demonstrated the formation of a noble HEA and determined its optical permittivity, highlighting plasmon resonances primarily in the MIR spectral range. These findings suggest that such HEAs could be used to realize perfect absorbers and emitters. Furthermore, noble HEAs exhibit efficient catalytic properties [12,13,[15], [16], [17], [18]]. As a result, this method can be leveraged to develop a plasmon-based efficient photocatalyst for artificial photosynthesis.

CRediT authorship contribution statement

Yoshiaki Nishijima: Writing – review & editing, Writing – original draft, Conceptualization. Teruaki Sudo: Writing – review & editing, Writing – original draft. Yasutaka Matsuo: Writing – review & editing, Writing – original draft. Saulius Juodkazis: Writing – review & editing, Writing – original draft.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors are grateful for partial support from the Japan Society for the Promotion of Science (JSPS), the Grants-in-Aid for Scientific Research, and JSPS Bilateral Joint Research Projects between Japan and Lithuania. This work was partially supported by the PRESTO and the Japan Science and Technology Agency (JST) (JPMJPR22B6). The authors are also grateful for the startup funding of the Nanotechnology facility at Swinburne and support for exploratory projects on IR sensors. Part of this work was supported by the ARIM of MEXT in Japan (JPMXP1223HK0070) and was conducted under the Cooperative Research Program titled Network Joint Research Center for Materials and Devices. We are grateful to Ayano Yamazaki, Yuko Mori, and Naomi Hirai of Hokkaido University for their helpful support with STEM-EDS, UPS, and XPS analyses. The authors are also grateful to Hidehiko Yoda, Utsunomiya University, for the mid-infrared ellipsometry.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2025.01.017.

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