# Low-Cost Optical Filters Based on SiOxCy:H and Ag Thin Films Fabricated by Plasma Enhanced Chemical Vapor Deposition and Sputtering

Ahmed Kotbi, Michael Lejeune, Pierre Barroy, Ilham Hamdi Alaoui, Wiaam

El Hakim, Frederic Lamarque, Andreas Zeinert

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Ahmed Kotbi, Michael Lejeune, Pierre Barroy, Ilham Hamdi Alaoui, Wiaam El Hakim, et al., Low-Cost Optical Filters Based on SiOxCy:H and Ag Thin Films Fabricated by Plasma Enhanced Chemical Vapor Deposition and Sputtering. Photonics, 2024, 11 (11), pp.1096. 10.3390/photonics1111096. hal-04804100

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Article

# Low-Cost Optical Filters Based on SiOₓCᵧ:H and Ag Thin Films Fabricated by Plasma Enhanced Chemical Vapor Deposition and Sputtering

Ahmed Kotbi<fnref n="1" />,*, Pierre Barroy<fnref n="1" />, Ilham Hamdi Alaoui<fnref n="1" />, Wiaam El Hakim<fnref n="2" />,
Frederic Lamarque<fnref n="2" /> and Andreas Zeinert<fnref n="1" />,*

**Abstract:** Hexamethyldisiloxane (HMDSO) is an organosilicon compound with a modifiable bandgap, depending on the deposition conditions. This material has many unique properties due to its stability, low toxicity, and strong adhesion, making it useful as a protective barrier against corrosion, moisture, and oxidation. In this work, HMDSO films were deposited on glass substrates by the Plasma Enhanced Chemical Vapor Deposition (PECVD) technique at different deposition times. The optical properties of HMDSO films, such as dielectric permittivity, refractive index, extinction and absorption coefficients, and band gap energy, are inferred from transmission and reflection spectra. As the deposition time increased, the real part of the dielectric constant, the refractive index, and the bandgap energy showed a decrease, dropping from 4.24 to 3.40, from 2.06 to 1.84, and from 2.85 eV to 2.03 eV, respectively. The latter result is determined using classical models such as the O'Leary-Johnson-Lim ('OJL') interband transition and the harmonic oscillator model. HMDSO and Silver are used in this study for the fabrication of optical filters using two types of structures, a multiple cavity metal-dielectric (MCMD) and the Fabry-Perot structure. The silver layers are deposited by a sputtering process. The MCMD optical filter shows a higher transmittance of about 30%, but a wide range of wavelengths is transmitted. In contrast, the Fabry-Perot filter showed high contrast but a lower transmittance of about 20%.

**Keywords:** thin films; PECVD; sputtering; HMDSO; silver; optical properties; OJL interband transition; harmonic oscillator; optical filters

## 1. Introduction

Hexamethyldisiloxane (HMDSO), chemical formula C₆H₁₈OSi₂, is an organosilicon compound used as a precursor in the fabrication of thin films [1,2]. These films are widely used for their dielectric properties in optical devices and sensors [3] and for electrical insulation in semiconductors. They also serve as protective barriers against corrosion, humidity, and oxidation, with applications in electronics [2]. Due to their biocompatibility and low toxicity [3], they are used in medical devices. HMDSO films adhere strongly to various substrates, whether metallic, ceramic, or polymer, thus providing a versatile and scalable solution for various industrial and biomedical applications. In addition, Hexamethyldisiloxane has the main advantage of having CH₃ groups, which can provide hydrophobic and organic character to the film surface [4,5]. One of the applications of HMDSO is in optical filtering. It can serve as a layer in an optical filter design because its optical properties can be adjusted based on the fabrication parameters. These filters

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**Citation:** Kotbi, A.; Lejeune, M.; Barroy, P.; Hamdi Alaoui, I.; El Hakim, W.; Lamarque, F.; Zeinert, A. Low-Cost Optical Filters Based on SiOₓCᵧ:H and Ag Thin Films Fabricated by Plasma Enhanced Chemical Vapor Deposition and Sputtering. *Photonics* **2024**, *11*, 1096. https://doi.org/10.3390/photonics1111096

Received: 8 November 2024
Revised: 18 November 2024
Accepted: 19 November 2024
Published: 20 November 2024

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**Copyright:** © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">¹ Laboratory of Condensed Matter Physics, University of Picardie Jules Verne, 33 Rue Saint Leu, 80039 Amiens, France; michael.lejeune@u-picardie.fr (M.L.); pierre.barroy@u-picardie.fr (P.B.); ilham.hamdi.alaoui@u-picardie.fr (I.H.A.)</footnote>

<footnote n="2">² Mechanical Engineering Department, Université de Technologie de Compiègne, 60203 Compiègne Cedex, France; wiaam.el-hakim@utc.fr (W.E.H.); frederic.lamarque@utc.fr (F.L.)</footnote>

<footnote>* Correspondence: ahmed.kotbi@u-picardie.fr (A.K.); andreas.zeinert@u-picardie.fr (A.Z.); Tel.: +33-3-22-82-78-27 (A.K.)</footnote>
can be used for the wireless actuation of micro-actuators, as using a laser source for
thermal energy may cause issues in many micro-actuators, leading to unintended actuations
due to irradiation. This issue can be addressed either by depositing an optical filter
directly on the micro-actuator or by applying it to a lens positioned above the actuators [6].
Plasma Enhanced Chemical Vapor Deposition (PECVD) is a suitable technique for the
deposition of this type of material. In the plasma phase, HDMSO decomposes to form
silica-based films (SiO₂) or organic–inorganic hybrid layers (SiOₓCᵧ:H), whose properties
can be adjusted depending on the deposition conditions [7]. PECVD is regarded as one of
the most promising techniques for large-scale deposition of high-quality coatings [8]. It
offers several advantages, such as low substrate temperature and the ability to produce
layers with varied properties by simply adjusting the conditions of deposition [9,10].

In this work, we deposited thin films of SiOₓCᵧ:H using HMDSO gas at different
deposition times using the PECVD technique. Optical properties of the HMDSO films were
modeled using commercial software to determine optical parameters at various deposi-
tion times, such as Dielectric permittivity, Refractive index, Extinction and Absorption
coefficients, as well as the Bandgap energy. The O'Leary-Johnson-Lim (OJL) interband
model [11] is an empirical model for the distribution of the electronic states of an amor-
phous semiconductor that is appropriate in this case. This model assumes that the energy
bands are parabolic, with tail states exhibiting an exponential decay in the band gap [12].
SiOₓCᵧ:H deposited by PECVD and silver deposited by sputtering were used in the fabrica-
tion of optical filters, utilizing both the multiple cavity metal-dielectric (MCMD) structure
and the Fabry-Perot structure.

## 2. Materials and Methods

Thin films were synthesized by PECVD using hexamethyldisiloxane vapor (C₆H₁₈OSi₂) as a precursor by controlling the total pressure at 13 × 10⁻³ Torr, RF power at 100 W, and HMDSO gas flow rate at 2 sccm. The glass substrates (1 × 1 cm²) were previously cleaned in consecutive ultrasonic baths of ethanol, acetone, and distilled water and then dried with compressed air. The substrates were etched with argon plasma to remove surface impurities before coating. The thicknesses of the layers grown during different deposition times of 20 s, 40 s, and 10 min were evaluated using a Bruker profilometer (Dektak XT), which gives an accuracy of about 1 nm. The thicknesses of the different layers show a linear growth variation from 20 nm to 160 nm. Silver thin films were deposited by direct current magnetron sputtering of a silver target with argon plasma in a commercial reactor (Cressington Sputter Coater 108 auto). The argon pressure was 0.1 mbar, and the current was 40 mA. The microstructure of SiOₓCᵧ:H and Ag films was studied by a Quanta 200 FEG scanning electron microscope (SEM). Using the Bruker–Dektak stylus profiler, the roughness and thickness of the SiOₓCᵧ:H and Ag layers were measured. Fourier transform infrared (FTIR) spectra were obtained for SiOₓCᵧ:H film and gas using a Bruker Vector 33 FTIR spectrometer. Optical transmittance and reflectance of the films were measured using a JASCO V-670 UV–vis–near-IR spectrometer with a PIN-757 horizontal sampling integrating sphere in transmission and reflectance modes.

Both OJL interband transition and Kim oscillator models were used in the analysis
of our reflectance and transmission spectra using the commercial software “CODE” de-
veloped by W. Theiss [13–15]. The CODE program allows us to determine the real and
imaginary parts of the dielectric permittivity, refractive index, extinction, and absorption
coefficients by implementing real physics models and comparing their outputs at multi-
ple wavelengths with real measurements. The design of all optical filters was optimized
using the commercial optical thin film software GENETICODE [14,16]. GENETICODE
uses Machine Learning in order to find an optimal solution amongst many potential ones
given a target design and constraints of optical properties and/or layer thicknesses. On
the other hand, GenetiCode uses a genetic algorithm to optimize the design of the coating.
Here is how it works: Initially, a number of coatings (each being a specific combination of
material and thickness for each deposition layer) are randomly selected. This set is referred
to as the population. For each coating, its fitness is evaluated. Then, new generations are created by producing two child coatings from two parent coatings. The selection of parents is guided by their fitness, meaning that more fit coatings have a higher chance of reproducing compared to less fit ones. During the transition from one generation to the next, the genes of the parents (i.e., the information about material and thickness) are exchanged so that the child's genes become a mixture of the parents' properties. This gene exchange is regulated by what is known as the crossover probability. Additionally, a gene may undergo random changes between generations, with this event governed by the mutation probability. Since genetic algorithms rely heavily on random numbers, it is unlikely to find a good (or optimal) solution on the first try. Therefore, it is recommended to perform several "evolutionary trials", which GenetiCode allows to be performed efficiently [17]. The multiple cavity metal–dielectric (MCMD) structure and Fabry–Perot cavity designs were our starting points for fabricating two optical transmission filters at 670 nm and 830 nm, respectively.

### 3. Results

#### 3.1. *Microstructural and Structural Properties*

The microstructure of SiOₓCᵧ:H and Ag thin films deposited on glass substrates was observed by scanning electron microscopy. Figure 1a,b illustrates the micrographs of different films prepared by PECVD and sputtering, respectively. As shown in the images, the films exhibit dense microstructures without cracks and without porosity. On the other hand, the surface roughness and morphology of SiOₓCᵧ:H and Ag films were evaluated by profilometer mapping. Figure 1b,c present 3D micrographs of SiOₓCᵧ:H and Ag thin films captured in a scanning area of (0.5 × 0.5) mm². These images clearly illustrate almost identical surface roughness for both films. Specifically, the average roughness for both films is about 0.01 µm. In the measurements shown in Figure 1c,d, a periodic structuring is visible on the surface. These structures are related to the scan parameters, particularly the scan pitch. If this structuring can be attributed to the profilometer needle, it is essential to discuss the scratch and wear resistance of the tested surface, as well as the durability of the SiOₓCᵧ:H layers, as reported in the work of Y. Leterrier et al. [18].

<figure><img src="image_4.png" /><figcaption>**Figure 1.** SEM images display the microstructure of the examined films: (a) Ag and (b) SiOₓCᵧ:H. Profilometer mapping of thin films of (c) Ag and (d) SiOₓCᵧ:H.</figcaption></figure>
The FTIR spectra of HMDSO samples, in both gas phase and thin film form, within the range of 400–3250 cm⁻¹, are depicted in Figure 2a,b. Each absorption spectrum was acquired over 30 scans to enhance the signal-to-noise ratio. The absorption peaks corresponding to the asymmetric stretching mode of Si-O-Si observed between 1000 and 1200 cm⁻¹ are clearly distinguishable in both samples. Additionally, the absorption peaks related to the Si-(CH₃)ₓ bending mode at 801 and 1260 cm⁻¹ are prominent. The absorption band of Si-O-Si near 500 cm⁻¹, associated with the rocking mode, is also evident. A peak corresponding to CH₂/CH₃ bonds emerges around 2900 cm⁻¹ in both the HMDSO-film and HMDSO-gas samples. Plasma treatment of HMDSO resulted in the broadening of the peaks. The observed absorption bands and their corresponding chemical bonds are detailed in Table 1, along with their wavenumbers and vibrational modes. Similar spectral patterns have been reported for HMDSO films by M. Goujon et al. [19]. These findings align with those reported in the literature [1,3,19–22]. On the other hand, Raballand et al. [23] demonstrated that the carbon content in SiO₂-like films derived from HMDSO is significantly influenced by the HMDSO flow rate. At a high flow rate, carbon becomes incorporated into the plasma-deposited films, resulting in SiO₂-like films with notable carbon content. Similar spectral patterns were observed in films deposited by PECVD [19], suggesting that HMDSO polymerization can proceed to form large (SiO₂)ₓ macromolecules composed of SiO₂ subunits with CO and CH₂/CH₃ groups. Following decomposition, a carbon-related peak at 2140 cm⁻¹ appeared, indicating a substantial carbon presence in the deposited films.

<table><caption>**Table 1.** IR absorption bands of species present in HMDSO.</caption><thead><tr><th>Species</th><th>Vibrating Mode</th><th>Wave Number (cm<sup>-1</sup>)</th></tr></thead><tbody><tr><td rowspan="3">Si-O-Si</td><td rowspan="3">Rocking vibration</td><td>400 [20]</td></tr><tr><td>459 [21]</td></tr><tr><td>500 Film; Our work</td></tr><tr><td rowspan="5">Si(CH<sub>3</sub>)<sub>x</sub></td><td rowspan="5">Bending vibration</td><td>804 [1]</td></tr><tr><td>800 [20]</td></tr><tr><td>795 [22]</td></tr><tr><td>801 Film; Our work</td></tr><tr><td>848 Gaz; Our work</td></tr><tr><td rowspan="7">Si-O-Si</td><td rowspan="7">Asymmetric Stretching</td><td>1020–1090 [3]</td></tr><tr><td>1072 [19]</td></tr><tr><td>1076 [21]</td></tr><tr><td>1075 [1]</td></tr><tr><td>1060 [20]</td></tr><tr><td>1074 [22]</td></tr><tr><td>1002 Film; Our work</td></tr><tr><td rowspan="5">Si(CH<sub>3</sub>)<sub>x</sub></td><td rowspan="5">Symmetric Stretching</td><td>1072 Gaz; Our work</td></tr><tr><td>1250–1260 [3]</td></tr><tr><td>1263 [19]</td></tr><tr><td>1265 [1]</td></tr><tr><td>1263 [20]</td></tr><tr><td rowspan="5">CO</td><td rowspan="5">Stretching</td><td>1260 [22]</td></tr><tr><td>1257 Film; Our work</td></tr><tr><td>1260 Gaz; Our work</td></tr><tr><td>2140 [22]</td></tr><tr><td>2140 Film; Our work</td></tr><tr><td rowspan="5">CH<sub>2</sub>/CH<sub>3</sub></td><td rowspan="5">Asymmetric Stretching</td><td>2966 [19]</td></tr><tr><td>2913 [22]</td></tr><tr><td>2921 [21]</td></tr><tr><td>2901 Film; Our work</td></tr><tr><td>2964 Gaz; Our work</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>Figure 2. FTIR spectra of HMDSO gas (a) and thin film (b).</figcaption></figure>

## 3.2. Optical Properties

The main model implemented in the CODE software for SiOₓCᵧ:H thin films was the O'Leary-Johnson-Lim model. The relationship between the distribution of electronic states and the optical absorption spectrum of an amorphous semiconductor has been described by O'Leary-Johnson-Lim in [11]. The OJL model is based on the assumption of parabolic conduction and valence bands with an electronic density of states decaying exponentially into the band gap. This model seems to agree successfully in the fitting of different amorphous semiconductors. For instance, there is an example in A. Gordijn et al. [24].

Also, it has been found that the vibrational modes in the SiOₓCᵧ:H thin films could be better taken into account by adding the extension model of the simple harmonic oscillator suggested by Kim et al. [25]. This model allows a continuous shift of the line shape between a Gaussian and a Lorentzian profile. The shift of the line shape between a Gaussian and a Lorentzian profile is achieved by a frequency dependence of the damping constant.

The transmission, reflection, and absorption values as a function of wavelength are presented in Figure 3a,b, which shows the variation of these parameters for SiOₓCᵧ:H layers depending on deposition time. Transmission (T) and reflection (R) are directly measured parameters, while absorptance (A) is calculated from the relation $A = 1 - T - R$. On the other hand, absorbance (Abs), defined by the logarithmic relation $Abs = -log(T)$ as presented in Figure 3c, provides insight into the interactions between light and the material. It can be observed that transmittance in the VIS-NIR range varies between 70 and 85%. The reflectance is relatively low, with values between 10 and 35%. This suggests that our materials are highly transparent to infrared radiation. As you can see in Figure 3b, the sample prepared with 10 min of plasma deposition shows the highest absorptance, attributed to its relatively greater thickness.

The optical properties of our materials were derived from the transmission and reflection spectra, with the findings displayed as a function of wavelength in Figure 4a-f. To analyze the optical spectra, the software “CODE” was used in order to determine the real and imaginary parts of the dielectric permittivity, the refractive index, the extinction, and the absorption coefficients by fitting the UV-VIS spectra. The error between the model and the measurement noted fit deviation (S) is calculated by the following relation:

$$S = \sqrt{\frac{\sum_{i=1}^{N} (y_{i}^{m}(\lambda) - y_{i}^{s}(\lambda))^{2}}{N - 1}}, \quad (1)$$

where $y_{i}^{m}(\lambda)$ is the value measured during a measurement at a specific length, $y_{i}^{s}(\lambda)$ is the value model, and N is the number of measured points. The calculated errors for both measurements (T and R) simultaneously were $3.61 \times 10^{-4}$, $4.05 \times 10^{-4}$, and $1.89 \times 10^{-4}$ for the three samples developed with 20 s, 40 s, and 10 min, respectively. Those were considered to be a good fit.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Measured transmittance, reflectance (a), absorptance (b), and absorbance (c) spectra of SiOₓCᵧ:H-based layers deposited with different deposition times.</figcaption></figure>

At first, the real parts of the dielectric permittivity decrease with deposition time, ranging from 4.24 to 3.40 at a wavelength of 550 nm. In contrast, the imaginary parts increase, going from 9.13 × 10⁻³ to 9.83 × 10⁻² at the same wavelength. For a fixed deposition time, both the real and imaginary parts gradually decrease as the wavelength increases, eventually reaching a plateau at longer wavelengths (as shown in Figure 4a,b, and Table 1). On the other hand, the refractive index n decreases with deposition time, ranging from 2.06 to 1.84 at a wavelength of 550 nm. Conversely, the extinction coefficients increase, from 2.12 × 10⁻³ to 2.70 × 10⁻². For a fixed deposition time, both the refractive index and the extinction coefficients gradually decrease as the wavelength increases (as shown in Figure 4c,d). Films deposited for 10 min exhibit a refractive index of 1.84, which aligns more closely with that of disordered carbon materials. In contrast, during 20 s of deposition, the refractive index reaches 2.06, a value characteristic of highly disordered carbon compounds. This suggests that shorter deposition times result in greater disorder within the material, while longer deposition times lead to a more ordered structure. The variation in refractive index can be associated with changes in material density. Thus, an increase in refractive index may indicate densification of the films as deposition time decreases [7]. The decrease in refractive index with increased deposition time could be related to a progressive change in structure, along with an increase in the degree of disorder and defects in an amorphous material at short deposition times [26]. In disordered materials, the refractive index is more sensitive to dispersion effects, as electronic states more strongly influence how light propagates. This can lead to a variation in the refractive index within certain wavelength ranges, depending on the density of electronic states and the type of disorder present [27]. The defects introduced by the disorder allow electronic transitions at lower energies, often resulting in increased absorption at specific wavelengths, which can also raise the refractive index just above this absorption region. Optical studies on amorphous materials, such as amorphous carbon and silicon nitride, show behavior similar to that observed in our study [28]. Furthermore, another study indicates that the introduction of disorder affects light transmission properties over a wide wavelength range: below a certain wavelength,
disordered structures transmit more light than ordered structures, whereas above this wavelength, ordered structures transmit more than disordered ones [29].

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Real part $\varepsilon_r$ (a), imaginary parts $\varepsilon_i$ of the dielectric constants (b), refractive index n (c), extinction coefficient k (d), absorption coefficient $\alpha$ (e), and band gap energy $E_g$ (f) of the SiO$_x$C$_y$:H films at different deposition times as a function of the wavelength.</figcaption></figure>

On the other hand, an increase was observed in the absorption coefficients, which rise from $4.35 \times 10^2$ to $6.20 \times 10^3$ cm$^{-1}$ at 550 nm, a decrease with increasing wavelength for the three samples was observed (see Figure 4e and Table 2). Table 2 summarizes the variation of these parameters at a wavelength of 550 nm for different deposition times. By properly controlling the deposition process, it is possible to deposit SiO$_x$C$_y$:H films with a specific refractive index profile. R. Rochotzki et al. [30] showed that the refractive index of SiO$_x$C$_y$:H films can be tuned over a wide range by changing the deposition conditions, such as pressure and power. Table 3 presents some literature-reported values of the refractive index of SiO$_x$C$_y$:H as a function of deposition parameters such as temperature, pressure, O$_2$ and N$_2$ ratio, and RF power. As you can see from Table 3, the refractive index varies from 1.39 to 2.1 at a wavelength of 632.8 nm. Studies on SiO$_x$C$_y$:H materials with spectroscopic ellipsometry show that the refractive indices of the layers can be tuned over the range of from 2.5 to 3.85 (measured at 600 nm) [31]. This shows the interest of this material as a layer in the design of optical filters.
<table><caption>**Table 2.** The real $ε_r$ and imaginary $ε_i$ dielectric constants, refractive index n, extinction coefficient k, absorption coefficient $α$, and optical band gap $E_g$ for SiOₓCᵧ:H at different deposition times (at =550 nm).</caption><thead><tr><th>Samples</th><th>ε<sub>r</sub></th><th>ε<sub>r</sub></th><th>n</th><th>K</th><th>a</th><th>E<sub>g</sub> (eV)</th></tr></thead><tbody><tr><td>20 s</td><td>4.24</td><td>9.13 × 10<sup>-3</sup></td><td>2.06</td><td>2.12 × 10<sup>-3</sup></td><td>4.35 × 10<sup>2</sup></td><td>2.85</td></tr><tr><td>40 s</td><td>3.93</td><td>4.93 × 10<sup>-2</sup></td><td>1.98</td><td>1.24 × 10<sup>-2</sup></td><td>2.86 × 10<sup>3</sup></td><td>2.30</td></tr><tr><td>10 min</td><td>3.40</td><td>9.83 × 10<sup>-2</sup></td><td>1.84</td><td>2.70 × 10<sup>-2</sup></td><td>6.20 × 10<sup>3</sup></td><td>2.03</td></tr></tbody></table>

<table><caption>**Table 3.** The variation of refractive index of SiOₓCᵧ:H as a function of deposition parameters such as temperature, pressure, O₂ and N₂ ratio, and RF power reported in the literature in comparison with our results.</caption><thead><tr><th>References</th><th>Flow rate</th><th>[7]</th><th>Deposition time</th><th>Power</th><th>[20]</th><th>200 sccm</th><th>[32]</th><th>4 sccm</th><th>Our Work</th></tr></thead><tbody><tr><td rowspan="4">Fixed parameters</td><td>Pressure</td><td>20 sccm</td><td>7 × 10<sup>-3</sup> Torr</td><td>5 min</td><td>-</td><td>0.9 Pa</td><td>-</td><td>7 × 10<sup>-3</sup> Torr</td><td>13 × 10<sup>-3</sup> Torr</td></tr><tr><td>Time</td><td></td><td></td><td></td><td>-</td><td>300 s</td><td>-</td><td>5 min</td><td>Varied</td></tr><tr><td>Power</td><td></td><td></td><td></td><td>-</td><td>-</td><td>72 W</td><td>200 W</td><td>100 W</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Studied parameter</th><th>Power</th><th colspan="2">O₂/HMDSO</th><th>Temperature</th><th colspan="2">N₂/HMDSO</th><th>Pressure</th><th colspan="2">Deposition time</th></tr><tr><td>Range</td><td>20 W</td><td>200 W</td><td>1/5</td><td>575 °C</td><td>0.4</td><td>20</td><td>0.08 mbar</td><td>20 s</td><td>10 min</td></tr><tr><td>Refractive index (at 632.8 nm)</td><td>1.45</td><td>1.9</td><td>2.1</td><td>1.51</td><td>1.39</td><td>1.47</td><td>2</td><td>1.75</td><td>1.62</td><td>1.48</td><td>2.04</td><td>1.82</td></tr></tbody></table>

Additionally, the optical bandgap energy ($E_g$) can be determined using the Tauc model, as described by the following equation [33]:

$$ \alpha h \nu = A (h \nu - E_g)^m \quad (2) $$

Here, $α$ represents the absorption coefficient, which is calculated using the “Code” software, $hν$ is the photon energy (where h is Planck’s constant and $ν$ is the frequency of the incident light), A is a constant, and m is an exponent that characterizes the nature of the optical absorption. For a direct forbidden transition, m = 3/2; for an indirect forbidden transition, m = 3; for a direct allowed transition, m = 1/2; and for an indirect allowed transition, m = 2. The bandgap energy ($E_g$) of the fabricated SiOₓCᵧ:H corresponds to a direct allowed transition and is obtained by plotting ($αhν$)² against the photon energy $hν$. Figure 4f illustrates the variation of ($αhν$)² as a function of photon energy $hν$ for films deposited at different deposition times. It can be observed that $E_g$ decreases as the deposition time increases, from 2.85 eV for 20 s of deposition to 2.03 eV for 10 min.

### 3.3. Optical Filters

Optical filters can be divided into several types; here, we had to choose between the following: transmission filters, which transmit the selected wavelength while absorbing other wavelengths, and absorption filters, which absorb the selected wavelength and reflect the others. In our case, we chose to fabricate transmission filters using two structures: a multiple cavity metal–dielectric (MCMD) structure composed of alternating layers of a high refractive index material (SiOₓCᵧ:H, n = 2.06 at $λ$ = 550 nm) and a “low refractive index material” (Ag, n ≈ 0.2 at $λ$ = 550 nm), and a structure similar to a Fabry–Perot filter, consisting of a layer of SiOₓCᵧ:H deposited between two Silver layers. The MCMD structure was used to fabricate a transmission filter at 670 nm according to the following design: 31 nm Ag/126 nm SiOₓCᵧ:H/44 nm Ag/67 nm SiOₓCᵧ:H (Figure 5a). On the other hand, the cavity Fabry–Perot was used to fabricate a transmission filter at 830 nm using three layers with thicknesses of 34 nm for Ag film, 353 nm for SiOₓCᵧ:H film, and 25 nm for Ag film (Figure 5b).
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Design of transmission filters realized with (a) multiple cavity metal–dielectric (MCMD) structure and (b) Fabry–Perot cavity.</figcaption></figure>

The thickness evolution over time for both materials, SiOₓCᵧ:H and Ag, was determined in order to identify the deposition time corresponding to the optimal thickness. The optimal thickness for each layer was determined with the help of the optical filter design software “Geneticode”. Figure 6 shows the evolution of this thickness for different deposition times for the two materials, SiOₓCᵧ:H and Ag.

<figure><img src="image_9.png" /><figcaption>**Figure 6.** The evolution of this thickness for different deposition times for the two materials, (a) SiOₓCᵧ:H and (b) Ag.</figcaption></figure>

The measured transmission response of optical filters is shown in Figure 7 for the two wavelengths, 670 nm and 830 nm. As can be seen, the wavelengths of 670 nm and 830 nm are transmitted, while the other wavelengths are rejected. The transmittance of a filter fabricated with the MCMD structure is about 30% for a wavelength of 670 nm, whereas, with the Fabry–Perot structure, it is about 20% for a wavelength of 830 nm. The full width at half maximum (FWHM) of the transmittance spectrum obtained with the MCMD structure is approximately 190 nm, and, for the Fabry–Perot structure, it is around 90 nm. This means that the MCMD structure transmits more than the Fabry–Perot structure, but it transmits over a wider range of wavelengths. Introducing a classic figure of merit for the selectivity, Lambda/DeltaLambda, where Lambda is the target wavelength, and DeltaLambda is the FWHM, we obtain a selectivity of 3.37 for the MCMD-structure-based filter and 9.22 for the Fabry–Perot structure-based filter.

Additionally, the manuscript presents the design and fabrication of wavelength-selective optical filters that are both cost-effective and high-performing. These filters are produced using simple, low-cost techniques and non-toxic materials. Furthermore, the fabrication process occurs at room temperature, allowing for the deposition of these filters
on flexible and soft polymer substrates. This approach paves the way for applications in flexible and portable optical devices and is particularly suited for areas where compatibility with non-rigid substrates is essential.

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Measured transmittance of real transmission filters realized with (a) multiple cavity metal–dielectric (MCMD) structure and (b) Fabry–Perot cavity.</figcaption></figure>

**4. Conclusions**

This study has focused on the fabrication of multilayer thin films of SiOₓCᵧ:H and Ag on glass substrates using both PECVD and Sputtering techniques. The influence of deposition time on the optical properties of SiOₓCᵧ:H films was studied. Reflectance and transmission spectra were analyzed to extract optical constants using the “CODE” software, including the real part εᵣ and imaginary part εᵢ of the dielectric constants, the refractive index n, the extinction coefficient k, the absorption coefficient α, and the bandgap energy E_g. With the increase in deposition time, the values of the real part of the dielectric constants, the refractive index, and the bandgap energy decreased, from 4.24 to 3.40, from 2.06 to 1.84, and from 2.85 eV to 2.03 eV, respectively. Conversely, the values of the imaginary part of the dielectric constants, the extinction coefficient, and the absorption coefficient increased from 9.13 × 10⁻³ to 9.83 × 10⁻², from 2.12 × 10⁻³ to 2.70 × 10⁻², and from 4.35 × 10² cm⁻¹ to 6.20 × 10³ cm⁻¹, respectively. Transmission optical filters based on the two structures, multiple cavity metal–dielectric (MCMD) and Fabry–Perot, were successfully fabricated. The optical filter fabricated with the MCMD structure at a wavelength of 670 nm showed higher transmittance compared to the Fabry–Perot structure, with about 30% transmittance but with a lower selectivity (3.22 using a classic Lambda/FHWM criterion). The Fabry–Perot structure, on the other hand, showed higher selectivity (9.22) but lower transmittance, around 20% at a wavelength of 830 nm.

**Author Contributions:** Conceptualization, A.Z., F.L., M.L. and P.B.; validation, A.K. and A.Z.; formal analysis, A.K.; investigation, A.K., M.L. and I.H.A.; data curation, A.K. and W.E.H.; visualization, P.B. and M.L.; writing—original draft preparation, A.K.; writing—review and editing, A.Z., M.L. and P.B., supervision, A.Z.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by PARS (ANR-DFG) project N°22003.

**Data Availability Statement:** The original contributions presented in this study are included in this article; further inquiries can be directed to the corresponding author.

**Acknowledgments:** Support by the French embassy in Kuala Lumpur, Malaysia is acknowledged by one of the authors (P.B.).

**Conflicts of Interest:** The authors declare no conflicts of interest.
## References

1. Gotoh, K.; Shohbuke, E.; Kobayashi, Y.; Yamada, H. Wettability control of PET surface by plasma-induced polymer film deposition and plasma/UV oxidation in ambient air. *Colloids Surf. A Physicochem. Eng. Asp.* **2018**, *556*, 1–10. [CrossRef]

2. Barni, R.; Zanini, S.; Riccardi, C. Characterization of the Chemical Kinetics in an O₂/HMDSO RF Plasma for Material Processing. *Adv. Phys. Chem.* **2012**, *2012*, 205380. [CrossRef]

3. Silva, M.L.P.; Tan, I.H.; Filho, A.P.N.; Galeazzo, E.; Jesus, D.P. Use of plasma polymerized highly hydrophobic hexamethyldisilazane (HMDS) films for sensor development. *Sens. Actuators B Chem.* **2003**, *91*, 362–369. [CrossRef]

4. Lamendola, R.; D'Agostino, R. Process control of organosilicon plasmas for barrier film preparations. *Pure Appl. Chem.* **1998**, *70*, 1203–1208. [CrossRef]

5. Kim, M.T.; Lee, J. Characterization of amorphous SiC:H films deposited from hexamethyldisilazane. *Thin Solid Film.* **1997**, *303*, 173–179. [CrossRef]

6. Carton, O.; Lejeune, M.; Lamarque, F.; Zaidi, S.; Zeinert, A. Thermo-mechanical characterization of optical thin films filters deposited onto shape memory alloy micro-actuators. *Smart Mater. Struct.* **2014**, *23*, 125035. [CrossRef]

7. Amri, R.; Sahel, S.; Gamra, D.; Lejeune, M.; Clin, M.; Zellama, K.; Bouchriha, H. Photonic band gap and defects modes in inorganic/organic photonic crystal based on Si and HMDSO layers deposited by sputtering and PECVD. *Opt. Mater.* **2018**, *76*, 222–230. [CrossRef]

8. Esena, P.; Zanini, S.; Riccardi, C. Plasma processing for surface optical modifications of PET films. *Vacuum* **2007**, *82*, 232–235. [CrossRef]

9. Alexandrov, S.E.; McSporran, N.; Hitchman, M.L. Remote AP-PECVD of Silicon Dioxide Films from Hexamethyldisiloxane (HMDSO). *Chem. Vap. Depos.* **2005**, *11*, 481–490. [CrossRef]

10. Cho, S.-H.; Park, Z.-T.; Kim, J.-G.; Boo, J.-H. Physical and optical properties of plasma polymerized thin films deposited by PECVD method. *Surf. Coat. Technol.* **2003**, *174–175*, 1111–1115. [CrossRef]

11. O'Leary, S.K.; Johnson, S.R.; Lim, P.K. The relationship between the distribution of electronic states and the optical absorption spectrum of an amorphous semiconductor: An empirical analysis. *J. Appl. Phys.* **1997**, *82*, 3334–3340. [CrossRef]

12. Musila, N.; Munji, M.; Simiyu, J.; Masika, E.; Nyenge, R. Optical Properties and Analysis of OJL Model's Electronic inter-band Transition Parameters of TiO₂ Films. *Traektoriâ Nauk. = Path Sci.* **2018**, *4*, 3001–3012. [CrossRef]

13. Theiss, W. Analysis of optical spectra by computer simulation—From basics to batch mode. In *Theiss Hard-Und Software for Optical Spectroscopy*; Wolfgang Theiss: Aachen, Germany, 2002.

14. Gao, X.-H.; Qiu, X.-L.; Li, X.-T.; Theiss, W.; Chen, B.-H.; Guo, H.-X.; Zhou, T.-H.; Liu, G. Structure, thermal stability and optical simulation of ZrB₂ based spectrally selective solar absorber coatings. *Sol. Energy Mater. Sol. Cells* **2019**, *193*, 178–183. [CrossRef]

15. Gao, X.-H.; Theiss, W.; Shen, Y.-Q.; Ma, P.-J.; Liu, G. Optical simulation, corrosion behavior and long term thermal stability of TiC-based spectrally selective solar absorbers. *Sol. Energy Mater. Sol. Cells* **2017**, *167*, 150–156. [CrossRef]

16. Köstenbauer, H.; Lorenz, D.; Winkler, J.; Theiss, W. P-145: Optimization of Molybdenum Oxides for Low-Reflectance Thin Films using Numerical Simulation. *SID Symp. Dig. Tech. Pap.* **2015**, *46*, 1741–1743. [CrossRef]

17. Theiss, W. Optical coating design by genetic algorithms. In *GnetiCode*; Wolfgang Theiss: Aachen, Germany, 2019; pp. 29–39.

18. Leterrier, Y. Durability of nanosized oxygen-barrier coatings on polymers. *Prog. Mater. Sci.* **2003**, *48*, 1–55. [CrossRef]

19. Goujon, M.; Belmonte, T.; Henrion, G. OES and FTIR diagnostics of HMDSO/O₂ gas mixtures for SiOx deposition assisted by RF plasma. *Surf. Coat. Technol.* **2004**, *189*, 756–761. [CrossRef]

20. Amri, R.; Hamed, Z.B.; Gamra, D.; Lejeune, M.; Bouchriha, H. Optical modeling and investigation of thin films based on plasma-polymerized HMDSO under oxygen flow deposited by PECVD. *J. Mater. Sci. Mater. Electron.* **2023**, *34*, 1413. [CrossRef]

21. Yuan, Q.H.; Wang, X.M.; Yin, G.Q.; Li, J.; Dong, C.Z. The Organosilicon thin Film Deposited Using an Atmospheric Pressure Dual-Frequency 50 kHz/33 MHz Frequency MicroPlasma Jet. *Contrib. Plasma Phys.* **2016**, *56*, 870–877. [CrossRef]

22. Ricci, M.; Dorier, J.-L.; Hollenstein, C.; Fayet, P. Influence of Argon and Nitrogen Admixture in HMDSO/O₂ Plasmas onto Powder Formation. *Plasma Process. Polym.* **2011**, *8*, 108–117. [CrossRef]

23. Raballand, V.; Benedikt, J.; Hoffmann, S.; Zimmermann, M.; von Keudell, A. Deposition of silicon dioxide films using an atmospheric pressure microplasma jet. *J. Appl. Phys.* **2009**, *105*, 83304. [CrossRef]

24. Gordijn, A.; Rath, J.K.; Schropp, R.E.I. Thickness determination of very thin amorphous and microcrystalline silicon layers using reflection/transmission measurements. *Appl. Phys. Lett.* **2004**, *85*, 5096–5098. [CrossRef]

25. Kim, C.C.; Garland, J.W.; Abad, H.; Raccah, P.M. Modeling the optical dielectric function of semiconductors: Extension of the critical-point parabolic-band approximation. *Phys. Rev. B* **1992**, *45*, 11749–11767. [CrossRef] [PubMed]

26. Shirai, K.; Gonda, S. Refractive indexes of amorphous boron films prepared by plasma deposition. *J. Phys. Chem. Solids* **1992**, *53*, 1081–1092. [CrossRef]

27. Mott, N.F.; Davis, E.A. *Electronic Processes in Non-Crystalline Materials*; Oxford University Press: Oxford, UK, 2012; ISBN 0191023280.

28. Jellison, G.E.; Merkulov, V.I.; Puretzky, A.A.; Geohegan, D.B.; Eres, G.; Lowndes, D.H.; Caughman, J.B. Characterization of thin-film amorphous semiconductors using spectroscopic ellipsometry. *Thin Solid Film.* **2000**, *377–378*, 68–73. [CrossRef]

29. Bellingeri, M.; Cassi, D.; Criante, L.; Scotognella, F. Light Transmission Properties and Shannon Index in One-Dimensional Photonic Media With Disorder Introduced by Permuting the Refractive Index Layers. *IEEE Photonics J.* **2013**, *5*, 2202811. [CrossRef]
30. Rochotzki, R.; Arzt, M.; Blaschta, F.; Poll, H.U. Optical properties of plasma polymer films (hexamethyldisiloxane). *Thin Solid Film*. **1993**, *234*, 463–467. [CrossRef]

31. Goyal, P.; Hong, J.; Haddad, F.; Maurice, J.; Roca, P.; Johnson, E. O pen Use of hexamethyldisiloxane for p-type microcrystalline silicon oxycarbide layers. *EPJ Photovolt*. **2016**, *7*, 70301. [CrossRef]

32. Amri, R.; Sahel, S.; Gamra, D.; Lejeune, M.; Clin, M.; Zellama, K.; Bouchriha, H. Photonic band gap and defect mode of one-dimensional photonic crystal coated from a mixture of (HMDSO, N₂) layers deposited by PECVD. *Superlattices Microstruct*. **2017**, *104*, 298–307. [CrossRef]

33. Makuła, P.; Pacia, M.; Macyk, W. How to Correctly Determine the Band Gap Energy of Modified Semiconductor Photocatalysts Based on UV-Vis Spectra. *J. Phys. Chem. Lett.* **2018**, *9*, 6814–6817. [CrossRef]

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