We have designed and fabricated TiN/SiO2/TiN–HfO2-based new metamaterial microstructures as an absorber of the visible wavelength, in the range of 400–700 nm, with exceptionally high absorption efficiency (>96%) for solar energy harvesting purposes and generation of heat upon absorption of electromagnetic energy. The finite element method-based COMSOL Multiphysics software simulations were used to optimize the structural parameters of the microstructures and visualize the electric field and electromagnetic power loss distribution in the structure. An optimized 2D unit cell of the structure consists of a 4 μm × 160 nm TiN base on a glass substrate covered with a 70 nm thick SiO2 film. A periodic structure of TiN straps (each 90 nm thick and 2 μm wide) is deposited over the SiO2. The straps are capped with a 40 nm thick layer of high-temperature dielectric HfO2 with a periodicity of 4 µm. This unit is symmetric along the other dimension and is repeated periodically along the horizontal direction. Similar optimized parameters were used for 7, 10, and 100 µm periodic structures to investigate the effect of grating structure pitch on the absorption of light. Although these microstructures were optimized for the visible light spectrum, they show absorption efficiency of >92% when integrated over a broadband wavelength spectrum ranging from 400 to 1200 nm. The experimental data show excellent agreement with the simulated results. We observe less than 5% difference between experimental and simulated absorption efficiencies for the investigated microstructures. Furthermore, we should emphasize that, to the best of our knowledge, this is the first study to experimentally report the light to heat conversion in metamaterials with micron-range size patterned structures.

There is significant interest in the development of broadband metamaterial solar absorbers (BMSAs) of sunlight with high absorption efficiency for energy harvesting purposes and high-temperature thermophotovoltaic applications. Different kinds of metamaterial nanostructures have been optimized and proposed using various simulation techniques for effective absorption efficiencies in the visible range of the spectrum.1–21 For example, Akafzade and Sharma introduced a metamaterial nanostructure consisting of a TiN/SiO2/TiN–HfO2 disk to be used as a broadband solar absorber approaching a simulated absorption of ∼98% integrated over the broadband spectrum ranging from 250 to 1100 nm.1 Some experimental works also have been conducted in this area of research.22–29 For example, Hou et al. proposed a nanostructure composed of tapered polyimide substrate and Al–Cr–SiO2–Cr–SiO2 thin film and experimentally achieved high average absorbance (>93%) over the range of wavelength from 300 to 2500 nm.27 

Theoretically, the total amount of light absorbed by the BMSA is given by the following equation:
A=1RT,
(1)
where A represents the total absorption, R is the reflectance, and T represents the transmission of incident light by the BMSA. To achieve maximum absorption, by some physical mechanism, reflected and transmitted light should be reduced to nearly zero. When the absorption of light is close to 100%, near-perfect absorption will be achieved. Perfect or near-perfect absorption is dependent on the materials and geometry of the pattern used to fabricate the device for light to heat conversion.

In general, the materials should have suitable optical properties, chemical stability, and adequate high-temperature tolerance. For example, titanium nitride (TiN) is a material of interest for BMSAs as a refractory plasmonic material owing to its high melting point (2930 °C), plasmonic resonance in the visible (VIS)-to-near-infrared (NIR) range, and chemical stability.19–25 Li et al. experimentally demonstrated that broadband metamaterial absorbers (BMAs) consisting of TiN show stability in physical and optical properties (in the visible range) after heat treatment at 800 °C and obtained integrated absorption of about 95% over the visible range.22 Qin et al. designed a BMA consisting of Ti and patterned TiN and experimentally reported broadband absorption greater than 90% over the optical region of the solar spectrum.23 

Similarly, hafnium dioxide (HfO2) is an exceptionally good dielectric material for high-temperature applications. For example, Liu et al. have investigated the optical properties of sputter-deposited HfO2 films and observed excellent antireflective properties of HfO2 films in the 3–5 and 8–12 μm thickness ranges.30 In addition, Fadel et al. also studied some of the optical properties of HfO2 films grown by electron beam evaporation. They determined the refractive index of the films to be close to 2 for wavelengths in the range of 350–2000 nm.31 Hafnium dioxide is characterized by optical transparency over a much wider range of wavelengths (250–2000 nm), higher density in the solid state, chemical stability, and a very high melting point of 2758 °C.31–36 Tiwari et al. have investigated the usefulness of HfO2 dielectric films as highly sensitive waveguide-coupled surface plasmon resonance sensors.31,37

In addition, Hao et al. provided a theoretical and numerical study of heat generation in plasmonic metamaterials upon absorption of light under light radiation39 using the theory provided by Loudon40 for electromagnetic energy propagation through an absorbing dielectric and Ruppin41 for electromagnetic energy density in a dispersive and absorptive material. In Ref. 39, Hao et al. stated that the absorbed electromagnetic energy upon absorption of light by metamaterial is dissipated by the dielectric or Ohmic losses and converted into heat.

Although there is a volume of research being conducted in this field, it still suffers from limited experimental work because of the difficulties in fabricating the proposed metamaterial nanostructures. In this investigation, we report on the design and fabrication of metamaterial microstructures as metamaterial broadband solar absorbers (BMSAs) with extremely high absorption efficiencies (>96%) integrated over the broadband wavelengths in the range of 400–700 nm and (>92%) integrated over the broadband wavelengths in the range of 400–1200 nm at normal incidence of unpolarized light. A set of devices consisting of a 1D periodic grating array of TiN (90 nm) of walls capped with high-temperature dielectric hafnium-dioxide (HfO2) (40 nm) walls on SiO2 (70 nm)/TiN (160 nm) film stack was optimized by utilizing the COMSOL Multiphysics software38 and fabricated using standard semiconductor fabrication process. These proposed microstructures were further studied experimentally for broadband absorption and heat generation as a result of the conversion of solar energy (electromagnetic energy) to thermal energy (dissipated heat).

For the proposed metamaterial structures, the design parameters were optimized using the finite element method (FEM)-based COMSOL Multiphysics software.38 Simulations are used to provide the maximum possible absorption efficiencies for the desired range of wavelengths. As required by simulations, a “physics-controlled mesh” was chosen in which the software determines the concentration and the size of mesh elements based on the wavelength of the desired purpose, the refractive index of the materials in each domain, and the size and dimensions of each domain of the defined unit cell. The size element was chosen to be “extremely fine” of free triangular type in the interface options.

The simulation started with using 2D space with electromagnetic waves, frequency domain physics selection in wave optics module. For simulating absorption efficiency, a unit cell of the structure was defined and periodic boundary conditions were applied to the vertical walls of the unit cell to imitate the infinite repetition of grating walls. Two periodic ports were designated for the incident and refracted light from the structure, where the top horizontal port is assigned as the input port for the incoming incident light and simulates the reflected light, and the bottom horizontal port is assigned as the output port for simulating the transmitted light. Every parameter in this structure was first optimized individually by keeping other parameters constant. Since the overall effect of these parameters is mutually dependent, for the next step, we ran a simulation in which all the parameters are changing slightly around their optimum values, simultaneously, to ensure the structure that we eventually predict is the best possible one. For the simulation of reflection, transmission, and absorption of incident light, a parametric sweep study on the desired wavelength range of incident light was performed. Figure 1 shows the optimized thickness of each layer for maximum absorption.

FIG. 1.

Optimized thickness of each layer for maximum absorption.

FIG. 1.

Optimized thickness of each layer for maximum absorption.

Close modal

The simulation was carried out for unpolarized visible light of 400–700 nm wavelength interval at normal incidence. The thickness of each layer was optimized before fabricating the devices. For 4 μm grating pitch BMSA, the value of the optimized thicknesses for TiN/SiO2/TiN–HfO2 were found to be 160/70/90/40 nm, respectively. These thicknesses were also confirmed for 7, 10, and 100 μm grating pitch BMSAs. Figure 2 shows the simulated absorptance as a function of the wavelength of normally incident unpolarized light for different grating pitch BMSAs.

FIG. 2.

Simulated absorptance of BMSAs as a function of wavelength for normally incident unpolarized light.

FIG. 2.

Simulated absorptance of BMSAs as a function of wavelength for normally incident unpolarized light.

Close modal

The absorption of incident light is dependent on the refractive indices (n, k) of the active layer. For the accuracy of the simulation, we employed infrared reflection and transmission spectroscopy to determine the refractive indices of the 100 nm thin TiN film for the 400–1200 nm range prior to the simulation since this layer is the active layer. In addition, since the glass is fused silica, we decided to determine the refractive index accurately for the simulation.

Figure 3(a) shows the real and imaginary parts of the refractive indices of 100 nm TiN film, whereas Fig. 3(b) shows the refractive index of the glass substrate as a function of wavelength. For SiO2 and HfO2 layers, the corresponding refractive indices data were used from COMSOL material library as “SiO2 (Silicon dioxide, Silica, Quartz) [Ghosh: α-Quartz, n(o) 0.198–2.0531 μm]”44 and “HfO2 (Hafnium dioxide, Hafnia) (Wood et al.: Cubic hafnia; n 0.361–5.135 μm).”45 

FIG. 3.

Measured refractive indices for (a) 100 nm TiN and (b) 1 mm thick glass substrate.

FIG. 3.

Measured refractive indices for (a) 100 nm TiN and (b) 1 mm thick glass substrate.

Close modal
The devices were fabricated in the Nanotechnology Research Center (NRC), a class-100 semiconductor fabrication facility. The fabrication steps are as follows;
SubstratepiranhaCleaningThinfilmstackdepositionDehydrationPhotoresistcoatingPhotolithographyexposureDevelopingphotoresistPhotoresistUVcureEtchingPhotoresistremoval
Figure 4 shows schematically the fabrication steps for the 4 μm pitch microstructure.
FIG. 4.

Schematics of the fabrication steps used for the metamaterial microstructure. (a) Color coding for used materials. (b) Deposited films stack on piranha-cleaned substrate. (c) Coating of photoresist. (d) Post photolithography exposure. (e) Post etching. (f) Final structure after remaining resist removing and cleaning.

FIG. 4.

Schematics of the fabrication steps used for the metamaterial microstructure. (a) Color coding for used materials. (b) Deposited films stack on piranha-cleaned substrate. (c) Coating of photoresist. (d) Post photolithography exposure. (e) Post etching. (f) Final structure after remaining resist removing and cleaning.

Close modal

1. Thin film growth

Device fabrication began with the deposition of a 160 nm thick layer of TiN on a piranha-cleaned glass substrate using a multi-gun AJA RF sputtering system. This layer was followed by the deposition of a 70 nm thick SiO2 and a 90 nm TiN film with the same sputtering equipment. The device was then transferred to an NRC homebuilt RF sputtering deposition system for the deposition of a 40 nm HfO2 thin film on top. KLA Tencor P6 Profilometer was used to measure the thickness of each deposited layer on simultaneously deposited reference layers on silicon wafers.

2. Photolithography process

The photolithography process was started with the films stack sample being dehydrated for 30 min at 150 °C and cooled down before spreading a monolayer of hexamethyldisilazane (HMDS), and a post-bake at 150 °C for 60 s, which serves as an adhesion promoter for the photoresist. Consecutively, 1.2 μm thick S-1813 positive photoresist was spread followed by a soft bake at 115 °C for 60 s. The photoresist was patterned using a custom-designed photomask on a broadband EVG aligner. The exposed sample was baked at 110 °C for 60 s and developed using MF-319 developer.

3. Etching process

Prior to the etching process, the samples were cured with a UV light source to increase the film to photoresist etch selectivity. The samples were etched in a Trion Deep Reactive Ion Etching (DRIE) equipment for etching HfO2, using a combination of argon (90%) and CF4 (10%) with an etch rate of 37 nm/min.42 For TiN etching, 30% aqueous hydrogen peroxide (H2O2) at 50 °C was used with an etch rate of 40 nm/min.43 Thus, the pattern was transferred to the two top layers (HfO2 and TiN). Post etching, the photoresist remover was applied to finalize the device, and the final step was to clean the device using de-ionized (DI) water and dry it with nitrogen gas.

Scanning electron microscopy (SEM), infrared spectroscopy (IR), and solar simulator (SS) technique were employed to investigate and characterize the device and its functionalities. Figure 5 shows an example of SEM images of patterned grating with a measured pitch of about 4 μm and trench width of about 2 μm obtained by a Zeiss Supra SEM.

FIG. 5.

SEM images of microfabricated grating structures of 4 μm pitch. (a) Measurements of grating pitch and width of trench. (b) Density of grating walls.

FIG. 5.

SEM images of microfabricated grating structures of 4 μm pitch. (a) Measurements of grating pitch and width of trench. (b) Density of grating walls.

Close modal

In addition, a V-570 UV-Vis spectrometer is used for measuring the reflectance (R) and transmittance (T) of BMSAs for incident light of wavelength range 400–1200 nm with a wavelength step of 1 nm. The absorption of the BMSAs was calculated by using the equation A = 1 − RT.

To measure the increase in temperature resulting from the absorption of the incident light and the generation of heat by the fabricated device, the setup shown in Fig. 6 was used.

FIG. 6.

Block diagram of the experimental setup for in situ thermal measurements on BMSAs due to generation of heat from near-perfect absorption of normally incident unpolarized white light.

FIG. 6.

Block diagram of the experimental setup for in situ thermal measurements on BMSAs due to generation of heat from near-perfect absorption of normally incident unpolarized white light.

Close modal

In this setup, a nearly circular spot size of ∼1 cm in diameter of unpolarized white light was used, and before each measurement, the intensity of incident light was measured near the top grating layer of BMSA. To ensure the accuracy of measurements, data collection was carried out in a dark room. The base temperature of BMSA was measured before each exposure and the thermocouple connection was covered to avoid any influence on the temperature measurements due to stray light interaction with the thermocouple.

Figure 7 shows the experimental and simulated absorption of the microfabricated structure of 4, 7, and 10 μm grating pitches for unpolarized light at normal incidence as a function of wavelength. From the simulated absorption curves, the 4 μm pitch device has broadband absorption (≳90%) over a wide wavelength range of 400–1100 nm with near-perfect absorption (>99%) in the wavelength range of 550–760 and 970–1020 nm. In addition, the experimental absorption of the 4 μm device has broadband absorption (≳90%) over a wide wavelength range of 400–1114 nm, which matches the simulated curve trend, with having a very high absorption (>90%) in the wavelength range of 576–930 nm.

FIG. 7.

Experimental and simulated absorption of the microfabricated structure of (a) 4, (b) 7, and (c) 10 μm grating pitches for unpolarized light at normal incidence as a function of wavelength.

FIG. 7.

Experimental and simulated absorption of the microfabricated structure of (a) 4, (b) 7, and (c) 10 μm grating pitches for unpolarized light at normal incidence as a function of wavelength.

Close modal

Furthermore, 7 and 10 μm devices have simulated broadband absorption (≳90%) over a wide wavelength range of 400–930 and 400–950 nm, respectively, which are smaller compared to 4 μm device. In addition, 7 and 10 μm devices have near-perfect absorption (>99%) in the wavelength range of 600–750 and 680–740 nm respectively, which are also smaller compared to 4 μm device. Therefore, the small features in metamaterial structures provide a wide range of broadband and near-perfect absorption.

The integrated simulated and experimental absorption for the visible range of wavelengths from 400 to 700 nm and for the wavelength range of 400–1200 nm is shown in Table I. The simulated and experimental results agree with about <5% difference. The difference is attributed to the nature of the complexity of the fabrication process such as film thickness variations, light diffraction, profiles of the structures that deviate from simulated vertical walls, the width of the walls, and the slight change in dielectric constants used in simulation and actual deposited material films. Table I shows the tabulated comparison of simulated and experimental integrated percentage absorption for the wavelength range of 400–700 and 400–1200 nm of all three devices.

TABLE I.

Simulated and experimental integrated % absorption for the wavelength range of 400–700 and 400–1200 nm of all three devices.

Simulated absorption (%)Experimental absorption (%)Absorption difference (%)
μm pitch device Visible (400–700 nm) 97.76 ∼94 <5 
Wavelength (400–1200 nm) 95.92 ∼94 <5 
μm pitch device Visible (400–700 nm) 97.37 ∼91 <10 
Wavelength (400–1200 nm) 93.61 ∼90 <5 
10 μm pitch device Visible (400–700 nm) 96.03 ∼93 <5 
Wavelength (400–1200 nm) 92.49 ∼91 <5 
Simulated absorption (%)Experimental absorption (%)Absorption difference (%)
μm pitch device Visible (400–700 nm) 97.76 ∼94 <5 
Wavelength (400–1200 nm) 95.92 ∼94 <5 
μm pitch device Visible (400–700 nm) 97.37 ∼91 <10 
Wavelength (400–1200 nm) 93.61 ∼90 <5 
10 μm pitch device Visible (400–700 nm) 96.03 ∼93 <5 
Wavelength (400–1200 nm) 92.49 ∼91 <5 

As simulation results show, the 4, 7, and 10 μm devices have near-perfect absorption at an incident wavelength of 700 nm, which can be incorporated with the enhanced evanescent resonant electric field induced between metal–dielectric–metal layers. Figure 8 shows the enhanced evanescent electric field (y component of the electric field) for 4, 7, and 10 μm devices at the incident wavelength of 700 nm. As shown in the figure, the enhanced electric field is concentrated at the bottom edges of the top TiN layer inside the SiO2 dielectric layer between the top and bottom of the TiN (metallic layer) and extended to the edge of the interface of TiN–HfO2 layers as well. It is known in interference theory46 for near-perfect absorption in metal–dielectric–metal structure metamaterial absorbers (MAs) that the thickness of the dielectric layer controls the constructive and destructive interferences. Furthermore, for near-perfect absorption, the total reflection should reach zero following the destructive interference conditions in multiple reflections. Thus, for near-perfect absorption, the optimized thickness of the dielectric layer between both TiN layers plays a major role and enhances the absorption by the top and bottom TiN layers. Furthermore, for 0.1 mW/cm2 power of incident light, 4, 7, and 10 μm devices have resonant electric fields of about 6 × 103, 5 × 103, and 4 × 103 V/m, respectively, which shows that smaller features enhance higher electric field.

FIG. 8.

Evanescent electric field for (a) 4, (b) 7, and (c) 10 μm devices for incident wavelength of 700 nm at near-perfect absorption conditions.

FIG. 8.

Evanescent electric field for (a) 4, (b) 7, and (c) 10 μm devices for incident wavelength of 700 nm at near-perfect absorption conditions.

Close modal

Figure 9 shows the electromagnetic power loss density distribution through resistive losses due to the absorption of incident electromagnetic energy. By analyzing the normalized electric field distribution over the grating structure, the mechanism of heat generation in different TiN layers can be understood. Figure 9 shows the correlation of electric field distribution and electromagnetic power loss density distribution in 4 μm device at 400, 700, and 1200 nm wavelengths. As shown in Figs. 9(a)9(f), the effect of heat generation is wavelength-dependent and decides whether the majority of the power loss is in the top TiN layer or bottom TiN layer. As shown in Fig. 9, for a 4 μm device, at 400 and 700 nm incident wavelengths, the electric field is mostly concentrated on the grating wall [Figs. 9(a) and 9(c), respectively], and the top TiN layer contributes to the electromagnetic (EM) energy losses [Figs. 9(b) and 9(d), respectively]. On the other hand, at a higher wavelength of 1200 nm, the electric field is distributed on the sides of the grating walls [Fig. 9(e)] and majority EM power loss at the bottom layer of the TiN as shown in Fig. 9(f).

FIG. 9.

The correlation of electric field distribution and electromagnetic power loss density distribution in 4 μm device at (a) and (b) 400, (c) and (d) 700, and (e) and (f) 1200 nm wavelengths.

FIG. 9.

The correlation of electric field distribution and electromagnetic power loss density distribution in 4 μm device at (a) and (b) 400, (c) and (d) 700, and (e) and (f) 1200 nm wavelengths.

Close modal

However, that is not the case for 7 and 10 μm devices. In both these devices, even at higher wavelengths, the majority of power loss is through the top TiN layer, as shown in Fig. 10. Figure 10 shows the EM power loss density distribution for 7 and 10 μm devices at a wavelength of 1200 nm.

FIG. 10.

The EM power loss density distribution for (a) 7 and (b) 10 μm devices at a wavelength of 1200 nm.

FIG. 10.

The EM power loss density distribution for (a) 7 and (b) 10 μm devices at a wavelength of 1200 nm.

Close modal

Figure 11 shows the electromagnetic power loss density distribution in 4, 7, and 10 μm devices at 700 nm wavelength where all three devices have near-perfect absorption. As shown in Fig. 11, smaller features have more amount of power loss since the 4 μm device has a maximum of ∼9 × 1012 W/m3 power density compared to ∼5 × 1012 and ≳3.5 × 1012 W/m3 power density for 7 and 10 μm devices, respectively.

FIG. 11.

The electromagnetic power loss density distribution in (a) 4, (b) 7, and (c) 10 μm devices at 700 nm wavelength where all three devices have near-perfect absorption.

FIG. 11.

The electromagnetic power loss density distribution in (a) 4, (b) 7, and (c) 10 μm devices at 700 nm wavelength where all three devices have near-perfect absorption.

Close modal

Figure 12 shows the increase in temperature (defined as ΔT = TT0, where T is the measured temperature after incident light absorption and T0 is room temperature) as a result of the conversion of light energy to heat in the device as a function of time for fixed light intensity. For all three devices, unpolarized white light of intensity of 9 mW/cm2 at normal incidence was used. At the first 200 s, the increase in temperature seems linear for all three devices. Beyond that time, it become nonlinear, trending toward saturation. We attribute this effect to the transfer of heat from the top TiN layer on grating walls to the bottom TiN layer through the dielectric SiO2 layer as shown by the simulation of the electromagnetic power loss density distribution through resistive losses. The total observed temperature change between 0 and 900 s for the 4, 7, and 10 μm devices are 2.4 ± 0.05, 1.9 ± 0.05, and 1.5 ± 0.05 °C, respectively. The difference in the temperatures is related to the level of light absorption in the devices discussed earlier. In relation to the experimental broadband absorption as mentioned in Sec. IV A, 4 μm device has an average integrated broadband absorption of about ∼94% in the wavelength range of 400–1200 nm, which is higher than the average integrated absorption of 7 and 10 μm, which are ∼90% and ∼91%, respectively. In addition, the small grating structure provides less surface area open to the environment, which can trap heat more efficiently since the rate of heat exchange to the environment is lower. Even though the 7 and 10 μm devices have similar experimental average integrated broadband absorption, the 7 μm device can trap heat more efficiently because of having small structural features and losing less heat to the environment. As it is evident from the data, the total generated heat depends on the pitch—with the smaller pitch, more light energy is converted to heat.

FIG. 12.

The measured generated heat as change in temperature of devices as a function of time. For all three devices, the incident light intensity was 9 mW/cm2.

FIG. 12.

The measured generated heat as change in temperature of devices as a function of time. For all three devices, the incident light intensity was 9 mW/cm2.

Close modal

In addition, to study the effects of the light intensity on the generated heat, the temperature measurements at different intensities of normal incident light were carried out. Figure 13 shows the measured temperature change as a function of the intensity of incident light after 2 min for a 4 μm device. As shown in the figure, the generated heat (increment in the temperature) is linearly dependent on the incident light intensity as it is a well-known phenomenon for heat generation in old nano particles.47 

FIG. 13.

Measured temperature change as a function of the intensity of incident light after 2 min.

FIG. 13.

Measured temperature change as a function of the intensity of incident light after 2 min.

Close modal

In conclusion, we successfully designed and fabricated various metamaterial microstructures as potential broadband absorbers of solar spectrum for solar energy harvesting and investigated the generation of heat experimentally. The proposed metamaterial microstructure has distinct advantage over the previously proposed metamaterial nanostructures,22–29 since it can be fabricated readily, as well as easily by using standard semiconductor fabrication technology tools and high-performance optical materials, namely, SiO2, TiN, and HfO2, and it provides similar experimental broadband absorption in visible–near-IR range of the spectrum and converts the absorbed electromagnetic energy to heat, which makes these devices a good candidate for high-temperature thermophotovoltaic, solar energy harvesting, and clean energy applications. The structural parameters of the microstructure are optimized by using finite element method (FEM)-based simulations, and the absorption characteristics of the optimized and fabricated microstructure are evaluated as functions of the normal incident wavelength of unpolarized light using simulations and experimentally. In addition, detailed simulated and experimental results for broadband absorption and heat generation due to resistive and Ohmic losses of electromagnetic energy are presented, which shows that the experimental performance of the BMSAs absorption is in good agreement with the simulated electric field and electromagnetic power loss distribution in the structures. Furthermore, it is shown that the absorbed light by BMSAs results in the generation of heat, and the generated heat depends on the microstructure of the BMSAs with smaller features trapping and generating more heat than bigger profiles. Furthermore, our results show the effect of the intensity of incident light on generated heat is linear.

The authors have no conflicts to disclose.

Vivek Khichar: Data curation (equal); Formal analysis (equal); Investigation (equal); Software (equal); Writing – original draft (equal); Writing – review & editing (equal). Nader Hozhabri: Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Ali R. Koymen: Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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