Machine learning optimized efficient graphene-based ultra-broadband solar absorber for solar thermal applications

Abstract

We designed an ultra-broadband graphene absorber structure with the applied resonator design based on the Al-AlSb-Cr structure, and a thin effective layer of graphene is inserted. To develop the role of the graphene in solar absorbers, the current structure investigates above 98% for 1500 nm bandwidth and 2800 nm (overall bandwidth) for 93.68%. In this study, the procedure of the investigated design in flow chat configuration, the multi-step presentation of the developed layers, and the analysis of the used parameters will be involved. The design is optimized using machine learning algorithm. The optimized design shows good performance compared to the other system. The newly investigated graphene design can be absorbed not only in visible places but also in near-infrared energy and ultraviolet zones. The other applications of the light trapping process, photovoltaic devices, and energy harvesting can also be used.

Introduction

Solar energy makes daily activities comfortable because it is a very simple process for generating energy and stands for clean energy¹. It can be used in a variety of ways, not only for small home installations but also for large industrial projects². The sun serves as the primary source of solar energy, which is particularly useful for all seasons^3,4. Moreover, a wide range of devices are available for harnessing solar energy, and its diverse applications further enhance the significance of the solar energy system^5,6.

Energy harvesting, also known as energy scavenging, refers to the process of capturing energy from a system’s environment and subsequently converting it into electrical power for use in actual processes^7–9. One of the most effective energy harvesting processes is solar harvesting, which is the conversion of the sunlight into heat or electricity^10,11. This renewable energy process effectively prevents the release of greenhouse gases, serving as the foundation for green energy systems^12,13. The electromagnetic harvesters, which convert electromagnetic transducers into radiofrequency signals or mechanical vibrations, are the most effective harvesters under the solar harvesting system^14–16. Applications for these types of harvesters include wearable devices, wireless sensor networks, and mechanical vibrations^17,18. Moreover, the energy harvesting process is also important for sustainability because it reduces the dependence on fossil fuels and minimizes large amounts of carbon emissions^19,20. B. B. Han and co-authors created a broadband solar absorber with a Ti resonator and TiC substrate that can give a radiation percentage of more than 97% with an associated bandwidth of 600 nm²¹. The multilayer absorber in Cr-GaAs-Ag combination can create a perfect absorption of 97.1% in a 1000 nm band rate with the invention of W. Li et al., and co-authors²².With the composition of the Ti and Si materials in the graphene type absorber, it was able to catch 97% absorption for 800 nm bandwidth by the investigation of Z. Liu et al., and co-authors²³. The new investigation of the diamond-shaped absorber by Y. Tang and co-authors can release 93.53% for the overall amount from UV to MIR parts²⁴. A plus-shaped solar design with the applied materials of Cr-InSb-Cr can give 93.1% for all regions of the study by A. H. M. Almawgani and co-authors²⁵.

For the TPV (thermo-photovoltaic) cell, S. Agarwal and co-authors invented a quad-helix material absorber structure with an effective rate of 92.38% between the 340 and 1680 nm wavelength range²⁶. S. Agarwal and co-authors invented a U-shaped gold resonator with the Si substrate with the variation bandwidth from 100 to 550 nm to give the high absorptance not only in the absorber but also in the sensor²⁷. With a gold and Cr structure (2-D materials) on a nanotype absorber, you can observe 100% absorptance with the varied bandwidth amount (nm) from 200 to 1000 by S. Agarwal and co-authors²⁸. P. Gao et al., and co-authors generated a solar absorber with a GaAs substrate part that can raise the resulting output for 95% at a 700 nm efficient bandwidth²⁹. A bloom-shaped absorber with the used materials of the InSb middle layer can create the solar radiation of 94.2% at the visible zone by the creation of F. Momeni and co-authors³⁰. With MSM-PD plasmonic-based design, we can study the creation of a plasmonic lens from the concentration of light energy between the subwavelength widths of 500 and 100 nm flanked with nanometal gratings by F. F. Masouleh and co-authors³¹. As a new creation of energy harvesting, it can be found that the simulation of helioscope performance can show the generated power of 96,993 kWh for a year by M. Nur-E-Alam et al., and co-authors³². With a structure of metal-semiconductor-metal in a photodetector, can enhance to rise 25 times optical absorption in grating results by C. L. Tan and co-authors³³.

When we create multiblocks for resonator design, we generate a new structure using aluminium (Al) for the resonator part and aluminium antimonide (AlSb) as the substrate layer, with chromium (Cr) material serving as the foundation layer. Aluminium has a silver-white color and low-density, ductile, and malleable properties³⁴. Aluminum and arsenide combine to form AlSb, a widely used semiconductor in electronic devices like rectifiers, thermistors, and transistors^35,36. The current project uses chromium as a foundation layer because of its high resistance to tarnishing and its usefulness in preventing corrosion from its outermost layer³⁷. Not only can visible areas absorb the newly investigated graphene design, but also near-infrared energy and ultraviolet zones in the current project. Additionally, we can use the light trapping process, photovoltaic devices, and energy harvesting in other applications.

Methodology

Adding the methodology can describe the specific parts of the proposed work, such as (i) procedure of the developed design, (ii) designing the structure using parametric numbers, (iii) structure and optimization, and (iv) equations for graphene and AM situations.

Procedure of the developed design

Before the presentation of the recent study, the first section we want to introduce is the procedure of the design to share knowledge about how to construct the absorber structure from the primary step to the final step of producing the perfect absorption. The developed design is configured by using many square shapes, and the procedure of the structure can be extinguished with a flowchart presentation as configured in Fig. 1. With the presentation of the steps in flow chat, we can check some instructions for the constructed design. As the first step in developing a solar structure, we need to select the proper materials for every layer and then build the new resonator design. Then, we can change the used parameter numbers to reach the best performance of the structure, and the incidence angle variation will be inserted to observe the design’s polarization effect.

Fig. 1.

The configuration of the developed structure’s procedure in a flow chat presentation.

Structural design with the use of parametric numbers

The developed structure is constructed with the muti squares in appropriate positions to form the ideal resonator design, and the absorber design is presented in different views with the x-y plane, x-z plane, and the three-dimensional plane as presented in Fig. 2. For the resonator view in the x-y plane, Fig. 2 (a) is distributed, and the used squares in height and width are also presented. The height of the first square h₁ is 220 nm, and the height of the other square presented in h₂ is 130 nm. The width of the squares used in the resonator design has the same number of w = 30 nm. The front view x-z plane in Fig. 2b with the configured heights of the layer and the used design width. The aluminum resonator height represents M = 600 nm, the AlSb substrate is A = 400 nm, and the Cr-based layer is R = 300 nm, respectively. The used structure width is D = 500 nm for the whole structure. The three-dimensional distribution (x, z, and y) plane in Fig. 2c shows the used materials in different color representations.

Fig. 2.

Design contribution for the recent graphene absorber design in the used parameters and different planes. (a) The used square blocks height and width in the resonator design in the x-y plane. (b) The heights of the absorber layers and the width of the whole graphene structure. (c) The three-dimensional x-z-y plane of the structure and the used materials in color representation.

Structure and optimization

To develop the current study efficiently, the COMSOL (Multiphysics) compilation has been used for the design construction section, and then, the method of Finite Element (FEM) applied to extract the resulting absorption outputs in exact numbers (percentages)^38–40. The exploration of the planar light source of the current structure, it is contributed type of periodic boundary condition according to the x and y axis. The contribution of the design to structural optimization and the varied absorption rates for each developed layer, from the Cr-based layer to the complete design (graphene inclusion), will be included in this section. Figure 3a configures the observation of the best performance (absorption rate) from the primary step (Cr-based) to the complete (graphene addition). The first ground layer with the applied Cr material is developed at 300 nm, and then the AlSb substrate part is overlapped at a height of 400 nm. Then, the Al resonator is deposited on the AlSb substrate, and the final step is complete with the inclusion of a thin layer of graphene. To mention the generated colour lines on the resulted figures, ‘A’ refers to the amount of absorptance, ‘R’ for the reflectance, and ‘T’ used for the transmittance rate. Figure 3b shows the resulting absorption situation for the first configuration of the Cr-based, with an output rate of 73.65% in the ultraviolet (100–400 nm) region, 85.71% in the violet (380–450 nm) spectrum, and 86.81% in the NIR (750–2500 nm) area. The overall average rate for the three mentioned areas is 84.36%. Figure 3c shows the resulting absorption situation for the second configuration of the AlSb substrate, with an output rate of 73.97% in the ultraviolet (100–400 nm) region, 79.86% in the violet (380–450 nm) spectrum, and 87.84% in the NIR (750–2500 nm) area. The overall average rate for the three mentioned areas is 87.04%. Figure 3d shows the resulting absorption situation for the third configuration of the Al resonator, with an output rate of 90.1% in the ultraviolet (100–400 nm) region, 93.87% in the violet (380–450 nm) spectrum, and 96.57% in the NIR (750–2500 nm) area. The overall average rate for the three mentioned areas is 92.59%. Figure 3e shows the resulting absorption situation for the final configuration of the perfect design in graphene inclusion, with an output rate of 90.32% in the ultraviolet (100–400 nm) region, 94.69% in the violet (380–450 nm) spectrum, and 97.1% in the NIR (750–2500 nm) area. The overall average rate for the three areas mentioned is 93.68%.

Fig. 3.

The design development and resulting absorption for each layer construction (A = Absorptance, R = Reflectance, T = Transmittance). (a) Design development procedure in structural optimization (b) The resulting absorption situation for the first configuration of the Cr-based. (c) The resulting absorption situation for the second configuration of the AlSb substrate. (d) The resulting absorption situation for the third configuration of the Al resonator. (e) The resulting absorption situation for the final configuration of the perfect design in graphene inclusion.

Equations for graphene and AM situations

To present the current study effectively, we also presented the equation section used in the performance of the graphene and the AM distribution. Before the presentation of the resulting percentage of the applied layer, we selected the four highest rates of the absorptions representing the different wavelength (λ) numbers of 0.95, 1.5, 1.9, and 2.3. With a thin graphene performance in the current design, the resulting outputs are 90.32% in the ultraviolet (100–400 nm) region, 94.69% in the violet (380–450 nm) spectrum, and 97.1% in the NIR (750–2500 nm) area, and the overall average rate for the three areas mentioned is 93.68%. With the validation of Fig. 4a, the observed output is greater than 98% for 1500 nm due to the wavelength deviation from 1 to 2.5 μm, and the average overall performance is 93.68% for 2800 nm. To observe the absorption rates properly, the following equations with respect to graphene are used⁴¹:

1

2

3

4

Fig. 4.

The observed absorption varied depending on the bandwidth and air mass conditions (A = Absorptance, R = Reflectance, T = Transmittance). (a) The resulting amounts at different wavelengths and selected wavelength numbers. (b) The resulting conditions of the absorbed and missed energy are presented with the AM distribution.

The applied symbols in the above equations are defined as: ‘∆’ for the used thin graphene, the temperature of the whole structure is the permittivity observed in air refers to ‘T_g’, the frequency number in the study is ‘ꞷ’, the used two constant numbers of the Plank and Boltzmann are ‘h’ and ‘K_B’, the resulting potential value is ‘u_c’, and ‘e’ for the amount of a charged electron⁴².

Air Mass (AM) = 1.5 means the standard amount of air mass, and we can also compute the recent explored situations in AM. We express the current resulting amount in AM conditions using Fig. 4b, which includes both the observed and missed energy sections. We use the following equations to calculate the numerical values for observed absorption rates in the AM distribution:⁴²

5

With the used symbols in the above-mentioned AM equation, the used symbol ‘µ_C’ for absorbed radiated energy, ‘I_AM1.5’ for the amount of standard AM configuration, and the reflected situation of the absorber is ‘R’⁴³.

Results and discussions

To compare the effects of the used parameters and the others, we can analyze the changing of the varied numbers for each used parametric number in each layer. By studying the parametric changing section of the paper, we can decide to choose the best performance of the structure with the appropriate parametric numbers. Figure 5a represents the changing parametric numbers in the resonator section with the aluminium height ‘M’ changing from 200 to 600 nm with the developing absorption rates in the UV zone, V region, NIR field, overall, and the maximum rate over the variation effects in a graph configuration. With the variation of the parametric numbers in the Al resonator part, the changed numbers from 81.98% at 200 nm to 85.73% at 600 nm at the wavelength amount (µm) of λ1 = 0.95, changed percentages from 86.1 to 92.83% for λ2 = 1.5, λ3 = 1.9 explores the rates from 82.49 to 97.67%, and λ4 = 2.3 distributes outputs from 80.62 to 99.67%. The effects of the changed parameters in Al resonator with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate are distributed in the graph exhibition of Fig. 5b. Figure 5c extinguishes the changing parametric numbers in the substrate section with the AlSb height ‘A’ changing from 100 to 500 nm with the developing absorption rates in the UV zone, V region, NIR field, overall, and the maximum rate over the variation effects in a graph configuration. With the variation of the parametric numbers in the AlSb substrate part, the changed numbers from 87.49% at 100 nm to 98.8% at 500 nm at the wavelength amount (µm) of λ1 = 0.95, changed percentages from 78.35 to 76.94% for λ2 = 1.5, λ3 = 1.9 explores the rates from 91.69 to 84.43%, and λ4 = 2.3 distributes outputs from 99.6 to 92.53%. The effects of the changed parameters in AlSb substrate part with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate are distributed in the graph exhibition of Fig. 5d.

Fig. 5.

Exploration absorption situations for the resonator and substrate parts with the parametric amount variations. (a) Resonator section with the aluminium height ‘M’ changing from 200 to 600 nm. (b) Al resonator with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate. (c) Substrate section with the AlSb height ‘A’ changing from 100 to 500 nm. (d) AlSb substrate with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate.

Figure 6a represents the changing parametric numbers in the based section with the chromium height ‘R’ changing from 300 to 700 nm with the developing absorption rates in the UV zone, V region, NIR field, overall, and the maximum rate over the variation effects in a graph configuration. With the variation of the parametric numbers in the Cr-based part, the changed numbers from 85.3% at 300 nm to 79.96% at 700 nm at the wavelength amount (µm) of λ1 = 0.95, changed percentages from 97.99 to 92% for λ2 = 1.5, λ3 = 1.9 explores the rates from 96.63 to 94.63%, and λ4 = 2.3 distributes outputs from 99.7 to 99.92%. The effects of the changed parameters in Cr-based with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate are distributed in the graph exhibition of Fig. 6b. Figure 6c extinguishes the changing parametric numbers in the width section ‘D’ changing from 100 to 500 nm with the developing absorption rates in the UV zone, V region, NIR field, overall, and the maximum rate over the variation effects in a graph configuration. With the variation of the parametric numbers in the structure width part, the changed numbers from 74.68% at 100 nm to 98.42% at 500 nm at the wavelength amount (µm) of λ1 = 0.95, changed percentages from 44.07 to 89.7% for λ2 = 1.5, λ3 = 1.9 explores the rates from 43.71 to 93.12%, and λ4 = 2.3 distributes outputs from 32.02 to 96.33%. The effects of the changed parameters in structure width part with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate are distributed in the graph exhibition of Fig. 6d.

Fig. 6.

Distributed absorption situations for the resonator and substrate parts with the parametric amount variations. (a) Based layer section with the chromium height ‘R’ changing from 300 to 700 nm. (b) Cr-based with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate. (c) Substrate width section ‘D’ changing from 100 to 500 nm. (d) Substrate width with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate.

With the graphene layer in the recent design, the effects of the graphene’s potential can be extracted with the changing numbers from 0.1 to 0.9 eV. Figure 7a represents the changing parametric numbers in the graphene section with the electron volt ‘eV’ changing from 0.1 to 0.9 with the developing absorption rates in the UV zone, V region, NIR field, overall, and the maximum rate over the variation effects in a graph configuration. With the variation of the electron volt numbers, the changed absorptions from 92.36% at 0.1 eV to 99.96% at 0.9 eV at the wavelength amount (µm) of λ1 = 0.95, changed percentages from 95.27 to 99.88% for λ2 = 1.5, λ3 = 1.9 explores the rates from 91.9 to 99.7%, and λ4 = 2.3 distributes outputs from 93.59 to 99.08%. The effects of the changed electron volts with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate are distributed in the graph exhibition of Fig. 7b.

Fig. 7.

Investigation absorption for the resonator and substrate parts with the parametric amount variations. (a) Electron volt values ‘eV’ changing from 0.1 to 0.9. (b) Electron volt values ‘eV’ with the contribution amount in the UV zone, V region, NIR field, overall, and the maximum rate.

With the different directions of the reflected rays from the sun to the resonator (top layer) of the absorber, we also need to study the varied absorption efficiency depending on the different angles to make the current structure a developed broadband absorber type. The current study can determine the situations of the polarization effect depending on the changing incident angles (from 0 to 80 degrees). The polarization determination will be classified into two different types of contribution of transverse in electric and magnetic techniques as included in Fig. 8. With the output numbers from the resulting TE and TM computation in the changing incident angles, the results are identical and the polarization effect can be performed in the current work. The changed absorptions from 99.81% at 0-degree to 48.37% at 80-degree at the wavelength amount (µm) of λ1 = 0.95, changed percentages from 99.77 to 41.7% for λ2 = 1.5, λ3 = 1.9 explores the rates from 99.58 to 40.49%, and λ4 = 2.3 distributes outputs from 98.55 to 44.55%. The outputs in color beneficiation of the angle variation effects can be figured out in Fig. 8a and b.

Fig. 8.

Situations of the polarization effect depend on the changing incident angles (from 0 to 80 degrees). (a) Contribution of Transverse in electric technique. (b) Contribution of Transverse in electric technique in color figuration. (c) Contribution of Transverse in magnetic technique. (d) Contribution of Transverse in magnetic technique in color figuration.

With the generation of the investigated electric and magnetic field conditions of the current absorber, we can improve output observation of the absorption contribution. According to the explored color range (from min to max), we can conclude the situations of the absorbed heat energy by the current structure in different parts of the constructed layers. The electrically deposited amount |E| can be determined in two planes of x-y and three-dimensional views with the selected wavelengths of 0.95, 1.5, 1.9, and 2.3 μm. Figure 9a and b show the various parts of the electric field for 0.95 μm in x-y and 3-D planes. Figure 9c and d shows the various parts of electric field for 1.5 μm in x-y and 3-D planes. Figure 9e and f show the various parts of the electric field for 1.9 μm in x-y and 3-D planes. Figure 9g and h show the various parts of the electric field for 2.3 μm in x-y and 3-D planes. Depending on the color rates in different layers of the structure, we can find that most of the absorbed heat energy is the resonator part, the second most absorbed layer is the substrate, and the ground layer is the minimum part of the absorbed heat energy.

Fig. 9.

The explored absorbed heat amount in electric field contribution in different parts of the absorber structure. The electrically deposited amount |E| in two planes of x-y and three-dimensional views for different wavelengths of (a) and (b) λ1 = 0.95 μm. (c) and (d) λ2 = 1.5 μm. (e) and (f) λ3 = 1.9 μm. (g) and (h) λ4 = 1.5 μm.

The magnetically deposited amount |H| can be determined in two planes of x-y and three-dimensional views with the selected wavelengths of 0.95, 1.5, 1.9, and 2.3 μm. Figure 10a and b show the various parts of the electric field for 0.95 μm in x-y and 3-D planes. Figure 10c and d shows the various parts of electric field for 1.5 μm in x-y and 3-D planes. Figure 10e and f show the various parts of the electric field for 1.9 μm in x-y and 3-D planes. Figure 10g and h show the various parts of the electric field for 2.3 μm in x-y and 3-D planes. Depending on the color rates in different layers of the structure, we can find that most of the absorbed heat energy is the resonator part, the second most absorbed layer is the substrate, and the ground layer is the minimum part of the absorbed heat energy.

Fig. 10.

The explored heat energy in electric field contribution in different parts of the absorber structure. The electrically deposited amount |E| in two planes of x-y and three-dimensional views for different wavelengths of (a) and (b) λ1 = 0.95 μm. (c) and (d) λ2 = 1.5 μm. (e) and (f) λ3 = 1.9 μm. (g) and (h) λ4 = 1.5 μm.

Machine Learning applied in the parametric variation section

The proposed work (multi-block design) absorber can also show the results of the changing parameters by Machine Learning for the resonator height, substrate layer, ground and structure width sections.

The first parametric number is ‘M’ for changing ML and the resulting R-square numbers (R²) explore 0.87507, 0.913002, 0.85877, 0.78963, and 0.74279 with 0.25 test size while the value of the mean square value distributes 1.43706 × 10^− 3. The results are given in Fig. 11.

Fig. 11.

The exploration of the Regressors with the respective actual values at 0.25 test value for (a) M₁ = 200 nm, (b) M₂ = 300 nm, (c) M₃ = 400 nm, (d) M₄ = 500 nm, (e) M₅ = 600 nm.

The second parametric number is ‘A’ for changing ML and the resulting R-square numbers (R²) explore 0.57873, 0.78674, 0.80634, 0.673407, and 0.650239 with 0.25 test size while the value of the mean square value distributes 1.244303 × 10^− 3. The results are given in Fig. 12.

Fig. 12.

The exploration of the Regressors with the respective actual values at 0.25 test value for (a) A₁ = 100 nm, (b) A₂ = 200 nm, (c) A₃ = 300 nm, (d) A₄ = 400 nm, (e) A₅ = 500 nm.

The third parametric number is ‘R’ for changing ML and the resulting R-square numbers (R²) explore 0.869154, 0.86824, 0.952213, 0.904038, and 0.92366 with 0.25 test size while the value of the mean square value distributes 0.22732 × 10^− 3. Results are given in Fig. 13.

Fig. 13.

The exploration of the Regressors with the respective actual values at 0.25 test value for (a) R₁ = 300 nm, (b) R₂ = 400 nm, (c) R₃ = 500 nm, (d) R₄ = 600 nm, (e) R₅ = 700 nm.

The fourth parametric number is ‘D’ for changing ML and the resulting R-square numbers (R²) explore 0.78796, 0.78654, 0.825465, 0.635309, and 0.904038 with 0.25 test size while the value of the mean square value distributes 1.22941 × 10^− 3. Results are given in Fig. 14.

Fig. 14.

The exploration of the Regressors with the respective actual values at 0.25 test value for (a) D₁ = 100 nm, (b) D₂ = 200 nm, (c) D₃ = 300 nm, (d) D₄ = 400 nm, (e) D₅ = 500 nm.

The other effective way to compare the current rates and formerly published results is to insert a table as a new section of the work as presented in Table 1.

Table 1.

Comparison table with the average amounts in different classifications.

References	Wavelength range (µm)	Absorption amount (%)	Bandwidth contribution (nm)	Angle of Incident (degree)	Generated polarization
Ref44	0.40–2.13	95.35	1730	60	Yes
Ref45	1.43–2.13	97.2	700	60	Yes
Ref46	0.20–2.28	95.82	2080	80	Yes
Ref47	1.00–2.00	97.1	1000	70	Yes
Ref48	0.20–3.00	93.2	2800	80	Yes
Ref49	0.20–2.00	95.3	1800	70	Yes
Ref50	1.53–0.30	96.6	1470	60	-
Ref51	0.20–3.00	94.13	2800	70	Yes
Ref52	0.20–0.70	97	500	80	Yes
The proposed design’s output	0.20–3.00 μm	94.13%	2800 nm	80	Yes

Conclusions

The combination of the multi-square blocks to form the new solar absorber design with the applied material of aluminium (Al) for resonator design and a graphene part is inserted between the Al resonator and the aluminium antimonide (AlSb) substrate in the development of the chromium (Cr) ground layer. With a high generated absorption efficiency of more than 98% (1500 nm bandwidth), the investigated absorber can help to develop the important role of graphene. With the investigation of the current study, the study of the construction stages, the analysis of the absorbed outputs by parametric variation, and the absorbed heat energy by electric and magnetic conditions can be studied.

Author contributions

Meshari Alsharari, Bo Bo Han: Conceptualization, Literature Review, Software development, Article draftingShobhit K. Patel, Khaled Aliqab: Methodology, Software development, Result analysis, Supervision Ammar Armghan, Om Prakash Kumar: Result analysis, Article proofreading, Supervision.

Funding

Open access funding is provided by Manipal Academy of Higher Education, Manipal. This work was funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No. (DGSSR-2024-02-01161).

Data availability

The data used to support the findings of this study are included in the article.

Declarations

Competing interests

The authors declare no competing interests.