Design of a highly efficient graphene-coated ultra-wideband solar thermal absorber for renewable mining energy applications using artificial intelligence optimization

Abstract

Although many technologies have advanced in electricity production, their carbon footprint remains a crucial factor in selecting the most sustainable option. Solar energy provides a promising solution, as it is a clean and renewable resource harnessed directly from the sun. Multi-layer type thermal absorbers are considered the most effective structures, and their efficiency can be further enhanced with the incorporation of advanced materials such as graphene and MXene. In the current study, the solar absorber is fabricated using Cr-Fe₃O₄-InSb materials, with a thin graphene film added to enhance overall thermal performance. The design features two square structures with a cylindrical resonator inserted at the center. The proposed structure achieves an impressive thermal absorption rate of 93.28% through a broad wavelength range of up to 2800 nm. Specifically, the structure can be configured to achieve a thermal absorption rate of 90.9%, 93.32%, and 94.72% for UV-Vis-NIR regions while maintaining these rates across the respective ranges: 90.9% in the ultraviolet, 93.32% in the visible, and 94.72% in the NIR, with the polarization-insensitive property applicable for incidence angles from 0 to 80 degrees. To extract precise performance values based on regression analysis for varying layer heights, machine learning techniques for a 0.25 test size and the R² value reach above 0.98. As a thermal energy innovation, the proposed absorber can be utilized in various thermal processes, including water heaters, cookers, solar ponds, fuel production, coffee roasters, swimming pool heating, and more.

Introduction

The growing global command for electricity, driven by newly investigated techniques, is leading to the depletion of natural resources [1]. Additionally, this increased demand contributes to CO₂ emissions, causing water and air pollution as well as climate change [2]. On a large scale, solar thermal energy can be developed for a large range of processes, from small residential to large industrial applications [3]. As a direct heating application, solar thermal systems are more efficient than photovoltaic processes, with temperatures typically operating at 200 °F or lower [4].

When we study the operation of the solar power system, the technique that we need to think about is photovoltaic technology [5]. This is the direct conversion technique of electricity from sunlight by using solar panels that are made with semiconductor cells [6]. Among all the photovoltaic processes, the most effective and popular way is the solar thermal system, and the CSP system (concentrated solar power) is also included [7]. With a CSP contribution, mirrors are used for receiving and reflecting the sunlight from a large area to a tiny patch that is proposed to capture the volume of the energy [8]. On the other hand, the role of solar collectors is to absorb heat and transfer it to various media such as oil, air, or molten salt [9]. These heated mediums are then circulated back to the designated area for heat utilization [10]. In larger institutions, the heat from the fluid can generate steam, and that drives the generator to produce the necessary output of electricity [11]. With a tungsten substrate, the broadband optical material structure can create 90% absorption between 0.3 and 2.0 μm wavelength range [12]. With a Ti-TiC-Si material absorber structure type, the solar thermal can achieve 95% for the 1200 nm band rate [13]. A new investigation of a Ti cross-shaped structure has shown 97% efficiency from 386 to 1178 nm [14]. For the thermal conversion procedure, the absorption efficiency is 95% with a large separation from 300 nm to 1777 nm for SiO₂ dielectric part inclusion [15]. The used materials of W and SiO₂ in the developing ultra-broadband absorber design can give a 98.9% between 260 and 1580 nm wide band rate [16].

With a new procedure of Cr- Fe₃O₄-InSb in the current investigation, a wide-band solar thermal absorber is developed at a perfect rate. The iron material in making solar resonator designs is also used widely because of its good absorption efficiency and heat conductivity [17]. The more magnetite in the particles, the higher the absorption rate [18]. Indium antimonide is used as a base material, and it is a crystalline type of indium (In) and antimony (Sb) [19]. InSb is also a narrow-gap type of semiconductor material and is mostly used in thermal imaging, infrared detectors, infrared astronomy, and infrared missile guidance processes [20]. The current design, based on a wide-band investigation of a multilayer structure with a wavelength range of 2800 nm, offers the following novel features:

• Achieved a thermal absorption rate of over 95% at 1400 nm.

• Structure optimized using Machine Learning.

• Absorption results are shown according to standard Air Mass 1.5.

• Configurable for various atmospheric regions, including UV, VIS, and NIR.

• Suitable for a wide range of thermal energy processing applications.

Design and Parameters

In constructing the absorber using COMSOL software, this section is crucial for extracting the optimal absorptance rate through the FEM technique [21]. The performance depends on factors such as the resonator design, applied parametric values, material types, and the use of a planar light source [22]. Two boundary conditions are used on the x–y–z axis for the Delaunay tessellation technique, and the lowest mesh size is 50.4 nm for the polarization-insensitive property for a 0–80 degree incidence angle. Refractive index amounts of the Cr by 3.21, Fe₃O₄ (2.3435), and InSb (1.617) have been used in the performed structure. The current resonator design is built up with a cylinder with a radius of r = 60 nm and surrounded with a rectangle. The outer rectangle has a length of S₁ = 300 nm with an S₂ = 250 nm width, and the inner rectangle has a 30 nm shorter length than the outer rectangle of P₁ = 270 nm length and P₂ = 220 nm width. The 3-D side (x-z-y) is presented in Fig. 1 (a), and the resonator shape (x-y) can be viewed from the top side in Fig. 1 (b). The front position (x-y) is included in Fig. 1 (c) to show the assigned parametric sections in the resonator of V = 900 nm, the Fe₃O₄ substrate with a length of I = 800 nm, and the InSb foundation layer height of B = 300 nm. The whole absorber structure is developed with a width of E = 500 nm.

Fig. 1.

The structure development in resonator design, using parametric numbers and material types. a The showcase of the 3-D part of the whole structure. b The outer and inner rectangles of the resonator design. c The three different parts in several parametric numbers and width contributions

With a design development category in the current work, the whole structural optimization is also added from the ground block to the complete performance as exposed in Fig. 2 (a). As a primary contribution of the current structure, the InSb-based part contributes with the varied percentages of 72.78% in the ultraviolet space, 81.94% spans in the visible area, and 87.72% attains in the NIR indication. The overall verification is 86.5% with a primary InSb-based layer development as indicated in Fig. 2 (b). Figure 2 (c) denotes the second layer configuration of Fe₃O₄-substrate with the varied percentages of 84.03% in the ultraviolet space, 92.4% spans in the visible area, and 90.3% attains in the NIR indication. The overall verification is 91.45% with a second Fe₃O₄-substrate section development. Figure 2 (d) indicates the resonator configuration (exclusion of graphene) with varied percentages of 90.68% in the ultraviolet space, 93.12% spans in the visible area, and 94.59% attains in the NIR indication. The overall verification is 92.24% with the resonator section development. Figure 2 (e) indicates the final design configuration (inclusion of graphene) with the varied percentages of 90.9% in the ultraviolet region, 93.32% spans in the visible area, and 94.72% attained in the NIR region. The overall verification is 93.28% with the complete current structure demonstration.

Fig. 2.

Structural optimization exploration in varied absorption ranges. a The whole structural optimization from the ground block to the complete performance. b The InSb-based part contribution. c The second layer consists of an Fe₃O₄ substrate. d The resonator is configured (excluding graphene). e The final design configuration (inclusion of graphene)

The layers deposited in the lithography design illustration in Fig. 3 with the used height and generated layers. The first step is an InSb layer with a 300 nm thickness in section (a), and the second step of the deposited section is an Fe₃O₄ substrate with an 800 nm thickness in section (b). The thin deposited graphene layer (0.34 nm) on the Fe₃O₄ substrate and the deposited top (resonator) section are in Figs. 3 (c) and (d), respectively. Figure 3 (e) is the whole structure’s front view with the deposited layers.

Fig. 3.

The deposited layers in lithography design illustration. a The first InSb-based layer with a 300 nm performance. b The second deposited Fe₃O₄-substrate section with an 800 nm height. c The thin deposited graphene layer (0.34 nm) on the Fe₃O₄-substrate section. d The deposited top section. e The whole structure front view with the deposited layers

A detailed study on the resonator changes is also added in the current work to present the increased rates as part of making a perfect resonator design. In Fig. 4, the performance of the rectangles and the comparison of the graphene exclusion and inclusion are presented. The red absorption color line for the two rectangles developed with varied percentages of 90.1% in the ultraviolet region, 93.2% spans in the visible area, and 92.6% in the NIR region. The overall verification is 91.58% with the rectangular resonator stage performance. With the exhibited absorption color lines, we verify the graphene effects according to the graphene inclusion and exclusion.

Fig. 4.

The performance of the resonator (rectangles and cylinder) and the comparison of the graphene exclusion and inclusion exhibition

In the developed work, the five denoted wavelengths (µm) of 0.26, 0.37, 0.5, 0.74, and 1.43 are expressed to show the different sharp points of the outputs. Figure 5 (a) contributes with detailed inclusion of bandwidth amount in 1400 nm for 96.78%, and the overall range is 93.28% by a 2800 nm wideband rate. With the perfect amounts in noted wavelengths (µm), 99.13% in 0.26, 99.42% for 0.37, 99.74% explores in 0.5, 99.93% exhibits in 0.74, and 99.77% in 1.43. As an equation section, some graphene equations are indicated as follows [23].

1

2

3

4

Fig. 5.

A detailed inclusion of bandwidth and wavelength amounts in showing output absorption. a The denoted five wavelengths (µm) of 0.26, 0.37, 0.5, 0.74, and 1.43 for exploring perfect outputs. b The output verification with the standard 1.5 AM

For equation numbers 1 to 4, the represented symbols are also needed to express their long forms. In this case, ‘Δ’ is used for the thin graphene inclusion, ‘Tg’ is the mentioned temperature, ‘ε_o’ is verified as air permittivity, ‘ω’ is frequency, ‘μ_c’ is the affected chemical potential [24].

The second part (Fig. 5 (b)) is expressed for the standard 1.5 air mass configuration with the area in the missed, performed, and AM parts, and the respective equation is also expressed.

5

With the explored AM equation, ‘η_A’ is overall absorption, AM (1.5) configuration in ‘I_AM1.5’, the current loss energy is denoted as ‘R’, and ‘λ_max’ and ‘λ_min’ are maximum and minimum rates for wavelength description [25].

Results and Discussions

As a parametric study section on the current work, the height and width of the structure can be identified according to their changes in the used parametric numbers. The variations in the Cr-resonator and Fe₃O₄-substrate are illustrated in Fig. 6 using color-based visual representations. As declared in the output section, the outputs are changed based on the height of the layer variation in Fig. 6 (a). When thickness is increased, the corresponding output values show significant variations: at 0.26 μm, the absorption increases from 93.34% to 95.85%; at 0.37 μm, it rises from 98.32% to 98.9%; at 0.5 μm, a slight decrease is observed from 99.56% to 98.1%; at 0.74 μm, the absorption improves from 98.36% to 98.48%; and at 1.43 μm, it increases from 96.33% to 96.88%. Figure 6 (b) is extracted to show the color validation of the Cr-resonator changes. As shown in section (c), increasing the Fe₃O₄ substrate thickness from 400 nm to 800 nm results in notable output changes: at 0.26 μm, the absorption improves from 81.2% to 99.14%; at 0.37 μm, it increases from 99.22% to 99.42%; at 0.5 μm, a slight decrease is observed from 99.41% to 98.73%; at 0.74 μm, the absorption rises from 98.3% to 99.93%; and at 1.43 μm, it increases from 97.83% to 99.77%. Figure 6 (d) is extracted to show the color validation on the Fe₃O₄-substrate changes.

Fig. 6.

Response for Parametric variation: a Resonator height variation from 500 nm to 900 nm; b Corresponding color plot illustrating resonator height changes from 500 nm to 900 nm; c Fe₃O₄ substrate thickness variation from 400 nm to 800 nm; d Corresponding color plot illustrating Fe₃O₄ substrate thickness changes from 400 nm to 800 nm

The InSb-based width changes are included in Fig. 7 with color exhibition figures. As illustrated in Fig. 7(a), varying the iron resonator height from 100 nm to 500 nm leads to noticeable output fluctuations: at 0.26 μm, the absorption decreases from 98.72% to 89.25%; at 0.37 μm, it reduces from 98.69% to 98.28%; at 0.5 μm, a slight decrease is observed from 99.96% to 99.15%; at 0.74 μm, the absorption drops from 99.98% to 98.63%; and at 1.43 μm, it decreases significantly from 98.56% to 90.2%. Figure 7 (b) is extracted to show the color validation on the InSb-based changes. As shown in section (c), increasing the width from 300 nm to 500 nm results in significant output variations: at 0.26 μm, the absorption improves from 76.95% to 99.14%; at 0.37 μm, it increases slightly from 99.37% to 99.42%; at 0.5 μm, the absorption rises from 99.26% to 99.73%; at 0.74 μm, it improves from 99.58% to 99.93%; and at 1.43 μm, the absorption increases from 97.54% to 99.77%. Figure 7 (d) is extracted to show the color validation on the width number changes.

Fig. 7.

Based on layer and width parametric numbers analysis. a The based height changes from 300 to 500 nm. b The verified color plot with the based height changes from 300 to 500 nm. c The width number changes from 300 to 500 nm. d The verified color plot with the width number changes from 300 to 500 nm

The variation in the radius of the cylinder inserted in the center of the resonator structure is also important in the performance of the absorption section. As demonstrated in Fig. 8(a), varying the radius of the central cylinder from 60 nm to 80 nm results in the following output changes: at 0.26 μm, the absorption slightly decreases from 99.14% to 99%; at 0.37 μm, it increases from 98.13% to 98.51%; at 0.5 μm, a significant improvement is observed from 95.77% to 99.84%; at 0.74 μm, the absorption rises from 95.04% to 99.9%; and at 1.43 μm, it increases from 93.98% to 99.9%. Figure 8 (b) is extracted to show the color validation on the radius changes. As illustrated in Fig. 8(c), varying the chemical potential values of 0.1–0.9 eV leads to notable changes in the output results: at 0.26 μm, the absorption decreases slightly from 99.5% to 99.12%; at 0.37 μm, it increases from 98.13% to 99.51%; at 0.5 μm, the absorption improves significantly from 95.77% to 99.84%; at 0.74 μm, it rises from 95.04% to 99.9%; and at 1.43 μm, the absorption increases from 93.98% to 99.81%. Figure 8 (d) is extracted to show the color validation of the potential number changes.

Fig. 8.

Cylinder radius and potential numbers analysis. a Radius changes from 60 to 80 nm. b Color plot. c The graphene potential changes. d The verified color plot for the potential change

The polarization-insensitive effect on the developed absorber structure can be analyzed with varied degrees depending on the configured modes of TE and TM displayed in Fig. 9 [26]. According to the identical results in TE and TM contribution outputs, there is polarization insensitivity, and percentages can be defined specifically [27]. When the TE and TM degree changes (0–80), the outputs are dropped from 99.14% (0-degree) to 10.12% (80-degree) at 0.26 μm, dropped from 99.42% to 62.82% at 0.37 μm, changed from 99.74% to 56.34% at 0.5 μm, observed from 99.93% to 54.45% at 0.74 μm, and extracted from 99.77% to 58.46% at 1.43 μm. Figures 9 (b) and (d) are extracted to show the color validation of the degree changes.

Fig. 9.

Polarization effect analysis of the developed structure. a The output displayed for TE degree variation (0–80). b The output displayed for TE variation color plot. c The output displayed for TM degree variation (0–80). d The output displayed with TM degree variation (0–80) with the color representative figure

This section also presents the resulting output as influenced by the electric and magnetic conditions. The deposited electric field is displayed with the varied wavelength numbers in Fig. 10. According to the representative color range, the resonator design is able to achieve higher efficiency (in the top and 3-D design). Figures 10 (a) and (f) are illustrated for the wavelength 0.26 μm, 0.37 μm for Figs. 10 (b) and (g), Figs. 10 (c) and (h) determine the wavelength 0.5 μm, 0.74 μm in Figs. 10 (d) and (i), and Figs. 10 (e) and (j) for 1.43 μm wavelength number respectively.

Fig. 10.

Two positions of the electric field condition on the varied wavelengths (µm). The top (x-y) conditions for the varied wavelengths (µm) of (a) 0.26, (b) 0.37, (c) 0.5, (d) 0.74, and (e) 1.43. The 3-D structure (x-z-y) conditions in the varied wavelengths (µm) of (f) 0.26, (g) 0.37, (h) 0.5, (i) 0.74, and (j) 1.43

The deposited magnetic display with the varied wavelength numbers is verified in Fig. 11. According to the representative color range, the resonator design is able to observe more efficiency (in the top and 3-D design). Figures 11 (a) and (f) are illustrated for the wavelength 0.26 μm, 0.37 μm for Figs. 11 (b) and (g), Figs. 11 (c) and (h) determine the wavelength 0.5 μm, 0.74 μm in Figs. 11 (d) and (i), and Figs. 11 (e) and (j) for 1.43 μm wavelength number respectively.

Fig. 11.

Two positions of the magnetic field condition on the varied wavelengths (µm). The top (x-y) conditions for the varied wavelengths (µm) of (a) 0.26, (b) 0.37, (c) 0.5, (d) 0.74, and (e) 1.43. The 3-D structure (x-z-y) conditions in the varied wavelengths (µm) of (f) 0.26, (g) 0.37, (h) 0.5, (i) 0.74, and (j) 1.43

The reported outputs applied by ML (machine learning) are displayed in this section based on the contributed parametric amounts in each layer [28]. To conduct a more in-depth analysis of the results, the current work employs the linear regression method, with output results based on the comparison between predicted and actual values, as illustrated in Figs. 12, 13, 14, 15 and 16 below [29]. As a preliminary tool in the solar absorber investigation, the ML model can be applied for the absorption efficiency with relation to the used structural parameters [30]. Although the use of linear regression can generate a simple framework, it is limited in its predictive capability for complex nonlinear interactions between material parameters and geometry [31]. Thus, the model can reduce the accuracy in the parametric section, and it is not appropriate for consideration in comprehensive optimization [32]. In future solar absorber design, machine learning optimization can be investigated with other methods, such as Random Forest, and the developed absorber adds the Random Forest result for the resonator analysis in Fig. 13.

Fig. 12.

Machine learning (ML) outputs for resonator height variations with regression analysis and corresponding actual output values (test ratio = 0.25): a V₁ = 500 nm, (b) V₂ = 600 nm, (c) V₃ = 700 nm, (d) V₄ = 800 nm, and (e) V₅ = 900 nm

Fig. 13.

Machine learning (ML) outputs for resonator height variations with Random Forest analysis and corresponding actual output values (test ratio = 0.25): a V₁ = 500 nm, (b) V₂ = 600 nm, (c) V₃ = 700 nm, (d) V₄ = 800 nm, and (e) V₅ = 900 nm

Fig. 14.

Machine learning (ML) outputs for substrate height variations with regression analysis and corresponding actual output values (test ratio = 0.25): a I₁ = 400 nm, (b) I₂ = 500 nm, (c) I₃ = 600 nm, (d) I₄ = 700 nm, and (e) I₅ = 800 nm

Fig. 15.

Machine learning (ML) outputs for base section height variations with regression analysis and corresponding actual output values (test ratio = 0.25): a B₁ = 100 nm, (b) B₂ = 200 nm, (c) B₃ = 300 nm, (d) B₄ = 400 nm, and (e) B₅ = 500 nm

Fig. 16.

Machine learning (ML) outputs for width variations with regression analysis and corresponding actual output values (test ratio = 0.25): a E₁ = 300 nm, (b) E₂ = 350 nm, (c) E₃ = 400 nm, (d) E₄ = 450 nm, and (e) E₅ = 500 nm

Figure 12 displays the ML output on the resonator height with the deposited R² in 0.90849482, 0.919179298, 0.8957310127, 0.9389731036, and 0.8174745946 for 0.470283847 × 10^− 3 MSE value and the split is 1:4 out of 1405 data points (test amount = 0.25).

Figure 14 displays the ML configuration on the substrate part with the deposited R² in 0.9641012458, 0.962902548, 0.905647292, 0.9635024123, and 0.8624675365 for 0.1026896019 × 10^− 3 MSE value and the split is 1:4 out of 1405 data points (test amount = 0.25).

Figure 15 displays the ML result on the substrate part with the deposited R² in 0.95491268226, 0.98165878423, 0.851771362, 0.91980765413, and 0.49943161316 for 0.5662832246 × 10^− 3 MSE value and the split is 1:4 out of 1405 data points (test amount = 0.25).

Figure 16 displays the ML result on the width with the deposited R² in 0.99491268226, 0.980508799612, 0.963093689, 0.93123253225, and 0.8335776889 for 0.5662832243 × 10^− 3 MSE value and the split is 1:4 out of 1405 data points (test amount = 0.25).

Table 1 shows the comparison of the different absorption rates.

Table 1.

Construct a table for the absorption rates comparison

References	Wavelength ranges (µm)	Outputs (absorption%)	Polarization conditions
Ref [33]	0.29–1.79	Above 90	Yes
Ref [34]	0.20–1.60	91	Yes
Ref [35]	1.53–0.30	93.6	-
Ref [36]	0.20–1.10	92.2	Yes
Ref [37]	0.20–3.00	94.52	-
Ref [38]	0.10–1.70	95.2	Yes
Ref [39]	0.20–3.00	94.13	Yes
Ref [40]	0.30–2.50	92.4	Yes
Proposed work’s results	2.60–1.20 μm	95.65%	Yes

Conclusion

The new investigation of a Cr-Fe₃O₄- An InSb metasurface broadband solar absorber with effective graphene for several air regions, including a thermal absorption rate of 90.9%, 93.32%, and 94.72% for UV-Vis-NIR regions. The design consists of two square structures with a cylindrical resonator placed at the center, providing an efficient resonator configuration. The developed structure achieves an impressive absorption rate of 93.28% across a broad bandwidth of 2800 nm. The multi-section design adopted in this work has been identified as an ideal structure for wide-band absorption. With the polarization-insensitive property applicable for incidence angles from 0 to 80 degrees and the machine learning optimized by the linear regression and the random forest method comparison with a 0.25 test size for an above 0.98 R² value. Solar thermal power generated from this absorber is suitable for a broad range of applications, from residential settings to large-scale industrial installations. As a thermal energy innovation, the absorber can be effectively used in processes such as water heating, cooking systems, solar ponds, fuel production, coffee roasting, swimming pool heating, and more. Additionally, machine learning techniques are used to both predict the absorption behavior and optimize the absorber’s design, resulting in maximized absorption efficiency.

Author contributions

Methodology, Y.S., and B.B.H.; software, S.K.P., B.B.H., R.G. and Y.S.; investigation, M.M.A., M.A.,and N.H.A.I.,; Formal Analysis, All authors; writing—original draft preparation, All authors; writing—review and editing, All authors.; All authors have read and agreed to the published version of the manuscript.

Funding

The authors extend their appreciation to Northern Border University, Saudi Arabia, for supporting this work through project number (NBU-CRP-2026-2461). The authors extend their appreciation tothe Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP.2/357/47.

Data availability

The data supporting the findings in this work are available from the corresponding author with reasonable request.

Declarations

Ethical Approval

Not Applicable.

Consent to Publish

Not Applicable.

Consent to Participate

Not Applicable.

Competing interests

The authors declare no competing interests.