TiN-Only Metasurface Absorber for Solar Energy Harvesting

Abstract

With global energy demand surging and traditional energy resources diminishing, the solar absorber featuring optimized design shows substantial potential in areas like power generation. This study proposes a solar absorber that is insensitive to wide-angle incidence and polarization. It has a cylindrical structure with square holes, which is constructed from titanium nitride (TiN). The calculation results indicate that, for plane waves, the average absorption of this solar absorber across the wavelength range of 300–2500 nm reaches 92.4%. Moreover, its absorption rate of the solar spectrum corresponding to AM1.5 reaches 94.8%. The analysis of the characteristics within the electric and magnetic field profiles indicates that the superior absorption properties arise from a cooperative resonance effect. This effect originates from the interaction among surface plasmon resonance, guided-mode resonance, and cavity resonance. In this study, the geometric parameters of the solar absorber’s structure significantly influence its absorption performance. Therefore, we optimized these parameters to obtain the optimal values. Even at a large incident angle, this absorber maintains high absorption performance and shows insensitivity to the polarization angle. The findings expected from this study are likely to be of considerable practical importance within the realm of solar photothermal conversion.

1. Introduction

New energy is an important direction of current energy development. It is sustainable and capable of offering stable energy support for the long-term progress of human society. As a prime example of new energy, solar energy is not only clean and pollution-free but also inexhaustible, which makes its position in the global energy structure increasingly prominent [1,2,3]. Solar absorbers are of importance in the exploitation of solar photothermal energy. They effectively take in solar radiation and transform it into heat. During the procedure of photothermal conversion, the surface plasmon resonance of metal materials plays an important role. By optimizing the surface structure of metal materials, different resonances are coupled, thus greatly improving absorption efficiency. Currently, solar absorbers, e.g., metallic nanoparticle-based absorbers, graphene absorbers, and metamaterial absorbers, possess substantial application prospects such as desalination of seawater, irrigation in agriculture, energy resupply in aerospace [4,5,6,7]. These advanced configurations leverage nanoscale light-matter interactions to optimize solar energy harvesting efficiency [8,9,10]. Solar absorbers possess substantial application prospects in areas like desalination of seawater, irrigation in agriculture, as well as energy resupply in aerospace. It is also evidenced that modifications in the polarization angle scarcely influence the absorption performance. The findings expected from this study are likely to be of considerable practical importance within the realm of solar photothermal conversion, effectively covering the visible and infrared light bands, and showing certain polarization-independent characteristics in the full-absorption band [11]. Elsharabasy et al. [12] engineered a broadband metamaterial perfect absorber featuring a Au-TiO₂-Au. This structure consists of concentric arrangements made up of crossed ellipses and quadruple split-ring resonators [12]. Zhang and colleagues [13] developed a broadband solar metamaterial absorber (BSMA). It spans from 280 to 2500 nm, featuring a structure composed of patterned Si₃N₄-TiN, SiO₂, and Ti. The average absorption achieves 97.77%. Many studies show that solar absorbers based on different materials and structural designs all exhibit significant light-absorption performance. Although these metamaterial solar absorbers perform well in absorption performance, and some even achieve high or even perfect absorption, their complex preparation processes and high costs limit their application in large-scale scenarios. Therefore, finding simple materials that can achieve efficient solar energy absorption has become a major challenge. Titanium nitride (TiN), as a newly synthesized artificial metal material, not only has excellent optical properties, enabling it to efficiently absorb solar energy, but also has good thermal conductivity, allowing it to quickly transfer heat energy and achieve effective energy transportation [14,15,16]. Its melting point attains a value as high as 2950 °C. Additionally, its structure and properties exhibit stability at elevated temperatures. Owing to its cost-effective production, this method has been extensively utilized in the development of solar absorbers [17,18,19,20,21].

Columnar structures are widely used in solar absorbers. Yu et al. designed a broadband solar absorber composed of a TiO₂-TiN nano-elliptical cylinder array, which achieved an average absorption of 95.68% in the wavelength range of 360–1624 nm [22]. Chen et al. proposed a solar absorber with a cylindrical array, which achieved a total solar absorption of 94% in the wavelength range of 300–2500 nm, providing a reliable thermal management solution for concentrated solar power systems [23]. We also focused on solar absorbers with square hole structures. Gao et al. [24] designed a TiN square-ring superstructure absorber. The thickness of the TiN square ring is 25 nm. It achieves an average absorption of 95.69% in the wavelength range of 280–2500 nm, supporting wide-angle incidence, and is insensitive to polarization. Song et al. [25] developed a four-layer metamaterial absorber of Ti/Si₃N₄/Ti-SiO₂, covering the wavelength range of 200–4200 nm with an average absorption of 98.16%. It had the characteristics of wide-angle insensitivity and high manufacturing tolerance. Pan et al. proposed an ultra-broadband absorber based on the TiN rectangular column-ring structure, which had an average absorption of 97.02% in the wavelength range of 300–4962 nm and was suitable for photovoltaic and infrared imaging applications [26]. All the above designs with square holes have good absorption performance. We referred to the above models and considered the manufacturing feasibility [27,28,29], so we controlled the difference between the radius of the circumscribed circle of the square hole and the radius of the cylinder to be approximately 30 nm. Therefore, we attempted to combine the advantages of the two and add square holes to the columnar structure to see if its performance can be improved. In addition, although TiN is widely used, most of the above structures are about the combinations of multiple materials, and there are relatively few studies using a kind of material just. Constructing the surface structure of an absorber with one kind of material can not only exhibit excellent performance but also avoid problems such as instability caused by the superposition of materials. Therefore, it is necessary to conduct further research on TiN-based solar absorbers.

In the present study, the finite-element method was employed to perform simulations and proposed a solar absorber that uses only titanium nitride (TiN). By discussing the absorption effect of 300–2500 nm plane waves and the absorptivity of the actual solar spectrum, we analyzed its absorption performance of solar radiation. By comparing the electric and magnetic field profiles, changes in local electric field intensity were identified, and the mechanism by which the solar absorber achieves efficient absorption was clarified. Meanwhile, the effect of geometric parameters on the absorber’s absorption characteristics was taken into account. Furthermore, the influence of the incident angle and polarization on the spectral absorption patterns was also analyzed. As a result, a thorough evaluation of the solar energy absorption capability of the absorber was conducted.

2. Models and Methods

Considering the significant characteristics of titanium nitride (TiN), including its high hardness, excellent chemical stability, and elevated melting point, TiN was chosen as the material in this study. In terms of micro-nano structures, through extensive literature comparison and analysis, we found that square-columnar and cylindrical solar absorbers each exhibit unique advantages. The square-columnar structure provides higher light-absorption efficiency due to its larger surface area, while the cylindrical structure is favored for its lower manufacturing complexity. Based on these findings, we proposed an innovative design that combines the advantages of these two structures, aiming to achieve better photothermal conversion performance [30]. We conducted a detailed analysis of the impact exerted by diverse structural parameters on the light-absorption efficacy [31]. Regarding the proposed structure, the finite-element approach was employed to optimize the parameters [32,33,34] with the aim of improving the absorption performance and exploring the maximum possible absorptivity within the required wavelength range. All geometric parameters were optimized based on COMSOL software (COMSOL 6.2).The configuration of the proposed solar absorber is illustrated in Figure 1. After optimization, the parameters are as follows: the height of the cylinder (h₁) is equivalent to the height of the square column(h₂), h₁ = h₂ = 2000 nm, the diameter (D) of the cylinder is 200 nm, the period (P) amounts to 300 nm, and the width (L) of the square-shaped column is 130 nm.

Material parameters are of great importance in research. The refractive index and the extinction coefficient together form the complex refractive index of the material. The complex refractive index exerts a direct impact on the way light interacts with the material. Consequently, it dictates the energy conversion efficiency of the solar absorber. In this context, the real part (n), which denotes the refractive index of the light-absorbing medium, is closely related to the velocity at which light waves propagate through the absorbing material [35]. It influences the propagation path and the refraction of light within the medium. The imaginary part (k) is governed by the degree of light wave attenuation during its propagation through the absorbing medium, which is directly related to the material’s ability to absorb light. As presented in Figure 2, the data from reference [36] were employed in our simulation process.

In this paper, the finite element method (FEM) is utilized to numerically simulate and analyze the proposed solar absorber [37,38,39]. This method is widely applied to the calculation of solar absorbers. The unit-cell model of the proposed solar absorption structure is depicted in Figure 3a. Above and below it, there are, respectively, an air layer and a perfect matching layer. To save simulation time, we took one unit cell and performed a parameter-sweep calculation in the 300–2500 nm spectrum range. A normally incident plane wave was adopted as the light source. Due to the fact that the structure is a periodic array, during the specific calculation process, a solitary unit cell featuring Floquet periodic boundary conditions was employed [40,41]. To simulate an infinite surface, periodic boundary conditions were applied to the walls in the x–z and y–z planes, as depicted in Figure 3b. The periodic ports illustrated in Figure 3c are denoted by arrows. The light is incident from the top through the specified periodic port, and a second port is added at the bottom. The upper horizontal port functions as the inlet for the incident light and simultaneously serves to model the reflected light. In the meantime, the lower horizontal port acts as the outlet port and is employed to simulate the transmitted light. In the simulation calculation, the setting of the grid deserves special attention. To a large extent, the grid determines whether the establishment and calculation of this model are reasonable. Since the cylindrical structure model is relatively complex, a relatively detailed meshing was carried out in this area. Looser meshes were adopted in the air and the perfectly matched layer. This approach not only ensures the accuracy of the calculation but also guarantees a reduction in computational costs [42,43]. Figure 3d outlines the grid used in the simulation of this study.

In the research of solar absorbers, theoretical calculations guide the final results. When light strikes the surface of TiN (which has a complex refractive index $n_2=n+ik$) from air (where the refractive index $n_1$ is approximately 1), Maxwell’s equations, in combination with the relevant boundary conditions, govern the values of the amplitude coefficients for reflection and transmission. For vertically incident light, the reflection coefficient r is determined by the complex refractive index [44,45]:

$$r={\displaystyle \frac{n_2-n_1}{n_2+n_1}}.$$

(1)

The reflectivity is $R\left(\lambda \right)$:

$$R\left(\lambda \right)={\displaystyle \frac{{\left(n-1\right)}^2+k^2}{{\left(n+1\right)}^2+k^2}}.$$

(2)

Provided that the TiN substrate has sufficient thickness, the transmittance is close to zero, that is, when T(λ) = 0, the light is completely reflected or absorbed. Therefore, the absorptivity A(λ) [46] is

$$A\left(\lambda \right)=1-A\left(\lambda \right)-T\left(\lambda \right).$$

(3)

Here, λ represents the wavelength of the incident light beam. To assess the practical solar absorption capability of the solar absorber, we examined its practical absorption characteristics by taking into account the AM1.5 solar irradiance spectrum [24]:

$$I_{abs}=A\left(\lambda \right)\cdot I_{AM1.5}\left(\lambda \right)$$

(4)

$$I_{loss}\left(\lambda \right)=I_{AM1.5}\left(\lambda \right)-I_{abs}\left(\lambda \right).$$

(5)

Here, $I_{AM1.5}\left(\lambda \right)$ corresponds to the solar spectrum distribution under AM1.5 conditions, $I_{abs}$ denotes the absorption spectrum, and $I_{loss}\left(\lambda \right)$ stands for the solar spectrum that is lost. According to the computations in Equations (4) and (5), The ratio of the total solar energy absorbed to the energy within the solar radiation spectrum provides the amount of energy that is actually absorbed [25]:

$$\alpha ={\displaystyle \frac{{\int }_{{\lambda }_2}^{{\lambda }_1}{I}_{abs}d\lambda }{{\int }_{{\lambda }_2}^{{\lambda }_1}{I}_{AM1.5}d\lambda }}.$$

(6)

Since solar energy is mainly concentrated in the wavelength band of 300–2500 nm, ${\lambda }_1$ = 300 nm and ${\lambda }_2$= 2500 nm.

3. Results and Discussions

Figure 4a shows that the average absorptivity of this solar absorber within the wavelength range of 300–2500 nm is 92.4%. Under the same conditions, the average spectrum absorptions of the planar unstructured titanium nitride (TiN), columnar TiN, and the absorber proposed by us within the same wavelength range are 30.1%, 91.2%, and 92.4%, respectively. In comparison, the absorber proposed by us has an average spectrum absorption more than three times that of the planar unstructured TiN. Since the materials used for them are the same, this is entirely attributed to the structural optimization. After the structural design, a remarkable enhancement occurs. This is attributable to the fact that the periodic array of TiN structures gives rise to a matched impedance, which mitigates solar reflection and substantially boosts solar absorption. Moreover, there exist four characteristic absorption maxima in the vicinity of ${\lambda }_1$ = 400 nm, ${\lambda }_2$= 1100 nm, ${\lambda }_3$= 1450 nm, and ${\lambda }_4$ = 2100 nm. The absorbance values at these wavelengths are 99.2%, 92.4%, 94.8%, and 99.1%, respectively. Additionally, by incorporating the AM1.5 solar radiation spectrum, we examined the actual absorption rate of solar energy by the solar absorber. As illustrated in Figure 4b, solar energy is predominantly distributed within the visible light spectrum, and our absorber demonstrates optimal absorption performance precisely within this wavelength band. At the 2500 nm wavelength band, the absorption of solar energy is nearly negligible. Although the absorption of our absorber declines beyond 2500 nm, this does not impact the overall actual absorption of solar energy. The spectrum absorptivity of the solar absorber reaches 94.8%. It is evident that the energy loss is minimal, with the ratio of energy loss to energy absorption being merely 0.052. This substantiates the superiority of our designed structure and offers compelling evidence for its promising potential in solar energy harvesting.

In

Table 1. Comparison of our designed absorption device with previous designs.

Reference	Absorption Band	Absorption	Structure
[47]	400–1500 nm	99.6%	TiN nanocone array/Al2O3/TiN
[48]	300–900 nm	93%	cross-based TiN/AlN/TiN
[22]	360–1624 nm	95.68%	TiO2-TiN nano-elliptical disk arrays
[23]	300–2500 nm	88%	TiN cylinder array/SiO2/TiN
proposed	300–2500 nm	92.4%	TiN

, we compare the absorption characteristics of TiN-based devices in prior works [22,23,47,48] with those of the proposed structure in the manuscript. The proposed design in this paper achieves a broad absorption band spanning 300–2500 nm. Reference [23] also reported the same range, while our structure exhibits a higher average absorption of 92.4%. Notably, our structure eliminates complex multilayer configurations (e.g., nanocone arrays in reference [47], cross-based layers in reference [48], or nano-elliptical disks in reference [22]) and employs a simplified single-material TiN architecture. This structural simplicity enhances the fabrication feasibility and provides potential application for broadband absorption.

The distribution of the electric field and the magnetic field inside the solar absorber are shown in Figure 5 and Figure 6. The absorber’s broadband absorption performance stems from three resonance mechanisms, each supported by distinct electric and magnetic field behaviors [49,50]. Surface plasmon resonance (SPR) is confirmed by the electric field intensity near the cylindrical periphery (Figure 5a–d), which increases with wavelength, driven by free electron oscillations on the TiN surface at shorter wavelengths [51,52]. When the frequency of the incident light matches the collective oscillation frequency of the free electrons on the metallic surface, a strong interaction will occur. This enables the light energy to be effectively coupled into the absorber and converted into the kinetic energy of electrons. Subsequently, the energy is dissipated in the form of heat energy through the processes, thus achieving a high absorption. While the corresponding magnetic field in Figure 6a–d shows localized hotspots near the same edge, spatially overlapping with electric field maxima. This coupling between SPR-induced electric dipoles and magnetic dipoles enhances energy retention at metallic-dielectric interfaces. Guided mode resonance (GMR) manifests in the electric field’s standing-wave pattern beyond 1100 nm (Figure 5e–h), where light undergoes multiple reflections and interferences, extending its propagation path [53,54]. Correspondingly, the magnetic field in Figure 6e–h exhibits periodic oscillations along the absorber, aligning with GMR’s phase-matched interference. Cavity Resonance (CR) plays a critical role in enhancing the absorber’s energy localization, as evidenced by both electric and magnetic field behaviors [48]. Figure 5a–d exhibits stronger field intensity compared to its surface. This contrasts with the weakening field in the cavity’s periphery, a hallmark of CR induced energy confinement. This phenomenon arises when the incident wavelength is smaller than the cavity’s cutoff wavelength, trapping light within the cavity and amplifying the field through resonant oscillations. Figure 6g,h reflects the influence of cavity resonance (CR) on energy redistribution. At wavelengths below the cavity’s cutoff condition, the magnetic field shifts toward the cavity interior due to confined modal profiles, further corroborating CR’s role in vertical energy trapping. The absorber’s symmetric geometry minimizes radiative losses, directing energy toward thermal dissipation. SPR enhances surface coupling, GMR prolongs light-matter interaction, and CR localizes energy. Together, SPR, GMR, and CR optimize broadband absorption through correlated electromagnetic field interactions.

Moreover, the geometric parameters of the structure of the solar absorber exert a remarkable influence on its absorption capabilities. Therefore, each parameter in this structure was optimized individually to ensure that the final determined structural parameters are optimal. Figure 7a shows that altering the height of the absorber’s cylinder significantly impacts the absorption ratio. As the cylinder height increases, the absorption ratio also increases, reaching its peak value when the height reaches 2000 nm. The change in height is capable of significantly altering the light scattering pattern and propagation path. It has an impact on the activation of surface plasmon polaritons and leads to a substantial variation in the region of interaction with the incident light [55,56]. Consequently, it significantly impacts the absorption performance. Furthermore, considering the cylinder’s diameter, as illustrated in Figure 7b, the absorption performance reaches its peak when the cylinder’s diameter is 200 nm. An appropriate diameter can better excite SPR and GMR phenomena, thereby enhancing absorption [57]. Figure 7c illustrates the impact of the period (P) for the absorber regarding its absorption characteristics. When the period reaches 300 nm, there is a remarkable enhancement in the absorption performance. However, as the period increases, the improvement in absorption performance becomes slow, and there is even no obvious increase. This implies that an augmentation in the period can boost absorption. However, if the period is excessively large, it has a negligible effect on the absorption result. Finally, Figure 7d illustrates the effect of the square column’s width on the absorption characteristics. Clearly, as the width of the square column increases, the absorber’s performance in absorption improves. Overall, alterations in the geometric parameters of the absorber play a crucial role in determining its performance. The optimized structural parameters provide guidance for the precision of the preparation process, aiming to maximize the efficiency of the solar absorber [58].

To investigate the relationship between structural dimensions and resonance modes, cylindrical column height (h₁) and square column width (L) were selected as observation parameters. Figure 8a and Figure 8b, respectively, depict the distribution of the electric field diagrams corresponding to the absorption peak at 1840 nm along the red line when different parameters are changed. As can be seen from the figures, at the titanium nitride metal-dielectric interface at the edge of the square hole, the incident light excites the collective oscillation of free electrons, leading to the enhancement of the local electric field and significantly improving the light absorption [59]. As h₁ increases, the effective optical thickness of the waveguide layer increases and the supported guided mode resonance wavelength experiences a red shift. At the same time, it can be observed that the square hole, as a resonant cavity, concentrates the energy within the cavity, causing cavity resonance. In Figure 8b, it can be seen that as L decreases, the local ability of the surface plasmon resonance weakens and the cavity resonance gradually becomes less obvious, resulting in a slight decrease in absorption [60]. In summary, the two parameters jointly optimize the synergistic effect of the guided mode resonance, cavity resonance, and surface plasmon resonance, enabling the absorption rate at 1840 nm to reach its peak.

Through extensive comparisons with the existing literature [24,25,26] and meticulous consideration of practical fabrication feasibility [27,28], we optimized structural parameters under mutual constraints. Our design carefully addresses critical manufacturing limitations including aspect ratio and vertical inclination. As demonstrated in references [61,62], which exhibit high absorption performance with identical vertical inclination to our proposed design, and their reported aspect ratios exceed 11. In contrast, our model adopts a more manufacturable aspect ratio of 10, well within the achievable range of standard fabrication processes. Furthermore, we incorporated the inevitable rounding of corners during machining into our simulations. While maintaining a cylinder radius of 100 nm, we ensured a minimum gap of approximately 30 nm between the circumcircle radius of square apertures and cylindrical outer boundaries, resulting in a corresponding square pillar width of 100 nm. Figure 9a presents comparative simulations with and without rounded corners to mimic actual fabrication processes. Analysis confirms negligible variation in absorption efficiency between these configurations, demonstrating our proposed solar absorber’s exceptional tolerance to typical manufacturing imperfections. This robust performance under practical fabrication conditions substantiates the design’s high technical feasibility for scalable production.

To further validate structural superiority, we conducted a comparative analysis of our square-aperture design with alternative geometric configurations as illustrated in Figure 9b, including pentagram and hexagram patterns. Although these star-shaped structures theoretically offer enhanced surface areas under comparable fabrication precision, experimental results reveal only negligible absorption enhancement relative to our original design. Such marginal performance gains fail to justify the substantially increased fabrication complexity arising from the multi-angle vertices inherent to these intricate geometries [63,64]. Consequently, the square aperture configuration was selected as the optimal architecture, achieving an optimal balance between optical performance and superior manufacturability [65].

As a broadband incoherent light source, the incident angle, polarization state, and spectrum distribution of sunlight directly affect the performance of the absorber [66]. In practical applications, sunlight does not directly irradiate the solar absorber vertically but at different angles [67,68]. Therefore, in the design of the absorber, it is crucial to consider the effect of the incident-light angle on absorption performance [69,70]. The spectral absorption characteristics of both transverse magnetic (TM) waves and transverse electric (TE) waves were analyzed under various incident angle conditions [71,72,73]. As presented in Figure 10a, the spectrum absorption behavior for TM waves under various incident angles is depicted. It is evident that when the incidence angle reaches 30°, the absorber’s average absorption ratio achieves 92.3%. Even when the angle of incidence is relatively large, at 60°, the absorption ratio remains at 77.1%. This maintenance of performance implies that the absorber continues to exhibit a high-level absorption ability at varying angles, signifying the stability of the absorber’s performance across different angles. In a similar vein, the alterations in the spectrum absorption characteristics of TE waves at diverse angles were also explored, and the findings are presented in Figure 10b. At an incidence angle of 60°, the average absorption for TE waves is 89.8%. Specifically, the absorber can effectively capture and absorb both TE and TM waves, which gives the absorber high angular sensitivity. Even as the incident angle of the light changes, the alteration in absorption performance remains negligible [74]. Figure 10c further illustrates the effect of the polarization angle on the spectrum absorption characteristics of the solar absorber. Owing to the isotropic properties and high degree of symmetry in the designed solar absorber structure, it demonstrates a high level of resistance to alterations in the polarization angle. This indicates that regardless of changes in the polarization angle of the incident light, the variations in the absorption characteristics of the absorber are barely noticeable [75,76]. This further bolsters its adaptability within practical scenarios, particularly in intricate lighting conditions, allowing it to uphold high efficiency.

4. Conclusions

In summary, a wide-angle, polarization-independent metamaterial solar absorber, made entirely of TiN, was proposed. Utilizing the finite-element method, the overall solar absorption within the wavelength range of 300–2500 nm was determined to be 92.4% and the absorption under the AM1.5 solar irradiance spectrum reached 94.8%. Analysis of the electric and magnetic field distributions showed that the synergistic effect of SPR, GMR, and CR enhances the light absorption efficiency of the absorber. Additionally, the effects of the geometric parameters of the solar absorber on its absorption characteristics were also investigated. Even at a relatively large incident angle of 60 degrees, the solar absorber still maintains excellent performance and achieves an absorption of 89.8%. This paper plays an exploratory role in the application of TiN materials in solar absorbers and in the optimization of solar absorbers.