High-Efficiency Broadband Selective Photothermal Absorbers Based on Multilayer Chromium Films

Abstract

Photothermal conversion is a pivotal energy transformation mechanism in solar energy systems. Achieving high-efficiency and broadband photothermal conversion within the solar radiation spectrum holds strategic significance in driving the innovative development of renewable energy technologies. In this study, a transmission matrix method was employed to design an interference-type solar selective absorber based on multilayer Cr-SiO₂ planar films, successfully achieving an average absorption of 94% throughout the entire solar spectral range. Further analysis indicates that this newly designed absorber shows excellent absorption performance even at a relatively large incident angle (up to 60°). Additionally, the newly designed absorber demonstrates lower polarization sensitivity, enabling efficient operation under complicated incident conditions. With its simple fabrication process and ease of preparation, the proposed absorber holds substantial potential for applications in photothermal conversion fields such as solar thermal collectors.

1. Introduction

The global energy shortage poses a severe challenge to human society, making the development and utilization of renewable energy a core issue for sustainable development. Among renewable energy sources, solar energy demonstrates tremendous potential due to its remarkable advantages, such as cleanliness, sustainability, and universal applicability, far surpassing traditional energy sources [1]. Additionally, solar energy offers further benefits, including low operating cost, minimal environmental impact, and widespread resource availability [2]. This not only reduces the dependence on fossil fuels but also effectively mitigates greenhouse gas emissions, providing crucial support in achieving sustainable development goals [3,4].

The utilization of solar energy primarily involves two pathways: photon-to-electricity conversion and photon-to-thermal conversion [5,6,7,8]. Among them, photon-to-thermal conversion technology stands out as a highly efficient and promising approach that converts solar energy into heat. It is widely applied in residential heating, seawater evaporation, desalination, and photothermal sensors [9,10,11]. In the process of solar energy utilization, solar thermal collectors play a crucial role in energy conversion. In particular, solar selective absorbers (SSAs) are extensively employed to enhance solar energy utilization efficiency and minimize energy loss through the precise design of the material composition and structural configuration of each layer. Developing high-performance, cost-effective SSAs with scalable production potential holds great significance for improving solar energy efficiency and accelerating the adoption of renewable energy technologies.

In previous research, high degrees of solar absorption have primarily been obtained through metal–dielectric multilayer films, graded-index films, or metamaterials [12,13,14,15,16,17,18]. While graded-index films and metamaterials can effectively absorb solar energy, their practical applications remain constrained owing to challenges such as complex fabrication processes or the need for additional post-processing. In contrast, metal–dielectric stacked multilayer structures offer a simpler fabrication process, lower cost, and easier scalability for mass production. Conventional metal–dielectric multilayer films typically adopt a three-layer configuration, utilizing the intrinsic absorption of the metal layer and the resonance cavity formed between the metal and dielectric layers to achieve the destructive optical interference of light, thereby enabling selective absorption of solar energy. To enhance the environmental corrosion resistance of thin-film devices, a protective layer is often coated on their surface [12].

From the perspective of electromagnetic field propagation, when electromagnetic waves reach the surface of a metal–dielectric multilayer planar film, electromagnetic and magnetic resonances, such as propagating surface plasmon (PSP) and localized surface plasmons (LSPs), are excited within the structure. This enhances the absorption of incident light. A common approach for broadband selective absorption is to design an absorber by overlapping multiple resonance absorption peaks at adjacent frequencies [19,20,21].

In previous studies by our research group, Li et al. designed four-layer metal–dielectric multilayer films that achieved an average absorption exceeding 95% in the 450–1000 nm range [22]. Then, by further increasing the number of layers to six, the high-absorption spectral range was extended to 250–1200 nm [23]. In an interference-based thin-film absorber, each layer can be composed of pure metals, semiconductors, dielectrics, or metal-based composite materials [24,25,26]. However, these studies still demonstrated certain limitations. For example, the absorption bandwidth was still confined to narrow ranges, failing to fully utilize the entire solar radiation energy. Additionally, absorbers incorporating precious metals incur high production costs, while multi-material absorbers often involve complicated fabrication processes. Therefore, designing a solar selective absorber capable of ultra-broadband absorption, simplified manufacturing, and low cost remains a significant challenge.

Based on prior research, this study proposes a new eight-layer metal–dielectric thin-film absorber. Simulation results showed that this absorber exhibited excellent broadband absorption efficiency, polarization robustness, and incident angular tolerance, showcasing broad application prospects. Although increasing the layer count can improve absorption efficiency by optimally tuning the optical interference effects in the multilayered structure, the resulting fabrication complexity and increasing process cost pose challenges that must be balanced in real-world applications. Through in-depth analysis of the performance of multilayer films, this work provides new research insights and solutions for efficient solar energy utilization.

2. Principle

As illustrated in Figure 1, the multilayer structure starts with a substrate, sequentially comprising a metal reflective layer, a transparent dielectric layer, an absorption layer, and a surface protection layer. When incident light irradiates multiple layers, its propagation and absorption processes are governed by the optical properties of each layer and interlayer interactions. The semi-transparent metal absorption layer directly absorbs a portion of the incident light energy, while the unabsorbed light undergoes multiple reflections between the reflection layer and the absorption one within the transparent one, where destructive interference occurs to dissipate the remaining energy. Additionally, the thickness of the surface protection layer is designed to correspond to a quarter-wavelength (λ/4) at the central wavelength to minimize surface reflection [27].

The performance of SSAs is characterized by their solar absorptance α and thermal emissivity ε [8,28]. The solar absorptance α can be expressed as

$$\alpha ={\displaystyle \frac{{\int }_{{\lambda }_0}^{{\lambda }_n}(1-R\left(\theta ,\lambda \right){)L}_{\mathrm{s}\mathrm{u}\mathrm{n}}d\lambda }{{\int }_{{\lambda }_0}^{{\lambda }_n}{L}_{\mathrm{s}\mathrm{u}\mathrm{n}}d\lambda }},$$

(1)

where R(θ, λ) represents the reflection spectrum of SSAs, L_sun denotes the standard AM1.5 solar radiation spectrum, and λ₀ and λ_n represent the lower and upper limits of the wavelength range, respectively. The average solar absorptance can be calculated by integrating R(θ, λ) across the solar spectral range.

As shown in Figure 2, the standard AM1.5 solar radiation spectrum (black) and 300 °C blackbody radiation spectrum (blue) are displayed. The solar radiation spectrum and the radiation spectrum of SSAs at the operating temperature are spectrally decoupled, indicating the feasibility of the SSAs’ design.

In the ideal scenario, as shown in Figure 2 (red), SSAs should exhibit a value close to the perfect absorptance (α ≈ 1) within the target absorption wavelength range while maintaining the minimum emissivity (ε ≈ 0) in the far-infrared thermal radiation region to maximize photothermal conversion efficiency and minimize thermal energy loss [29]. The red line shows the spectral absorption characteristics of an ideal absorber. However, a persistent discrepancy exists between theoretical predictions and practical performance. At 2500 nm, the absorption spectrum of the designed absorber fails to present the ideal step-like transition from unity absorption to near-zero. As shown in Equation (2) below, the average thermal emissivity of SSAs is expressed as

$$\epsilon ={\displaystyle \frac{{\int }_{{\lambda }_0}^{{\lambda }_n}E\left(T,\lambda \right)\left[1-R\left(\theta ,\lambda \right)\right]d\lambda }{{\int }_{{\lambda }_0}^{{\lambda }_n}E\left(T,\lambda \right)d\lambda }}.$$

(2)

The thermal emissivity ε can be calculated based on the reflection spectrum R(θ, λ) and Planck’s blackbody radiation E(T, λ) in Equation (3) below, which are functions of incident angle θ and temperature T, respectively.

$$E\left(T,\lambda \right)={\displaystyle \frac{8\pi hc}{{\lambda }^5}}{\left[exp\left({\displaystyle \frac{hc}{\lambda k_{\mathrm{B}}T}}\right)-1\right]}^{-1},$$

(3)

where h is the Planck constant, c is the speed of light in vacuum, and k_B denotes the Boltzmann constant, which connects temperature with energy at the molecular scale.

According to the photon energy conservation principle, the relationship between absorption A(λ), reflection R(λ), and transmission T(λ) should satisfy

$$T\left(\lambda \right)+R\left(\lambda \right)+A\left(\lambda \right)=1$$

(4)

When the thickness of the reflection layer exceeds the skin depth of the metal, the transmission T(λ) can be approximated to be 0. Consequently, Equation (4) simplifies to R(λ) + A(λ) = 1.

3. Structure and Simulation

3.1. Multilayer Structure and Numerical Simulation Results

Figure 3a illustrates a schematic diagram of an eight-layer metal–dielectric stacked thin-film structure, designed for solar selective broadband absorption. In this configuration, Cu serves as the high-reflection layer material, mainly utilizing its high reflectivity in the long-wavelength regime to effectively suppress the thermal radiation loss. The absorber employs alternating layers of SiO₂ (as a transparent layer) and Cr (as an absorption layer) deposited atop the Cu layer, achieving optimized solar absorption. The synergistic combination of these two materials yielded stacked films with relatively easy preparation and exceptional broadband optical absorption capability.

In this structure, the thickness of each layer is denoted as h_i (i = 1, 2, 3, 4, 5, 6, 7, and 8). The precise modulation of the thicknesses of individual layers enabled fine tailoring of the optical absorption performance, allowing the absorber to meet application-specific optical requirements. This design strategy provides significant implications for solar photothermal conversion devices, substantially enhancing the overall energy-harvesting performance.

The proposed multilayer films can be considered isotropic and homogeneous, allowing the optical properties to be analyzed through the fundamental principles of Maxwell’s equations [30]. To this end, the eight-layer Cr-SiO₂ stacked thin-film structures, deposited on Si and K9 glass substrates, were designed using the transfer matrix method, and the optical properties were systematically investigated. In the simulations, the optical constants for SiO₂, Cr, and Cu materials were sourced from the optical constants database provided by Palik [31], and the same dataset was consistently applied in subsequent finite-difference time-domain (FDTD) simulations [32].

To optimize the multilayer film design, the Global-Modified LM (Levenberg–Marquardt) algorithm embedded within the software was applied to optimize the parameters, ensuring the optimal performance of absorbers. The specific geometric parameters of each layer are summarized in

Table 1. Parameters of the designed multilayer films.

Parameter	Material	Symbol	Quantity
Anti-reflection layer	SiO2	h1	70.3 nm
Absorption layer	Cr	h2	2.3 nm
Transparent layer	SiO2	h3	91.4 nm
Absorption layer	Cr	h4	4.4 nm
Transparent layer	SiO2	h5	82.2 nm
Absorption layer	Cr	h6	7.2 nm
Transparent layer	SiO2	h7	179.5 nm
Reflection layer	Cu	h8	>100 nm

.

As shown in Figure 3b, the absorption spectrum of the absorber demonstrates an average absorption of up to 94% across the entire solar radiation spectrum (300–2500 nm) for unpolarized light at normal incidence. Detailed analysis reveals four distinct absorption peaks at 360, 470, 870, and 1710 nm, corresponding to 99.93%, 99.97%, 99.99%, and 98.13%, respectively. The absorption peaks primarily originate from multiple vertically oriented optical resonant cavities within the device, efficiently capturing and dissipating incident light across different wavelengths, thereby enabling strong multi-band absorption. The electromagnetic waves form high-intensity standing-wave distributions within the cavities, significantly enhancing the localization and coupling efficiency of optical energy, which in turn improves the overall absorption performance. Relying on a multi-cavity cooperative resonance mechanism, the absorber achieves broadband and high-efficiency light absorption across the visible-to-near-infrared spectrum. It exhibits excellent spectral selectivity and angular stability, providing a robust design strategy and practical feasibility for developing high-performance solar absorbers.

A critical performance metric for SSAs is maintaining a high absorption at various incident angles. Figure 4 displays the absorption spectra for unpolarized light at different incident angles. The data demonstrate that the absorption decreases less significantly with incident angles up to 60°, indicating that the absorber exhibits angular robustness for working under wide-incident-angle conditions.

To further investigate the spectral response characteristics, the absorption spectra at five wavelengths for unpolarized light at various incident angles were calculated, as shown in Figure 5. The absorption remains above 80% for wavelengths up to 2000 nm within the incident-angle range of 60°, with an average absorption exceeding 95%. These results confirm that the designed SSA can provide a high-solar-absorption spectrum even at high incident angles across a broad spectral range.

3.2. Effect of Polarization

Polarization insensitivity is a critical issue for practical applications, since this ensures high absorption efficiency for light illumination with a variety of polarization states. This characteristic is particularly vital when dealing with natural light (which is typically unpolarized) or light sources with randomly varying polarization directions. Figure 6 demonstrates the absorption spectra for unpolarized, p-polarized, and s-polarized light at different incident angles.

At normal incidence (Figure 6a), the absorber maintains an average absorption exceeding 94% for all three polarization modes, in agreement with the optical principle and prediction. When light is incident at non-zero angles, the absorption characteristics exhibit a certain polarization sensitivity. As the incident angle increases, the differences between the three polarization modes become more pronounced. In particular, at 60° incidence, the difference in absorption between p- and s-polarized light reaches 11%, while the unpolarized curve lies in the middle due to the effect of polarization-sensitive interference to enhance the intensity of the electric field concentrated in the multilayered stack in favor of the p-polarized light.

In this study, FDTD simulations were employed to analyze the polarization-dependent characteristics of the designed structure. The simulation domain comprised a single unit cell with a periodicity of 300 nm × 300 nm in the x- and y-directions. Periodic boundary conditions were applied along the x- and y-directions to simulate an infinite periodic array, while perfectly matched layers were implemented in the z-direction to absorb outgoing waves and eliminate the boundary reflections that could distort the computational results. In addition, both transverse-magnetic (TM)-polarized and transverse-electric (TE)-polarized plane waves were utilized as incident sources in the simulation to investigate the structural response to polarized light.

As depicted in Figure 7a, the absorption, reflection, and transmission spectra for the TM-/TE-polarized light at normal incidence on the multilayer structure are presented. As shown in the figure, the spectral responses for both polarization states are highly consistent across the entire operating wavelength range. This phenomenon can be attributed to the boundary conditions derived from Maxwell’s electromagnetic theory. In isotropic, linear, and non-magnetic material systems, under normal incidence, the tangential field components of TM and TE waves at interfaces share analogous continuity requirements—specifically, satisfying E_1t = E_2t and H_t1 = H_2t—which leads to converging propagation characteristics for both polarization states within the structure. Moreover, since the multilayer structure lies in manipulating optical path differences and optimized admittance matching, both of which remain polarization-insensitive under normal incidence conditions, similar electromagnetic responses are consequently achieved for both TM and TE modes.

The comparison with the absorption spectra simulated by Film Wizard under the same conditions as in Figure 7b shows that certain discrepancies exist between the two computational methods, while consistent average absorption is observed across the operational wavelength, demonstrating robust absorption performance. This result validates the high reliability of FDTD simulations in modeling the absorption of multilayer films and confirms the polarization-independent optical response of the designed structure to normally incident polarized waves.

To elucidate the physical mechanism underlying the high absorption of the proposed ultra-broadband solar selective multilayer films, FDTD simulations were performed to calculate the electric field distributions at different wavelengths for a TM-polarized wave at normal incidence, as shown in Figure 8a. The results reveal that, across the entire solar range, the electric field is predominantly confined to the interfacial regions between the topmost metal and dielectric layers. Figure 8b–d further illustrate the electric field distributions at 300, 1000, and 2000 nm, respectively. As observed in Figure 8b, within a short-wavelength range of 300–500 nm, the electric field is not only concentrated at the surface metal–dielectric interface but also exhibits significant enhancement within the structure inside. This phenomenon predominantly originates from the strong penetration capability of short-wavelength light, which can penetrate more deeply into the multilayer films and establish standing waves, thereby inducing localized electric field amplification. In the infrared spectral regime, however, the electric field is predominantly confined to the metal–dielectric surface, with negligible penetration into the interior of the structure.

The results discussed above show the absorption characteristics of the SSA for polarized light at normal incidence. However, in practical applications, both the polarization angle φ and incident angle θ critically influence absorption performance, requiring further study of their angular dependencies.

As shown in Figure 9a,b, FDTD simulations were conducted at normal incidence to analyze the polarization-dependent absorption performance by systematically varying the azimuthal angle φ of TM-polarized illumination. The corresponding absorption profiles, presented in Figure 9c, reveal that the SSA exhibits negligible variation in absorption across the solar spectrum as the polarization state rotates from TM (φ = 0°) to TE (φ = 90°), demonstrating a remarkable polarization insensitivity. This distinctive performance is attributed to the rotational symmetry of the designed absorber around the z-axis, which ensures polarization-independent absorption capability at normal incidence, enabling highly efficient light harvesting even for diverse polarization conditions.

Complementary to the polarization-independent behavior, the absorption spectra, according to the incident angle, of the SSA for TM-polarized light were also investigated. The simulation result is shown in Figure 9d. As the incident angle gradually increases from normal incidence to 60°, the high-absorption regime of the designed SSA exhibits a gradual reduction trend in spectral bandwidth. Notably, for θ ≤ 40°, the absorption is negligibly changed, demonstrating highly stable absorption characteristics with respect to the incident angle.

Within the solar spectral range of 300–2500 nm, the absorber retains an ultra-broadband absorption response exceeding 84%, even at high incident angles up to 60°. These results further confirm that the designed SSA exhibits exceptional robustness with respect to incident angle for polarized illumination. A comparison with the unpolarized incidence angle results in Figure 4 indicates that the multilayer structure not only exhibits lower sensitivity to the polarization of incident light but also accommodates the variation in incident angle.

3.3. Effect of Layer Count

An analysis of the spectral absorption performance of multilayer films under unpolarized illumination at normal incidence according to the layer count is shown in Figure 10. The results indicate that increasing the layer count progressively broadens the high-absorption spectral bandwidth and significantly enhances the overall absorption. Detailed data are tabulated in

Table 2. Performance of Cr/SiO₂ multilayer structures with varying layer counts in the 0.3–2.5 μm wavelength region.

Layer Count	4	6	8	10	12
Average absorption	69.77%	82.3%	94.26%	96.5%	97.07%

.

For the eight-layer structure, the absorber showed an average absorption surpassing 94%; on the other hand, by further extending the layer count to 10–12, the average absorption will increase up to 96–97%. This progression suggests that moderately increasing the layer count will enhance the optical absorption to trap the light, especially in the longer-wavelength region, thereby significantly improving light-harvesting efficiency. However, the gain in absorption performance tends to be saturated beyond eight layers, with diminishing marginal improvements. Moreover, a higher layer count results in other issues of increased fabrication complexity, higher costs, potential structural stability issues, and so on, which must be considered in applications. Therefore, the balance of the absorption efficiency with manufacturability will be a critical issue in the design of multilayer thin-film absorbers.

3.4. Admittance

To further uncover the high-efficiency absorption mechanism of the proposed SSA in the ultra-broadband spectral range, optical admittance analysis can be employed to probe its spectral response and energy dissipation pathways. In this experiment, a SiO₂ substrate established the initial optical state of the multilayer films at the coordinate (n_sub,0). According to the admittance formula, the admittance trajectory evolves in a spiral manner as light propagates through the stratified layers, generating characteristic circular or arc-shaped paths. The terminal admittance of each layer is jointly determined by the optical properties of the material (refractive index and extinction coefficient) as well as its geometric thickness. When the system admittance perfectly matches the air admittance (Y_air = 1), the admittance trajectory eventually terminates at the air point (1, 0), thus achieving minimal light reflection. For each operational wavelength, achieving precise admittance matching constitutes an essential prerequisite for attaining strong broadband absorption performance.

The admittance trajectory analysis at λ = 480 nm, as geometrically mapped in Figure 11, reveals a characteristic spiral propagation through successive material interfaces in the designed SSA. Colored curves explicitly track the admittance evolution dynamics across each stratified layer. The numerical results show the terminal admittance coordinates at (1.12, −0.07), with the corresponding reflectance of R ≈ 0.4%, which aligns with the computational results derived from the methodology given above. Throughout the entire solar spectrum, absorption predominantly depends on the terminal coordinates of the admittance trajectory at each wavelength.

3.5. Thermal Emissivity

Figure 12 shows a schematic diagram of thermal radiation and the reflection spectrum of the designed absorber (black) in the wavelength range of 0.3–10 μm simulated by TMM, at normal incidence and under room-temperature conditions, respectively. In terms of the spectral data, the thermal emissivity is calculated to be about 0.2, as derived from Equation (2).

Table 3. Thermal emissivity of multilayer films with temperature.

	Angle	0°	10°	20°	30°
Temperature
300 K		0.20348	0.21603	0.21904	0.22405
400 K		0.20727	0.21468	0.21587	0.21785
500 K		0.22156	0.22602	0.22557	0.22487
600 K		0.2473	0.24988	0.24801	0.24495

presents the thermal emissivity values at various temperatures, showing a steady increase in thermal emissivity with temperature. Remarkably, even at 600 K, the thermal emissivity of the solar–thermal conversion structure remains low at 0.25, indicating that this multilayer configuration functions as a highly efficient selective solar absorber for energy-harvesting applications.

4. Conclusions

This study presents the design and analysis of a high-performance solar selective absorber featuring an eight-layer Cr-SiO₂ stacked structure optimized for broadband solar energy harvesting in the 300–2500 nm wavelength region. Through strategic material selection and optimization of the layer thickness, the absorber exhibited excellent absorption characteristics, with an average absorption of 94% over the broadband range. Remarkably, even at a large incident angle of up to 60°, the average absorption exceeded 84%, showcasing its outstanding incident-angle stability. Furthermore, the structure exhibits robust polarization, ensuring stable absorption performance under complicated illumination conditions. Thermal analysis revealed a low room-temperature emissivity of 0.2, minimizing radiative heat losses. These factors contribute to this absorber being recognized as a promising candidate for high-efficiency solar thermal collection systems, photothermal conversion devices, and renewable energy applications.