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Abstract
Broadband light absorbers are attractive for their applications in photodetection and thermo-photovoltaics. Metal-black porous coatings have been experimentally proven to have broadband light absorption. However, a theoretical model is of importance for the design and fabrication of metal-black absorbers. Here we propose a three-dimensional cluster-structure model to simulate the absorption of metal-black films. Based on experimental data, a model of uniform clusters formed by nanoparticles with Gaussian random distribution in position was constructed for the gold-black absorbers. The absorption spectra were simulated with this model by finite-difference time-domain method. The gold-black absorbers were fabricated by the one-step magnetron sputtering process. The average absorption of gold-black absorbers with sputtering pressure of 50, 65 and 80 Pa were 72.34%, 87.25% and 91.08% in the visible spectral range and 81.77% (80 Pa) in 3–12 µm infrared spectrum. The high broadband absorption was attributed to the multiple scattering of incident light inside the gold-black porous structure. The simulations showed good agreements with experimental results with an error of 2.35% in visible spectrum and 1.82% in 3–12 µm infrared spectrum. To verify the applicability of this model, aluminum-black absorbers with different thicknesses were fabricated, and the absorption error between simulation and experimental results was 3.96%. This cluster model can be a good tool to design ultrabroadband absorbers based on metal-black porous structures.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Broadband light absorbers with high absorption are attractive for their applications in photodetection [1,2], thermal detectors [3], thermal/electrical interconnects [4] and imaging devices [5]. Nanostructures, such as plasmonic blackbody [6,7] and graphene solar absorber [8], have been intensively investigated to improve the absorption and broaden the bandwidth [9–11]. For example, Giessen’s group reported a multilayered palladium-based absorber produced by electron-beam lithography (EBL) lift-off technique. The absorber exhibited a reflection lower than 0.5% at visible wavelength [12]. Søndergaard and his coworkers reported a meta-absorber with ultra-sharp convex metal grooves achieved by focused ion beam (FIB) milling technique [13]. The absorber demonstrated an average absorption of 96% from 450 nm to 850 nm spectrum. More recently, Liu et al. proposed a carbon-black/anodic aluminum oxide absorber with an average reflection of 2.5% in 2.5–15.3 µm spectrum by Ar+ ion irradiation [14]. There have been many reports on experimental studies of broadband absorbers from visible to infrared wavelength range by different methods. However, most of them were based on complicated and time-consuming nanofabrication such as FIB and EBL techniques, which restricts its mass production and applications. Metal-black porous structures [15,16] have gained popularity owing to their ultrabroadband absorption characteristics and easy fabrication. Instead of complicated nano-scale fabrication, metal-black porous structures were achieved by thermal evaporation or magnetron sputtering method in an inert gas environment. Collisions with the gas molecules allow vaporized metallic atoms to coalesce into nanocrystalline chains which then diffuse towards the cooled substrate to form a loosely cluster layer [17,18]. The fabrication of metal-black porous structure is cost-effective compared with the afore mentioned approaches. The candidate metals for metal-black porous structures can be many metals, such as Au [19,20], Ag [21], Cr [22] and W [23]. The porous structures form micro cavities which in turn trap the light from getting out. Metal-black films are very attractive absorbers in hot electron physics due to the large uniform plasmonic absorption [24–27].
In order to study the growing process of porous structures, Eden model [28], diffusion-limited aggregation (DLA) model [29] and cluster-cluster aggregation (CCA) model [30,31] were proposed based on different simulation methods. Eden model was an early model used to study the formation process of uniformly distributed nanoparticles. The fractal growth was ignored in this model, it was too simple to simulate the actual aggregating process. DLA model proposed by Witten and Sander [32] improved Eden model. The migration motion of atoms was taken into account, and the fractal morphology during film growth could be simulated by DLA model. On this basis, Ball and his coworkers [30] proposed the CCA model to explain the fractal structure of aerosol and colloidal aggregation in the atmosphere. For the metal-black porous structure, Zaeschmar’s group [33] developed fractal impedance networks and simulated infrared transmission and reflection of a gold-black layer in 3–100 µm wavelength range. O’Neill et al. [34,35] utilized the effective medium theories to describe the optical properties of gold-black films in visible and near-infrared spectra. Recently, Munir et al. [36] proposed a fractal lossy antenna model for simulating the directional absorption of gold-black films in near-infrared.
In this paper, a different three-dimensional (3D) simulation model of uniform clusters formed by nanoparticles with Gaussian random distribution in position was established for visible to mid-infrared spectra based on experimental results. The parameters used in the model were adopted from experimental results of gold-black absorbers prepared in our lab. The ultrabroadband gold-black absorbers were prepared by sputtering at low pressure. When the sputtering pressures of gold-black films were 50, 65 and 80 Pa, the average absorption were 72.34%, 87.25% and 91.08% in visible spectrum. The simulated results showed good agreements with experimental measurements with an error of 2.35% in visible spectrum and 1.82% in 3–12 µm infrared spectrum. Aluminum (Al)-black absorbers were fabricated to verify the applicability of this proposed model. The error between simulation and experimental absorption was 3.96% in visible spectrum. The results indicated that this cluster model can be of an alternative to design ultrabroadband absorbers based on metal-black porous coatings.
The paper is organized as follow: In section 2, the fabrication process of gold-black absorbers is described and the simulation model is introduced. In section 3, the experimental results and simulations are presented and compared. In section 4, the experimental results of the Al-black films optimized with the cluster model are presented to verify the model. In section 5, we summarize and draw the conclusions.
2. Manufacturing process and characteristic simulation of gold-black absorbers
2.1 Fabrication and characterization
The gold-black coating was done by magnetron sputtering processes. Polished Si (1 0 0) wafers and quartz glasses were cleaned by sonication in acetone for 15 mins followed by 15 mins in ethanol. After sonication, the Si wafers and quartz glasses were washed with deionized water and blow-dried in nitrogen gas then were used as substrate. The sputtering chamber was first evacuated to the pressure of 10−4 Pa then filled with Ar and N2 (1:1) gases to desired pressure for sputtering process. The pressure was varied from 50 to 80 Pa. 99.99% pure Au as a target material was sputtered via a direct current sputtering at electrode voltage of 0.4 kV and current 0.48 A. The target-to-substrate distance was 10 cm, and the substrate rotated at 6 rpm. When the pressure of the sputtering chamber was restored to one atmospheric pressure, a gold-black film was coated on the substrate. The overall procedure to prepare the gold-black absorbers on a substrate was presented schematically in Fig. 1.
The morphology and thickness of gold-black films were characterized by a scanning electron microscopy (SEM, Carl Zeiss, Supra 55). The mass density was measured by using an electronic microbalance (Mettler Toledo, AL104). A high-resolution X-ray diffraction (XRD, Rigaku, Ultima IV) was used to analyze the composition of the absorbers. The reflection and transmission spectrum of the film was measured with an ultraviolet-visible (UV-Vis) spectrophotometer (Shimadzu, UV-2600). In addition, the infrared absorption characteristics of gold-black films were analyzed with a Fourier Transform Infrared spectrometer (FTIR, Bruker, Tensor 37) for optimization. All measurements were performed at room temperature.
2.2 Simulation model
The reflection and transmission of gold-black coatings were calculated using finite-difference time-domain (FDTD) method. The FDTD method is a numerical analysis technique in which the time-dependent Maxwell’s equations [37] are discretized using central-difference approximations to the space and time partial derivatives. As a time-domain method, it has been widely used in the electromagnetic field simulation. The needed parameters for FDTD simulation are the spatial distributions, structures, and permittivity of the materials. In this paper, we supposed that the absorber was composed with many homogeneously distributed 3D gold-black clusters, and each cluster consisted of many gold nanoparticles with Gaussian random distribution in position. Figure 2(a) is the top-view of nine clusters formed with nanoparticles. The Gaussian distribution in position was in radial direction. Figure 2(b) is the vertical cross-section of one single cluster. In a cylindrical coordinate, suppose that the Gaussian distribution in position is symmetric in radial directions. The density of the nanoparticles [38] can be expressed as:
Fig. 2. (a) Top-view schematic of nine clusters formed by nanoparticles with Gaussian random distribution in position. (b) Vertical cross-section of one single cluster.
The nanoparticle diameter and cluster diameter of this model were depended on sputtering pressure of gold-black absorbers, which was consistent with experimental SEM measurements. The permittivity of Au was taken from Palik et al. [39]. Besides, the boundary conditions along the arrangement of clusters of the simulation region were set as periodic and as perfectly matched layer (PML) conditions in z-direction. The light source was a broadband (0.3–12 µm) plane wave, with normal incidence angle to the absorber. The reflection and transmission were calculated by means of frequency-domain power detector with the following formula,
3. Measurements and simulated results
Figures 3(a)–3(f) present the top-view and cross-sectional SEM image of gold-black coatings sputtered for 30 min under Ar + N2 (1:1) pressure of 50, 65 and 80 Pa, respectively. It can be seen that the gold-black coating has a porous nanostructure, formed with many clusters. The average diameter of the cluster increased with the increase of sputtering pressure. The thickness of the gold-black coating increased obviously as sputtering pressure increased under same sputtering time, where the thicknesses were 300, 500 and 710 nm at 50, 65 and 80 Pa, respectively. Figure 3(g) is a photo of the gold-black absorber sputtered on a 4-inch Si substrate at 65 Pa, which exhibits black color and high uniformity in a large area. To verify the crystalized structure of gold-black absorbers, the XRD diffraction patterns of gold-black absorbers with different sputtering pressure are examined in Fig. 3(h). With the sputtering pressure increased, the intensity of these diffraction peaks also increased. The sharp peaks located at 2θ = 38.2°, 44.4°, 64.6° and 77.5° corresponded to bulk-gold (1 1 1), (2 0 0), (2 2 0) and (3 1 1) diffraction (JCPDS No. 04–0784), respectively. The XRD data indicated that the gold-black absorber retained the crystalized structure of bulk-gold. In addition, in order to determine the cluster diameter of the gold-black absorbers, the top-view SEM images of Figs. 3(a)–3(c) were analyzed using Otsu method [40]. The diameters of 400 clusters were measured on the SEM images. 3, 5 and 10 top-view SEM images were used for the cluster diameter analysis for 50, 65 and 80 Pa gold-black films since at higher pressure, the diameter of the cluster was bigger, therefore more images were needed. Each image had 1280 × 960 pixels. The resolution of the image was 256 dot per inch (dpi), the scanned area of the sample was 3 × 3 µm. Therefore, the resolution on the gold-black film samples analyzed with top-view SEM was 2.4 nm in one direction and 3.1 nm in perpendicular direction. The algorithm of 8-point connected method (counting average distance of lateral, vertical and diagonal connections) was used to determine the diameter of each cluster because of the irregular shape. The diameter was defined as the average value of lateral, vertical and diagonal connection distances of a cluster. It was the twice the radius. The cluster diameter distribution of gold-black clusters was obtained in Fig. 3(i), which appeared a Gaussian distribution under different pressures. The average cluster diameter increased as the increasing of sputtering pressure. The average cluster diameters of gold-black absorbers under 50, 65 and 80 Pa were 190, 390 and 560 nm, respectively.
Fig. 3. (a)–(f) SEM top-view (top) and cross-sectional (bottom) images of gold-black absorbers on Si substrate in Ar and N2 (1:1) pressure of 50 Pa (a) and (d), 65 Pa (b) and (e), and 80 Pa (c) and (f), with a scale bar of 500 nm. (g) A photo of a gold-black absorber sputtered on a 4-inch Si substrate at 65 Pa. (h) X-ray diffraction patterns under sputtering pressures of 50, 65 and 80 Pa. (i) Cluster diameter distribution obtained from top-view SEM images of the gold-black absorbers at different sputtering pressures.
The sputtering power, mass density and filling factor are listed in Table 1. The sputtering power of gold-black films at different pressure remained the same. The mass density was measured by using a microbalance of substrate without and with deposited gold-black films. The filling factor was obtained by comparing the measured density to the density of bulk-gold [41]. When the sputtering pressure increased from 50 to 80 Pa, the mass density of gold-black coatings decreased from 0.823 g cm−3 to 0.537 g cm−3, which was only 2.78–4.26% of the bulk-gold density, exhibited extremely low mass density.
Table 1. Sputtering power, mass density and filling factor of gold-black absorbers with different pressures.
The reflection and transmission spectra of gold-black absorbers were investigated in the visible region. The gold-black absorbers with different pressures were deposited on quartz glasses to determine their transmission properties. In order to exclude the influence of the substrate, the transmission of the film on the substrate and the transmission of the substrate were measured. According to the sample transmission expression [42],
where ${T_{all}}$, ${T_{gold}}$ and ${T_{sub}}$ are the transmissions of the gold-black film on a substrate, the gold-black film and the substrate, respectively. We measured the transmission of the film with quartz substrate and the transmission of quartz substrate without the film, then calculated the transmission of the gold-black film according to Eq. (3). The results are shown in Fig. 4(a). One can see as the sputtering pressure increasing, the transmission of gold-black absorbers decreased. The average transmission of gold-black absorbers with 50, 65 and 80 Pa in visible range were 25.12%, 10.68% and 7.18%, respectively.Fig. 4. Optical properties of the gold-black film absorbers under sputtering pressure of 50, 65 and 80 Pa in UV to Vis spectral range. (a) Transmission spectra (Tgold = Tall / Tsub). (b) Reflection spectra [Rgold = Rmeasure - RSi(Tgold2)]. (c) Calculated absorption spectra (Agold = 1- Tgold - Rgold).
Then, the gold-black absorbers were deposited on Si substrate to determine the reflection properties. The measured reflection (${R_{measure}}$) includes the reflection of gold-black films (${R_{gold}}$) and the part reflected by the substrate.
where ${R_{measure}}$, ${R_{Si}}$ are the measured total reflection and the reflection of the Si substrate, respectively. ${T_{gold}}$ is transmission of the gold-black film. According to Eq. (4) the reflection of the gold-black film (${R_{gold}}$) can be calculated. The results are shown in Fig. 4(b). The average reflections of gold-black coatings were 2.54%, 2.07% and 1.74% for 50, 65 and 80 Pa. In addition, the common feature for all absorbers was that these films had low reflection at wavelengths below 500 nm due to the interband transition of gold [43].With the results of Figs. 4(a) and 4(b), the absorption can be calculated as follows: Absorption = 1 – Reflection – Transmission, as shown in Fig. 4(c). The average absorption of gold-black absorbers at 50, 65 and 80 Pa were 72.34%, 87.25% and 91.08% in visible region. The highest absorption reached 94.26% at 622 nm of 80 Pa gold-black film. The optical properties of gold-black absorbers were dominated by many clusters formed in gold-black films. These clusters worked as many blackbody cavities, allowing the incident light to undergo multiple scattering inside gold-black absorbers, resulting in a high absorption and a black-color appearance [44,45]. With the increasing of sputtering pressure, the filling factor of gold-black absorber decreased, and the thickness increased. There was more space in the film, which facilitated the multiple scattering of incident light, resulting in better absorption performance.
To compare the gold-black absorber with other commonly used absorbers in visible spectral range, we calculated the average absorption coefficients ${\alpha _\lambda }$ from the following formula,
where d and Agold are the thickness and absorption of films. In the visible range, the average absorption coefficient of gold-black absorber prepared at 80 Pa was calculated as 3.01 µm−1, which was higher than 1.1 µm−1 of black nickel-phosphorus [46] and 0.7 µm−1 of vertically aligned carbon nanotube arrays [47]. The results indicated that the gold-black film was a very good alternative as a visible light absorber.To analyze the absorption mechanism of gold-black absorbers, we proposed a 3D cluster model of the gold-black film. Figures 5(a)–5(c) are cross-sectional SEM images of 80 Pa gold-black absorber with sputtering time of 3, 10 and 30 min. The insets were the corresponding top-view SEM images. The SEM images at different sputtering time demonstrated that the gold-black films had a Stranski-Krastanov growth mode. Many uniform and fine gold atomic groups formed on the substrate at the beginning of sputtering. With the increasing of sputtering time, more gold nanoparticles were added to the boundary of the clusters at random positions, forming many uniform gold-black clusters. The process of adding the particles to the cluster boundary was repeated until the cluster was formed. Therefore, the position of gold nanoparticles formed an intermediate aggregated Gaussian random distribution, further formed a single cluster. Consequently, in our model, the clusters were considered to have a uniform distribution. But the position of nanoparticles in each cluster had a Gaussian distribution, as shown in Fig. 5(d). The mentioned CCA model proposed the aggregation of nanoparticles in a low pressure gas. This model explained the process of aggregation of clusters into bigger clusters. In the CCA model, the aggregation formed a fractal structure of the cluster. In the model we proposed the cluster was formed by nanoparticles with Gaussian distribution in position. We did not treat the cluster as a fractal structure. Hence, the model we proposed was a different model of the formation of metal-black films based on experimental results. A simulation model of 3 × 3 clusters was established. According to the SEM images of gold-black coatings under different pressures, the gold-black models with different heights and cluster diameters were established. The diameter of single gold particles varied between 15–20 nm. The cluster diameters in this model were 190, 390 and 560 nm corresponding to the pressure of 50, 65 and 80 Pa. The cluster heights were set as 300, 500 and 710 nm at 50, 65 and 80 Pa in the simulations, same as the experimental values (Fig. 3). The number of nanoparticles in each single cluster of this model at 50, 65 and 80 Pa were 164, 952 and 2200, respectively, which was consistent with the filling factor (Table 1). Then, the reflection and transmission were calculated using FDTD method. In addition, in order to reduce the uncertainty of random distribution, we calculated the reflection and transmission spectra of each model 20 times and took the average.
Fig. 5. (a)–(c) Cross-sectional SEM images of 80 Pa gold-black absorber with various sputtering time, the scale bar is 300 nm. The insets are the corresponding top-view SEM images, the scale bar of the inset is 1 µm. (d) Schematic image of the gold-black cluster model. (e)–(g) The experimental measurements and simulations of transmission, reflection and absorption spectra of the gold-black absorbers in visible range. The inset in (g) is the simulated absorption of 80 Pa gold-black absorber.
The experimental (solid line) and simulated transmission spectra (dashed line) with different pressures were shown in Fig. 5(e). The average simulated transmission under 50, 65 and 80 Pa were 27.89%, 11.85% and 8.25% in visible range, respectively. The results showed that the average difference between the experimental and simulated results is 1.67%. Figure 5(f) shows the experimental and simulated reflection spectra of the gold-black model with different pressures in 320–800 nm. The simulated reflection of the gold-black model with 50, 65 and 80 Pa exhibited an average reflection of 3.36%, 1.91% and 1.58% over the whole spectral range. The ultra-low reflection was attributed to the multiple scattering of incident light. Compared with measured reflection, there was an average difference of 0.38%. Subsequently, the simulated and experimental absorption were displayed in Fig. 5(g). The calculated absorption of the model with 50, 65 and 80 Pa were 68.75%, 86.24% and 90.17%. One can see that the simulations based on the gold-black uniform clusters model with nanoparticles of Gaussian random distribution in position fitted well with the experimental results with an error of 2.35%. Besides, the inset in Fig. 5(g) is the simulated absorption of 80 Pa gold-black absorber. There was a peak of absorption, with an absorption of 95.04% at 583 nm, which might be attributed to the hybridization of plasmon resonances of close proximity clusters [48].
To evaluate the necessity of using Gaussian distribution in nanoparticle position of the gold-black cluster model, we also calculated the absorption of clusters with nanoparticles of uniform distribution in position of this gold-black model. We used the same diameter and number of nanoparticles in two models. Figures 6(a)–6(c) displays the comparison of transmission, reflection and absorption of the two simulated models and experimental results with pressure of 80 Pa. Compared with the Gaussian distribution of nanoparticles in position, the transmission and reflection calculated by uniform distribution model differ greatly from experimental results, as shown in Figs. 6(a)–6(b). The average absorption of uniform distribution model was 76.31% in visible range, which was quite different from experimental results with an error of 16.04%, as shown in Fig. 6(c). This may be attributed to the fact that model of uniform distribution in nanoparticle position does not consider the cluster growth of the film, which leads to larger transmission and lower absorption. Therefore, the Gaussian distribution of nanoparticles in position is extremely important for designing this gold-black cluster model. Besides, in order to analyze the effect of different number of cluster layers in the height (z) direction on the absorption of the gold-black model, we determined that the overall height of the absorber was 600 nm. Then, we calculated the absorption of 1 cluster layer of 600 nm, 2 layers of 300 nm, 3 layers of 200nm and 4 layers of 150 nm, as shown in Fig. 6(d). The average absorption in visible range of 1, 2, 3 and 4 layers were 88.03%, 87.78%, 87.29% and 87.28%, respectively. The results showed that the number of layers had little effect on the absorption in the model. This gold-black model provided a theoretical reference for the production of porous structures in visible spectral range.
Fig. 6. (a)–(c) Comparison of transmission, reflection and absorption of simulated Gaussian distribution, simulated uniform distribution in nanoparticle in position and experimental results under 80 Pa. (d) Absorption spectra of the gold-black model with different number cluster layers.
Optical imaging devices in the mid-infrared (MIR) range play important roles in many applications such as thermography surveillance, automotive safety and astronomy. Emission wavelength in the atmospheric transmission windows of 3–5 µm and 8–12 µm spectral ranges attracted more attentions due to the low attenuation from water vapor, dust or other atmospheric influences [49]. Therefore, to verify the performance of the gold-black cluster model at MIR wavelength ranges, we investigated the absorption properties of 80 Pa gold-black film on Si substrate [50] in 3–12 µm infrared spectrum. Figure 7(a) reveals the simulated reflection, transmission and absorption spectra of the gold-black model in the range of 3–12 µm. The simulated average reflection and transmission in 3–12 µm were 10.94% and 5.77%. The simulated average absorption was 83.29%, demonstrating an ultrabroadband high absorption in MIR region. Additionally, Fig. 7(b) compared the simulated and experimental absorption. The measured average absorption of the 80 Pa gold-black film was 81.77% in the wavelength range of 3–12 µm. The theoretical simulation showed a great agreement with the experimental measurements with an error of 1.82%.
Fig. 7. (a) Simulated reflection, transmission and absorption spectra of 80 Pa gold-black model in 3–12 µm range. (b) Simulated and measured absorption spectra in the range of 3–12 µm.
4. Verification of the cluster model with Al-black absorbers
To verify the applicability of this cluster model for other metal-black films, Al-black porous absorbers with different thickness were fabricated by thermal evaporation as validation. Figures 8(a)–8(c) present top-view SEM images of the Al-black absorbers with evaporation time of 10, 20 and 30 s, where the thickness is 1.09, 2.06 and 2.90 µm, respectively. The insets are the corresponding cross-section SEM images. To obtain the cluster diameter of Al-black absorbers, 3 top-view SEM images with 15 × 15 µm area were scanned. We tried to zoom in further, but we did not get a sharp image. The reason was probably due to the conductivity of Al-black film was lower than the gold-black film. The resolution of the images was same as the gold-black films. Therefore, the corresponding resolution on the Al-black films samples analyzed by SEM was 11.7 nm and 15.6 nm in perpendicular directions respectively. The average cluster diameter with 10, 20 and 30 s evaporation time were 0.15, 0.21 and 0.27 µm by image processing of Otsu method [40]. Because the resolution of the top-view SEM image was low, the diameter of the Al-black nanoparticles was obtained from the cross-section SEM images. The cross-section SEM image had 1280 × 960 pixels, same as the top-view SEM image. The resolution of the image was 256 dot per inch (dpi). The cross-sectional scanned area of the sample was 5 × 5 µm. Thus, the resolution of the cross-sectional SEM images was 3.9 nm and 5.2 nm in perpendicular directions. Then, the diameter of Al nanoparticles was obtained from the cross-sectional SEM images. The diameter of single Al particle varied from 7 to 10 nm. Besides, mass density of Al-black film was measured 0.932 g cm−3. Thus, the filling factor was calculated as 34.52%. The nanoparticles diameter and cluster diameter of the Al-black absorber are different from gold-black absorbers, so the parameter of Al-black cluster model needed to be modified accordingly. The number of nanoparticles in a single Al-black cluster at 10, 20 and 30 s were set as 1230, 4140 and 9870, consistent with the filling factor. Figures 8(d)–8(f) present the experimental measurements and simulated results of transmission, reflection and absorption of Al-black absorbers with different evaporation time in visible spectral range. The experimental average transmission of 10, 20 and 30 s were 34.53%, 13.37% and 11.25% in visible spectral range. Simulated transmission spectra showed an average difference of 1.74%, where the average transmission of 10, 20 and 30 s Al-black films were 36.91%, 14.68% and 12.8%, respectively. Figure 8(e) shows the reflection of Al-black absorbers. The average reflection of 10, 20 and 30 s Al-black films were 3.09%, 1.37% and 0.68%. The simulated spectra showed an average reflection of 5.22%, 1.95% and 1.20% at 10, 20 and 30 s Al-black model. The average difference from the experimental results was 1.07%. Figure 8(f) shows the comparison of absorption from experimental measurement and the simulations. The average experimental absorptions were 62.39%, 85.26% and 88.07% of 10, 20 and 30 s Al-black absorbers. The average simulated absorptions of Al-black cluster models were 57.87%, 83.36% and 85.90%, resulting in an average error of 3.96% between experimental results and simulation. These results demonstrated that this cluster model is not only suitable for gold-black absorbers, but also for other metal-black structures, which can be of an alternative approach to design ultrabroadband absorbers based on metal-black coatings.
Fig. 8. (a)–(c) Top-view SEM images of the Al-black absorbers with the evaporation time of 10, 20 and 30 s, the scale bar is 3 µm. The insets are the corresponding cross-sectional SEM images, the scale bar of the inset is 1 µm. (d)–(f) Optical properties of Al-black absorbers with the evaporation time of 10, 20 and 30 s in visible spectral range with experimental measurements and simulations. (d) Transmission spectra (TAl = Tall / Tsub). (e) Reflection spectra [RAl = Rmeasure - RSi(TAl2)]. (f) Calculated absorption spectra (AAl = 1- TAl – RAl).
5. Conclusion
In summary, a gold-black uniform clusters model formed by nanoparticles with Gaussian random distribution in position was proposed based on the experimental results. Ultrabroadband gold-black absorbers were fabricated by a one-step magnetron sputtering. The optical properties of the fabricated coatings were analyzed in visible and MIR wavelength range. The average absorption of gold-black coatings with 50, 65 and 80 Pa were 72.34%, 87.25% and 91.08% in visible spectrum and 81.77% (80 Pa) in 3–12µm infrared spectrum respectively, demonstrating that gold-black films can be used as effective broadband light absorbers. The high absorption was attribute to multiple scattering of incident light inside the gold-black absorber. Moreover, the absorption spectrum of gold-black films was simulated with this proposed model. The simulated absorption of the gold-black model with 50, 65 and 80 Pa were 68.75%, 86.24% and 90.17% in visible spectrum and 83.29% (80 Pa) in 3–12 µm infrared spectrum. The simulation results showed good agreements with experimental results with an error of 2.35% in visible range and 1.82% in 3–12 µm. Besides, Al-black absorbers were fabricated to verify this proposed cluster model. The absorption error between experimental and simulated results was 3.96%. This cluster model we proposed can be of an alternative approach to design ultrabroadband absorbers based on metal-black porous coating, which has great potential in the fields of photoelectric detection, infrared scene generation and hot electron physics.
Funding
National Natural Science Foundation of China (61835001, 61875011); China Postdoctoral Science Foundation (2020TQ0036).
Disclosures
The authors declare no conflicts of interest.
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