2.1.

Design

In the design of radiative coolers, one of the most important parameters is the complex refractive index $N=n-\mathrm{i}k$, where the optical constants $n$ and $k$ represent the refractive index and extinction coefficient, respectively, and $k$ is related to the absorption coefficient $\alpha$ by $\alpha =4\pi \mathrm{k}/\lambda$. As shown in Fig. 1, the optical constants $n$ and $k$ of various materials (${\mathrm{SiO}}_2$, ${\mathrm{HfO}}_2$, ${\mathrm{TiO}}_2$, ${\mathrm{Al}}_2{\mathrm{O}}_3$, and ${\mathrm{Ta}}_2{\mathrm{O}}_5$), which are widely used in radiative cooling due to their high absorption in the 8 to $13\mu \mathrm{m}$ waveband,^24,27,28 are plotted for comparison.

Fig. 1

Optical constants $n$ and $k$ of the materials in the 8 to $13\mu \mathrm{m}$ spectrum:^25,26 (a) optical constants of ${\mathrm{SiO}}_2$, (b) optical constants of ${\mathrm{Ta}}_2{\mathrm{O}}_5$, (c) optical constants of ${\mathrm{TiO}}_2$, (d) optical constants of ${\mathrm{Al}}_2{\mathrm{O}}_3$, (e) optical constants of ${\mathrm{HfO}}_2$, and (f) optical constants of Ag.

To improve the reflection in the solar spectrum, high-index and low-index materials in the solar spectrum are needed in the structure. ${\mathrm{SiO}}_2$ with its refractive index of approximately near 1.44 in the solar spectrum and low absorption in the near-ultraviolet band is mostly used as the low-refractive-index material in the solar spectrum. Furthermore, ${\mathrm{SiO}}_2$ also has a very high absorption in the 8 to $13\mu \mathrm{m}$ spectrum and its extinction coefficient $k$ reaches a value of over 1.5 in the 9 to $10\mu \mathrm{m}$ waveband. As for high-index materials in the solar spectrum, both ${\mathrm{Ta}}_2{\mathrm{O}}_5$ and ${\mathrm{TiO}}_2$ are considered. The refractive index of ${\mathrm{Ta}}_2{\mathrm{O}}_5$ is 2.1 and that of ${\mathrm{TiO}}_2$ is 2.2 in the solar spectrum. Although ${\mathrm{TiO}}_2$ has been used in many kinds of structures of photonic radiative coolers,²¹ ${\mathrm{Ta}}_2{\mathrm{O}}_5$ is a comparatively better material in making radiative coolers. However, ${\mathrm{TiO}}_2$ has a much higher absorption in the near-ultraviolet band than ${\mathrm{Ta}}_2{\mathrm{O}}_5$. Furthermore, the TiO generated during the ${\mathrm{TiO}}_2$ coating process affects the experimental results. By contrast, ${\mathrm{Ta}}_2{\mathrm{O}}_5$ is a more stable material. In the solar spectrum, ${\mathrm{HfO}}_2$ has low absorption in the near-ultraviolet band and can be a good material for optimizing reflection in the solar spectrum. However, its $k$ is low in the 8 to $13\mu \mathrm{m}$ waveband. In addition, ${\mathrm{HfO}}_2$ is a comparatively rare and expensive material. ${\mathrm{Al}}_2{\mathrm{O}}_3$ is a cheap and well-known oxide, and it has the highest absorption in the 11 to $13\mu \mathrm{m}$ spectrum among the aforementioned oxides. It is also used as the adhesion layer between the Ag layer and other oxide layers to enhance bonding, thus improving the reliability of the photonic radiative cooler. So we finally chose ${\mathrm{SiO}}_2$, ${\mathrm{Ta}}_2{\mathrm{O}}_5$, and ${\mathrm{Al}}_2{\mathrm{O}}_3$ as the materials of oxide layers instead of ${\mathrm{HfO}}_2$ and ${\mathrm{TiO}}_2$.

The design began with calculating the optical properties of multilayered thin films, and the ultimate absorptivity, reflectivity, and transmissivity of a given wavelength were determined through iterative calculation by choosing the $n$, $k$, and $d$ of each individual layer in the 8 to $13\mu \mathrm{m}$ waveband. The optical constants $n$ and $k$ of different materials vary in different ways in the 8 to $13\mu \mathrm{m}$ waveband, so we set some initial structures of different arrangements of layers, using commercial software (FilmWizard, Scientific Computing International, United States), which can optimize each layer with a given target.

Because ${\mathrm{SiO}}_2$ is mostly used as a low-refractive-index oxide, we only tried different high-refractive-index oxides for the optimal design. Initially, we designed two types of radiative coolers composed of 10 alternating layers of ${\mathrm{SiO}}_2$ (400 nm) and ${\mathrm{Ta}}_2{\mathrm{O}}_5$ (400 nm) or ${\mathrm{Al}}_2{\mathrm{O}}_3$ (400 nm) and Ag (200 nm) on the substrate; the structures were named structures 1 and 2, as shown in Fig. 2(a). To improve the reflection in the solar spectrum, we use 4 layers of alternating ${\mathrm{SiO}}_2$ (50 nm) and ${\mathrm{Ta}}_2{\mathrm{O}}_5$ (50 nm) layers, and one layer of Ag (200 nm) at the bottom, as the reflection segment, which is responsible for increasing the reflection of incident light. On top of the reflection segment is the absorption segment with 12 layers of alternating ${\mathrm{SiO}}_2$, ${\mathrm{Ta}}_2{\mathrm{O}}_5$, and ${\mathrm{Al}}_2{\mathrm{O}}_3$ layers in different orders; the structures were named structures 3 to 6, as shown in Fig. 2(b). During optimization, some single layers may be reduced to meet the demand for less thickness. The reason that our initial structures have so many layers and arrangements is to give the optimization more room to adjust.

Fig. 2

(a) Initial structures of 10 layers of ${\mathrm{SiO}}_2$ and ${\mathrm{Ta}}_2{\mathrm{O}}_5$ or ${\mathrm{Al}}_2{\mathrm{O}}_3$ and (b) initial structures of 10 layers of ${\mathrm{SiO}}_2$, ${\mathrm{Ta}}_2{\mathrm{O}}_5$, and ${\mathrm{Al}}_2{\mathrm{O}}_3$ in different arrangements. (A: ${\mathrm{Al}}_2{\mathrm{O}}_3$, B: ${\mathrm{SiO}}_2$, C: ${\mathrm{Ta}}_2{\mathrm{O}}_5$, unit: nm, and SUB: Si).

Then we used the global optimization of the software and set 100% as the optimization target of absorption in the 8 to $13\mu \mathrm{m}$ waveband. After extensive numerical optimization, satisfactory results were obtained, as shown in Fig. 3. Taking structure 3 as an example, the average emissivity in the 8 to $13\mu \mathrm{m}$ spectrum of structure 3 slightly increased from 85.8% to 86.6%, but the total thickness of the structure significantly decreased from 3.8 to $2.58\mu \mathrm{m}$. Similarly, the other five structures all showed a significant reduction in thickness and an obvious performance improvement. The results showed that a thin film using global optimization has a much better performance than simply changing the thickness and ratio of different materials, especially in reducing the thickness.

Fig. 3

(a)–(f) Schematic diagram and optical performance of the structures before and after the global optimization. (A: ${\mathrm{Al}}_2{\mathrm{O}}_3$, B: ${\mathrm{SiO}}_2$, C: ${\mathrm{Ta}}_2{\mathrm{O}}_5$, unit: nm, and SUB: Si).

${\mathrm{Al}}_2{\mathrm{O}}_3$ has a better adhesive force with the Ag layer than other oxides, so we use an ${\mathrm{Al}}_2{\mathrm{O}}_3$ layer as the bonding layer to improve the bonding force between the selective interference absorption layers and the metal reflector layer to prevent the film from cracking or delamination. For the same reason, to increase the adhesion between the metal reflector layer and the substrate, we chose to coat a very thin layer of Ni on the substrate before coating the Ag layer. The use of adhesion layers helps to improve the reliability. Finally, the main materials of our structures used in the actual coating situation are ${\mathrm{SiO}}_2$ and ${\mathrm{Ta}}_2{\mathrm{O}}_5$. The change of coating conditions such as coating methods, deposition temperature, and deposition rate will cause the change of film optical constants. Different from the conventional coating of oxides in EBE condition, with the combination of the Ag layer, the deposition temperature of the multilayer thin films is the room temperature without extra heat gain to avoid the Ag layer from oxidation.

To obtain the reliable optical constants of film materials in the EBE condition in this work, we measured the ellipsometry parameters psi and delta of ${\mathrm{SiO}}_2$ and ${\mathrm{Ta}}_2{\mathrm{O}}_5$ films deposited at certain deposition temperatures and deposition rates in the 250 to 2500 nm and 8 to $13\mu \mathrm{m}$ spectra and fitted the optical constants in these spectra (Fig. 4). This makes our optimization more accurate and reliable than previous works. During the same process of design and optimization used before, we get two structures that meet the actual experimental conditions in our laboratory as the final structures (Tables 1 and 2). They both have a satisfactory performance of high reflectivity in the solar spectrum and high absorptivity/emissivity in the 8 to $13\mu \mathrm{m}$ spectrum.

Fig. 4

Optical constants $n$ and $k$ of oxides in the solar spectrum and atmospheric window fitted by ellipsometry. (a) ${\mathrm{SiO}}_2$ in the 250 to 2500 nm waveband. (b) ${\mathrm{SiO}}_2$ in the 8 to $13\mu \mathrm{m}$ waveband. (c) ${\mathrm{Ta}}_2{\mathrm{O}}_5$ in the 250 to 2500 nm waveband. (d) ${\mathrm{Ta}}_2{\mathrm{O}}_5$ in the 8 to $13\mu \mathrm{m}$ waveband.

Table 1

Structural parameters of structure A.

Table 2

Structural parameters of structure B.

Compared with prior works that simply changed the numbers of layers or thicknesses of each layer in optimizing the structures of the radiative coolers, this work has the following advantages.

2.2.

Fabrication

The thin-film radiative coolers were prepared by conventional EBE. When the chamber pressure reached $1\times {10}^{-3}\mathrm{Pa}$, the ion source was turned on for bombardment cleaning of the substrate. The samples were not heated during the coating process. The Ag film was deposited by thermal evaporation, and the ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ta}}_2{\mathrm{O}}_5$, and ${\mathrm{SiO}}_2$ films were deposited by EBE. The deposition rate of Ag film was $1.0\mathrm{nm}/\mathrm{s}$. The deposition rates of the ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ta}}_2{\mathrm{O}}_5$, and ${\mathrm{SiO}}_2$ films were 0.8, 0.2, and $0.8\mathrm{nm}/\mathrm{s}$, respectively, and the deposition of the oxide dielectric films was assisted by the ion beam. The quartz crystal oscillator was used to monitor the deposition of the films to accurately control the thickness of each layer. Finally, the thin-film radiative coolers were fabricated by following the designed optimal structures.^29,30

2.3.

Characterization

The test of the cooling effect was carried out under direct sunlight on a rooftop in Shanghai on June 10, 2023. We selected a large polystyrene box covered with aluminized mylar as a frame. Inside it were two small hollow polystyrene boxes covered by the radiative cooler and the uncoated substrate respectively, creating two sealed small air pockets. Thermocouples were used to record the temperature changes in different areas. One thermocouple went through the small hollow polystyrene box and was connected to the bottom of the radiative cooler, and one thermocouple went through another small hollow polystyrene box and was connected to the bottom of the uncoated substrate. Another thermocouple was used to record the temperature change inside the large polystyrene box. We calibrated all of the thermocouples before the experiment. A clear polyethylene film was wrapped around the whole structure, and the part where the probe is inserted was also sealed, creating a sealed big air pocket to prevent non-radiative heat exchange from air flow. The solar irradiometer was set next to the large polystyrene box to measure the solar illumination. All of the devices were connected to the laptop to record the data every second. The schematic and physical diagrams of the temperature test structure are shown in Fig. 5.

Fig. 5

Schematic and physical diagram of the temperature test structure.