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Abstract
We propose a simple structure for passive sky radiative cooling made of a surface-textured layer of silica on a silver substrate. Using electromagnetic simulations, we show that the optical properties of such structures are near-ideal, due to the large reflectivity of silver in the solar spectrum and the large emissivity of silica in the infrared. Surface texturation is key to obtain near-unity emissivity in the infrared. By using thin transparent layers sandwiched between silver layers at the bottom of the structures, resonant absorption can be obtained, leading to coloration while keeping acceptable radiative cooling power. Using multiple resonator increases the color palette that can be obtained.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surfaces exposed to the sky exchange radiative energy with the atmosphere when it is opaque, and with the cold outer space in the transparency regions of earth atmosphere. In the later case, due to the temperature difference of the two body, large heat fluxes between the surface and the sky can be obtained leading to efficient cooling of the surface, if its emission in the transparency windows of earth atmosphere in the infrared is large. During daytime, reflection of sunlight is required to conserve this cooling power. This is the so-called daytime sky radiative cooling principle [1]. Applications of this phenomena are various, from thermal management of objects, like solar cells [2–6] or thermophotovoltaic cells [7] to production of energy via negative electroluminescence [8] or thermoelectricity [9,10]. During the past years, many studies focused on spectral tailoring of structures using various materials and geometries in order to obtain large reflectivity in the spectral range where the solar spectrum extends and large emissivity in the transparency regions of earth atmosphere. One-dimensional stacks of semiconductors thin layers [11–18] have shown great potential despite their simplicity. Another approach investigated was reflection of sunlight by backscattering instead of using a silver layer. In this framework, nanoparticles [19–21] and nanofiber networks [22] have been shown to be efficient. More complex 3D structures were also studied [1,23,24], as well as structural materials [25] and insulating aerogels [26]. For aesthetic purpose, a coloration of the surface may be desired by keeping radiative cooling capacity [27,28]. This would allow colored object, such as building walls or car body paints to keep relatively low temperature under sunlight illumination. Since ideal radiative coolers reflect most of the incident solar energy, including the visible part, it results in a whitish coloration. To obtain coloration while keeping acceptable radiative cooling power, narrowband absorption in the visible are required. This can be obtained with resonant phenomena, like Tamm plasmons [29], Fabry-Pérot resonances [30] or localized surface plasmon resonances [22]. In this article, we first present a baseline structure for sky radiative cooling application composed of a surface-textured silica layer deposited on a silver substrate. This type of structures has already been proven to be efficient in various studies, due to the possibility to excite surface phonon-polaritons in order to obtain quasi-perfect emissivity [2,5,19,22,24]. Using electromagnetic simulations, we determine the optical properties of the structures, and an in-depth analysis is performed to explain the origin of the near-ideal optical properties of the structure. Radiative cooling power of the simulated structure is then calculated. For 1D structures like the one we present in this study, Fabry-Pérot resonance are particularly efficient [30] in order to obtain sharp absorption peaks in the visible range. Resonator made of transparent layers sandwiched between silver thin layers can therefore be added to the silica-silver structure to produce coloration while keeping acceptable value of radiative cooling power. Investigation of this structure is performed, and the variation of colors with radiative cooling power is analyzed. To extend the gamut of obtainable color, we propose to stack multiple resonators that produce multiple absorption peaks in the visible range. We demonstrate that new colors can be obtained, but in the detriment of radiative cooling power, and therefore that it is necessary to find a compromise between coloration and radiative cooling efficiency.
2. Non-colored conventional radiative cooling
We first demonstrate the efficiency of textured-silica on silver structures for maximizing the radiative cooling power. Silver, being the material that have the largest reflectivity in the solar spectrum, is used to reflect incident solar radiation. On the other hand, silica is a large bandgap semiconductor and a polar material, which usually results in large transparency in the solar spectrum and emissivity in the infrared. To simulate the optical properties of the structure, we apply the Rigorous Coupled Wave Analysis approach using the RETICOLO software [31]. Optical indices of materials are required for simulations. We used measurements values provided by [32] for silver. For silica, values measured with reflectometry are taken from [33]. The spectral hemispherical emissivity of a single silica layer as a function of its thickness is plotted in Fig. 1(a). When the thickness increases, its emissivity tends to also rise, but at different rates for different spectral regions, depending on the value of the extinction coefficient of silica at each wavelength. For wavelengths between $0.3~\mathrm{\mu}$m and $4~\mathrm{\mu}$m, values of the extinction coefficient are close to $0$, so that the emissivity of the silica layer doesn’t increase much and stays very low. For wavelengths larger than $4~\mathrm{\mu}$m, the extinction coefficient is larger and the emissivity gets values close to $1$ for layer thicknesses larger than about $100~\mathrm{\mu}$m. At wavelengths around $9~\mathrm{\mu}$m, the spectral hemispherical emissivity displays a dip of emission due to large values of the reflection coefficient of silica in the restrahlen band. In the end, a few hundred-micron thick silica layer being extremely transparent in the spectral region where the solar spectrum extends, and emissive in the infrared, it is a promising material for building a radiative cooler. For reflection of incident solar radiation, an Ag substrate is considered at the bottom of the layer. The spectral emissivity of the Ag-SiO$_2$ structure, for a $500~\mathrm{\mu}$m thick silica layer, is plotted in Fig. 1(b), along with the normalized solar spectrum [34], blackbody spectrum at $300$ K and the atmosphere transmittance in the infrared [35].
Fig. 1. (a): Spectral hemispherical emissivity of a single SiO$_2$ layer as a function of its thickness. (b): Spectral hemispherical emissivity of a $500~\mathrm{\mu}$m SiO$_2$ layer on silver substrate, along with the normalized solar spectrum (orange curve), blackbody spectrum at $300$ K (red curve) and the spectral earth atmosphere transmittance (blue curve).
One can observe that the structure displays good reflectivity in the solar spectrum, and high emission in the transparency regions of earth atmophere, except in the restrahlen bands of silica. This dip of emissivity is decreasing the radiative cooling power, since it occurs partially in the spectral region where the atmosphere is transparent, and also near the maximum emission of Planck’s blackbody at $300$ K. This problem have been overcome in [36] by adding a polymer layer on top of the silica layer. Here, to tackle this problem, we propose to use surface texturing to avoid adding another material the the system. Gratings have the ability to scatter evanescent waves and couple them with propagating modes in order that they can be detected in the far-field. Since the surface electromagnetic density of states is large at these wavelengths due to the presence of surface phonon-polariton resonances, it results in an increase of emission. We considerer hereafter two types of gratings: a 1D lamellar one, and a 2D cubic one. The periodicity of the grating and its height are set at $5~\mathrm{\mu}$m. The filling factor is chosen to be $0.5$. These parameters are chosen because these are the characteristic dimensions that can be synthesized for large surface synthesis by ion etching processes, and also. Figures 2(a) and 2(b) displays the spectral and angular emissivity of the structure with a 1D lamellar gratings, for the transverse magnetic (TM) and transverse electric (TE) polarizations, respectively. It is observed that emission inside the resltrahlen band become high for TM modes, but not for TE modes.
Fig. 2. Spectral and directional distribution of emissivity of the structure with a 1D lamellar gratings. (a): for TM modes. (b): for TE modes. Spectral and directional distribution of the structure with a 2D cubic gratings. (c): for TM modes. (d): for TE modes.
As a consequence, since the unpolarized spectral emissivity is the arithmetic mean of the two components, it is observed in Fig. 3 that the enhancement of the spectral hemispherical emissivity with a 1D gratings is moderate. Since 1D gratings are polarized [37,38], we then consider the 2D cubic grating in order to obtain an emissivity enhancement in any direction. Figures 2(c) and 2(d) show that in this case, both polarization are affected by the gratings. As a consequence, the enhancement due to gratings is even larger than with a 1D one, as seen in Fig. 3. In the end, for a Ag-SiO$_2$ structure with a 2D gratings, the spectral emissivity obtained displays large values in the infrared and large reflectivity in the solar spectrum, which is near-ideal for radiative cooling .
Fig. 3. Spectral hemispherical emissivity of the structure with flat surface, 1D lamellar grating and 2D cubic grating.
To emphasize this, we calculate the radiative cooling power $Q_{\textrm {cool}}$ of the structure [11]. It reads
whereWe also define the net radiative cooling power between the atmosphere and the sky in absence of sunlight, $Q_{\textrm {radnet}}$ as
In Table 1, values of the radiative cooling power $Q_{\textrm {cool}}$ and its components $Q_{\textrm {radnet}}$ and $Q_{\textrm {solar}}$ are displayed for the flat SiO$_2$ structure, the 1D lamellar and 2D cubic gratings. An increase of $Q_{\textrm {radnet}}$ is observed when going from a flat layer to a 1D and 2D gratings. This is due to the increase of emission in the infrared. However, $Q_{\textrm {solar}}$ also increases due to the slight decrease of reflectivity that can be observed with the presence of a grating. In the end, an increase of cooling power of $25~\textrm {W}\textrm {m}^{-2}$ is obtained with the addition of a 2D gratings, and a maximum value of radiative cooling power of $114~\textrm {W}\textrm {m}^{-2}$ is reached. These performances are slightly lower than [36], where a radiative cooling power of $127~\textrm {W}\textrm {m}^{-2}$ was reported. The advantage of our structure is that it is not necessary to add a polymer layer on top of the surface to reduce the dip of spectral emissivity. It is worth mentioning that the proposed structures can be easily synthesized by deposing a thin silver layer at the bottom of a silica substrate by magnetron sputtering for example. The surface texturation can be created with focused ion beam techniques or ion etching.
Table 1. Values of radiative cooling power and its components for the structure with flat surface, 1D and 2D gratings.
3. Colored structured for radiative cooling
For the sake of aestheticism, one could desire a colored structure that is also able to dissipate heat, or at least to mitigate the net heat flux between the surface and the sky in order to decrease its equilibrium temperature. As explained in the introduction section, coloration by reflection is obtain by absorbing radiation in the visible range, which decreases the radiative cooling power. To obtain coloration without altering the radiative cooling power too much, narrowband absorption is therefore required.
It was shown in [30] that Fabry-Pérot interferences produced by resonators made of a transparent layer sandwiched between thin silver layers can produce absorption peaks. By tuning the size of the transparent layers, the spectral position of the peak can be tuned, leading to different colors. We use the same principle for the structure presented above, and the resulting colored radiative cooler is presented schematically in Fig. 4(a). The resonator is made from the bulk Ag substrate, an Ag layer of thickness $d_1$ and a transparent HfO$_2$ layer sandwiched in between, with thickness $t_1$. Note that even if we chose HfO$_2$ as a material for the resonator, any transparent layer in the visible can be used for this purpose. The optical indices of HfO$_2$ used in the RCWA simulations are taken from [32]. For different sizes of the HfO$_2$ layer, the spectral reflectivity at normal incidence of the structure is plotted in Fig. 4(b). It is observed that the presence of the resonator doesn’t impact the emissivity in the infrared, that stays large due to the textured SiO$_2$ layer. For short wavelengths, the reflectivity stays large except for absorption peaks in the visible. Therefore, the structure displays good properties for colored radiative cooling. In the following, an estimation of the color that can be obtained and the drop of radiative cooling power due to coloration will be estimated. To convert a reflection spectrum into an estimation of the color, we use the standard CIE model [39,40]. Using the three standard color matching functions $\bar {x}$, $\bar {y}$, $\bar {z}$, calculated spectral reflectivity of the structure $R(\lambda )$ and the standard D65 illumination $I(\lambda )$, the coordinates $X$, $Y$, $Z$ in the CIE color space are computed as
Fig. 4. (a): Proposed structured for colored radiative cooling: a resonator made of a thin HfO$_2$ layer sandwiched between the Ag substrate and a Ag thin layer is added to the structure. (b): Spectral reflectivity at normal incidence for different sizes of the HfO$_2$ layer $t_1$.
To get insights on the color appearance, the parameters in the XYZ space can be transposed in the Lab space using the relations
Quantitative description of the color such as the lightness $L$, the chroma $C=\sqrt {a^2+b^2}$ and the hue $h=\arctan \left ( \frac {b}{a} \right )$ can then be calculated. Eventually, the saturation $S$ can be calculated as
and is a quantitative description of the vividity of the color.In Fig. 5(a), the saturation of the color is represented as a function of the size of the HfO$_2$ layer thickness $t_1$, with the thickness of the Ag layer $d_1$ fixed at $30$ nm. Each circles are filled with the corresponding estimated color. It is observed that three saturated colors can be obtained, yellow, magenta and cyan, with magenta having the larger saturation peak, similarly as in [30]. Here, only three color can be obtained due to the narrowband nature of the absorption in the visible, only one on the primary color (red, blue and green) can be absorbed. The structure will therefore either reflect a mix of red and green (yellow), a combination of red and blue (magenta) or a combination of blue and green (cyan). In Fig. 5(b), the drop of radiative cooling power, defined as the ratio between the cooling power of the colored structure and the one of the conventional radiative cooler, is plotted. As expected, absorption peaks in the visible induce a drop in radiative cooling power due to solar absorption. When the colors are saturated, the radiative cooling power stabilizes to approximately one-third of its initial value. This means that despite solar absorption, the structure still display a positive value of radiative cooling power. In conclusion, our structure is well adapted for colored radiative cooling. Magenta, cyan and yellow can be obtained by keeping positive values of the radiative cooling power. Since the color palette obtainable is restraint, we propose in the next part to extend the principle of Fabry-Pérot interference to obtain new colors with multiple cavities.
Fig. 5. (a): Saturation of the color and estimated color of the structure as a function of the thickness of the HfO$_2$ layer $t_1$. (b): Decrease of radiative cooling power as a function of the thickness of the HfO$_2$ layer $t_1$.
As mentioned previously, with one absorption peak, only one primary color is absorbed by the structure. To obtain blue, red and green by reflection, it is necessary to absorb two primary colors and reflect only one. It was shown in [41,42] that multilayer structures containing several transparent layers sandwiched between thin metallic layers can produce multiple interference peaks. We demonstrate this effect in Fig. 6, where the spectral emissivity is plotted as a function of the thickness of the HfO$_2$ layers for a single resonator and a double one. For the double resonator, we consider though the whole study that the thicknesses of both HfO$_2$ layers are equal, such as $t_1=t_2$, and that $d_1=30$ nm. One can see that the addition of a resonator induces the apparition of a new interference peak. The spectral position of the peaks can be tuned by varying both the size of the transparent layers and the thin Ag layers. Varying the size of HfO$_2$ layers can move the positions of the absorption peaks, but not independently, as it can be observed in Fig. 7(a), where the spectral reflectivity of a structure with a double resonator is plotted for $d_1=d_2=30$ nm and several values of $t_1$. It is also possible to tune the relative position of the two peaks from each other by varying the size of the second silver layer $d_2$, as shown in Fig. 7(b). This means that the positions of the two peaks can be tuned independently which will allow to control the coloration of the structure by varying these two parameters.
Fig. 6. Spectral emissivity as a function of the thickness of the HfO$_2$ layer. (a): for a single resonator. (b): for two resonators. Here, the thickness of both silver thin layer are fixed at $30$ nm, and the thicknesses of both HfO$_2$ layers are equal ($t_1=t_2$)
Fig. 7. Spectral reflectivity of the double resonator structure. (a): For several values of $t_1=t_2$ and $d_1=d_2=30$ nm. (b): For $t_1=t_2=80$ nm, $d_1=30$ nm and several values of $d_2$.
By playing on the size of the various layers, we can obtain spectral absorption peaks that matches the different primary colors. For example, in Fig. 8(a), red color is obtained by absorbing blue and green color. In Fig. 8(b), blue color is obtained by absorbing green and red color. Eventually, green color can be obtained by absorbing blue and red color, as seen in Fig. 8(c). This demonstrate the ability of multiple resonator structures to tune the color over a large gamut.
Fig. 8. Spectral reflectivity of the structure with two resonators, and its color estimation, along with the three color matching functions corresponding to blue, red and green color. (a): production of red color by absorption of blue and green light, with $t_1=60$ nm and $d_2=33$ nm. (b): production of blue color by absorption of green and red light with $t_1=85$ nm and $d_2=50$ nm. (c): production of green color by absorption of blue and red light with $t_1=70$ nm and $d_2=10$ nm.
To illustrate this, we plot in Fig. 9(a) the chromaticity diagram of the CIE model. In the diagram, the black dots represent the color that can be obtained with a single resonator structure, by varying $t_1$. The white dots represent the three colors that have been obtained in Fig. 8. One can observe that the addition of a resonator extended the gamut of color that can be obtained. It is also worth noticing that various nuances of color can also be obtained, but not represented here. In Fig. 9(b), we schematized the different color that can be obtained, and also display the solar power absorption that is induced by the corresponding spectrum. Blue, red and green color, the primary ones, are at the corner of the triangle. Between them, mix of the colors, yellow, cyan and magenta, are displayed. One can notice that blue, red, and green color lead to a larger solar absorption than cyan, yellow and magenta, since they require two absorption peaks to occur. We recall that in Table 1, the net radiative cooling power between the structure and the sky can be as large as $187~\textrm {W}\textrm {m}^{-2}$, which means that even with blue, red and green color, the net radiative cooling power would still be positive, although rather small.
Fig. 9. (a): Chromaticity diagram. The black dots represent the coordinates of the color that can be obtained with a single resonator structure, when varying $t_1$. The white dots represent the color obtained in Fig. 8. (b): Schematic of the color that can be obtained with the resonating structures and their corresponding absorbed solar power.
In summary, the structure that we proposed, consisting of a thick textured SiO$_2$ surface on top of a Ag substrate displays good properties for radiative cooling. By using resonators consisting of HfO$_2$ layers sandwiched between thin Ag layers, it is possible to produce various colors. Despite a decrease of radiative cooling performances due to solar absorption, positive values of radiative cooling power are reached even with solar absorption.
4. Conclusions
We have presented a numerical study of radiative cooling for non-colored and colored surfaces. The convectional radiative cooler consists in a textured SiO$_2$ layer deposited on Ag substrate, which despite its simplicity, displays adequate optical properties for radiative cooling, with a radiative cooling power estimated up to $114~\textrm {W}\textrm {m}^{-2}$. One of the key element of the structure is surface texturation, that reduces reflection in the infrared region, especially in the restrahlen bands of SiO$_2$. For maximum efficiency, the texturation needs to be two-dimensional, to impact on both polarization of light and allow a strong emission in all directions. We have also shown that the proposed structure can be used for colored radiative cooling by adding resonators made of transparent HfO$_2$ sandwiched between Ag layers. The presence of resonators induce absorption peaks, whose spectral position can be tuned to overlap with the visible range, producing several colors. For a single resonator, three colors can be produced, cyan magenta and yellow, with decreased values of radiative cooling power compared to the conventional non-colored one. However, the values of radiative cooling power remains positive despite solar absorption. To obtain more colors, we have demonstrated that multiple resonators can be used and effectively produce blue, red and green color by using multiple absorption peaks. In conclusion, this work presented new insights on the design of efficient radiative cooler, as well as structural colors. This paves the way toward energy efficient colored surfaces, and can be used for various applications such as colored buildings, car paints, jewelry, clothing or other aesthetic objects.
Funding
Agence Nationale de la Recherche (ANR-17-CE06-0002-01); Programme d'aide à l'Accueil en Urgence des Scientifiques en Exil (PAUSE).
Acknowledgments
The authors acknowledge Lionel Simonot for fruitful discussions.
Disclosures
The authors declare no conflicts of interest.
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