Efficient realization of daytime radiative cooling with hollow zigzag SiO2 metamaterials∗

Huawei Yao(姚华伟) Xiaoxia Wang(王晓霞) Huaiyuan Yin(殷怀远) Yuanlin Jia(贾渊琳) Yong Gao(高勇)Junqiao Wang(王俊俏) and Chunzhen Fan(范春珍)

1School of Physics and Microelectronics,Zhengzhou University,Zhengzhou 450001,China

2Department of Physics,Shanghai Polytechnic University,Shanghai 201209,China

Keywords: daytime radiative cooling,hollow zigzag metamaterials,net cooling power,emissivity

1. Introduction

With the increasing demands of modern refrigeration,the corresponding emission of greenhouse gases poses a threat to people’s lives, especially from traditional refrigeration methods such as air conditioners which consume a lot of electric energy and generate net heat, which further aggravates CO2emission and increases temperatures.It is becoming extremely urgent to find an effective method to reduce temperatures and energy consumption. Recently,the passive cooling technique has aroused widespread interest, which can reduce the target object temperature below the ambient one without any energy consumption.It is regarded as an alternative way to achieve effective cooling,in which refers to reflecting the sunlight in the solar spectrum and pumping heat from objects to cold outer space via the atmospheric window.[1–3]Catalanottiet al.realized a selective surface at the atmospheric window and demonstrated practical cooling during nighttime operation in 1975.[4]Since then, nighttime coolers have been extensively studied and improved cooling performances were reported.[5–10]However, to achieve selective radiation in daytime, the radiative cooler needs to have approximately unit reflection at the solar spectrum and high emission at the atmospheric window while considering the non-radiative condition.[11,12]

In order to meet the necessary requirements,a multilayer structure,[13]a photonic metamaterials structure[14–18]and a random particle structure[19,20]were proposed to achieve daytime cooling. Rephaeliet al.achieved a metal–dielectric photonic structure to get high-performance daytime radiative cooling.[21]Ramanet al.proposed a seven alternating layers of SiO2and HfO2on the top of Ag layer which had a reflectivity of 97%. They experimentally verified 4.9◦C of cooling temperature under direct sunlight in 2014.[22]Chenet al.proposed a three-layer radiator with silicon nitride, amorphous silicon and aluminum,which achieved an average temperature reduction of 37◦C by eliminating parasitic thermal load.[23]Kecebaset al.investigated a similar periodic radiator with a seven-layer structure and replaced the top layer with Al2O3to improve the net cooling power.[24]Jeonget al.put forward a structure with eight alternating layers of SiO2and TiO2, and the average emissivity was 84% in the atmospheric window.[25]The combination of polymer layers such as PDMS,[26]PMMA[27]and PTFE[28]has also been tested for daytime radiative cooling. Photonic metamaterials could prevent high solar absorption in the solar spectrum with a large emissivity in the atmospheric window. Wuet al.designed a two-dimensional antenna composed of a low loss alternating Al2O3and SiO2multi-layer structure, which possessed both selective MIR emissivity and low solar absorption.[29]Zhuet al.proposed a micro photonic design consisting of a twodimensional silica pyramid array and a 100µm-thick uniform silica layer atop the bare solar cell.[30]Jeonget al.presented a periodic multilayer structure based on PDMS, which verified that patterned metamaterials could obtain high emission.[31]Gentleet al.reported that embedded microparticles into polymer could also achieve a radiative cooling effect in 2010.[32]In the subsequent research,random SiO2or TiO2microparticles in a polymer layer exhibited superior performance for daytime radiative cooling with high emissivity in the atmospheric window and low absorptivity in the solar spectrum region.[33–35]Although much progress had been achieved in the previous works, it is still difficult to realize ideal broadband selective absorption in the atmospheric window with a simple inorganic radiative cooler.Thus,it is necessary to design photonic metamaterials to improve their emissivity and maintain high reflectivity.

In this study, we have proposed a novel metamaterial to achieve a broadband absorption spectrum,which incorporates a patterned SiO2layer and Si3N4and Ag layers. The radiative cooler exhibits an average reflection of 92.0%in the solar spectral region and an average emissivity of 98.7% in the atmospheric window simultaneously. The electric field distributions at the resonant peak positions are carefully examined to figure out the origin of the high emissivity. Tunable average emissivity of our proposed structure is explored in detail with different geometric parameters and incident angles. Finally,cooling performance in the steady and transient state is examined respectively and its cooling ability persists when considering non-radiative heat exchange.

2. Model and method

2.1. Model design

Figure 1(a) depicts the three-dimensional configuration of our designed radiative cooler, which consists of hollow zigzag SiO2metamaterials deposited on Si3N4and silver substrate. The Si3N4and SiO2has extremely low loss in the solar spectrum and a strong absorption peak in the atmospheric window,[36]serving as the absorptive segments. The hollow zigzag structure with a gradual refractive index is designed to improve the anti-reflection performance of the proposed model. Figure 1(b) is the cross-section view of the metamaterials and the geometric parameters are clearly indicated.The periodicity is taken as 7 µm along thexdirection. The inner and outer heights of hollow SiO2areh2=2.6 µm andh1=3µm. The inner and outer widths of the patterned SiO2arew2=3.5 µm andw1=7 µm. The tilted angle off thexaxis is taken asθ. Here it is set as 63◦. The thicknesses of the Si3N4and Ag films areh3=0.8µm andh4=0.2µm,respectively. The absorption spectra and field distribution are numerically investigated with the finite difference time domain method. The incident plane electromagnetic wave is in thezdirection and the electric field polarization is alongxdirection. A perfectly matched layer (PML) is set surrounding the unit cell in thezdirection. The periodic boundary condition is applied along thexandydirections. The mesh size of each layer is 20 nm in thezdirection and 50 nm in thexandydirections. The refractive index of Si3N4and SiO2are obtained from the reference data.[37,38]The dielectric properties of the silver film are taken from Ref. [38]. With the solutions of Maxwell’s equations on electromagnetic waves,we can finally obtain the optical spectrum. To obtain our designed metamaterials in the lab, silicon can be employed as the substrate of the radiative cooler and it does not influence the optical properties of the upper structure. The silver layer was firstly deposited on the silicon wafer by using dc magnetron sputtering, and then layers of Si3N4and SiO2were deposited.[39]After that, an array of grooves on the top of the SiO2layer could be fabricated with lithography and the inductively coupled plasma reactive ion etching method.[40]A sacrificial layer was deposited on the silica layer to obtain the triangular prism patterns through the lithography and wetetching process.[41]Then, a SiO2layer was deposited on the triangular prism patterns and the sacrificial layer etched away with a specific solution to get the hollow zigzag SiO2metamaterials.

Fig. 1. Schematic diagram of thermal metamaterials. (a) 3D illustration.(b)Crosssection view. Parameters: h1 =3µm,h2 =2.6µm,h3 =0.8µm,h4=0.2µm,w1=7µm,w2=3.5µm,θ =63◦.

2.2. Radiative cooling power

In order to evaluate the cooling performance of the thermal emitter, it is necessary to obtain its net cooling power(Pnet). Usually, it is determined by four factors in the daytime environment. Namely, the infrared radiation of radiative cooler,solar irradiance,atmospheric thermal radiation and non-radiative radiation. The net radiative cooling powerPnetis defined as[42]

Pcond+convis the power absorbed by conduction and convection

HereTambis the ambient temperature,Tis the radiator surface temperature.IB=(2hc2/λ5)/[ehc/kBT −1]stands for the blackbody radiation andεatm(λ,θ)=1−t(λ)1/cos(θ)is the angular atmospheric emissivity.h,c,kB, andhcindicate the Planck constant,the speed of light,Boltzmann’s constant,and the heat transfer coefficient,respectively.ε(λ,θ)is the emissivity of the film andAis the surface area of the radiative cooler. According to Kirchhoff’s law, the absorptivity of an object is equivalent to emissivity in a thermodynamic equilibrium state. The mean solar reflectivity and emissivity can be obtained with the integral formula.[43]The column water vapor is assumed to be 1.0 mm and the air mass is 1.0 in this calculation. The global AM1.5 solar spectrum in Eq. (4) is

987 W·m−2of direct normal irradiance.[44]The ambient temperature is taken as 300 K in our analysis.

3. Results and discussion

The absorption spectra of our designed radiative cooler as a function of the incident wavelength from 0.3 µm to 15 µm is shown in Fig. 2. It can be clearly observed that the proposed structure can simultaneously achieve high reflection in the solar band and high emission in the atmospheric window.In addition, the average emissivity is as high as 98.7% near the atmospheric window,which enables the structure to radiative cool maximally. Yellow and cyan colored spectra indicate AM1.5 solar power density and atmospheric transmittance in the atmospheric transparency window for reference. It illustrates that the radiative cooler has a broad near-unit absorptivity region in the atmospheric window embodying high performance for daytime radiative cooling.

Fig.3. (a)The absorption spectra of the thermal metamaterial with the resonant positions are marked with I,II,III,IV,and V.(b)The electric field distributions at(I)8.1µm,(II)8.7µm,(III)9.3µm,(IV)10.0µm,(V)11.1µm. Parameters: w1=7µm,θ =63◦,h2=2.6µm.

Fig.2. Absorptivity of the hollow zigzag SiO2 thermal metamaterials in the wavelength from 0.3µm to 15µm. Parameters: w1 =7µm,h2 =2.6µm,θ =63◦. Emissivity curve of the radiative cooler (red), the scaled AM1.5 solar spectrum(yellow)and the atmospheric absorption spectrum(cyan)are plotted for reference.

To fully explore the physical origin of the high absorption in the atmospheric window,the resonant positions are marked in the absorptivity spectrum in Fig.3(a). It is clearly found the minimum absorptivity is still around 0.95 in the atmospheric window. The electric field distribution at resonant positions of 8.1µm,8.7µm,9.3µm,10.0µm and 11.1µm are illustrated in Fig.3(b)(I–V). The electric field mainly focuses on the top of the hollow zigzag structure at 8.1µm in Fig.3(I).It moves to the lateral sides of the hollow zigzag structure in the lower position as shown in Fig. 3(II). The electric field is confined around the two lateral regions in Fig. 3(III) at the resonant peak 10.0µm. However,it penetrates the cavity in Fig.3(IV).At a larger resonant wavelength of 11.1µm,the electric field intensity in the cavity gradually decreases. The intensity at resonant peak position V is less than that of(I,II,III and IV),indicating that the hollow zigzag structure plays a major role in the overall enhanced absorption. The graded refractive index(moth eye effects) can be employed to explain the high absorptivity in the atmospheric window.[29]The hollow zigzag structure can be viewed as an infinite number of thin layers.The index of each thin layer is lower than the lower adjacent layer when the groove width of the air decreases. Thus, the effective refractive index of the material changes continuously along the depth direction and a multilayer antireflective constitution occurs.[45–48]The imaginary part of the dielectric constant in Si3N4and SiO2is extremely low in the solar region.Therefore, the reflectivity is not affected by the thickness of SiO2.

Fig.4. (a)Absorptivity with different depths h2. (b)The emissivity in relation with different depths. (c)Net cooling power with different depths.Parameters: w1 =7 µm, θ =63◦. (d) Absorptivity with different angles θ. (e) The emissivity with different angle θ. (f) Net cooling power in relation with different angles θ. Parameters: w1=7µm,h2=2.6µm. (g)Absorptivity with different widths w1. (h)The emissivity with different widths w1. (i)Net cooling power with different widths w1. Parameters: h2=2.6µm,θ =63◦. The ambient temperature is 300 K.

Figure 4 presents the absorptivity in our designed metamaterials with different geometric parameters. Here the structure width is taken as 7 µm andθ=63◦. With the increase ofh2from 2.0 µm to 2.4 µm, the absorption spectrums shift to the high frequency region. To better reflect the tendency of the absorptivity, the average emissivity with different depths is shown in Fig. 4(b). With a largerh2, the average emissivity first increases and then decreases. It reaches a maximum value at 2.6 µm. The relevant net cooling power at different depths is shown in Fig. 4(c). The trend of cooling power is consistent with the average emissivity and reaches the highest value of 100.6 W·m−2at 2.6µm. The dependence of the absorption spectrum with differentθis shown in Fig.4(d). The absorptivity is above 92% in the atmospheric window. With a larger angle, the enhanced electric field around the edges is no longer the same. The electric field inside the cavity varies as well. Therefore, the absorptivity no longer overlaps in the wavelength ranging from 8µm to 13µm.To clearly reveal the influence of the angleθ,the average emissivity with differentθis illustrated in Fig.4(e). The average emissivity increases from 50◦to 63◦and then decreases from 63◦to 70◦with an angle interval of 2◦. The average emissivity and cooling power of the absorber are closely related to the widthw1in Fig.4(g).Whenw1is taken from 3µm to 7µm,the emissivity is getting larger in Fig. 4(h). The net cooling power with differentw1follows the same trend in Fig.4(i). Whenw1is getting larger,the emissivity increases as well. Therefore,the optical geometry parameters can be obtained to get the desired emissivity in the atmospheric transparency window.

It should be pointed out that the tunable emissivity can be achieved with different incident angle. Thus,the effect of incident angle on emissivity is taken into consideration in Fig.5.This is more in line with the fact that the position of the sun changes every day. The high average emissivity is approaching 1.0 and it keeps as a constant between 0◦and 30◦. When the incident angle exceeds 60◦, the average emissivity drops gradually. However, the average emissivity remains above 0.83. Namely,the emissivity can persist above 0.83 for angles of incidence less than 80◦. Our results demonstrate that the proposed emitter can absorb the energy of incident wave almost perfectly with incident angle smaller than 80◦,embodying excellent radiation performance in the atmospheric transparency window.

Fig.5.Emissivity as a function of various incident angles in the atmospheric transparency window.

The net cooling power of our proposed structure as a function of emitter surface temperatureTis demonstrated in Fig. 6. The influence of parasitic convection and conduction are in the absence (red curve). The net cooling power of the radiative cooler is 100.6 W·m−2at the ambient temperature 300 K, which is due to its near-ideal emissivity and excellent heat dissipation performance in the atmospheric window. Moreover, the radiative cooler can reach an extremely low equilibrium temperature at 257 K. The influence of the non-radiative heat exchange coefficients is also taken into consideration. Here the coefficient is taken ashc= 3, 6,9(W·m−2·K−1). With the increasedhc,the cooling power decreases rapidly when it is lower than the ambient temperature.Especially,the cooling effect persists even with a largerhc.

Fig.6. The net cooling power of the proposed cooler with different hc.

The net cooling power of the proposed cooler with different non-radiative heat exchange coefficients in Fig.6 represents a steady-state process. However,the transient process of the radiative cooler under ambient temperature conditions is demonstrated in Fig.7,which can be obtained by solving the differential equation[49]

whereCcoolerrepresents the heat capacitance and determined from the sum rule of multilayer design. The initial temperatures of the radiative cooler and ambient temperature are taken as the same. Herehcis set as 6 W·m−2·K−1. The temperature variation of the radiative cooler as a function of time at different ambient temperatures is shown in Fig. 7(a). When the ambient temperature is 280 K,the cooling capacity of the radiative cooler is very limited. With the increase of the ambient temperature to 300 K,the cooling capacity of the radiative cooler increases to a value of 13◦C. An obvious drop of the temperature is found when the ambient temperature is 320 K.It indicates that the surface temperature of the radiant cooler finally decreases to 287 K,verifying the cooling ability of our designed cooler. Considering the transient process,the radiative cooling power versus time is considered in Fig. 7(b). It verifies that our designed emitter has excellent cooling performance. Meanwhile, the net radiative cooling power (Pnet)shown with the blue line and radiative power(Prad)in red gradually decrease with time. When the equilibrium process is approached, the net radiative cooling power becomes 0 and the radiative power is 165 W·m−2,which is employed to eliminate the non-radiative radiation and the absorbed sun power.

Fig.7. Temperature evolution of the radiative cooler versus time at 280 K,300 K and 320 K ambient temperature. (b) Prad and Pnet of the radiative cooler versus time under 300 K ambient temperature.

4. Conclusions

In summary, we have numerically described and investigated the emission properties of hollow zigzag SiO2metamaterials to achieve efficient daytime radiative cooling. A broadband absorption in the atmospheric window and a high reflectivity in the solar spectral can be simultaneously achieved.It can be analyzed with electric distribution and it originates from the graded refractive index of the hollow zigzag structure. The effects of the structure widthw1, the depth of the grooveh2, the degree of zigzagθand incident angle on the absorptivity are fully analyzed. Moreover,tunable ideal emissivity can be maintained at large angles, which is a desirable feature in maximizing the cooling power. The hollow zigzag SiO2metamaterial structure can achieve 100.6 W·m−2and a drop of 13◦C for daytime cooling. When non-radiative exchange is considered, the proposed radiative cooler can still achieve effective cooling. Therefore, the designed structure not only provides potential applications in the radiative cooling system of buildings, solar cells and sensors, but also provides an insight into designing radiative coolers and related photonic structures.