Every object with finite temperature emits heat by thermal radiation. If an object radiates more energy than it absorbs from its surroundings, it loses energy and cools down. This phenomenon occurs generally at night when the object is not subject to solar irradiation, and forms a basis of nocturnal radiative cooling^1-3. However, it has been recently suggested that a material that reflects solar energy but radiates in an atmospheric window (wavelengths 8 μm<λ < 13 μm) can lose energy during the day ⁴. This observation has stimulated studies on diurnal radiative cooling, in which an object can cool down even under solar illumination without consuming external energy^5-9. Therefore, diurnal radiative cooling has been evaluated as an alternative cooling technology for future.

For efficient radiative cooling, two conditions should be satisfied. The absorptivity of the object should be near zero in the ultraviolet (UV) to near-infrared (NIR) range, and should radiate its energy with near-unity efficiency in the wavelengths at which electromagnetic radiation can be transmitted through the atmosphere (the “atmospheric window”). To meet those conditions, structured materials such as photonic crystals¹⁰, micro/nanoporous structures^11-17, multilayer^{18, 19}, and mixtures of dielectric particles^20-23 have been used for their ability to manipulate optical responses. However, the spectra of such media cannot be changed after fabrication. Therefore, many efforts have been devoted to find optical materials and structures that have switchable thermal characteristics.

An interesting example is the use of vanadium dioxide (VO₂). It is a phase change material that has an insulating phase at temperature T below the critical temperature T_c and metallic phase at T > T_c. The phase transition of VO₂ has been used to develop active emitters and absorbers^24-26, switchable polarization rotators²⁷, waveguides²⁸ and nanoantennas²⁹. T_c of pure VO₂ is 68 °C, but can be set to around room temperature by doping molybdenum, tungsten and/or strontium^30-37 and by growing VO₂ thin film on TiO₂ substrates^{38, 39}. This relatively low T_c of VO₂ encouraged the development of an active radiative cooler⁴⁰ based on the transmissive filter placed on a switchable emitter and a photonic-based thermostat⁴¹ consisting of repeated layers of VO₂ grown on TiO₂ film and zinc selenide. Such active thermal devices radiate only at T > T_c and thus lose their thermal energies as temperature increases while maintaining temperature similar to ambient as temperature decreases. Here, we develop a switchable radiative cooler by combining two parts: an emitter that uses doped VO₂, and a solar reflector that has optimized one-dimensional multi-stacked photonic crystals. The emitter part is designed to selectively radiate in the atmospheric window whereas the solar reflector blocks solar irradiance in UV to NIR regime. Thus, the cooler exhibits positive cooling power at T > T_c and negative cooling power at T < T_c. Therefore, it maintains a moderate temperature that is resilient to environmental changes. Simulation using a diurnal cycle of outdoor temperature and solar radiation proved that the radiative cooler is capable of switchable diurnal radiative cooling. In comparison to other static radiative cooler, the switchable radiative cooler exhibits minimal variation of temperature, and is therefore useful in various applications including air conditioning and heating.

The optical behavior of VO₂ can be described as Fig. 1(a). In the infrared range, VO₂ responses as a metal well above T_c and as an insulator well below T_c. To avoid an unphysical result, we assume that the permittivity of VO₂ changes continuously and smoothly in a narrow transition range [T_c − Δ T, T_c + ΔT]. Thus, the permittivity of VO₂ is modelled individually in three distinct regimes: insulating, transition and metallic regime (Fig. 1(a)). For insulating and metallic regime, we use permittivities of doped VO₂ presented in ref.⁴⁰. In the transition regime, we assume that permittivity changes as an arctan function (Fig. 1(b)):

${\textit{ε}}_{\rm{transition}}={\rm{arctan}} \left(\frac{T-T_{{\rm{c}}}}{{\rm{Δ}} T} \times 10\right) \times \frac{{\textit{ε}}_{\mathrm{\rm{m}}}-{\textit{ε}}_{\mathrm{\rm{i}}}}{2 {\rm{arctan}} 10}+\frac{{\textit{ε}}_{\mathrm{\rm{m}}}+{\textit{ε}}_{\mathrm{\rm{i}}}}{2}\;, $ (1)

where ε_m and ε_i are permittivity in the metallic and insulating phase, respectively. Throughout this paper, we set T_c = 298 K and ΔT = 2 K. In the transition regime, both the real and imaginary parts of ε_transition change smoothly (Figs. 1(c) and 1(d)).

To minimize the absorption of solar irradiance and maximize thermal energy radiated through the atmospheric window in a switchable way, we combine an emitter and a solar reflector separated by a spacer (Fig. 2) on a SiO₂ substrate. The emitter part is composed of stacked layers of silver (200 nm), silicon (700 nm) and VO₂ (10 nm) from bottom to top. A 300 nm-thick spacer made of poly(methyl methacrylate) (PMMA) is deposited on the emitter. The top of the spacer is the solar reflector consisting of three stacked photonic crystals. Each photonic crystal (PC_i) is a distributed Bragg reflector (DBR) that is designed to suppress absorption at a target wavelength λ_i where λ₁ = 0.52 μm, λ₂ = 0.76 μm and λ₃ = 1.18 μm. Thickness of each layer is set as λ_i/4n following the design rule of DBRs⁴².

The transfer-matrix method was used to calculate the absorptivity and reflectivity spectra⁴³. We examine absorptivity and reflectivity of the emitter part and solar reflector part individually. The emitter works as a metal-insulator-metal structure at T > T_c. The Fabry-Pérot resonance due to the cavity results in high absorptivity near the atmospheric window (Fig. 3(a)). In contrast, the emitter behaves as an insulator deposited on a metal and mostly reflects at T < T_c (Fig. 3(b)). Therefore, the emitter performs the switching of radiation in the atmospheric window. Meanwhile, the solar reflector reflects solar irradiance in the UV to NIR range (Fig. 3(c)). The high reflectivity of the solar reflector originates from the optimization of photonic crystal structures. The average absorptivity of the solar reflector at λ < 2 μm is 5.9 %. The combined structure of emitter separated by a spacer from the solar reflector has low absorption in UV to NIR and switchable absorption in the atmospheric window simultaneously. Absorptivity in UV to NIR is low in both metallic and insulating phases; the combined structure absorbs 7.6 % in average. In contrast, absorptivity in the atmospheric window are remarkably distinct in two phases. The absorptivity is high in the metallic phase, but low in the insulating phase ( Figs. 3(d) and 3(e)). Average absorptivity is 78 % in the metallic phase and 18 % in the insulating phase. At oblique incidence, the absorptivity remains high in the atmospheric window (Fig. 3(f)).

To evaluate the cooling flux, we consider blackbody radiation, solar irradiance, thermal exchange with atmosphere, and two other heat exchange channels⁴:

$ $$\begin{array}{rl}P\left(T\right)=& P_{\mathrm{r}\mathrm{a}\mathrm{d}}(T)-P_{\mathrm{s}\mathrm{u}\mathrm{n}}\\ & -P_{\mathrm{a}\mathrm{t}\mathrm{m}}\left(T_{\mathrm{a}\mathrm{m}\mathrm{b}}\right)-P_{\mathrm{c}\mathrm{c}}(T,T_{\mathrm{a}\mathrm{m}\mathrm{b}}),\end{array}$$ $ (2)

where T is the temperature of the switchable radiative cooler, T_amb is ambient temperature, and P_rad (T) corresponds to radiation flux emitted by the cooler:

$ P_{\rm{rad}}(T)=\iint_{0}^{\infty} I_{\rm{BB}}(T, \lambda) E(T, \lambda, \theta) {\rm{d}} \lambda {\rm{cos}} \theta {\rm{d}} \Omega\;, $ (3)

where λ is the wavelength, θ is the polar angle, and $\int {\rm{d}} \Omega = 2{\rm{π}} \int_0^{\rm{π} /2} {\sin } \theta {\rm{d}}\theta$ is the angular integral over a hemisphere. E is the emissivity of the cooler and is equal to the absorptivity according to Kirchhoff's law⁴⁴. Since E of VO₂ depends on its temperature, we use E(T, λ, θ) instead of E(λ, θ).

$ I_{\rm{BB}}(T, \lambda)=\frac{2 {\rm{hc}}^{2}}{\lambda^{5}} \frac{1}{{\rm{e}}^{{\rm{hc}} /\left(\lambda k_{\rm{B}} T\right)}-1}\;, $ (4)

is the spectral radiance density of a blackbody at temperature T, where h is Planck constant, c is the speed of light in free space, and k_B is the Boltzmann constant. The second term represents absorbed thermal flux due to solar irradiance:

$ P_{\rm{sun}}=\int_{0}^{\infty} E(T, \lambda) I_{\rm{AM} 1.5}\left(\lambda\right) {\rm{d}} \lambda\;, $ (5)

where I_AM1.5 is the AM1.5 spectrum of the solar illumination. Thermal flux absorbed by the atmospheric heat exchange is

$$$\begin{array}{rl}{P}_{\mathrm{a}\mathrm{t}\mathrm{m}}\left(T_{\mathrm{a}\mathrm{m}\mathrm{b}}\right)=& {\iint }_0^{\mathrm{\infty }}{I}_{\mathrm{B}\mathrm{B}}(T_{\mathrm{a}\mathrm{m}\mathrm{b}},\lambda )E(T,\lambda ,\theta )\\ & \cdot E_{\mathrm{a}\mathrm{t}\mathrm{m}}(\lambda ,\theta )\mathrm{d}\lambda \cos \theta \mathrm{d}\mathrm{\Omega },\end{array}$$$ (6)

where E_atm = 1−t(λ)^1/cosθ is the emissivity of the atmosphere where t(λ) is the transmittance of the atmosphere in the zenith direction^{1, 45}. The last term is associated with conduction and convection given as

$ P_{\rm{cc}}\left(T, T_{\rm{amb}}\right)=h_{\rm{cc}}\left(T_{\rm{amb}}-T\right) \;,$ (7)

where h_cc is the heat transfer coefficient due to conduction and convection. We use h_cc = 6.9 Wm⁻²K⁻¹ throughout the calculations.

The cooling flux P(T) under normal incidence of solar energy is calculated using Eq. (2) to (7). For simplification, we first treat E as a temperature-independent value. We calculate the cooling flux of the cooler by assuming that VO₂ is either metallic or insulating regardless of temperature (Fig. 4(a)). When VO₂ is assumed to be metallic, it has positive cooling flux above T = 297.8 K and negative cooling flux below it. As expected, the cooling flux when VO₂ is insulating is lower than that when it is metallic. The cooling flux is zero at T = 306 K for the insulating case.

In reality, E of VO₂ varies with T and thus, E should be treated as a function of temperature. Cooling flux is expected to be equal to that of metallic case at T > T_c + ΔT and to that of insulating case at T < T_c − ΔT. In the vicinity of T_c, it is assumed to change continuously and smoothly. We use Eq. (1) to calculate emissivity of the radiative cooler, then obtain the cooling flux in the transition regime when T_amb = 303 K (Fig. 4(b)). The cooling flux varies by amount of more than 100 Wm⁻² across the transition regime. In the atmospheric window, the cooler radiates approximately P_rad = 179 Wm⁻² when the cooling is turned on (T = T_c + ΔT) and P_rad = 47 Wm⁻² when the cooling is turned off (T = T_c − ΔT). The switchable radiative cooler is in thermal equilibrium at T = 298.3 K, which corresponds to room temperature.

To confirm the cooling visually, we calculate how temperature of the switchable radiative cooler changes over time. Temperature variation obeys the thermal balance equation:

$ C \frac{{\rm{d}} T}{{\rm{d}} t}=A P\left(T, T_{\rm{amb}}\right)\;, $ (8)

where A is the area of the cooling surface, and t is time. C is the heat capacitance, which can be obtained by summing the heat capacitances of all layers as

$ C=A \sum\limits_{j} c_{j} \rho_{j} t_{j}+C_{0}\;, $ (9)

where c_j, ρ_j and t_j is the specific heat, density and thickness of j-th layer, respectively. The summation applies to layers shown in Fig. 2 and a substrate of 500 μm-thick silicon dioxide (SiO₂). The specific heat and density (Table 1) are obtained from ref.^{46, 47} for PMMA, ref.^{48, 49} for silicon, ref.^{48, 50} for silver, ref.^{48, 51} for SiO₂, and ref.^{52, 53} for VO₂. Strictly, specific heat of VO₂ depends on its temperature, but we use the specific heat at room temperature because the variation range is small (< 3 Jg⁻¹K⁻¹). To test the cooling ability, we additionally include C₀ = 1.325×10⁵ JK⁻¹ as the heat capacitance of an object to be cooled; it corresponds to a block of SiO₂ of unit area and 0.05 m thickness.

We simulate temperature variation in time under T_amb = 303 K by using Eq. (2) and Eq. (9). For various initial temperature ranging from 280 K to 320 K, temperature converges to 298.3 K (Fig. 5(a)). It shows that the cooler is turned on at T > 298.3 K but turned off at T < 298.3 K. The switchable cooling is also confirmed by cooling flux which is positive at T > 298.3 K and negative at T < 298.3 K ( Fig. 5(b)). The thermal equilibrium temperature can be tuned by designing the solar reflector part. Therefore, the switchable radiative cooler provides a pathway to constantly control the temperature at a desired value.

The practicality of the switchable radiative cooler is assessed by simulating a cycle of temperature during a day. To emulate the outdoor condition, we use ambient temperature and solar irradiance I measured on July 15, 2018 in Pohang, Korea by the Korea Meteorological Administration⁵⁴ (Fig. 5(c)). Initial temperature of the switchable radiative cooler is set equal to that of ambient. During the whole day, the cooler has T < T_amb, with the maximum decrement of 8.5 K (Fig. 5(d)). For comparison, we also plot the temperature of the radiative cooler when the cooling is turned on and off at all temperature. In all cases, temperature gets lower before 6 am when the sun rises. When the cooling is turned off, temperature increases as time passes until it reaches the equilibrium and then decreases again after the sunset. On the other hand, when the cooling is turned on, temperature decreases by approximately 10 K as a result of high cooling power. Temperature variation during a day exceeds 10 K in both cases. In contrast, the switchable radiative cooler shows a minimal change of temperature, resilient to the surrounding environment.

In conclusion, we present a switchable radiative cooler made of doped vanadium dioxide. The cooler emits energy in the atmospheric window only above room temperature as a result of Fabry-Pérot resonance. Thus, the cooling is conditionally turned on and off depending on the temperature. We demonstrate the switchable radiative cooling by calculating cooling flux for various temperature ranges. The switchable cooling is further supported by simulating a cycle of temperature for a day using the measured temperature and solar irradiance data. We confirm that the cooler can maintain its temperature robustly under natural weather conditions. To further improve the cooling effect of the switchable diurnal radiative cooler, the design can be optimized to have unity (zero) reflectivity in the UV to NIR range and emissivity in the atmospheric window at T > T_c (at T < T_c) or to have the highest cooling flux by various optimization methods and machine learning^55-57. The switchable radiative cooler will facilitate self-adaptive control of thermal energy and can be implemented in a variety of applications such as passive cooling in environmentally-benign buildings and vehicles.