Radiative sky cooling: fundamental physics, materials, structures, and applications

2.1 Thermal radiation fundamentals

Thermal radiation fundamentally arises from random energy level transitions in matter. For any object with finite temperature, energy transfer is thus realized by the resulting emission of energy in the form of electromagnetic waves, which consist of finite quanta of energy, or photons. Based on these considerations, the temperature-dependent emission is given by Planck’s law of blackbody radiation [29]:

where I_BB is the spectral irradiance per unit area per unit wavelength, h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, and T denotes the temperature in K. By integrating the spectral irradiance over area and the whole wavelength range, it can be found that the total emitted power is proportional to the fourth power of the emitter temperature, as described by the Stefan-Boltzmann law:

where P is the total emissive power, A is the surface area of the emitting object, σ is the Stefan-Boltzmann constant, and ε=∫0∞ dλIBB∫0π/2d(sin2θ)ε(θ, λ)/∫0∞ dλIBB denotes the averaged emittance of the object. Note that ε(θ, λ) is an angular and spectral dependent parameter as discussed in [1], [2], [17]. For an ideal blackbody emitter, ε=1 for all angles and wavelengths. On a related note, Kirchhoff’s law states that for arbitrary matter absorbing and emitting thermal radiation under thermal equilibrium, its emittance is equal to its absorptance. Recently, a more generalized form of Kirchhoff’s law has been derived by Greffet et al. [30] that extends to any finite size object, including those with temperature variations across their surface. Hence, the emittance of an object is generally considered equivalent to the absorptance, which helps derive the atmospheric transmittance from the atmospheric emittance.

2.2 Tropospheric temperature and atmospheric transmittance

The temperature of the cosmic microwave background radiation is around 3 K [31], while the sun is approximately a blackbody at an effective surface temperature closer to 5800 K. This enormous temperature difference, combined with heat transfer in the upper atmosphere, gives rise to a complex, altitude-dependent temperature profile [32], featuring a tropospheric temperature of about 50 K below standard room temperature (300 K) [2], which can serve as a potential radiative heat sink for ground level cooling. The exact cooling strongly depends on geographic location and climate, thus requiring a detailed calculation [33]. For simplicity, we will focus on ground level cooling. Exchange with the troposphere on the ground is limited by the atmospheric absorption spectrum [2], [27], [28], [34], [35], [36], [37], [38], which features a strong water vapor absorption band centered around 6 μm and beyond 20 μm, as well as a carbon dioxide absorption band that peaks around 15 μm. These absorption bands leave behind an atmospheric transmission window from 8 to 13 μm. Equivalently, if we assume that the entire atmosphere is radiating at ambient temperatures (~300 K), the effective transmittance within the atmospheric window is far above zero, as depicted in Figure 1. Furthermore, the atmospheric emittance is not only wavelength dependent, but also zenith angle dependent, as expressed by the following equation [2]:

Figure 1:

The atmospheric transmittance spectrum at zenith angles of 0°, 60°, and 75°; it is highest in the 8–13 μm transparency window. Results are adapted from [2].

Here ε_a(θ, λ) denotes the atmospheric emittance at any arbitrary zenith angle θ, based on Kirchhoff’s law, equal to the atmospheric absorptance as well. On the other hand, because water vapor absorption dominates the atmospheric absorptance within the atmospheric window, the transparency of the sky is quite sensitive to precipitable water vapor concentration, which is correlated with relative humidity (RH) and ground temperature [39], [40], and thus varies geographically. Its influence is illustrated in Figure 2: higher precipitable water vapor concentration leads to stronger absorption within the atmospheric window. Similarly, the atmospheric window dependence on RH was demonstrated in [41] by modeling transmittance characteristics during the summer solstice at two locations. The atmospheric transmittance within the 8–13 μm spectral window is higher in Perth than in Brisbane despite the close ambient temperatures, due to lower water vapor concentration in Perth than in Brisbane as reflected by the mean RH. In short, atmospheric transmission varies with geography in a well-understood manner.

Figure 2:

The computed atmospheric transmittance spectrum, computed using the Lowtran model. The temperature of the lowest kilometer of atmosphere is assumed to be 21°C, the ozone content assumed to be 0.35 atm·cm, and aerosols are of urban type with a 23 km visual range. Different precipitable water vapor levels are shown as red, green, and blue curves in the figure. These results have been adapted and replotted from [2].

2.3 Principle of cooling

Developing radiative coolers for various applications requires rigorous engineering and design. In this subsection, we review the physics of radiative cooling by the steady-state energy balance equation and summarize the design considerations for radiative coolers.

When a radiative cooler of surface area A is exposed to the sky, the cooling power P_cool here is the net outgoing radiative energy flux, which is given by

where Prad(T)=A ∫​ dΩcosθ ∫0∞ dλIBB(T, λ)ε(λ, θ) is the thermal emission of the radiative cooler with operating temperature of T, and ∫​ dΩcosθ is the integration of the solid angle over the hemisphere. The atmospheric radiation at a temperature T_amb is given by Patm= A ∫​ dΩcosθ ∫0∞ dλIBB(Tamb, λ)ε(λ, θ)εatm(λ, θ),  where ε_atm(λ, θ) denotes the spectral and angular atmospheric emittance that can be calculated by Eq. (3). Balanced with other energy fluxes (e.g. incident solar power, convective, and conductive heat transfer), the maximum cooling power determines the lowest temperature achievable. Initially, nighttime radiative cooling appeared much more promising thanks to the absence of solar irradiance, and constituted the focus of the early work [42], [43], [44], [45], [46]. Enabled by recent advances in photonic design, daytime radiative cooling below ambient temperature has been demonstrated by Rephaeli et al. [16]. Such a cooling structure is engineered to be spectrally selective: (1) highly emissive between 8 and 13 μm to maximize P_rad(T); (2) weakly emissive outside the atmospheric window to reduce parasitic radiation P_rad(T_amb); (3) either highly reflective or transparent in the solar spectrum to suppress sunlight absorption.

When designing a practical, efficient radiative cooling system, one must also consider other heat transfer pathways. Generally, the net power of the cooling system P_net is defined as

where P_cool denotes the radiative cooling power, P_abs.sun is the total absorbed solar power only relevant for daytime applications, and P_{non−radiative} corresponds to non-radiative heat transfer (i.e. convection and conduction). According to (5), solar absorption and non-radiative heat transfer act as parasitic cooling losses, thereby reducing the overall cooling efficiency and increasing the cooling time to reach thermal equilibrium. Remarkably, it has been experimentally demonstrated that significant temperature reduction up to 40 K below ambient has been reached by radiative cooling within 1 h [47]. For systems with greater heat loads (e.g. CPV and TPV), it is also expected that the temperature will quickly reach steady state due to significant heating, for example, temperature varies instantaneously with solar irradiance in [48]; in such cases, radiative cooling can still serve as a complementary passive cooling method to reduce overall system temperature. By eliminating those parasitic heat transfers, the lowest temperature achievable by radiative cooling is essentially the tropospheric temperature, which is ~50 K below ambient. Indeed, Chen et al. [47] have demonstrated a sub-freezing radiative cooling system with considerably reduced parasitic heat transfer (e.g. no convection in the vacuum chamber and Sun shade to block solar irradiance). The lowest temperature measured is 42 K below ambient, far lower than the previous under-optimized experimental demonstration [17].

2.4 Below-ambient cooling vs. above-ambient cooling

Radiative cooling can be categorized as either below-ambient or above-ambient, depending on specific applications. The target cooling temperature of a radiative cooler determines the desired spectral emittance profile; namely, a broadband cooler is needed for above-ambient cooling, while a selective cooler is needed for below-ambient cooling. The broadband cooler should have emittance close to one throughout the IR spectrum, and negligible absorptance in the solar spectrum for daytime cooling. On the contrary, a spectrally selective cooler will have emittance close to one only in the atmospheric window (8–13 μm) and minimal emittance elsewhere. Next, we will interpret such design requirements into the temperature and spectrum dependence of P_cool(T).

P_cool(T) must be positive to ensure net cooling of a system. For above-ambient cooling (i.e. T>T_amb), the thermal radiation outside the atmospheric window from the cooler to the ambient (i.e. above-ambient cooling) becomes beneficial and adds up to higher total cooling power P_cool(T); thus, a broadband design is preferable to deliver more cooling gain (see Figure 3). For below-ambient cooling (i.e. T<T_amb), parasitic thermal emission outside 8–13 μm from atmosphere heats up the cooler, resulting in a negative cooling power for the broadband. In contrast, a spectral selective cooler that can eliminate such undesired absorption of radiation from ambient and maximize P_cool(T) is the best for below-ambient cooling. At T=T_amb, the net thermal radiation outside the 8–13 μm wavelengths from the coolers to the ambient becomes zero; essentially, both designs deliver the same cooling power (see the dashed lines in Figure 3). To summarize, cooler designs should be adopted for different cooling targets. Note that the calculation in Figure 3 only considers the primary atmospheric window from 8 to 13 μm, and has neglected the secondary atmospheric window that exists between 16 and 22 μm. Our simulation has shown that, with the presence of the secondary window, full-spectrum radiation coolers can generate 10–20 W/m² more cooling power than the selective radiative coolers only focusing on 8–13 μm. Consequently, the temperature range in which the selective radiative coolers (from 8 to 13 μm) are preferable needs to be at least ~5 K lower than the ambient instead of just below-ambient, which is in good agreement with Figure 1c in [47]. The secondary window, however, contributes only ~10% of the total cooling power at near-ambient temperature due to much lower transmittance (see Figures 1 and 2) and deviation from the wavelength range (i.e. around 10 μm) wherein IR blackbody radiation peaks. Since the impact of the secondary window on radiation cooling is fairly insignificant, it can be neglected in general. In the next section, we describe specific materials and structures that are suitable for either type of cooling.

Figure 3:

The net cooling power, as defined by Eq. (4), as a function of the object temperature and effective sky temperature for two cases: (A) a full-spectrum radiative cooler and (B) a selective radiative cooler. The horizontal dashed line indicates an ambient temperature of 300 K, and the black solid line illustrates zero cooling power. As in [49], sky radiation inside the atmospheric window is assumed to be emitted 3–5 km above ground at the effective sky temperature. The atmosphere is opaque outside the transparency window (8–13 μm). For realistic non-zero atmospheric transmittance outside 8–13 μm, full-spectrum radiative coolers may have slightly higher cooling power than selective radiative coolers (approx. 20 W/m²) at ambient temperature [50].

3.1 Bulk and gaseous material radiative coolers

In the early stage, plastic has been investigated as a prospective candidate for radiative coolers. Polyvinyl chloride (PVC) [5], polyvinyl fluoride (PVF) [1], [6], [42], [53], [54], and polymethylpentene (TPX) [52] were shown to have high emittance in the atmospheric window. Most plastic coolers reported in the literature were aluminized at the back to block transmission without adding significant absorption outside the atmospheric window. Although the TPX and PVF emittance spectra match the atmospheric window, as shown in Figure 4A [2], [52], TPX is slightly better, due to its higher emittance near 8 μm.

Figure 4:

(A) Transmittance spectrum of aluminized polyvinyl fluoride (TEDLAR) cooler (red) and polymethylpentene (TPX) cooler (blue); adapted from [2], [52]. Strong emittance can be observed within the atmospheric window. (B) the measured reflectance spectrum of 10 μm SiO film on aluminum (Al). The spectrum is adapted from [2]. (C) The measured reflectance for TM (red) and TE (blue) polarizations incident on a 1.34 μm SiO_0.6N_0.2 film on Al. Compared to SiO, a broader peak is found within the atmospheric window. The spectrum is adapted from [56]. (D) The measured transmittance spectrum of ethylene gas in a 1.1-cm-thick gas slab. The spectrum is adapted from [58].

Alternative bulk materials, such as oxide and nitride, have been investigated extensively in the pioneering works of Granqvist et al. It was found that SiO, with its strong lattice absorption near 10 μm, can serve as a selective radiative cooler. The optimal thickness of 1 μm was found to be most effective in reducing reflection [2], [11]. Like the previous structure made from plastic coolers, an Al back reflecting layer was coated by evaporation [2], [11]. The structure and the reflectance of the SiO cooler are shown in Figure 4B [2]. However, the emittance of SiO within the atmospheric window is not strong enough to yield a significant improvement in the cooling effect compared with a blackbody cooler during a nocturnal test. The SiO cooler cooled to 13.8°C below ambient, while the blackbody cooler cooled to 13.4°C below ambient [2]. Therefore, a stronger cooler consists of silicon nitride (Si₃N₄), and the Al back reflector was fabricated in the following work [10]. Si₃N₄ has been explored again in a more recent work, showing a capability of sub-freezing temperature cooling (−22.2°C) [47]. The optical properties of silicon oxynitride (SiO_xN_y) have also been studied [55], [57], with its application as a selective cooler examined in [56]. As shown in Figure 4C [56], a 1.34-μm-thick SiO_0.6N_0.2 (x=0.6 and y=0.2) on the Al back reflector exhibits a strong emittance peak that matches the atmospheric window. The peak is related to the Si–O and Si–N bonds [67], [68] and the shoulder near 8.5 μm is related to the Si–H bond [67]. The net result was an equilibrium temperature of 16°C below ambient during nighttime, 2°C lower than what was achieved by a blackbody cooler [56]. For above-ambient cooling, it was found that fused silica is a suitable cooler with its high emittance across a broad wavelength range except for a dip within the atmospheric window. It is demonstrated to be able to cool an underlying Si wafer by 12°C [19]. Soda-lime glass or low-iron glass, commercially used as cover glass for PV, was found to be slightly better than fused silica for above-ambient cooling [69].

Radiative coolers in gaseous state have also been considered for radiative cooling applications. It is shown that for ammonia gas (NH₃), the IR absorption corresponding to the N atom moving perpendicularly to the H₃ plane is broadened by the rotational absorption so that it covers the atmospheric window [59]. Theoretical modeling showed that a slab of NH₃ gas can potentially cool down to 20°C below ambient during nighttime [59]. Similarly, with out-of-plane bending vibrations, ethylene (C₂H₄) also exhibits strong emittance in the atmospheric window, as shown in Figure 4D [58]. When encapsulated in an IR transparent container, C₂H₄ is a good candidate for radiative coolers that reached 10°C below-ambient cooling during daytime without direct sunlight [58]. Eriksson et al. showed that a mixture of C₂H₄ and C₂H₄O has higher cooling power, compared with either C₂H₄ or C₂H₄O [56].

3.2 Composite radiative coolers

As an alternative to bulk and gaseous material radiative coolers, composite material coolers consisting of two or more different materials were investigated, and were shown by several groups to have emittance properties suitable for radiative cooling. Commercially available white paints containing 35% TiO₂ provide a maximum 15°C drop in temperature with indirect sunlight, clear sky, and low absolute humidity; however, concerns regarding the true spectral selectivity of these TiO₂ paints were raised by Granqvist and Hjortsberg in their letter to the editor [70]. Additional experiments that applied white pigmented paints consisting of TiO₂/BaSO₄ or TiO₂/ZnS in alkyd resin binder on Al panels showed a 9–12°C temperature drop under nocturnal conditions [8].

The development of nanomaterials offered more choices of cooler design. Suryawanshi and Lin fabricated and tested three types of above-ambient radiative coolers consisting of carbon-based nanomaterials [nanodiamond powder (NDP), multi-wall carbon nanotubes (CNTs), or carbon black (CB)] dispersed in acrylate (AC) emulsion with the Al back panel [60]. It was found that the composite cooler with a CNT gives the best performance among the three, as shown in Figure 5A. Furthermore, 1 wt% of CNT in AC can lower the temperature by 17°C from 87°C [60]. Similarly, nanoparticles that have absorption bands that match the atmospheric window were added to polymeric binders to form radiative coolers for below-ambient cooling. It was found that the two IR absorption bands of SiO₂ and SiC nanoparticles, as shown in Figure 5B, are complementary to each other. Therefore, when the two nanoparticles are mixed together in the polyethylene film, the emittance spectrum matches well with the atmospheric window [61]. The estimated result from the model proposed in [61] showed that a 25°C temperature drop below ambient can be achieved when there are limited non-radiative heat transfer and no sunlight. Other than polyethylene, PVF and polyvinylidene fluoride are also good polymeric binders for SiO₂ and SiC nanoparticle composite radiative coolers [71].

Figure 5:

(A) Operating temperature vs. time for carbon-based nanomaterial-composite coolers. The cooler with multiwall carbon nanotubes (CNT-AC) gives the best performance. Adapted with permission from [60]. Copyright (2009) American Chemical Society. (B) The transmittance spectrum of SiO₂ nanoparticles in polyethylene binder (blue) and SiC nanoparticles in polyethylene binder (red). The transmittance spectrum of the polyethylene film itself [61] is shown in green. The two nanoparticle emission peaks are complementary to each other, and both fit within the atmospheric transparency window.

3.3 Nanophotonic radiative coolers

Nanophotonics opens up new possibilities to tailor the emittance spectrum via properly designing periodic nano/micro-structures, in analogy with prior efforts in photovoltaics [72] and TPV [73], [74]. Similarly, for radiative cooling, the large degree of freedom in engineering nanophotonic structures potentially allows for better cooling performance than bulk material or composite coolers. It is proposed that a bar array consisting of α-quartz gives strong selective thermal emission within the atmospheric window while preserving the solar absorption of the underlying structure (Si nanowire array on Al) [63]. The simulation showed that the temperature drop during daytime can be as large as 31.4°C with a nonradiative heat exchange coefficient equal to 6 W/(K m²) [63]. Stronger selectivity in thermal emittance can be achieved by more complex PhC structures. Rephaeli et al. proposed a structure consisting of two layers of quartz and SiC 2D PhC on top of a 1D chirped dielectric stack and silver (Ag) substrate [16]. As shown in Figure 6A, the structure proposed has a strong emittance spectrum that matches well with the atmospheric window due to the phonon-polariton resonances of quartz and SiC. Meanwhile, the introduction of a chirped dielectric reflector and the intrinsically low solar absorption of both quartz and SiC strongly suppressed solar absorption so that below-ambient cooling can be achieved during daytime [16]. The simulation showed that with the optimized PhC structure, a temperature of 7°C below ambient can be reached with a non-radiative heat exchange coefficient of 12 W/(K m²) [16]. In experimental demonstrations, it was shown that a much simpler nanophotonic cooler structure also cools to 4.9°C below ambient under direct sunlight [17]. Figure 6B shows the emittance spectrum of the fabricated radiative cooler. The SEM cross-section of the cooler which consists of seven alternating layers of SiO₂ and HfO₂ on top of Ag is shown in the inset [17]. The significance of the result is that a properly designed one-dimensional photonic film that is feasible for large-scale fabrication could achieve below-ambient cooling in daytime. However, a low-density polyethylene film, serving as a convection barrier, is used in the experiment. The non-radiative heat transfer was therefore strongly suppressed, giving more significant below-ambient cooling effect. Fortunately, such below-ambient cooling in daytime can be achieved even without convection barriers [66]. Using multilayer polyester stacks, Gentle and Smith demonstrated 2°C below-ambient cooling under mid-summer sunlight without using convective barriers [66].

Figure 6:

(A) The numerically optimized photonic crystal cooler for a below-ambient cooler under direct solar exposure. Reprinted with permission from [16]. Copyright (2013) American Chemical Society. (B) The measured emittance spectrum of the fabricated 1D photonic crystal cooler with feasible structures and excellent emittance within the atmospheric window. Adapted with permission from Macmillan Publishers Ltd (Nature) [17], copyright (2014). (C) The measured emittance spectrum of a bare silicon wafer (black), a bare silica slab (blue) and a 2D photonic crystal of silica (red). It can be seen that the emission of silica in the atmospheric transparency window can be enhanced by the 2D square lattice structure. The figure is adapted from [19]. (D) Simulated emittance spectrum of bare low-iron soda-lime glass (blue) and 2D photonic crystal-enhanced bare low-iron soda-lime glass (red). A similar effect of enhanced emission within the atmospheric window is observed. The broad emission spectrum and low solar absorption is ideal for above-ambient daytime cooling. The figure is adapted from [64].

For above-ambient cooling during daytime, nanophotonic coolers also showed promising performance. It was proposed by Zhu et al. [18] that a 2D square lattice of SiO₂ pyramids can reduce the temperature of the underlying Si solar cell by 17.6°C. Later, their experiments demonstrated that a 2D PhC consisting of a square lattice of air holes on SiO₂ cools the underlying Si wafer by 13°C [19]. Figure 6C shows the emittance spectrum of the SiO₂ PhC and its top-view SEM cross-section in the inset. Apparently, the PhC structure enhances the thermal emittance of bare SiO₂ within the atmospheric window, yielding an equilibrium temperature that is 1°C lower than the case with bare SiO₂ [19]. A similar 2D PhC structure can enhance the thermal emittance of low-iron soda-lime glass as well. It is shown in Figure 6D that a square lattice of air holes on low-iron soda-lime glass (structure cross-section in the inset) provides an almost uniform emittance that is close to unity in mid-IR and is highly reflective in the solar spectrum, which is close to the ideal case for above-ambient radiative cooling during daytime [64]. Simulations showed that such radiative cooler design cools a photovoltaic diode of a specific energy conversion device with high heat load, known as TPV, by 91°C from 161°C, which will be discussed in detail in Section 4. The amount of cooling can significantly increase the efficiency of the TPV system and improve the reliability thereof.

3.4 Summary

Various radiative coolers can be quantitatively compared by the cooling parameters defined in a way similar to [2]. From the discussion in Section 2, radiative coolers for below-ambient or above-ambient cooling have different ideal emittance spectra. Therefore, a pair of cooling parameters should be defined to capture the different requirements. Following the work by Granqvist et al. [2], the spectrally averaged hemispherical emittance inside the atmospheric window ε_ave−in is defined as

where ε(λ)=∫0π/2d(sin2θ)ε(λ, θ) and I_BB(λ, T) is Planck’s blackbody radiation function from Eq. (1). The spectrally averaged hemispherical emittance outside the atmospheric window ε_ave−out is defined as

It should be noted that this term is different from the spectrally averaged hemispherical emittance over the entire spectrum ε_ave defined by Granqvist et al. But it can be derived from ε_ave by substituting the first term in the numerator of Eq. (7) with εave∫0∞ dλ IBB(λ, Ta). One important reason of picking these two parameters, as pointed out by Granqvist et al. [2], is that they do not depend strongly on the operating temperature of the cooler and can be easily used to estimate the cooling power at certain temperatures. For some of the radiative coolers discussed above, their cooling parameters are mapped in Figure 7. For the coolers labeled with *, the cooling parameters are calculated based on published spectra and are limited by the spectral range presented. The top-left corner of the plot (blue shaded region) corresponds to the ideal emittance profile of a cooler for below-ambient cooling, while the top-right corner (red shaded region) corresponds to the ideal emittance profile of an above-ambient cooler. It is apparent that most demonstrated and proposed coolers lie in the top-left corner, and are therefore more suitable for below-ambient cooling. However, two designs (silica PhC (2015) [19] and PhC (2016) [64]) lie in the top-right corner, and are both strong candidates for above-ambient cooling. The map shows that bulk material coolers such as SiO_0.6N_0.2 and Si₃N₄ and gaseous coolers such as C₂H₄ and NH₃ already have good emittance spectra that are suitable for below-ambient cooling. Besides, although the absolute cooling of PhC designs is not always as good as bulk material coolers developed much earlier, their solar absorption can be suppressed much more significantly. This is an unprecedented advantage that enables below-ambient cooling even under direct sunlight. Remarkably, the map shown in Figure 7 clearly differentiates the performance of different coolers for both above-ambient and below-ambient cooling. It also allows a quantitative comparison between different cooler designs, as well as estimating their cooling power. In the next section, we consider how various materials and designs can be applied to specific applications.

Figure 7:

Cooling parameters of selective radiative coolers. The top-left corner (blue shaded region) implies the best below-ambient cooling performance. The top-right corner (red shaded region) implies the best above-ambient cooling performance. Data points with * were calculated by the author, using detailed spectra previously presented in the references. Reference list: PVC (1967) [5], TPX (1979) [2], PVF (1979) [2], SiO (1980) [11], SiO (1981) [2], 10 cm C₂H₄ (1981) [58], Al₂O₃ (1982) [75], Si₃N₄ (1982)* [10], 2 cm NH₃ (1982) [59], 5 cm NH₃ (1982) [59], SiO_0.6N_0.2 (1984) [56], PhC (2013)* [16], PhC (2014)* [17], Silica PhC (2015)* [19], PhC (2016)* [64].

4.1 PV cooling

PV, especially solar PV, is an alternative energy source that has the potential to reduce our dependence on fossil fuels for the 21st century. A typical commercial solar module has an efficiency of 20%, which means that up to 80% of solar irradiance is dissipated as heat, thereby increasing the module temperature. On average, one-sun solar modules can operate 20–40°C higher than the ambient temperature. Self-heating becomes even worse for CPV as well as TPV since the incoming light can be orders of magnitude higher than that of one-sun solar modules. For the short term, the elevated temperature directly reduces the power conversion efficiency of PV cells, for example, temperature coefficient of −0.45%/°C for crystalline silicon. In the long run, the aging rate for solar modules can double with every 10°C increase in average temperature [77], caused by thermally activated degradation processes, such as corrosion and potential-induced degradation [78], [79]. Hence, cooling photovoltaic cells can dramatically improve performance and reliability, leading to greater energy yield.

4.1.1 One-sun solar PV

Low IR emissivity can exacerbate self-heating in PV [18], [19], [20], [21], [22], [69]. As shown in Figure 4 in [22], the emittance of bare silicon in the IR spectrum is very low; therefore, it emits negligible thermal radiation. Indeed, bare silicon cells can operate up to 20°C higher than glass-encapsulated modules [18], [19], [22], which has much higher emittance. Nonetheless, its emittance still drops significantly within the atmospheric window, preventing heat exchange with the cold universe. Additionally, the emittance of glass decreases rapidly at an angle of incidence θ greater than 50°, further suppressing thermal radiation (see Figure 4 of [22]). Note that the rear side of the solar modules also exchanges thermal radiation with the ground. During the day, the ground underneath the solar modules can be at a lower temperature than the ambient owing to shading, potentially providing considerable cooling power. The PVF backsheet (an encapsulant polymer) has a hemispherical emittance, ε_ave≈0.85, still lower than the unity. As a result, there is still room to improve the radiative cooling of the top (glass) and bottom (PVF backsheet) layers of solar modules. This brings about a question of the maximum temperature reduction achievable by radiative cooling for a one-sun solar module. Reference [18] shows a temperature difference of 5.2°C between fused-silica glass (ε_ave≈0.73) and ideal radiative cooler (ε_ave=1) as the top layer for solar panels. The cover glass of commercial solar modules, however, has higher hemispherical emittance ~0.84 than fused-silica glass; thereby the actual cooling gain may have been overestimated in [18]. Indeed, simulation results in [22], [69] predict a temperature reduction of only 1–2°C by radiative cooling when commercial glass is considered (see Figure 8). Zhu et al. [19] experimentally demonstrated radiative cooling on solar cells by using a PhC emitter as the top layer (its emittance is plotted in Figure 6C). Figure 9A illustrates the experimental setup, and the steady-state temperature of the solar absorber with the PhC emitter was measured to be ~ΔT≈1.3°C cooler than that of fused silica in [19] (ΔT is expected to be slightly lower for PhC vs. commercial cover glass) (see Figure 9B). Even such a modest temperature change can yield an ~0.13% absolute increase in efficiency for Si solar modules. Given the efficiency plateau of Si-based PV in the recent decade [80], radiative cooling gives a new perspective for further improving the efficiency of Si solar modules. Moreover, the time to failure of solar modules follows the Arrhenius relation (i.e. it is proportional to exp(−E_A/kT), where E_A≈0.89 eV is the activation energy [81]). Radiatively cooling the solar module by 1–2°C can extend lifetime by up to 20%, substantially increasing the lifetime electricity yield. Hence, radiative cooling can improve the performance and reliability of one-sun solar modules considerably.

Figure 8:

Simulated temperature reduction obtained by different cooling schemes (S. Cooling: selective-spectral cooling; R. Cooing: radiative cooling; S.&R. Cooling: selective-spectral cooling and radiative cooling combined). The simulation assumes that the wind speed is approximately 0.5 m/s giving an effective convective coefficient h=10 W/(K m²), conductive heat transfer only at the module edges through metal frames is neglected, and the ambient temperature T_A and solar irradiance are 300 K and 1000 W/m², respectively. The atmospheric transmittance data are for New Delhi in spring, with perceptible water vapor (PWV)=18 mm. © 2017 IEEE. Reprinted, with permission, from [22].

Figure 9:

(A) Experimental setup for radiative cooling in [19]. The left picture shows the apparatus and solar absorbers on a rooftop. The chambers were tilted at 60° to maximize solar absorption. Shown on the right is the normal view SEM image of the 2D silica photonic crystal structure (PhC) consisting of a square lattice PhC of 10 μm deep air holes with a periodicity of 6 μm fabricated on a fused silica wafer. (B) Temperature measurement of solar absorbers underneath different top layers on a clear day in winter. The measurement was performed with a windshield to reduce the convection coefficient to 6.5–9.1 W/(K m²).

4.1.2 CPV and TPV

Radiative cooling is of great interest to systems that are under excessive heat dissipation and require energy-efficient and effective cooling schemes. In this context, radiative cooling appears particularly appealing to CPV and TPV systems.

CPV, an extension of one-sun PV, operates under concentrated sunlight (up to 100-fold), resulting in severe self-heating. Despite the use of traditional passive cooling, the operating temperature of CPV under 24 suns can still reach up to 140°C [82], considerably lowering the power output as well as shortening the lifespan. So far, most work on cooling techniques for CPV has been limited to heat sinks [83], cycling coolants [84], and forced air cooling [85], all of which can add up the cost of CPV systems and reduce the overall energy efficiency. Recently, by coating the bottom aluminum chassis with an additional thermal radiation layer to enhance thermal radiation, Nishioka et al. [48] successfully achieved temperature reduction by 10°C corresponding to 1% absolute improvement in efficiency for triple-junction CPV systems under 820 concentration factor (see Figure 10). Note that the enhanced thermal radiation in [48] is purely from improved heat exchange with the ground. Extra cooling gain can be obtained by reconfiguring the CPV system to direct the enhanced thermal radiation toward the sky, whose temperature is much lower than the ground.

Figure 10:

The recorded (A) operating temperature and (B) efficiency of triple-junction concentration photovoltaic systems under 820 suns concentration with and without thermal radiation coating in [48].

Likewise, TPV can also experience radiative heat stress on the order of hundreds of suns in vacuum (to thermally isolate the thermal emitter), resulting in a severe thermal management challenge. The temperature of TPV systems with only passive cooling can easily go beyond 200°C, and the consequent efficiency drop can be over 50% [23]. Zhou et al. [64] proposed a setup for radiatively cool outdoor TPV applications. The setup consists of a cooling radiator on top of a heat spreader to thermally concentrate the radiative cooling power on the PV cells underneath. Using an opto-electro-thermal coupled simulation framework, a temperature drop of 90°C of TPV cells by radiative cooling has been predicted in [64] (see Figure 11A). With sufficient cooling concentration factor (area ratio between the radiative cooling emitter and the PV cell), below-ambient cooling of TPV during daytime can be realized by employing low-iron soda-lime glass as the radiative cooler, allowing TPV exceeding the optimal efficiency at room temperature (see Figure 11B). The design of radiative cooling in [64] is also transferable to indoor TPV, though the indoor background temperature bounds the lowest achievable cooling temperature.

Figure 11:

(A) The design of an outdoor TPV system with radiative cooling. The thermal emitter and PV cell are both enclosed in a vacuum for mutual thermal isolation. The area of the radiative cooler and heat spreader is larger than that of the PV cell to improve cooling power. (B) Operating temperature of PV cell as a function of the cooler-to-cell area ratio. The convection coefficient is set to be 2.5 W/(K m²).

4.2 Emissive energy harvester

The earth is constantly radiating approximately 10¹⁷ W to the cold universe [49]. In principle, if properly utilized, radiation from the earth is sufficient to meet the electricity need for the entire humanity. However, effective strategies to harness such energy have not been fully explored. Recently, a device named emissive energy harvester (EEH) that can transfer heat from a heat sink to sky through radiative cooling from a cold reservoir and convert part of the heat flow into useful work has been proposed [49], [76] (see Figure 12A). Coupled Carnot’s law to the steady-state heat flow, the maximum output power from the engine is P_Cool×(T_Hot/T_Cold−1), where P_Cool is the net radiative cooling power from the cold reservoir to the sky described by Eq. (4). At a fixed T_Hot and T_Sky, P_Cool increases with T_Cold whereas the Carnot efficiency of the engine decreases. Hence, there is an optimal temperature of the cold reservoir that maximizes the power at a given T_Hot and T_Sky. Figure 12B–C summarizes the performance of an ideal EEH (Carnot limited) with different emission bandwidths [76]. The power density can reach up to ~300 W/m² (equivalent to a solar cell with 30% efficiency under one sun) with heat sink at a temperature of 500 K. It should be noted that, at high heat sink temperature that gives an optimal T_Cold above the ambient, it is not desirable to confine the wavelength range of thermal radiation within the atmospheric window because of the additional outgoing heat from the colder reservoir to the surrounding background.

Figure 12:

(A) Schematic of an EEH. Heat flows from the heat sink to the cold reservoir through the engine, which converts part of the heat into useable energy; the rest of the heat is radiated to the sky by the cold reservoir (or to the surroundings with non-zero emissivity outside the atmospheric window). Carnot-limited output power (W/m²) of an ideal EEH that (B) only emits between 8 and 13 μm wavelengths with a unity emissivity and (C) emits as a blackbody upwards placed outdoor at an ambient temperature of 300 K.

Ideally, in analogy to PV, EEHs can be realized by a semiconductor p-n junction. However, dominant Auger recombination and generation in mid-IR bandgap semiconductors makes such a design impractical. As shown in Figure 13, much more promising candidates have been proposed, that is, rectenna-based and cold carrier EEHs [49], [76], both of which will be discussed in detail as follows.

Figure 13:

(A) Design of a rectenna-based EEH, where the electrical signal is coupled to IR radiation collected by antennas. (B) Illustration of a cold carrier EEH. Electrical current is extracted by energy-selective metallic contacts. The back reflector is used to reduce radiative heat transfer between the cold electrons and the heat source. Reproduced from [76], with the permission of AIP Publishing.

4.3 IR detectors and electronics