1. Introduction

Radiative cooling (RC) stands up as a promising alternative to reduce the energy consumption of different systems such as housing air conditioning [1] and fresh air pre-cooling systems [2]. Due to its characteristics, RC operates without an external power supply and it has been shown—both theoretically and experimentally—that RC can operate continuously 24 hours a day, even under direct sunlight. The RC effect occurs due to the transparency of Earth’s atmosphere between 8 and 13 $\mu$m and to the temperature difference between objects at the Earth’s surface ($\sim$300 K) and the deep space ($\sim$3 K). A heat exchange process takes place via thermal radiation that passes through the first infra-red (IR) atmospheric transparency window (IRAW), enabling the passive cooling of an object at the Earth’s surface. This radiative heat transfer mechanism is passive and it does not require any power supply or moving parts, thereby making RC advantageous compared to active approaches based on refrigeration cycles. In the last decades, the interest in RC due to its economic and environmental relevance has resulted in studying different cooling configurations and applications, where radiative coolers have been analyzed, simulated, optimized, and fabricated. For example, some remarkable approaches are metal-dielectric nanophotonic structures [3–6], thin-film heterostructures [7], double-layer nanoparticle-based coatings [8], microsphere-based photonic random media [9–13], aerogels [14,15], and porous polymer-based coatings [16–22].

RC can also be used as a passive cooling strategy for photovoltaic (PV) cells to improve their performance. PV cells are one of the keystones to dealing with global warming and environmental damage. Countries worldwide have implemented PV plants to reduce fossil fuel energy consumption and, consequently, dampen the environment’s harm. Even though PV cells have been studied for decades, commercially, their efficiency remains low ($\sim$20%) due to different effects, e.g., Auger recombination [23]. Furthermore, parasitic absorption (i.e., absorption of photons that cannot generate photocurrent) also reduces efficiency due to heat generation.

PV cells’ temperature under operation conditions is approximately 60 °C [24,25]. This operating temperature is detrimental to the PV cell performance (resulting in a PV efficiency reduction of about 0.45%/°C, [26]) and service lifetime [27]—considering that PV cells performance is tested under room temperature conditions. Several attempts have been made to incorporate active and passive cooling solutions to improve PV efficiency under typical operating conditions. Those approaches include airflow and forced water flow, phase change materials, liquid immersion, heat pipes, and heat sinks [28].

Radiative cooling has recently been considered as a simple, cost-efficient, and passive solution that could generate power gains beyond what glass covers in solar cell modules already achieve due to thermal emission. Up to date, most RC approaches have focused on high mid-IR emittance materials that are nearly transparent in the visible. For example, Zhu et al. [29] demonstrated that a micro-photonic structure made of SiO$_2$ could decrease the operating temperature of a bare solar cell by 18.3 °C when placed on top of the device. Ahmed and coworkers [30] found that Polydimethylsiloxane (PDMS) on glass integrated with a photovoltaic-thermal module could reduce the operating temperature and increase the relative efficiency of the solar cell by 1.7 °C and 0.5%, respectively, compared to a regular glass encapsulated PV thermal module. Other works have focused on integrating RC into concentrating photovoltaics (CPV). For example, Zhou et al. [31] have used soda-lime glass with an Al back reflector to cool down low-bandgap PV diodes in a CPV system, reducing its operating temperatures by 10 °C, translating into a relative increase of 5.7% in open-circuit voltage and an estimated increase of 40% in a lifetime at 13 suns. Wang et al. [32] showed that for a GaSb CPV system integrating soda-lime glass-based radiative coolers in sealed chambers, a temperature drop of 36 °C could be achieved and a 27% relative increase of open-circuit voltage.

All-photonic theoretical approaches that maximize thermal emittance and reflect light in the wavelength ranges where photons are not converted into photocurrent have also been recently proposed. These stacks use multilayer dielectric coatings composed of Al2O$_3$/SiN/TiO$_2$/SiN [33–35] to further increase power gain by exhibiting broadband IR emittance, antireflection at solar wavelengths, and high reflectivity in the wavelength ranges of 0.3-0.375 $\mu$m and 1.1-4 $\mu$m (Fig. 1(a) and 1(d)). These ideal optical characteristics minimize heat gain due to inefficient light-electricity conversion while providing radiative cooling. More complex systems that use 1D multilayer stacks and 2D photonic crystals have also been investigated and showed that an increase of 6.9% in absolute efficiency could be achieved compared to a bare cell working under standard conditions [36]. So far, these solutions have not been demonstrated experimentally because they involve sophisticated nanofabrication to form a multilayer stack, including the alternating deposition of different layers of dielectric materials such as silica, alumina, titania, and silicon nitride. Therefore, implementing all-photonic approaches that use multilayer coatings is hindered in the photovoltaic industry because of the fabrication costs and limited manufacturing feasibility and scalability. This challenge can be overcome by developing an all-photonic approach based on the surface structuring of a single material. Recent works have shown the effectiveness of a single-material-based radiative cooling approach comprising a flat base thin layer and photonic patterning. For example, Perrakis et al., [37] studied the use of combined micro and nano structuring, achieving efficiencies of 3.1 %; Zhao et al., [38] proposed a silica grating that exhibits high IR emittance; and Long et al., [39] explored silica disks showing remarkable cooling effects. Here, we propose a strategy based on a single patterned material that simultaneously maximizes thermal radiation and light trapping while exhibiting high reflectance in the UV (0.3-0.375 $\mu$m) and sub-bandgap (1.1-4 $\mu$m) wavelength ranges. We investigate patterned surfaces of soda-lime glass and PDMS as these are materials commonly used in PV panel covers due to their optical transmittance at solar wavelengths and high thermal emissivity in the mid-IR, as well as their durability and UV and mechanical resistance. To estimate the enhancement in PV efficiency improvement—thanks to the proposed all-photonic strategy—a numerical approach based on the rigorous coupled-wave analysis (RCWA) method and an electrical-thermal model was implemented. The results show that the hemisphere-based photonic structures can increase the maximum produced PV power by 18.1% and 19.7% for soda-lime and PDMS, respectively, compared to a reference cell that includes a standard 3200 $\mu$m-thick glass cover (Fig. 1(a) and 1(b)). This demonstrates that broadband IR emittance, antireflection at solar wavelengths, and high reflectivity in the UV and near-IR can be achieved simultaneously by surface structuring of a single material. Thanks to its simplicity, this approach could be applied during the production process or directly on the surface of already fabricated solar panels, paving the way to real implementation in the photovoltaic industry.

 

Fig. 1. Schematic of a solar cell and its properties. (a) depicts a solar panel energy balance and (b) shows the reference solar cell. (c) show the complex permittivity of silicon and (d) the optical properties of silicon and the reference cell. Additionally, the solar spectrum, AM 1.5, (yellow) and the atmospheric transmittance in the IR (light blue) along with the ideal reflectivity (red dashed line) and emissivity (green dashed-dotted line) that this work aims for, are included for reference.

Download Full Size | PDF

2. All-photonic radiative cooler design

An optical and a coupled electrical-thermal mathematical model was developed to design an all-photonic strategy for thermal management and evaluate PV performance improvements. First, the RCWA method [40,41] is used to compute the absorptivity, reflectivity, and transmissivity of the studied structures. Then, as usual, the structures’ emissivity is obtained by invoking Kirchhoff’s law of thermal radiation. To study the effect of the proposed all-photonic structure on a realistic PV system, all calculations of optical properties were done considering a base stack that exhibits optical properties comparable to a real solar cell. The stack—from now on called the base PV stack—is based on a silver substrate [42], a lightly boron p-doped silicon PV cell of 250 $\mu$m thickness (resistivity of $\sim$14 $\Omega$ cm, 1$\times$10$^{15}$ cm$^{-3}$), and a Si$_{3}$N$_{4}$ anti-reflective coating (ARC) of 75 nm [43]. The model incorporates the silicon complex permittivity at 300 K presented in [44] that captures silicon optical features in the UV, VIS, and IR. These optical properties were benchmarked against measurements (see Supplement 1, Section 3). Figure 1(c) shows the real and imaginary parts of the silicon complex permittivity, and Fig. 1(d) shows the optical properties of the base PV stack (solid blue line) considered in the analysis (Ag/Si/Si$_{3}$N$_{4}$). Note the difference in the scale between 0.3 to 4.0 $\mu$m and 4.0 to 30 $\mu$m. The effect of the proposed hemisphere photonic cover on top of the above-mentioned base stack was studied and compared to a reference cover glass of 3200 $\mu$m, whose geometry is shown in Fig. 1(b), and its optical properties are displayed in Fig. 1(d) (gray dotted line). Additionally, Fig. 1(d) shows the solar spectrum (AM 1.5) and the atmospheric transmittance in the IR along with the ideal reflectivity (red dashed line) and emissivity (green dashed-dotted line) that this work aims for.

Once the optical properties of the cell are calculated, the PV cell characteristics (i.e., net cooling power, the PV cell’s operating temperature, the maximum power point, and the IV characteristics) are obtained using a coupled electrical-thermal mathematical model (based on [45,46]). To determine the net cooling power and the operating temperature, an energy balance (Eq. (1) and Fig. 1(a)) of the cell under steady-state condition is considered:

This balance allows for the calculation of the net power, $P_{net}$, per unit area flowing in or out of the cooler surface depending on the operating conditions ($P_{net} = 0$ for steady-state conditions). Note that the Eq. (1) considers the PV cell characteristics such as output power ($P_{mpp}$) and non-thermal radiation ($P_{rad, cell}$), since the PV cell should be considered as an energy converter and not only as an absorber to avoid overestimating the output electrical power, according to [45,46].

The term $P_{cooler}$ in Eq. (1) is the radiated power from the emitter

Additionally, the heat transfer coefficient for convection and conduction imitates outdoor conditions; this power is calculated as $P_{cc} = h_{cc}(T - T_{amb})$—considering $h_{cc} = 12$ W/m$^{2}$K and $T_{amb} = 298$ K. Additionally, the so-called non-thermal radiation, $P_{rad,cell}$, obtained using

In the last three equations, $q$ is the electric charge, $V$ and $V_{mpp}$ is the voltage and the voltage at the maximum power point, respectively, $k_{B}$ is the Boltzmann constant, and $c$ is the speed of light. We implemented the model presented in [46] and considered other relevant PV cell parameters such as series and shunt resistances to obtain a realistic but conservative estimation of the cooling effect provided by the photonic coolers. The IV characteristics are obtained considering:

Usually, the encapsulation of commercial PV cells considers, among other layers, a thick layer of transparent glass. This cover is transparent for above-bandgap photons, and it helps to cool down the PV cell since it exhibits high emissivity in the IR. However, that emissivity shows dips in the wavelength range of the atmospheric window—due to the light and optical phonons interaction—that is detrimental to the cooling effect. Moreover, there is significant absorption in the UV and sub-bandgap regions that are detrimental to the lifetime and efficiency of the cell. To alleviate these effects and using the mathematical approach mentioned above, we designed an all-photonic structure by pursuing the ideal optical properties shown in Fig. 1(d), i.e., improve UV and sub-bandgap reflectivity as well as infrared emissivity.

To this end, first, we studied the influence of a flat material (soda-lime and PDMS) thickness on top of the base PV stack in the UV and solar spectrum (0.3–1.1 $\mu$m), sub-bandgap (1.1–4.0 $\mu$m), and mid-IR (4.0–30 $\mu$m) to understand how reflectivity and emissivity behave for a range of thicknesses from 25 to 300 $\mu$m. Secondly, based on the results for flat materials, we designed an all-photonic structure to improve solar cell thermal management. Thirdly, to evaluate PV cell improvements, the coupled electrical-thermal model is used to evaluate the PV cell characteristics and the output power enhancement due to the proposed hemisphere-based photonic structure. The results are then compared to flat layers of equivalent thickness and a reference cell that considers a standard 3200 $\mu$m-thick glass cover. Finally, to predict the behavior of the proposed design, we calculated the output power for different values of solar irradiance.

To assess if there is an optimal flat-cooler thickness that maximizes the reflectivity and emissivity in the desired wavelength range, the optical properties of soda-lime and PDMS flat coolers with thicknesses ranging from 25 to 300 $\mu$m were analyzed (Fig. 2). In particular, Fig. 2(a) displays the silicon absorptivity averaged for a wavelength range $\lambda \in [0.3,1.1]$ $\mu$m (see Supplement 1, Section 2 for details of calculations) as a function of cover thickness. The PDMS based cooler exhibits a higher light absorption due to the lower reflectivity as shown in Fig. 2(b). Furthermore, Fig. 2(c) shows the averaged reflectivity of a flat material on the base PV stack in the sub-bandgap region ($\lambda \in [1.1, 4.0]$ $\mu$m). In this case, similarly to Fig. 2(b), PDMS exhibits less reflectivity than soda-lime. For both materials, the reflectivity decreases monotonically as the cooler’s thickness increases; however, this effect is more pronounced for the PDMS. In fact, when considering the reference cell (Fig. 1(b)) the values of average reflectivity and emissivity are 69.6 % and 84.1 %, respectively. Unlike average reflectivity, average emissivity (Fig. 2(d)) for $\lambda \in [4.0,30]$ $\mu$m increases asymptotically to approximately 83% for soda-lime and 90% for PDMS (See Supplement 1, Section 2 for details).

 

Fig. 2. Optical properties of flat soda-lime and PDMS on the reference stack Si$_{3}$N$_{4}$/Si/Ag. (a), (b), (c), and (d) show the averaged absorptivity, reflectivity, and emissivity in different regions of the spectrum. (e) and (f) display the optical properties of a 300 $\mu$m soda-lime and PDMS stack.

Download Full Size | PDF

To help elucidate the average optical properties behavior, Figs. 2(e) and (f) show the reflectivity and absorptivity/emissivity of soda-lime and PDMS for layers of 300 $\mu$m. We chose 300 $\mu$m to see the characteristics of optical properties in the wavelength ranges under study. Soda-lime exhibits higher reflectivity in the sub-bandgap region since PDMS has absorption peaks due to CH$_{3}$ vibration [51,52]. On the contrary, emissivity in the IR of soda-lime is lower since dips due to bulk phonon resonance excitation are more pronounced. Considering the behavior of optical properties for flat surfaces, we designed an all-photonic structure (Fig. 3(a)) able to, in part, reflect UV light, enhance light-trapping of photons able to generate photocurrent, reflect light in the sub-bandgap region, and efficiently emit thermal radiation in the entire mid-IR. This structure is based on either soda-lime or PDMS hemisphere on a flat layer of the same material below. This flat base layer below the hemisphere, if carefully designed, helps to improve the emissivity without sacrificing reflectivity in the sub-bandgap region. Note that the designed photonic cooler is integrated onto the base PV stack (Si$_{3}$N$_{4}$, Si, and Ag).

 

Fig. 3. Proposed all-photonic approach for thermal management and improved PV performance. It consists of soda-lime or PDMS hemispheres on a flat layer of the same material. The photonic structure is integrated on the modeled PV base stack (Si$_{3}$N$_{4}$/Si/Ag). (a) shows the proposed photonic stacking. (b) shows the properties of the soda-lime photonic structure, and (c) shows the properties of PDMS photonic structure, both compared to a flat cooler.

Download Full Size | PDF

For the calculations of the optical properties, hemispheres were discretized in thin layers, and the results obtained with the RCWA code were benchmarked against SiO$_{2}$ sphere-based photonic structures previously reported in the literature [53] (see Supplement 1, Section 1 for details). Properties of soda-lime and PDMS are obtained from [54,55] and [56,57], respectively (See Suppl. document, Section 3 for details).

Figures 3(b) and 3(c) show the spectral hemispherical absorptivity for $\lambda \in [0.3,1.1]$, reflectivity for $\lambda \in [0.3,4.0]$, and the emissivity for $\lambda \in [4.0,30]$ of the proposed photonic structures compared to their counterpart flat radiative coolers. In order to find the proposed designs, an extensive search considering different geometrical parameters (radius, period, and thickness of the flat layer below the hemispheres) was done.

The results for the best performing soda-lime and PDMS structures are shown in Figs. 3(b) and 3(c), respectively. First, Fig. 3(b) shows the properties of a soda-lime all-photonic cell design, which considers hemispheres of 9 $\mu$m in diameter on top of a 75 $\mu$m layer compared to a flat counterpart of 79.5 $\mu$m. Likewise, Fig. 3(c) shows the properties of a PDMS all-photonic cell design considering hemispheres of 8 $\mu$m diameter and a layer of 75 $\mu$m, also compared to its flat counterpart of 79 $\mu$m—both in a periodic cell of (17.3, 10) $\mu$m. In both cases, the use of hemispheres increases the emissivity of the structures in the atmospheric window. This phenomenon has been studied for silica and soda-lime spheres, and it is attributable partly to surface-phonon polariton outcoupling as well as to a broadband impedance matching between the material, and free space [12,53,58].

Additionally, the light trapping effect in the useful part of the solar spectrum can be attributed to the lower reflectivity due to the impedance matching; therefore, more photons are reaching the silicon since, in that spectral region, both soda-lime and PDMS are mostly transparent. It is worth mentioning that both designs exhibit a reflectivity between 40% and 50% (since transmissivity is negligible) for the UV light. Nevertheless, there is still room for improvement, as further enhancing the reflectivity for UV light reduces heating and degradation of solar cells.

To evaluate the proposed PV cells’ performance, we calculated the IV characteristics and the maximum power generated by the cell. Figures 4(a) and 4(b) show the current-voltage characteristics and Figs. 4(c) and 4(d) display the output power. For the soda-lime photonic structure, the hemispheres increase 5.3% and 0.90% in the short-circuit current and the open-circuit voltage, respectively, compared to its flat counterpart. We also compared the soda-lime design to the standard encapsulation thick glass of 3200 $\mu$m. In that case increments of $J_{sc}$ and $V_{oc}$ reached values of 18% and 2.0%, respectively. On the other hand, for the PDMS structure, the performance enhancement when comparing the all-photonic approach to its flat counterpart is 5.2% for the $J_{sc}$ and negligible in the case of $V_{oc}$. As PV cells are characterized in standard conditions, i.e., 298 K and 1000 W/m$^{2}$ (AM1.5G), then the output power at ambient temperature was also included for comparison in Figs. 4(c) and 4(d) using squares and circles for flat materials and hemispheres, respectively. This is useful to evaluate the best-case scenario for an optimal thermal management approach. Even though the proposed designs increase the total output power, there is still room for improvement by reducing the operating temperature to reach ambient temperature. As expected, when the proposed hemisphere structures are placed on the base PV stack, they exhibit higher performance compared to their flat counterparts and the reference cell (Table 1). There is an increment of 18.1% and 19.7 % when comparing $P_{mpp}$ for the soda-lime and PDMS materials, respectively, to the reference cell. This increment translates to approximately 3.4 % and 3.7 % relative efficiency improvements. Notably, the equilibrium temperature for all the proposed structures are similar—only 1 $^{\circ }$C difference. Even though the reflected power for the proposed designs is higher than the reference cell, its increment is not significant. This fact illustrates that the performance improvements due to incorporating the proposed all-photonic structures are attributable to the cooling effect, the silicon absorption enhancement by light trapping, and the sub-bandgap reflectivity. The coolest temperature is reached using a flat PDMS structure; however, the maximum power point is reached using hemispheres of PDMS, followed by the soda-lime hemispheres.

 

Fig. 4. Electrical properties and output power. (a) and (b) IV curves for the photonic and flat designs considering soda-lime and PDMS, respectively. (c) and (d) Output power for the photonic and flat designs considering soda-lime and PDMS, along with output power obtained at ambient temperature.

Download Full Size | PDF

Table 1. Comparison of quantities of interest for the different designs.

View Table

Finally, we estimated the output power under different irradiance conditions in order to predict the effect of different climate scenarios (Fig. 5). The output power of the hemisphere structures is higher than the flat structures for the entire analyzed range, reaching its maximum for maximum irradiance. Moreover, for high solar irradiance ($\sim$1000 W/m$^{2}$), the difference between the hemispheres and flat structures is 5.7% and 5.6% for soda-lime and PMDS, respectively. For low irradiance ($\sim$500 W/m$^{2}$), however, the difference between the PDMS cells decreases to 5.0% while for soda-lime structures is only 5.4%.

 

Fig. 5. The output power of different designs under different irradiance conditions.

Download Full Size | PDF

3. Conclusions

In conclusion, we present a new all-photonic strategy for thermal management and PV performance improvement based on a structure composed of hemispheres on a flat layer. The investigated photonic structures are evaluated as solar photovoltaic panel covers, considering soda-lime (glass) and PDMS, as both materials are commonly used for such purposes in real PV applications. An optical and a coupled electrical-thermal model was developed to evaluate the PV cell characteristics and, consequently, the efficiency enhancement due to the proposed hemisphere-based photonic structure. The results were compared to flat layers of equivalent thickness and a reference cell that considered a standard 3200 $\mu$m-thick glass cover. It was shown that when the hemisphere-based photonic structure is implemented, the solar cell’s performance increases independently of the studied materials, highlighting the approach’s potential. Notably, incorporating this type of photonic cooler impacts the temperature reduction, the PV cell absorption, and the structure UV and sub-bandgap reflectivity, thereby increasing the output power by 18.1 % and 19.7 % for soda-lime and PDMS, respectively, when compared to the reference cell. In sharp contrast to previously reported multilayer all-photonic approaches for PV thermal management, our strategy is based only on one single patterned material that simultaneously maximizes thermal radiation and light trapping in the solar spectrum while exhibiting significant reflectance in the UV (0.3-0.375 $\mu$m) and sub-bandgap (1.1-4 $\mu$m) spectral regions. The use of a single patterned material is more suitable for manufacturing feasibility, scalability, and mass-production in the photovoltaic industry, as the cover fabrication process can be simplified, overcoming the challenge of alternating deposition of different dielectric layers. This work, therefore, sets the guidelines for designing a simple and robust strategy to increase the PV efficiency by simultaneously exploiting all-photonic passive thermal management and solar energy harvesting.