Supporting Information A comprehensive photonic approach for solar cell cooling Wei Li 1, Yu Shi 1, Kaifeng Chen 1,2, Linxiao Zhu 2 and Shanhui Fan 1* 1 Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA 2 Department of Applied Physics, Stanford University, Stanford, California 94305, USA * email: shanhui@stanford.edu 1. Photonic cooler design for photovoltaic modules with large incident angle range. Reducing reflection loss of the glass surface in the useful solar spectrum is an important feature of our photonic cooler design. In general, the photonic cooler can be designed for photovoltaic modules either with or without sun tracking. Specifically, the photonic cooler design in Fig. 3 in the main text is designed for solar irradiance from normal or in small incident angles. In this case, it will be suitable for photovoltaic modules with tracking systems such as dual axis solar trackers or single axis solar trackers. However, our photonic cooler can also be designed to work with large incident angles for photovoltaic modules without sun tracking such as the case of roof-top residential application. Below in Fig. S1 we provide a photonic cooler design, showing that it can still reduce the refection loss even in the high incident angles. More details about the layer thickness of the design are presented in Supporting Information Table S1.
Figure S1 Photonic cooler design for large incident angles. a, b, Angle-dependent reflection spectra of a glass substrate with photonic cooler (a) and without photonic cooler (b) over the solar wavelength. The region between the two white dashed lines indicates the useful solar spectrum in the wavelength range of 0.375 to 1.1 µm. c, Averaged solar reflectance of a glass substrate with photonic cooler (red line) and without photonic cooler (blue dashed line) over the useful solar spectrum in the wavelength range of 0.375 to 1.1 µm. d, Global horizontal irradiance (GHI) and solar zenith angle in a clear day in California in July, 2015. Data obtained from NREL [1]. Fig. S1a shows the angle-dependent reflection spectra of a glass substrate with photonic cooler over the solar wavelength. As a comparison, the angle-dependent reflection spectra of a bare glass substrate is also plot in Fig. S1b. To compare the reflection characteristics of these two cases, we calculate the averaged solar reflectance R in the useful solar spectrum in the wavelength range of 0.375 to 1.1 µm as: R = 1.1 0.375 1.1 dλ I AM1.5 (λ) r(λ,θ) 0.375 dλ I AM1.5 (λ) 2
This averaged solar reflectance R is plotted as a function of incident angle for both photonic cooler and bare glass substrate, shown in Fig. S1c. One can see that the photonic cooler can reduce the reflection loss of the glass in a large incident angle range from 0 to 65. This incident angle range corresponds to a time range from 7:00 to 17:00 in California in July 2015 (Fig. S1d). For incident angle range from 65 to 90, the photonic cooler and the bare glass substrate have similar solar reflectance. Therefore, this photonic cooler can be designed to work with large incident angles without having negative effect for the whole day operation. 2. Photonic cooling effects on photovoltaic modules made of cell II. Below we provide experimental result of solar absorption spectrum of an encapsulated cell made of cell II, as well as the thermal calculation, showing the cooling effects on cell II under various non-radiative heat transfer conditions: Figure S2 Photonic cooling effects on photovoltaic modules made of cell II. a. Experimentally measured solar absorption spectra of bare cell II (blue) and an encapsulated cell II (red), with the normalized AM1.5 solar spectrum plotted for reference. b. Under AM1.5 illumination, operating temperature of the solar panel made of cell II, without a photonic cooler (purple), with a photonic cooler (red), and in the ideal situation (green), as a function of h 1, with a fixed h 2 = 5 W/m 2 /K. c, Under AM1.5 illumination, operating temperature of the solar panel made of cell II, without a photonic cooler (purple), with a photonic cooler (red), and in the ideal situation (green), as a function of h 2, with a fixed h 1 = 10 W/m 2 /K. 3
As shown in Fig. S2a here as well as Fig. 2a in the main text, one can see that the bare cell II has a substantial absorption in the sub-band-gap region. The encapsulation process even further enhances the absorption in the sub-band-gap as well as UV wavelength region, due to the absorption of EVA (Fig. S2a). The absorption represents a parasitic heat source that does not contribute to current generation. We then calculate the cooling effects on the encapsulated cell II with our photonic cooler under various non-radiative heat transfer conditions, shown in Fig. S2b and S2c. In particular, in a typical outdoor condition with non-radiative heat transfer coefficient as h 1 = 10 W/m 2 /K and h 2 = 5 W/m 2 /K, the operating temperature of the encapsulated cell II can readily be lowered by 7.7 C with current photonic cooler design and by 11.4 C with an ideal photonic cooler. Compared with the 5.7 C temperature reduction from cell I, we observe a much stronger cooling effect. 3. An example of a concentrated photovoltaic system with 10 Suns intensity concentration and incident angle range from 0 to 30. 4
Figure S3. A concentrated photovoltaic system design with 10x concentration factor and incident angle range from 0 to 30. 4. Layer thickness parameters for various photonic cooler designs. Below we provide the layer thickness parameters for various photonic cooler designs. Photonic cooler I is designed for photovoltaic modules with solar irradiance from normal or with small incident angles (Fig. 3c in the main text). Photonic cooler II is designed for photovoltaic modules with large incident angles (Supporting Information Section 1). Photonic cooler III is designed for concentrated photovoltaic system with incident angle range from 0 to 30 ((Fig. 5b in the main text). Layer number is counted from bottom to top. Layer Number Materials Thickness (nm) Layer Number Materials Thickness (nm) I II III I II III 1 Al 2 O 3 81 102 86 24 SiN 61 64 69 2 SiN 60 86 62 25 Al 2 O 3 172 172 186 3 TiO 2 89 19 90 26 SiN 67 65 68 4 SiN 59 83 62 27 TiO 2 102 93 101 5 Al 2 O 3 154 189 168 28 SiN 69 64 66 6 SiN 55 66 62 29 Al 2 O 3 194 165 175 7 TiO 2 84 106 87 30 SiN 69 62 63 8 SiN 56 67 58 31 TiO 2 104 90 92 9 Al 2 O 3 145 187 157 32 SiN 68 64 66 10 SiN 54 68 58 33 Al 2 O 3 182 170 180 11 TiO 2 83 105 86 34 SiN 68 64 68 12 SiN 54 69 59 35 TiO 2 105 90 102 13 Al 2 O 3 141 191 158 36 SiN 70 62 70 14 SiN 55 69 59 37 Al 2 O 3 194 169 185 15 TiO 2 83 105 87 38 SiN 67 64 71 16 SiN 53 69 60 39 TiO 2 104 97 102 17 Al 2 O 3 142 185 163 40 SiN 68 65 70 18 SiN 56 68 60 41 Al 2 O 3 180 178 182 19 TiO 2 82 102 92 42 SiN 80 66 82 5
20 SiN 55 67 66 43 TiO 2 25 100 23 21 Al 2 O 3 152 176 181 44 SiN 77 67 83 22 SiN 57 64 69 45 SiO 2 95 87 100 23 TiO 2 82 91 103 Table S1. Layer thickness parameters for various photonic cooler designs References 1. Andreas, A, Wilcox, S. (2012). Solar Resource & Meteorological Assessment Project. (SOLRMAP): Rotating Shadowband Radiometer (RSR); Los Angeles, California (Data); NREL Report No. DA-5500-56502. http://dx.doi.org/10.5439/1052230 6