1 The role of light scattering in the performance 2 of fluorescent solar collectors 3 Nazila Soleimani,a Sebastian Knabe,b Gottfried H. Bauer,b Tom 4 Markvart,a Otto L. Muskensc a 5 Materials Research Group, School of Engineering Sciences, University of Southampton, 6 Highfield, Southampton. SO17 1BJ b 7 Institute of Physics, Carl von Ossietzky University of Oldenburg, D-26111 Oldenburg, 8 9 Germany c SEPnet and Department of Physics and Astronomy, University of Southampton, Highfield, 10 Southampton. SO17 1BJ 11 12 Nazila.Soleimani@soton.ac.uk; T.Markvart@soton.ac.uk; O.Muskens@soton.ac.uk 13 14 Abstract. A fluorescent solar collector (FSC) is an optoelectronic waveguide 15 device that can concentrate both diffuse and direct sunlight onto a solar cell. 16 The electrical output of the device depends strongly on the photon fluxes that 17 are absorbed, emitted and trapped inside the FSC plate; for this reason, it is 18 important to study the photon transport losses inside the collector. One of the 19 losses in FSC is investigated to be scattering which increases the probability 20 of the escape cone losses. The purpose of this work is to determine the 21 scattering contributions in FSC by using angle dependence of light internally 22 reflected in the FSC. The cause of the scattering in spin-coated PMMA on 23 top of the glass collector is identified to be roughness from the top surface 24 rather than bulk losses. This loss can be suppressed using an index-matching 25 planarization layer. 1 26 Keywords: Fluorescent solar collector; Solar energy; Scattering; Scattering 27 measurements. 28 29 1 Introduction 30 In a typical fluorescent solar collector (FSC), the luminescent light is trapped by total internal 31 reflection (TIR) and guided to the edge of the plate where it can be harvested by a solar cell. 32 One objective of the collector design is to reduce the size of the solar cell with respect to the 33 area which collects light. Unlike their geometric counterparts, fluorescent collectors can 34 accept light from a wide angle of incidence and are thus able to make use of the diffuse light.1 35 The photon flux at the edge of an idealized FSC is the product of the absorbed solar flux, the 36 fraction of the trapped luminescence, and the geometric ratio of the area of the face directly 37 exposed to sunlight Af divided by the area Ae of the edge that is covered by the solar cell. The 38 geometric gain Ggeom of the FSC is then given by: 39 G geom Af (1) Ae 40 Weber and Lambe (1976) initially suggested the concept of luminescence trapping for solar 41 concentrators, which they named the luminescent greenhouse collector2. In experimental FSC 42 devices, the emitted photon flux is less than ideal due to several loss processes, including 43 reabsorption and scattering.1,2,3,4,5 44 In this work, we investigate the effect of surface scattering in realistic FCS devices based on a 45 dye-doped PMMA layer on top of a glass slide. To characterize the photon transport inside the 46 collector we monitor the angular distribution of a collimated light beam which enters the 47 collector from the edge, after propagation and total internal reflection. We find that the 48 surface scattering process is described well by Fraunhofer diffraction at surface 49 inhomogeneities of a size of several m. 50 2 51 2 Theory 52 We calculate the effect of diffraction due to surface roughness on the FSC efficiency using the 53 model developed by Weber and Lamb.2 In their model, they included the guiding of light in 54 the FSC at angles larger than the critical angle for total-internal-reflection, c. Attenuation of 55 reflected light by reabsorption is taken into account through an effective absorption 56 coefficient e, while Fresnel reflection losses at the interface between the low-index FSC and 57 the high-index solar cell is included through Fresnel’s reflection coefficients for s- and p- 58 polarized light. 59 In addition, we include here losses caused by angular spread of the reflected light due to 60 surface roughness. The effect is included as a divergence of angles with a Gaussian profile of 61 1/e half-width . Around the critical angle, this additional spread in angles results in part of 62 the light to be lost within the escape cone. The angular distribution of light remaining after 63 one reflection from the rough surface can be approximated from the convolution of the unit 64 step function with the Gaussian diffraction function, resulting in the error function 65 P()=erfc[(c-)/]/2. Under the condition that the scattering is only a small correction on 66 the distribution function, the sequence of total internal reflections can be written as a 67 multiplication of a number of error functions where the number is given by the amount of 68 internal reflections from the rough surface. Inclusion of this effect in the Weber and Lambe 69 model results in a total collection efficiency Q C given by QC (2L) 1 L dy 0 70 /2 d 0 /2 1 2 erfc ( c ) / N R ( , ) sin d c exp e ( L y ) / sin sin exp e ( L y ) / sin sin 2 [2 rs ( , ) r p ( , ) ]. 2 71 Here the number of total internal reflections from the rough surface is given by 72 2L y N R ( , ) cot cot , 2T (2) (3) 3 73 where we have introduced the FSC thickness T. The brackets indicate the floor function which 74 rounds NR to the largest previous integer. 75 Results were calculated for the collection efficiency of the FSC for a representative collector 76 with index nc=1.5 coupled into a semiconductor of index ns=3.35. We assumed a thickness 77 given by T=L/50, which is typical for a medium-scale FSC device with a geometric gain of 78 50. Different values of T will only change the total amount of scattering loss, not the 79 qualitative response. Figure 1a shows computed values obtained by numerical integration of 80 Eq. (2). The curve in absence of surface scattering (closed circles) corresponds to the Weber 81 and Lambe result.2 Introduction of a surface roughness characterized by a =1.5° divergence 82 results in a reduction of the efficiency by several percent (open circles). Also shown are the 83 total (triangles) and relative (diamonds) scattering losses, where the latter is normalized to the 84 collection efficiency for a smooth film (=0). The right-hand panel in Fig. 1 shows the 85 absolute and relative scattering losses as a function of for a value of eL=10-2, i.e. low 86 reabsorption. Above =1°, the scattering loss increases roughly linear with the diffraction 87 width . The loss percentage of 5% for 2.5° indicates the importance of surface 88 roughness optimization in experimental FSC. For comparison we have also shown the results 89 for T=L/5.2, which corresponds to the small-scale experimental configuration in this work. As 90 can be seen the scattering loss does not scale linearly with the system size, i.e. the number of 91 internal reflections, indicating that the majority of the loss is accumulated during the first few 92 reflections. This can be understood from the fact that the angular range around the critical 93 angle gets depleted of photons after the first few internal reflections and therefore the effect 94 saturates. 4 95 96 Figure 1. (Left) collection efficiency for the FSC as a function of eL calculated using the 97 modified Weber and Lambe model Eq. (2), for a perfectly smooth surface (, closed dots) 98 and a surface roughness characterized by ° and T=L/50 (open dots). (Triangles, blue) 99 Absolute scattering loss and (diamonds, red) relative scattering loss normalized to the result for 100 . (Right) (Triangles, blue) Absolute and (diamonds, red) relative scattering loss at eL = 101 10-2 as a function of the 1/e half width of the diffraction cone, for T=L/50 (symbols) and for 102 T=L/5.2 (dashed lines). 103 2 Method 104 2.1 Sample 105 The substrate used in this study was a BK7 glass slide with dimensions of 26×26×5 mm3. 106 Before depositing the layers the slides were thoroughly cleaned. A solution of 9% - 10% 107 PMMA dissolved in Chlorobenzene (Micro Chem) was spin-coated (Laurell EDC-650- 108 15TFM) at a speed of 4000 rpm for 1 minute. The thickness of the spin-coated layer was 109 measured by using a profilometer (Talysurf-120 L, Taylor Hobson Ltd.) and was found to be 110 24.85 μm. The surface morphology of the PMMA layer was characterized using Atomic 111 Force Microscopy. Figure 4 shows a representative AFM image revealing that the layer shows 112 a roughness of around 48 nm over a typical correlation length of several m. This roughness 113 may be associated with the relatively large thickness of PMMA required for fluorescent 114 conversion in a realistic FSC, resulting in height variations during the spin-coating process. 5 115 However, fluctuations may also be intrinsic to the polymer itself. Large scale heterogeneities 116 have been observed even in very pure PMMA, and its nature may be related to local 117 alignment of polymer chains and strain produced during the drying process.6 118 119 Figure. 2. Atomic Force Microscopy measurement of the PMMA layer, 120 showing height fluctuations of ~48 nm over a distance of several m. 121 122 2.2 Scattering setup 123 For the characterization of light scattering, the samples were illuminated with a laser beam 124 impinging from one side-edge of the glass. The sample was placed at the center of a circular 125 goniometer table illuminated with a laser. A silicon photodiode (SM05PD1A, Thorlabs) was 126 mounted at the edge of the table as shown in Fig. 3. The distance between the sample and the 127 detector was 27 cm. A pinhole with a diameter of 1 mm was placed in front of the silicon 128 photodiode which gives a solid angle for collection of 0.2°. A frequency of 185 Hz was 129 applied via a chopper to the beam and the current was detected by a photodiode connected via 130 a lock-in amplifier (SR810). The lock-in amplifier was used to decrease the noise of the 6 131 measurement by locking in to the chopper frequency and the average of two current 132 measurements, captured 1 second apart, was taken. The interface of this setup was 133 programmed in Labview (8.6) software. A sample holder was fixed to the center of the 134 goniometer table. The laser beam was aligned perpendicular to the surface of the sample, and 135 the photodiode could be rotated around the table for measuring the scattered intensities at 136 different angles. The scattered light intensity was measured between 0° and 180° with a 137 scattering angle increment of 0.5°. 138 139 Figure 3. Schematic of the experimental setup for the angle-dependent scattering 140 measurements. 141 2.3 Scattering measurement of FSC by angular dependence method 142 This section describes the method for measuring the scattering of PMMA spin coated on top 143 of the BK7 glass by illumination from one edge in different incident angles and detection 144 from another edge. 7 145 146 Figure 4. PMMA spin coated glass illuminate with laser light from one edge and the 147 scattered light was detected from another edge at different angles, θ1=15° and 148 N=14.21mm, M=11.79 mm. The error in this experiment was 0.8 mm which is the 149 width of the laser beam. 150 The distance of M (distance from detector inside of the glass) can be calculated by sin 1 151 n 2 for n2=1.5 and n1=1 sin 2 n1 152 tan 2 D 2N , N=26-M . (4) (5) 153 Values for N for different incident angle from one edge are shown in Table 1. If N <26 mm, 154 the probability that the light is totally internally reflected increases if 90-θ2 is more than the 155 critical angle. 156 157 Table 1. Distance from the incident beam inside of the glass for different incident angle, the 158 error in this calculation is 0.8 cm, given by the width of the laser beam. Angle of incidence No. of TIRS Distance M(cm) 0° 0 N.A. 15° 1 14.21 35° 2 6.04 45° 3 4.77 159 8 160 For incident angles less than 8.3° there is no reflection inside of the collector. For incident 161 angles between 8.3° to 24.6° there is one reflection inside of the collector, for the incident 162 angles between 24.6° to 40.5° there are two reflections inside the collector, and for the 163 incident angle of 45° there are three reflections inside the collector. 164 165 166 3 Results 167 Values of the intensity of scattered light measured over a range of angles are plotted in Fig. 5 168 for three different angles of incidence of 15º, 35º and 45º. To compare the results the 169 maximum intensity for all the measurement was defined as 0º. Clearly, the light cone 170 transmitted through the PMMA-coated FSC is considerably broadened compared to a bare 171 glass slide. As seen in Table 2, the angular width of the scattered intensity cone increases for 172 larger angles of incidence up to 45°. The width here is determined as the length over which 173 the intensity drops to 1/e of the maximum. The measurements at 15° and 35° show the same 174 width, which can be understood from the fact that the second internal reflection takes place at 175 the opposite glass surface without PMMA. As we will show below, the observed behavior is 176 consistent with diffraction of the laser beam caused by the roughness of the PMMA layer. 177 In a simple model, we include the diffraction by describing the reflected light as a collection 178 of diffraction-limited cones with an aperture given by the correlation length of the surface 179 roughness. 180 9 Intensity (norm.) 1.00 -5 Glass 15 35 45 Gaussian 0.50 -4 -3 -2 181 0.00 -1 0 1 Scattering angle ( ) 2 3 4 5 182 Figure. 5. Angular dependence of normalized intensity for different incident 183 angles for 670 nm incident light. Lines: Gaussian fits. 184 Table 2. Beam width for different incident angles of incidence. Angle of incidence 0° laser beam 1/e half-width of the scattered beam (º) 0.6 15° 1.3 35° 1.4 45° 1.6 185 186 187 Thus, if we consider the PMMA surface as a collection of uncorrelated areas, the angular 188 distribution of the reflected intensity can be fitted to the Fraunhofer diffraction formula for the 189 circular aperture, given by7 190 I I0 G 2 2 J 1 ( ka sin ) ka sin 2 r 2 2 (6) 191 where the G=πa2, a is the radius of the aperture, r is the distance from observation point to 192 shadow area, λ is the wavelength of the incident, J1 is the Bessel function of the first order and 193 k is the optical wavenumber. 10 194 Equation (6) gives us the intensity of the scattered light in different detection angles known as 195 the Airy pattern. We note that the use of a Gaussian angular spread in Eq. (1) is a good 196 approximation as the central lobe of the Airy pattern shows close agreement with a Gaussian 197 profile.7 Good agreement is obtained for a radius of the aperture of 11 µm for the data taken at 198 670 nm wavelength and at 15º angle of incidence, as shown in Fig. 7. 199 200 201 Figure 6. Scheme showing PMMA spin coated on top of the glass illuminate 202 with laser light from one edge in incident angle of 15° and the forward 203 scattered light detected at different angles. The roughness from spin coated 204 PMMA is assumed to produce an effective circular aperture when the laser is 205 reflected by the rough layer. 11 1.00 15°, 670 nm Intensity (norm.) Fraunhofer diffraction, 670 nm -5 206 0.50 -4 -3 -2 0.00 -1 0 1 2 Scattering angle (degree) 3 4 5 207 Figure 7. Normalized angular dependence of I in 15° incident angles in 208 PMMA side for 670 nm. The solid line was fitted by using equation 4, circles 209 indicate the experimental results. 210 211 The validity of the diffraction model can be verified by changing the optical wavelength. 212 Figure 8 shows the scattered light intensity measured over a range of angles when we 213 illuminate the sample from one edge at 15 degree through the PMMA part at different 214 wavelengths of respectively 401 nm, 532 nm, 633 nm , and 670 nm. Clearly, the scattered 215 light cones show a decrease in width for decreasing wavelength. 216 The Fraunhofer diffraction for the circular aperture was calculated when the size of the 217 particle is fixed at 11 µm while the wavelength was decreased according to the used lasers. 218 We find good quantitative agreement with our experimental results in Fig. 8 (lines), showing 219 that the diffraction pattern gets more and more compressed into a narrow cone around the 220 forward direction for shorter wavelengths. 12 1.00 15°, 670 nm Fraunhofer diffraction, 670 nm 15°, 633 nm Intensity (norm.) Fraunhofer diffraction, 633 nm 15°, 532 nm Fraunhofer diffraction, 532 nm 0.50 15°, 401 nm Fraunhofer diffraction, 401 nm 221 0.00 -1 0 1 Scattering angle (°) 222 Figure 8. Comparison of normalized scattering intensity at wavelengths of 223 670 nm, 633 nm, 532 nm, and 401 nm detected over a range of angles with 224 illumination from 15° incident angles through the PMMA part of the sample. -5 -4 -3 -2 2 1.00 3 4 5 15 °, without optical gel 15 °, with optical gel Intensity (norm.) Gaussian -5 225 0.50 -4 -3 -2 0.00 -1 0 1 2 Scattering angle (degree) 3 4 226 Figure 9. Comparison of intensity of scattered light at a wavelength of 670 227 nm detected over a range of angles with illumination from 15° incident 228 angles once when the PMMA top surface covered with the optical gel 229 (circles, blue) and without optical gel (diamonds, green). 5 13 230 To further investigate the cause of the scattering in spin coated PMMA on top of the BK7 231 glass, the top surface in PMMA (n=1.49) part was covered by optical gel with refractive index 232 of 1.4646(THORLABS). The surface tension of the gel produced a smooth film which 233 compensated the surface roughness of the PMMA layer. Subsequently, the irradiance of 234 scattered light as a function of angle was measured when illuminating the sample at a 15º 235 angle of incidence. The results are compared with a measurement taken on the same sample 236 before the gel was added. Results are shown in Fig. 9. As we can see, application of the 237 optical gel results a decrease of the angular width of the scattering cone. This effect 238 unambiguously shows that the cause of the scattering in spin coated PMMA on top of the 239 glass is the surface roughness. Compared to the surface scattering contribution, the bulk 240 scattering in this type of sample is negligibly small, i.e. of order 10-5 cm-1.6 241 It is relevant to consider whether diffraction effects play a role in the situation that the 242 illumination is provided by mutually incoherent fluorescent molecules. To assess this we have 243 to compare the divergence of a point source with the diffraction provided by the surface 244 roughness. For example, when a point source illuminates an area of 10 m at a distance of 1 245 mm from the source, this corresponds to a divergence angle of 10-2 radians or 0.5º, i.e. smaller 246 than the typical diffraction broadening in our samples. Therefore surface scattering losses are 247 relevant for incoherent fluorescence emission at propagation distances larger than several 248 hundred m, which is the case in FSC. 249 250 4 Conclusion 251 In summary, the contribution of light scattering in fluorescent solar collectors (FSC) based on 252 a spin-coated dye/polymer layer was investigated. Measurements of the transmission cones as 253 a function of total internal reflections (TIR) revealed that the predominant loss factor is 254 surface scattering at the top layer, caused by roughness of the spin-coated PMMA. 14 255 Good agreement is obtained when we consider the PMMA roughness as an coherent aperture 256 with a circular shadow therefore the angular distribution of the scattering intensity can be 257 fitted using far-field Fraunhofer diffraction. The width of the scattered beam increases when 258 the wavelength is increased from 401 nm to 670 nm, in good agreement with Fraunhofer 259 diffraction for a circular aperture at different wavelengths where the size of the aperture is 260 fixed to the value of 11 µm. This value is of the same order as the correlation length of the 261 height variations observed in AFM measurements. The value of the scattering was found to 262 decrease significantly when we cover the top surface with optical gel, which unambiguously 263 shows that surface scattering is the predominant loss factor in our FCS compared to bulk 264 scattering effects. Surface roughness is caused by to the large required thickness of the 265 PMMA-dye layer for the operation of the FSC. Our results indicate that the performance of 266 the FSC can be improved by using a subsequent planarization with a thin index-matching 267 layer of low roughness. 268 269 Acknowledgements The authors would like to thank L. Danos for help with the 270 experimental setup. This project was funded partly through UK SUPERGEN (Sustainable 271 Power Generation and Supply) PV21 Programme. 272 References 273 1. A. Goetzberger, W. Greubel, Solar energy conversion with fluorescent collectors, Appl. 274 Phys. 14,123–139 (1977). 275 2. W.H.Weber and J. Lambe. Luminescent greenhouse collector for solar radiation. 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