1. Introduction

Luminescent solar concentrators (LSCs) operate on the principle of down-conversion of solar radiation. Incident sunlight is absorbed, re-emitted in a specific spectral range, and transferred by total internal reflection to photovoltaic (PV) cells at the edges of the LSC. Research in the design and development of LSCs began in the 1970s [1], but early work used organic dyes as the active material. In spite of high quantum yield (QY), drawbacks such as photo-bleaching from solar irradiation and large self-absorption (SA), where the fluorescent species re-absorb their emitted photons, limited their efficiencies [2]. The field remained dormant until recently, when advances in materials science renewed interest in LSCs by making other viable candidates available, such as semiconducting polymers, quantum dots (QDs) and specialized dyes [3–6]. Advances in patterning techniques have further allowed various optical modifications to limit SA [7–9]. Theoretically, the energy conversion efficiency of LSCs can be as high as 24% [10], but the highest efficiency experimentally achieved is considerably lower [6] as LSCs suffer from some typical problems. These include inadequate utilization of the solar spectrum [11], large SA, low QY and photo-degradation. And finally, practical LSCs require that the fluorescent material be embedded in a polymer or glass plate. This often gives rise to luminescence quenching [12], further reducing the device efficiency. Here, we attempt to alleviate some of these shortcomings through rational design of both the active material and the geometry of QD-based LSCs.

2. Experiments

Over 60% of the total solar photon flux occurs at wavelengths greater than 600 nm [13]. As a result, fluorescent materials with broad absorption bands extending into the near-infrared are preferable to those that absorb only in the visible part of the solar spectrum [14]. We use lead sulfide (PbS) QDs as our active material. Figures 1a and 1b (solid lines) show the spectral absorption and emission for a solution of PbS QDs (Evident Technologies), 2.2 nm in diameter. A basic evaluation of the viability of PbS QDs as the active material in an LSC coupled to silicon (Si) PV cells has yielded encouraging results [15], but has simultaneously exposed a shortcoming in the form of photo-instability. When suspended in a solution, these QDs photo-oxidize within minutes of exposure to sunlight, resulting in a corresponding rapid decrease of the photocurrent. This is shown in Fig. 2c (open circles) as the normalized short circuit current (I_LSC) generated by a Si PV cell.

 

Fig. 1 (a) Absorption spectra for PbS QDs in solution and for two representative QD-PMMA composite samples, one prepared by secondary dispersion (SD) and one by radical polymerization (RP). (b) Emission spectra for the same. The individual Stokes shifts are indicated by double headed arrows in part (a). (b, insets) Spatially-resolved emission maps showing the emission wavelength over a 1 × 1 mm² area of the SD (left) and the RP (right) samples.

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Fig. 2 (a) Solid and (b) hollow CLSCs with 60, 80 and 100 µM of QDs (left to right). The scale bar represents 1.0 cm. (c) Normalized I_LSC measured immediately after photo-exposure for QD solution (open circles) and a QD-PMMA composite (filled circles).

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One option for stabilizing the QDs is by encapsulating them in a suitable host material where they can be easily dissolved and uniformly dispersed without aggregation or phase separation. We use polymethylmethacrylate (PMMA) as our choice of the host due its low absorptivity in the visible and infrared spectral regions. QD-PMMA composite samples are typically prepared by secondary dispersion (SD) [16] where the PMMA pellets are dissolved in toluene, an appropriate ratio of the PMMA and QD solutions mixed and cured in molds. Figures 1a and 1b (open squares) show the absorption and emission spectra of a QD-PMMA composite that we have prepared using SD. Both are spectrally blue-shifted compared to the solution data, and the QY reduced by approximately 70%. These are attributed to oxidation of the QDs during the dispersion process. Further, these samples are not homogenous, as is seen in the spatially-resolved spectral scan of Fig. 1b (left inset) taken over a 1 × 1 mm² region with a 5 µm spatial resolution. The peak emission wavelength varies over a range of almost 60 nm, and such non-uniformity is not entirely atypical in composites prepared this way [16].

A second method to encapsulate QDs into PMMA solids was suggested in [17] which involves the thermally-driven radical polymerization (RP) of a QD-monomer mixture using an initiator. QDs are dissolved in methylmethacrylate (MMA) monomer solution and a radical initiator, azobisisobutyronitrile, added to the mixture to start the polymerization. This mixture is then poured into molds to allow the process to complete, which requires up to 24 hours. The absorption spectrum of RP samples prepared following [17] is unshifted from the solution spectrum (Fig. 1a, solid circles), implying no oxidative size reduction of the QDs. The emission (Fig. 1b, solid circles) is red-shifted and we believe this to be a result of inter-dot energy transfer facilitated by close packing of QDs in the composite. While sometimes such close-packing may lead to sample inhomogeneity and luminescence quenching, the QY is approximately twice that of the SD samples. Further, the spatial scan (Fig. 1b, right inset) reveals spectral uniformity with the emission wavelength not varying by more than 10% over the scanned area. Given these results, we use RP to synthesize our samples. Figure 2c compares I_LSC as a function of time immediately following photo exposure for both the solution and the QD-PMMA composites prepared by RP taken under external ambient conditions. The QD-PMMA sample does not display the instability of the solution and we have verified that I_LSC remains stable over hundreds of hours for the composites.

The concentration factor C in LSCs is calculated as: C = η_opt × G, where G is the geometric factor (ratio of the top surface area to that of the edges) and η_opt the optical efficiency, a product of the absorption, retention and quantum efficiencies. Concentrators will work efficiently only if η_opt remains undiminished as G increases. As an example, our 1 × 3 inch rectangular QD-PMMA LSC yielded η_opt = 4% and G = 2.3 (resulting in C = 0.1). But when scaled up to 12 × 12 inches, in spite of G = 19, increased SA reduced η_opt to 1% making the total concentration effect just marginally better (C = 0.19) instead of several times greater. Cylindrical geometry for LSCs was first proposed in [18] as a means of enhancing the geometric factor G without using more active material in the volume. We fabricate both solid and hollow cylindrical LSCs (CLSCs) (Figs. 2a and 2b) using PbS-PMMA composites prepared by RP. The sample nomenclature follows the QD concentration in the total volume. Both CLSCs are 25 mm long and have an outer radius R₁ = 6 mm and the hollow CLSC has an inner radius R₂ = 3.8 mm (Fig. 3a ) with an index matched transparent core. For operational purposes the PV cell would attach to the end of the CLSC, as shown in Fig. 3a (the solar radiation incidence direction is indicated by dashed arrows).

 

Fig. 3 (a) Schematic of a PV cell attached to a hollow CLSC. Arrows show directionality of incident radiation. (b) The curves show calculated values of the ratio of transmission from hollow and solid CLSCs varying with QD concentration. Legend represents values of R₂/R₁. Squares denote experimental data for R₂/R₁ = 0.6.

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Of the three major factors that determine η_opt, absorption, retention and QY, only the last is unaffected by sample geometry. We begin by calculating the difference in solar flux absorption between the solid and hollow CLSCs when each has the same total number of QDs. Consequently, the concentration of QDs in the active volume is higher in the hollow CLSC. We calculate the transmitted intensity T using T = T₀e-^Npσ where T₀ is the incident solar intensity (calculated from an incident solar flux of 1000 W/m²), p is the path length through the active volume and σ is the absorption cross-section of a single PbS QD [15]. We find that hollow CLSCs absorb more sunlight over all. Figure 3b plots the ratio of transmittance, T_hollow/T_solid varying with QD concentration for different values of R₂/R₁. The squares represent experimental values of this ratio for R₂/R₁ = 0.6 averaged over three samples, and show a similar trend to the calculated results. The slight discrepancy is due to the convolution of other effects in the experimental measurement such as the size inhomogeneity of QDs in the samples that introduce uncertainty in the absorption cross section values, and unavoidable scattering and re-absorption effects that are ignored in the calculations.

We perform a similar calculation to estimate SA as we did for solar absorption, with a few alterations. T₀ is now the emission from QDs in the volume of the LSC and the path of the radiation, p, is a trace along the CLSC axis, because the down-converted emission travels along the axis to the ends (sketched in Fig. 4a ). As in a flat panel, in a solid CLSC SA occurs throughout the volume of the sample, but in a hollow CLSC there are regions (the core with no QDs) where there is no SA, shown as dashed lines in Fig. 4a. The percentage of the intensity of down-converted emission transmitted to the end of the CLSC is calculated for different shell thicknesses and plotted in Fig. 4b. A solid cylinder (R₂ = 0) transmits least implying SA is highest. As QD concentration increases, SA increases in both hollow and solid CLSCs and the difference between the two geometries is reduced. The best way to quantify the extent of SA experimentally is by measuring the spectral shifts [5] in the emission rather than intensity. The sample is excited by a collimated beam from a laser tuned to 632 nm and the excitation spot is continuously varied along the length of the cylinder while the emission is collected at the end (inset, Fig. 4c). As the distance d between excitation and collection increases, the photons emitted by the QDs travel a longer distance, and have a higher probability of being re-absorbed and then re-emitted at longer wavelengths. The final effect is a net red-shift of the emission spectrum, as is observed between the emission spectra in Fig. 4c. The spectra corresponding to d = 20 mm is red-shifted compared to the spectra at d = 0 mm. Plotting the emission peak as a function of d for one hollow and one solid CLSC in Fig. 4d we find a smaller red-shift in the hollow CLSC (8 nm) than in the solid one (18 nm), which agrees with our calculations that hollow CLSCs exhibit less SA.

 

Fig. 4 (a) Schematic showing possible travel paths towards the ends for photons emitted in the active volume of a hollow CLSC. The regions where SA might occur are shown by thicker lines. (b) Calculated values of percentage of intensity of down-converted emission transmitted at the end of the solid and hollow CLSCs as a function of QD concentration for different values of shell thickness of the hollow structures. Legend represents values of R₂/R₁ (c, inset) Measurement scheme used to determine SA experimentally. (c, main) Spectral emission of the 100 μM solid CLSC at d = 0 and 20 mm. (d) λ_PEAK of the solid and hollow CLSCs as a function of d for QD concentration 100 μM.

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Figure 5 summarizes our final efficiency measurements averaged over three samples of each geometry, all with comparable G. The optical efficiency η_opt, plotted as a function of QD concentration, is calculated as η_opt = I_LSC /(I_PV × G) where I_PV is the short circuit current generated by the PV cell without an LSC. η_opt continuously increases with sample concentration, something not always observed [5], a result of larger Stoke’s shift and lower SA in PbS QDs. The flat LSC and solid CLSC both absorb approximately 50% of the incident light for the highest QD concentration, and the SA for both is almost the same, with the 100 μM sample transmitting a very small fraction of its emission to the edges. We cannot measure escape cone losses independently from SA losses in our samples, but the total retention efficiency calculated from η_opt yields values of 31% and 43% for the flat LSC and the solid CLSC, respectively. Within the error bars, these two do not have significantly different performances, as we would expect in LSCs with similar G and concentration of active materials, no matter what the geometry. Between the hollow and solid geometries, the hollow CLSC absorbs between 20 to 30% more sunlight based on our experimental data and calculations (Fig. 3b). By contrast, it consistently has lower SA and transmits almost 55% more emission to its edges for the 100 µM sample (Fig. 4b), also supported by the smaller spectral red-shift (Fig. 4c). The enhanced absorption and reduced SA add up to the higher η_opt we observe for the hollow CLSCs in Fig. 5. Its retention efficiency is 53% for the most concentrated sample.

 

Fig. 5 Optical efficiency plotted as a function of QD concentration for rectangular flat LSC (squares), solid CLSC (filled circles) and hollow CLSC (open circles) samples. Data repeated after six months are shown for solid (filled triangles) and hollow (open triangles) CLSCs for 60-100 µM QD concentrations.

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Figure 5 shows additional η_opt data for the solid and hollow CLSCs re-taken after a period of six months (solid and hollow triangles). While the QD-PMMA composites are stable for hundreds of hours, it appears they degrade on a longer time scale. Within the error bars, the 60 μM samples appear stable, but the more concentrated ones exhibit distinctly worse performance. This may be a result of the fact that more concentrated samples have a higher probability of inter-dot energy transfer events, so darkening of a fraction of QDs in them results in a net increase in overall luminescence quenching [19].

A primary consideration in the design of LSCs is the volume of active material used. Our results are significant because they demonstrate that a simple re-structuring of the cylindrical geometry to form hollow structures, while maintaining the same G, can lead to both higher absorption and reduced self-absorption, resulting in a better performing CLSC module while not requiring more of the active component. Theoretical studies [18] have suggested that an array of CLSCs may have higher efficiencies than the sum of the individuals due to reduced external reflection losses. If this proves correct in practice, then an array of hollow CLSCs would provide an even more attractive route as it would not only reduce external losses, but be a means to overcoming the more fundamental problem of scalability. The biggest drawback in our study is the decrease in QY when the QDs are encased in PMMA, but it has been possible to arrest this problem in core-multishell CdSe QDs [20]. If a similar solution were found for the PbS QDs, our CLSCs would achieve optical efficiencies several times better than observed here. An array of hollow cylindrical LSCs would offer cumulatively higher efficiency compared to a both a flat LSC and a solid CLSC array of the same geometric factor.