Luminescent solar concentrators (LSCs) use dye molecules embedded in a flat-plate waveguide to absorb solar radiation. Ideally, the dyes re-emit the absorbed light into waveguide modes that are coupled to solar cells. But some photons are always lost, re-emitted through the face of the LSC and coupled out of the waveguide. In this work, we improve the fundamental efficiency limit of an LSC by controlling the orientation of dye molecules using a liquid crystalline host. First, we present a theoretical model for the waveguide trapping efficiency as a function of dipole orientation. Next, we demonstrate an increase in the trapping efficiency from 66% for LSCs with no dye alignment to 81% for a LSC with vertical dye alignment. Finally, we show that the enhanced trapping efficiency is preserved for geometric gains up to 30, and demonstrate that an external diffuser can alleviate weak absorption in LSCs with vertically-aligned dyes.
©2010 Optical Society of America
Luminescent Solar Concentrators (LSCs) aim to reduce the cost of solar electricity by using an inexpensive collector to concentrate solar radiation without mechanical tracking [1–8]. Sunlight is absorbed by fluorescent dye molecules that are integrated in a thin, flat-plate waveguide. These dyes re-emit the captured photons at a lower energy for ultimate collection by solar cells mounted on the waveguide.
Here, we present a two part study on the effects of dye alignment in LSCs using polymerizable liquid crystals as a scaffold [9, 10]. In Part I we investigate LSCs whose dye molecules are aligned perpendicular to the plane of the waveguide, resulting in an improved coupling between the waveguide and dye re-emission and an enhanced LSC-performance. In Part II  we align dye molecules in-plane with the waveguide, causing the LSC absorption to be linearly polarized. This allows for a strategy in which linearly polarized LSCs replace conventional linear polarizers for energy harvesting in displays.
The essential processes within an LSC are shown in Fig. 1a . The efficiency of re-emission is given by the photoluminescent efficiency of the dye, ηPL. Ideally, photons re-emitted within the LSC are trapped in the waveguide by total internal reflection and guided to the edge of the plate. The fraction of photons confined within the waveguide is the trapping efficiency, ηtrap. Finally, a solar cell attached to the edge of the waveguide absorbs the photons and converts their energy into electricity. The geometric gain, G, of the LSC is defined as the area of the collector plate divided by the area of the solar cell. Increasing this figure of merit without compromising efficiency is the key to reducing the cost of solar electricity.
As a photon propagates within an LSC it may be re-absorbed by other dye molecules when a finite overlap exists between the absorption and emission spectra of the dyes. For n re-absorption events in the waveguide the LSC efficiency scales as (ηPLηtrap )n. LSC performance consequently depends on three key parameters: ηPL , η trap, and n. Many dyes already have ηPL → 1, especially in the visible spectrum, and the reduction of the re-absorption probability, i.e. n, especially for high geometric gains, has recently been the emphasis of several publications [7, 12–14].
Here, in Part I of our study, we focus on the trapping efficiency, for which large improvements are possible, since ηtrap is theoretically predicted to be approximately 75% for a conventional waveguide. Following the suggestion of Debije et al.  we directly address trapping losses by controlling the orientation of the dye molecules. Conventional LSCs employ randomly aligned dyes that collectively emit photons isotropically; see Fig. 1a. This yields a trapping efficiency of ηtrap ~0.75 for a waveguide refractive index of nS = 1.5. Instead, it is possible to align the dyes vertically so their transition dipoles couple more strongly into the waveguide, as illustrated in Fig. 1b. We employ a homeotropic liquid crystal matrix to align rod-shaped dye molecules perpendicular to the waveguide, as illustrated in Fig. 1c. Orienting the molecules at a right angle to the surface reduces the absorption of perpendicular incident radiation. Consequently, we employ an optical diffuser above the LSC to scatter incident light.
First, we derive theoretical predictions for the trapping efficiency as a function of the refractive index of the waveguide and the angle of the transition dipole. We also derive an expression for ηtrap of an isotropic LSC as a function of the angle of the incident light. Second, the trapping efficiency is determined experimentally for both vertically aligned and isotropic dye systems and compared to theoretical predictions. We demonstrate that vertically aligned (homeotropic) LSCs employing the rod shaped dye molecule, Coumarin 6 (3-(2-Benzothiazolyl)-N,N-diethylumbelliferylamine) exhibit higher efficiencies than conventional LSCs that rely on isotropic Coumarin 6 in a PMMA (poly(methyl methacrylate)) host matrix. Third, the performance of the LSCs as a function of incident angle is studied for the vertically aligned dipoles and contrasted to the performance of the isotropic system. Furthermore, the effect of the addition of an external diffusing layer to the vertically aligned and isotropic LSCs is characterized. Finally, the overall efficiency of the isotropic and vertically aligned LSCs is assessed as a function of geometric gain and compared to Monte Carlo simulations based on LSCs employing isotropic and homeotropically aligned dye systems.
2. Trapping efficiency – theoretical predictions
To assess the effect of dye molecule alignment on the trapping efficiency of LSCs, we first assume that a transition dipole aligned parallel to the long axis of electronic symmetry of the molecule determines the molecular emission pattern . We then calculate the fraction of photons trapped in a waveguide as a function of dipole orientation, θD, and the refractive index of the waveguide, nS, and cladding media, nC.
The expression for the time-averaged power density of a Hertzian dipole oriented along the z-axis  can be extended to arbitrary inclination, θD (see Fig. 2a for a schematic representation of the dipole orientation). The obtained expression for the power density, is integrated over the solid angle from θC to π - θC, where θC is the critical angle . Normalizing by the total power emitted by the dipole yields the following expression for the trapping efficiency of aligned dyes:
The trapping efficiency of aligned dyes as a function of θD is plotted in Fig. 2b for three different waveguide-refractive indexes. The trapping efficiency is maximum for a dipole aligned with the z-axis (θD = 0°), varying from ηtrap = 91% for a dipole embedded in a nS = 1.5 medium to ηtrap = 95% for nS = 1.7. The calculations assume an air cladding (nC = 1). The lowest trapping efficiency is calculated for a dipole lying in the plane of the waveguide (θD = 90°), ranging from ηtrap = 66% for nS = 1.5 to ηtrap = 73% for nS = 1.7.
Figure 2c presents the calculated trapping efficiency as a function of nS for perpendicular, in-plane and isotropic dipoles. Achieving ηtrap > 90% in an LSC based on isotropic, randomly-oriented dye molecules, requires a waveguide with refractive index nS > 2.2. The practicality of the various approaches to improving trapping efficiency is discussed below.
The trapping efficiency of an isotropic dye system can also be calculated from Eq. (1) Assuming that the exciton alignment within the LSC is also isotropic yields the familiar result for the isotropic trapping efficiency:
However, if there is no energy transfer or other dispersion of exciton alignment within the LSC, then the angular distribution of excited dyes depends on the angle of the incident light, θI, as measured within the LSC [7, 18]. Integrating over all solid angles, and normalizing gives the following expression for trapping efficiency for an isotropic dye system as a function of the angle of the incident light:Fig. 2a). Solving Eq. (3) for s and p polarized light we find that considering the angle of the incident light makes a small correction to the usual expression for the trapping efficiency of an isotropic LSC.
For p-polarized incident light we obtain:18]. The most important consequence of considering the anisotropic initial distribution of excited dipoles is a reduction in the expected trapping efficiency from ηtrap = 75% for an nS = 1.5 index waveguide under normally-incident light to ~ηtrap = 71%; see Fig. 2d.
3. Device fabrication and experimental techniques
Vertically aligned and isotropic dyes are incorporated in scaffolds of a homeotropic polymerizable liquid crystal mixture or PMMA, respectively. The substrate is a 1-mm-thick glass with a refractive index, n = 1.7 (SF10, Schott). Glass substrates are cut with a dicing saw to the desired dimensions. The geometric gain, G, of an LSC is defined as the ratio of the face area versus edge area. When solar cells are attached to each edge of a square collector, G = L/(4t), where L is the length of the LSC and t is the thickness. For the experimental assessment of the trapping efficiency the glass substrates are cut to squares of 2 × 2 cm. Measurements of the external quantum efficiency (the fraction of incident photons converted to current in the attached solar cells) employ substrates with a substrate size of 7.6 × 9.5 cm. The glass substrates are thoroughly cleaned with a detergent solution, DI water, and solvents.
The polymerizable homeotropic liquid crystal host used in this study is UCL018 (Dai Nippon Ink and Chemicals, Inc.). This mixture includes a polymerizable nematic liquid crystal, homeotropic dopant molecules, and a photo-initiator. The dye molecule used for the experiments is Coumarin 6. Coumarin 6 has a high photoluminescence efficiency (measured to be 78%, which is in close agreement with literature ) and is known to possess a relatively high dichroic ratio . Coumarin 6 is also characterized by a large Stokes shift, which makes this dye especially suitable in an LSC [21, 22]. In a vial, UCL018 (40%) is added to Coumarin 6 (0.40% total weight ~1% solid weight content). FC-4430 (NovecTM, 3M) is used as a surfactant (0.40%) and taken from a pre-prepared solution of 5% FC-4430 dissolved in toluene. To these substances, toluene is added (59.2%) and gently stirred. All percentages of the separate components are given relative to the total weight of the mixture. When the components are well dissolved (after being stored for approximately an hour in the dark at room temperature) the solution is filtered and spin-cast on the glass substrates. The spin-speed is adjusted to yield a peak-absorption of around 40% (optimized for specific experiments). A typical spin-cast recipe uses an acceleration of 500 rpm/sec and a spin speed of 1250 rpm for a duration of 15 seconds. Directly after spinning, the samples are placed for 1 minute on a hotplate at 50°C in still air to help alignment and to let the sample dry. Subsequently, the samples are cooled down to room temperature for 1 minute before placing them under a UV lamp (365 nm) for 2 minutes to cure.
Isotropic LSCs use PMMA (Sigma Aldrich) as a host matrix. In a vial, PMMA and toluene are added to a concentration of 150 mg/mL. The vials are heated (at 70°C) and stirred to dissolve the PMMA. Coumarin 6 is added to obtain a concentration of 1.5 mg per mL of toluene (equal to a 1% solid weight content). After all components are well dissolved the solution is filtered and spin-cast on a clean glass substrate. Also here, the spin-speed is adjusted to obtain the desired peak-absorption within the sample. All thin film absorption measurements are obtained using an Aquila spectrophotometer at 30° incidence.
The edges of the glass substrates coated with PMMA or the liquid crystal mixture are cleaned before optical characterization with a solvent to remove material that might incidentally have spilled on the edges during the spin-casting process. The edges for all the reported experiments are smooth. We do not observe a difference in out-coupling from the edges for the Coumarin 6-doped LSCs when we use roughened or smooth edges.
The trapping efficiency of conventional, isotropic LSCs and vertically-aligned LSCs is measured with the use of an integrating sphere (see Fig. 3a for a schematic of the set-up). The samples are placed in the center of the sphere and excited by a monochromatic beam incident normal to the face of the samples. The beam is created by coupling a 150W Xenon lamp into a monochromator and chopping it at 73 Hz. The photoluminescence of the LSCs is detected through a photo-detector mounted on the integrating sphere. The trapping efficiency is given by the ratio between the number of photons emitted from the edges of the LSC to the total number of photons that are emitted from both the face and the edge of the LSC. In the absence of self absorption losses, the trapping efficiency is independent of the fraction of incident light absorbed by the sample. We discriminate between face and edge emission by selectively blocking the edge emission with a black marker. The blackening with a black marker is tested to block over 98% of the transmission and internal reflections. The responsivity of the sphereis given by the fraction of directly incident photons that is ultimately detected by the photo-detector mounted on the sphere. We account for the difference in responsivity of the integrating sphere and the photo-detector for clear edged and black edged samples by placing either a clear edged sample or a black edged in the center of the sphere.
The angular dependence of the absorption within isotropic and homeotropic (vertically aligned) LSCs is obtained from the edge emission as a function of the angle of the incident light beam. Not only is the fraction of photons emitted from the edge of the LSC directly proportional to the number of photons absorbed within the waveguide, it is the best measure of the performance of the LSC overall. Furthermore, it allows us to probe the angular distribution of excited dyes within the LSC, which, for the isotropic LSCs, will depend on the angle of the incident light. As outlined in Section 2, increasing the incident angle will increase the number of excited vertical dipoles and hence result in an enhancement in the trapping efficiency. A schematic representation of the set-up used to test the angular dependence of the LSC performance is presented in Fig. 3b. One of the edges of the LSC is placed into the opening of an integrating sphere, while the other three edges of the glass are blackened out to prevent indirect radiation reaching the edge inserted into the sphere. The LSC is excited in the center of the waveguide with a λ = 408 nm laser, whose power is monitored over time with the use of a beam-splitter and a second photo-detector. The remainder of the opening in the sphere is blocked and a spectral filter is used to prevent scattered laser light from reaching the photo-detector that has been mounted directly onto the sphere.
Holographic diffusers are obtained from Edmund Optics with ~90% transmission efficiency under varying diffusive strengths. The diffusive strength (10°, 30° and 60° for the holographic diffusers used in this experiment) is the maximum angle to which at least 0.1% of the light is scattered given a collimated beam incident normal to the surface. The holographic diffuser is placed at a distance of 1mm in front of the LSC (see Fig. 3b) and the laser beam is positioned to be incident normal to the diffuser surface.
The external quantum efficiency of an LSC, the ratio of electrons out to photons in, is measured using two GaAs solar cells from Spectrolab, each with an external quantum efficiency of ~85% at the emission wavelength of C6 and cut into 3.8 cm × 0.34 cm strips. The cells are connected in series, and attached to one of the short edges of the LSC with index matching fluid (Norland Products). The other 3 edges are blackened out with a black marker to prevent indirect luminescence from reaching the solar cell. The absorption within the films peaked at 42% for both the isotropic and homeotropic LSCs. Figure 3c presents a schematic of the EQE-set-up. Concentration factor-dependent measurements are obtained by directing an excitation beam perpendicular to the LSC so as to create an excitation spot of ~1 mm2, while the distance, d, between the spot and the solar cell is varied. This is an experimentally convenient technique to simulate the performance of LSCs at different geometric gains. It provides a lower bound for the performance since the average path-length is slightly longer than a uniformly illuminated LSC. The measured photocurrent was multiplied by the factor, g, which corrects for the different angle subtended by the solar cell at each spot distance: .
Experimental results are compared to simulations using a Monte Carlo ray-tracing model [23–26], extended to consider dye molecules with arbitrary orientations. The LSC components are modeled by their experimentally measured spectral absorption coefficients, photoluminescence spectra, including self-absorption, photoluminescence quantum efficiency, and refractive indices. In particular, we use the experimentally determined absorption and emission spectra of Coumarin 6, and the glass waveguide is modeled by SF10 parameters . The refractive index of the organic film was simulated as nS = 1.5 for the PMMA film and nS = 1.6 for the UCL018 film. The bi-refreingence of the UCL-018 is Δn = 0.17  and has not been taken into account in the presented simulations. The PL efficiency of Coumarin 6 is ηPL = 78% and the EQE of the solar cell combined with the in-coupling is simulated to be 85%. The thickness of the PMMA and UCL018 films were adjusted to result in a absorption of 42% in the films, identical to experimental conditions. To match our experimental procedures, the input light is defined monochromatically at normal incidence for both s and p polarizations. For these simulations an input photon count of 30,000 was used that resulted in uncertainties of less than +/− 0.5%.
We simulate EQE as a function of G for two different experimental configurations. The first configuration simulates the spot excitation technique and calculates the number of photons coupled to one of the edges as a function of the distance between that edge and the spot excitation. The correction factor presented above is then used to account for the different angle subtended by the solar cell at each spot distance, and multiplying by the EQE of the solar cell attached to the edge yields the EQE of the LSC. The second configuration simulates EQE versus G for a uniformly illuminated LSC. The fraction of photons coupled to the four edges is multiplied by the EQE of the GaAs solar cell to obtain the EQE of the LSC.
4. Experimental results
Figures 4a and 4b summarize the trapping efficiency for isotropic and vertically-aligned LSCs, respectively. The total absorption within both samples is 40%. One can observe a clear enhancement of the edge emission for the vertically aligned LSC over the isotropic LSC. To allow for a more quantitative assessment of the enhancement in edge emission, Fig. 4c presents the trapping efficiency for both the isotropic and the homeotropic LSCs. The trapping efficiency of the vertically aligned LSC is measured to be 81%, while the isotropic dye system results in a trapping efficiency of 66%. To the best of our knowledge, the vertically-aligned device exhibits the highest measured LSC trapping efficiency to date, although we note that the trapping efficiency of LSCs with dielectric mirrors has not been explicitly reported . Comparing these measured trapping efficiencies to theoretical predictions for ηtrap presented in Fig. 2, however, shows that the measured trapping efficiency of the vertically aligned and the isotropic LSC is lower than theoretically predicted. We demonstrate below that this is due, at least in part, to imperfect vertical alignment.
Next, we measure optical absorption as a function of the incident angle of the excitation beam for vertically aligned LSCs and isotropic LSCs. Increasing the coupling of radiation into the waveguide by aligning the transition dipole moment of the dyes perpendicular of the waveguide is expected to come at the expense of a reduced capability to absorb perpendicularly incident radiation.
Figure 5a presents the power emitted from the edge of the vertically aligned LSC and the isotropic LSC as a function of incidence angle, θ. The measured power is normalized to the edge emission at normal incidence. We correct for the expected increase in pump absorption at higher incidence resulting from the increased path length in the film by multiplying the measured edge power by a factor, with θI being the internal angle in the film (assuming ns = 1.5 for PMMA and ns = 1.6 for UCL018), α is the absorption coefficient and t is the thickness of the film. The product αt is determined from the absorptionat normal incidence. The change in reflection off the face of the sample with increasing incident angle is calculated to be ~2% and is neglected. The edge output of the isotropic sample is observed to increase slightly with excitation angle, while the edge emission power of the homeotropically aligned LSC increases dramatically. The vertically-aligned dipoles absorb more light at higher incident angles, whereas absorption by randomly-aligned dipoles is constant. Both measurements are corrected for the varying photon path-length as a function of excitation angle.
We also include the dependence of the trapping efficiency on the incident angle of light. Isotropic dipoles are only weakly dependent on the incident angle of the excitation light (see Eqs. (4) and (5)). The increase in ηtrap over the measured angles for the isotropic LSC is calculated to be ~3% for p-polarized light, and 0% for s-polarized light. The trapping efficiency is constant over all excitation angles for an LSC employing perfectly aligned vertical dipoles. Thus, the edge emission of the vertically-aligned sample should follow the sin2 θINT behavior of the absorption in the film. We normalize the theoretical prediction of the edge power to the measured edge power at 45°. The fact that the absorption of the vertically aligned LSC deviates from the behavior of a perfectly aligned homeotropic system suggests that the actual alignment in the film is not ideal, partly explaining the lower value for the measured trapping efficiency than the theoretical models predict.
To alleviate the weak absorption of homeotropically aligned LSCs under perpendicularly-incident light, we employ external holographic diffusers. The edge power of the LSC is monitored as a function of diffuser strength and is presented in Fig. 5b. The edge power is normalized to the edge power measured without the presence of the diffuser. The initial drop in edge-power at a diffuser strength of 10° results from the non-unity transmission efficiency of the diffuser. The vertically aligned, homeotropic LSC shows a clear improvement with increasing diffuser strength. The edge emission for the system that included the 60° diffuser is 10% better than the system without diffuser, and 20% better than the LSC result for the 10° diffuser. As expected, the isotropic LSC does not show an overall enhancement in performance due to the presence of the diffusers.
In Fig. 6 , we plot the external quantum efficiency for vertically-aligned and isotropic LSCs as a function of G. Consistent with an enhanced trapping efficiency of the homeotropic, vertically aligned LSCs, their performance is approximately 16% better than the isotropic LSCs for all measured concentration factors. The presence of an external diffuser is expected to further improve the performance of a vertically aligned LSC. The results presented in Fig. 5b suggest that for our imperfectly vertically-aligned LSC one can expect a 10% enhancement in EQE under normal incidence excitation due to the addition of a 60° diffuser. The enhancement is expected to be much greater if the alignment is perfected. We also simulate the performance of the isotropic and homeotropic LSCs as a function of concentration factor. To test the accuracy of the spot excitation-technique, we simulated both spot-illuminated waveguides (open squares) and uniformly illuminated waveguides (open circles) of various sizes. The Monte Carlo simulations closely resemble the experimentally obtained results demonstrating that the spot illumination technique accurately represents the concentration dependence of quantum efficiency, at least for these LSC samples.
5. Discussion and conclusions
We have enhanced the overall performance of LSCs by 16% by aligning the dipole moment of dye molecules perpendicularly to the waveguide. The improvement is due to an increase in trapping efficiency. We measure ηtrap = 81% for an LSC employing vertically aligned dye molecules compared to ηtrap = 66% for an LSC based on randomly oriented dye molecules. The increase is consistent with theory that models the system using Hertzian dipoles embedded in a waveguide. This theory also predicts small but significant changes to the commonly-cited trapping efficiency of LSCs employing isotropic dipoles. For example, the trapping efficiency of a waveguide of n = 1.5 under normally incident light is ~71% as compared to 74.5% under the standard analysis. We have also demonstrated that an external diffusing medium can help alleviate reduced absorption of incident sunlight by vertically aligned dipoles. All LSCs must be packaged to protect the surfaces of the waveguide, and the diffuser can be incorporated within the front surface of the LSC package without significant additional structural complication.
Finally, dye alignment is not the only means of enhancing the trapping efficiency of LSCs. It is also possible to increase the trapping efficiency by employing wavelength selective mirrors [8, 29, 30] or high refractive index waveguides. But dielectric mirrors require many layers to achieve omni-directional reflectivity at the luminescent wavelengths and high transmission for the broadband solar excitation at all incident angles. The fabrication of such mirrors may prove costly. Materials with high refractive indices are also typically more costly than conventional glasses and plastics. Consequently, aligning the transition dipoles of dye molecules perpendicular to the waveguide may be the most promising path to higher efficiency LSCs.
This material is based upon work supported as part of the Center for Excitonics, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001088. We also wish to express our gratitude to Dr. Hiroshi Hasebe of Dai Nippon Ink and Chemicals, Inc. for his generous donation of the polymerizable LC materials.
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