Simulations of luminescent solar concentrator bifacial photovoltaic mosaic devices containing four different organic luminophores

In this article, various design configurations of luminescent solar concentrator photovoltaic (LSC-PV) devices have been simulated using Monte Carlo raytracing. These LSC PV devices are composed of mono-crystalline silicon solar cells and cubical poly (methyl methacrylate) lightguides, each containing one of the following dyes: Lumogen F Red 305, Lumogen F Orange 240, Perylene Green, or Perylene-diimide di-tert-butylphenyl, which results in different device colors. In these devices, mono-crystalline silicon bifacial PV cell are placed in between the vertical edge(s) of neighboring cubical lightguides whereas monofacial PV cells are positioned at the bottom of a lightguide. Each device is made out of five cubical 10 × 10 × 10 mm3 lightguides, meaning that the PV cells measure 10 × 10 mm2. The main research goal of this article is to evaluate the optical and electrical performance of five of such configured LSC-PV devices. Hence, the spectral distribution of irradiance received by the edges and bottom of the devices has been simulated as well as the optical efficiency of these surfaces and the power conversion efficiency of each device. The theoretical results for power conversion efficiency are in the range of 13.3% to 18% under irradiance of 1000 W/m2 and depend on the dyes applied. Hence, this article demonstrates the potential for energy generation by these colorful LSC-PV technologies, which we have called Mosaic devices.


I. INTRODUCTION
L UMINESCENT solar concentrator photovoltaic (LSC-PV) devices consist of transparent optical lightguides typically made of a polymer or glass containing luminophores with one or more photovoltaic (PV) solar cells mounted on one or more edges and sometimes rear of the lightguide [1], [2]. The luminophores of the LSC-PV devices absorb a fraction of the incoming irradiance, re-emitting it at usually longer wavelengths (connected downshifting). Preferably, emission takes place in spectral regions where the associated PV cells have a high external quantum efficiency. In this process photons are spectrally shifted and optically concentrated by total internal reflection to PV cells in order to be converted to electricity [3]- [8].
LSC-PV devices have shown relative insensitivity to the incidence direction of illumination, which often is a challenge for conventional PV modules [9]. Combined with other attractive features including color tunability [10], transparency, geometry flexibility, configuration versatility, and electrical interconnection invisibility [7], [11], [12], LSC-PV devices or modules could be seamlessly integrated into the urban built environment by means of building integrated PV or as smart windows for controlling the light entering room spaces [13]- [16].
Furthermore, LSC-PV technologies can be applied in such diverse applications as the automotive [17] or agricultural sectors [18], [19]: LSC-PV modules are already applied in greenhouses for combined electricity generation and spectral shifting of incoming irradiance to reddish light, which is assumed to stimulate plant growth [20], [21], or even in the production of hydrogen [22] or fine chemicals [23].
Over the past decade, there have been significant advancements and rapid growth in the field of LSCs [24]. At present, several groups in the LSC PV community are interested in bringing results obtained in the laboratory into practice by the development of small scale applications [25]- [27].
For some applications in buildings and the automotive sector, efficiencies greater than the world record of 7.1% reported by Sloof et al. [28] will be desirable using nontoxic colorful luminophores. Therefore, this article aims to determine the optical power efficiency (1) and power conversion efficiency (2) of LSC PV devices with an attractive mosaic geometry deploying bifacial silicon solar cells [29]   dyes rather than quantum dots [30]- [32] or rare earth elements [33]- [36]. In this article, we present Monte Carlo ray-tracing simulations of the optical and electrical performance of these LSC-PV mosaic devices using lightguides made of poly(methyl methacrylate) (PMMA) doped with a variety of perylene dyes including Lumogen F Red 305 (LR 305), Lumogen F Orange 240 (LO 240), Perylene Green (PG), and perylene-diimide (PDI) di-tert-butylphenyl (bPDI-3).
In these devices mono-crystalline silicon bifacial and monofacial solar cells (mono c-Si) are mounted on the edges and bottom of cubical lightguides, which when attached, collectively form an array of lightguides with bifacial solar cells between them and monofacial solar cells at their rears. Thus, four 10 × 10 × 10 mm 3 lightguides are adhered each by one edge to a central lightguide by four bifacial solar cells, see Fig. 1. Various modifications of this design configuration have been explored using cubical lightguides containing different luminophores in a variety of colors. This concept can be developed with customization of geometry in a scalable device, see Fig. 2.

A. Materials and Simulation Set Up
In this simulation study, PMMA was used as the host material as an inexpensive and easily processable material, widely   [37]. The PMMA was doped with one of four organic dyes, namely LR 305, LO 240, PG, or PDI-3 (see Fig. 3 for the chemical structures of the luminophores). The edge-mounted bifacial silicon solar cells (with a refractive index of n PV = 3.4 at 550 nm) were modeled as receiver planes to convert the waveguided photons into electricity: Table I summarizes the  electrical characterization of the bifacial silicon solar cells. LR 305 and LO 240 dyes (BASF) have close-to-unity photoluminescence quantum yields (PLQY), around 95%, and good photostability under ultraviolet (UV) and visible lights [38], [39]. The PG dye has a large Stokes shift (98 nm) but relatively low PLQY (26%) [40]. The bPDI-3 fluorophore is a promising derivative of perylene diimide (PDI) with a PLQY of 98% [41]- [43]. Fig. 4 shows the absorption and photoluminescence spectra curves of the luminophores. The Stokes shifts of the red, orange, green, and bPDI-3 dyes were, respectively, 27, 7, 98, and 9 nm.
In the simulation, we calculated the mean free path (MFP) for the bPDI-3 luminophore using the Beer-Lambert law and the wavelength-dependent optical cross-section as well as molar absorptivity coefficient (see Supporting Information, part A). The optical cross-section of other luminophores were obtained via measurement at The Netherlands Organization for Applied Scientific Research (TNO) and the MFP values were computed at different concentrations accordingly (see Supporting Information, part B). The MFP is defined as the average distance that a photon can travel freely without being scattered or absorbed by luminescent particles. This photon-luminophore interaction is more likely to occur at higher concentration of the luminophores, resulting in shorter MFPs [44], [45].  The properties of the lightguides and solar cells were imported into the commercially available LightTools (Synopsys) software for ray-tracing simulations [29], considering absorption, refraction, reflection, dye emission, and transmission. LightTools is a 3-D design and optical engineering software, which can support complex ray-tracing simulations, optimization, visual prototyping, and can generate photorealistic renderings of illumination applications [46], and was used due to its ability to handle complex 3-D geometries and simulate the LSC-PV devices under standard test conditions (STC), which are defined by an irradiance of 1000 W/m 2 with an AM 1.5 spectrum and a cell temperature of 25°C. Monte Carlo ray-tracing has previously proven to be useful for predicting performance of LSC-PV devices [47]. For this article, incident photons were traced from their entry into a cubical LSC-PV device until lost from the system or collected by the attached bifacial solar cells [48].

B. Design Configuration
We designed and modeled five different mosaic LSC-PV devices based on five cubical lightguides containing different luminescent materials and number of bifacial silicon PV cells mounted on the edges and/or bottom sides of the lightguides: see Table II for a list of configurations. An example configuration is depicted in Fig. 5, see also [29]. Five cubical LSCs and their bifacial solar cells are attached around a single cubical lightguide. In this concept, the PV cells also were mounted on the bottom side of cubical LSCs to maximize the device efficiency.

C. Simulation Assumptions
In this simulation study, we assumed the following. 1) The organic luminophores have a high quality and photostability with constant quantum yield over the entire wavelength range. 2) Luminophores have good solubility in the host-matrix material (PMMA).

3) Ideal optical interfaces between host matrix material and
PV cells without any irradiance losses. 4) PV cells with efficiency of 21% without any defects or reflection losses. 5) An ideal aperture surface without structures that could scatter incoming irradiance back to the surroundings as well as ideal transmission.

III. RESULTS
The simulation assumed incident light could only enter the lightguide via the top surface: the sides were effectively "masked" for purposes of this article. Please notice that in an actual device, of course, the light would be capable of entering through the unadorned edges of the outer cubes. Fig. 6 depicts the spectral distribution generated at the lightguide edges and passing through the bottom of the cubical lightguides at the middle of the emission faces, and the solar spectrum (AM 1.5) received by the top surface of LSCs. In addition, the spectrum distribution passing through the bottom side of a simulated clear PMMA is also shown in this figure.
The spectral irradiance at the bottom of the cubical LSCs containing LR 305 and LO 240 dyes naturally contain less power for wavelengths in the absorption range of the embedded dyes but produce a higher power flux around 650 nm and 580 nm, respectively, the emission range of the dyes. In contrast, the LSCs containing PG and bPDI-3 supply a reduced power to the bottom cell even at their peak emission wavelengths, likely a result of their lower FQYs. The edgemounted bifacial cells show power flux corresponding to the range of dyes' emission peak, as nonscattering lightguides are assumed.
The optical power efficiency, η PE , of the cubical LSCs is calculated using the resulting data of raytracing simulation through where G PV the irradiance on both surfaces of the bifacial PV cells in (W/m 2 ) and G in is the incident solar irradiance on the aperture area of the cubical LSC-PV device in (W/m 2 ). As the spectral composition incident to the PV is different from the original solar spectrum, it is necessary to use the spectral response to calculate the power production of LSC PV devices.  The power conversion efficiency (PCE) of an LSC PV device η dev [7] is calculated via (2) Fig. 7 displays the simulated optical efficiency of the LSC-PV devices as a function of the dye concentration when exposed to STC with 70% direct and 30% diffuse irradiance. The optical efficiency at the edges and bottom of the lightguide of cubical LSCs decreases with increasing dye concentration because higher dye concentrations result in increased reabsorption losses due to the overlap of the absorption and emission spectra of the dyes. Device 4, with the larger Stokes shift bPDI-3 dye showed a generally higher optical performance under all dye concentrations. Fig. 8 depicts the simulated power losses of the LSC-PV devices as a function of dye concentration. The losses stem from the limited PLQY of the dyes, emission and/or re-emission of light outside the "capture cone" of the lightguide, and lightguide absorption, all of which can influence negatively on the performance of LSC-PV devices.
The PCE of the LSC-PV devices were calculated according to (2) and are presented in Fig. 9(left), which shows the PCE of the devices with only edge-mounted bifacial solar cells increases with the concentration of LF 305, LO 240, PG, bPDI-3 dyes, whereas the PCE of LSC-PV devices with edge-and bottommounted bifacial PV cells decreases smoothly with the increase of the dye concentration, see Fig. 9(right).
The two figures can be explained by the increase in incident dye-emitted irradiance on the edge-mounted PV cells and a decrease in the incident solar irradiance on the bottom-mounted solar cells with increasing dye concentration. While the increase in dye concentration led to an increase in irradiance for the solar cells attached on the edges, given that the dye quantum yields and emitted light transport are not 100% efficient, there is a significant decrease in the incident irradiance for the PV cells placed on the bottom sides of lightguides. Table III summarizes the optical and electrical efficiencies of cubical bifacial LSC-PV devices with different luminophores obtained through ray tracing simulation: the highest power efficiency of 84.6% and power conversion efficiency of 18% (at 5 ppm) were obtained for the LSC-PV device 4 under STC with a 70% share of direct irradiance and 30% share of diffuse irradiance.
We performed preliminary investigations on the effect of dimensional variations of these cubical LSCs and PV on the performance of LSC-PV devices, see Fig. 10. According to our observations, an increase in the dimensions of cubical lightguides and the size of solar cells led to a slight decrease  in the PCE of devices, mainly due to increased probability of reabsorption events.

IV. DISCUSSION AND CONCLUSIONS
In this article, we have shown a novel mosaic configuration for LSC-PV devices using colorful cubical lightguides made of PMMA containing four different organic fluorophores; LR 305, LO 240, PG, and bPDI-3. Mono c-Si solar cells were located between the lightguides and mounted on the bottom sides of the lightguides to convert the incident unabsorbed irradiance into electricity. We have configured five LSC-PV devices to evaluate their optical performance and electrical performance by using Monte Carlo ray tracing simulations executed in LightTools software.
The spectral distribution of irradiance on the edges and bottom sides of the devices was investigated, as well as the electrical power production of these LSC PV devices. According to the ray tracing simulations, the theoretical power conversion efficiency under ideal circumstances is in the range of 13.3% to 18% at irradiance of 1000 W/m 2 and depend on the dyes applied. The highest optical power efficiency of 84.6% and PCE of 18% were obtained for the LSC device consisting of five cubical lightguide (10 × 10 × 10 mm 3 ) containing bPDI-3 dye at 5 ppm, with 4 edge-and 5 bottom-mounted bifacial solar cells. Hence, this article demonstrates the potential for energy generation by this new type of LSC PV devices.
While the system efficiency is lower than the silicon PV cells alone, the LSC performance is considerably greater than the moderate efficiencies reported in the literature. But the reader should be aware of the fact that the primary goals of LSC-PV devices is not to compete with the efficiency of conventional solar PV modules, because their customizable design features, such as color, transparency, and shape, are prevailing for integration purposes. Once a simple assembly technique is created, these mosaic-LSC devices could allow for intricate, high-efficiency devices with a high degree of artistic beauty. It is anticipated that this device could find application in higher-end applications requiring greater efficiency where aesthetics is also of utmost importance, allowing some leeway for the additional costs required to produce these specialized systems.