We developed an optical model for simulation and optimization of luminescent down-shifting (LDS) layers for photovoltaics. These layers consist of micron-sized phosphor particles embedded in a polymer binder. The model is based on ray tracing and employs an effective approach to scattering and photoluminescence modelling. Experimental verification of the model shows that the model accurately takes all the structural parameters and material properties of the LDS layers into account, including the layer thickness, phosphor particle volume concentration, and phosphor particle size distribution. Finally, using the verified model, complete organic solar cells on glass substrate covered with the LDS layers are simulated. Simulations reveal that an optimized LDS layer can result in more than 6% larger short-circuit current of the solar cell.
© 2015 Optical Society of America
Improving the conversion efficiency of solar cells and reducing manufacturing costs are of paramount importance for future growth of the photovoltaic industry. Conventional solar cells suffer from inefficient solar spectrum harvesting. This significantly limits their conversion efficiency, especially in the UV and near-UV region where high-energy photons lead to substantial thermalization losses. In the case of an ideal single-junction solar cell with the optimal bandgap, these losses sum up to almost 50% of the total energy available in the solar spectrum [1–3]. Therefore, advanced techniques towards more efficient solar spectrum utilization are of great interest. Among the most widely researched concepts are the multi-junction devices in which different parts of the incident spectrum are distributed among solar cells of different bandgaps [4,5], and the spectrum conversion concepts in which the wavelength and energy of the incident photons are shifted to better match the spectral responsivity of a single-junction solar cell [3,6].
Luminescent down-shifting (LDS) is one of the promising spectrum conversion approaches that can improve the conversion efficiency of single-junction solar cells in the short-wavelength spectral region [7,8]. It is based on the application of photoluminescent (PL) materials that shift UV and near-UV photons into the visible spectrum, where they can be harvested more efficiently by the solar cell. Different types of PL materials have been proposed for this application, such as organic dyes [9,10], semiconductor quantum dots [11,12], and phosphor particles . Among them, phosphor particles show many advantages such as large Stokes shift, high photoluminescence quantum yield, and long-term stability. However, there are also challenges with respect to their application in solar cells. First, phosphor particles exhibit weak absorption which requires a sufficient amount of them incorporated in the layer, leading to either thick LDS layers or layers with high particle volume concentrations. And second, the size of the phosphor particles is relatively large, which, when the particles are embedded in a polymer binder, results in pronounced light scattering inside the LDS layer that limits transmission of light to the device .
The ability of phosphor-based LDS layers to improve the conversion efficiency of solar cells depends heavily on the composition of the LDS layer, namely the layer thickness, the volume concentration of phosphor particles, the size of the particles, and the optical properties of the materials. All these parameters and properties are interdependent and need to be optimized simultaneously, which presents a challenging and time consuming experimental process. Numerical simulations can provide rapid and cost-efficient optimization of LDS layers, however their reliability greatly depends on the accuracy of the optical models on which they are based. In recent literature, different optical models were proposed for simulation of LDS layers. One group of models follows the thermodynamic modelling approach in which a detailed balance between the absorbed light and the spontaneous emission is applied [15,16]. The approach, however, grows in complexity with finer discretization (mesh) of the simulation domain, and it is often limited in geometry (typically to block-shaped slabs). Another group of models is based on geometric ray tracing. In this case, individual photons are traced through the LDS layer and their interaction with luminescent centers (e.g. particles or quantum dots) inside the layer is taken into account [17–19]. This approach, however, often requires a large number of luminescent centers to be included in the model, which in turn requires a large number of photons to be traced for accurate simulation of the layer, and this may increase the computation time tremendously.
In this paper, we present a newly developed optical model for simulation of LDS layers that is also based on geometric ray tracing in three dimensions. However, as the main difference to existing models, we treat the entire LDS layer as an effective medium and apply an effective approach to scattering and photoluminescence modelling. This approach helps to reduce the complexity and simulation time considerably. The model enables complete optical simulation of LDS layers comprised of phosphor particles embedded in polymer binders and takes all the structural parameters and material properties into account. The model is implemented into the existing optical simulator CROWM , which expands its applicability not only to single LDS layers but also to complete solar cell structures, including thick and thin films. Verification of the model is performed on realistic fabricated LDS layers with phosphor particles. Finally, using optical simulations based on the verified model, we investigate the potential of luminescent down-shifting based on phosphor-filled layers for improved solar spectrum harvesting in organic solar cells. The optimal parameters of LDS layers for this application are also discussed.
To verify the developed optical model presented in this work, realistic LDS layers were fabricated using the following materials: phosphor powder – a modified structure of Lu3Al5O12Ce3+ (GAL 545L, Intematix Corp., USA), “low-index matrix” (LIM) polymer binder QSil 218 (ACC Silicones Ltd., UK), and “high-index matrix” (HIM) polymer binder SA-251P (Nagase ChemteX Corp., Japan). Phosphor powder was first added to liquid binder under continuous stirring, and then the solutions were doctor-bladed on top of 1 mm thick float-glass substrates. LIM-based layers were dried at 100 °C for 60 min, whereas HIM-based layers were first dried at 140 °C for 30 min, then cooled to 7 °C for 10 min, and finally hardened upside-down for 10 min under UV illumination to avoid particle sedimentation. Further details can be found in . Additionally, pure binder layers (without phosphor particles) in thicknesses of about 150 – 600 μm were also fabricated for acquisition of their refractive indices (see below).
The extensive verification of the optical model required a large number of LDS layers to be fabricated. The following parameters were changed systematically in the layers: (i) the binder material (either LIM or HIM), (ii) the thickness of the layer d (150 – 600 μm), (iii) the particle volume concentration PVC (6, 13, and 18%), and (iv) the particle size distribution (PSD). Three different particle size distributions (Large, Normal, Small) were obtained by wet sieving the GAL phosphor particles through a nylon grid mesh. It was observed that in each case the distribution could be approximated as Gaussian. The mean particle size dp and the standard deviation σp were determined by the particle analyzer LS-100Q (Beckman-Coulter, Krefeld, Germany) as follows: (a) Normal PSD, dp = 15.00 μm, σp = 7.39 μm, (b) Large PSD, dp = 18.80 μm, σp = 6.50 μm, and (c) Small PSD, dp = 11.34 μm, σp = 4.82 μm.
The thicknesses of the dried layers were determined using the confocal microscope Nikon Eclipse L150. The surface morphology of the layers was measured using the KLA-Tencor AlphaStep D-1000 stylus profilometer.
The total reflectance R and the total transmittance T were measured in the wavelength range of 300 – 800 nm using the PerkinElmer Lambda 950 UV-VIS double-beam spectrophotometer equipped with an integrating sphere.
The photoluminescence (PL) properties of GAL phosphor particles, namely the excitation and the emission spectra and the quantum yield PLQY, were determined in a previous work . The values and the dispersion of the real part of the refractive index of GAL were taken from literature , whereas the imaginary part was estimated from the measurements using a novel technique that will be published elsewhere. The refractive indices of float glass substrate and both binder materials were determined using the software NIKA . The software employs an iterative algorithm based on the one-dimensional transfer matrix method that enables extraction of complex refractive indices directly from the measured R, T and d data of the characterized sample (either a single layer or a stack of layers). Refractive indices of float glass substrate, GAL particles, LIM binder, and HIM binder at the wavelength of 600 nm are 1.52, 1.81, 1.46, and 1.61, respectively. Full refractive index dispersion curves of all four materials are shown in Fig. 1.
3. Optical model
In terms of optical simulation, LDS phosphor-filled polymer layers present complex structures with many interdependent optical effects taking place under external illumination. All these effects need to be accurately taken into account by the optical model. For convenience, we divide them into two groups. In the first group are optical effects common to most homogeneous layers and multilayer structures: reflection and refraction at the interfaces, absorption within the materials, scattering in the case of textured interfaces, interference of light in the case of thin films, etc. In the second group are optical effects induced by the phosphor particles: volumetric light scattering at the particles, and photoluminescence (PL) of the particles. All these effects from both groups are governed by the optical properties of the materials (complex refractive indices and PL properties) and the structural parameters of the LDS layer (layer thickness, particle volume concentration, and particle size distribution).
In this work, we present an advanced optical model developed for optical simulation of phosphor-filled LDS layers. The model is primarily focused on accurate description of the optical effects from the second group mentioned above, whereas the effects from the first group can be handled in conjunction with any of the conventional optical models and simulators (optical simulator CROWM was used in our case ).
The framework of the developed optical model is three-dimensional incoherent ray tracing (geometric optics). This is justified since the thicknesses of the LDS layer are typically in the range of hundreds of microns and, therefore, incoherent light propagation through the layer is expected. To describe volumetric scattering at the phosphor particles, however, we do not follow the conventional approach in which phosphor particles are located at specific locations inside the LDS layer. Instead, to reduce the complexity of ray-tracing and limit the required computation power, we introduce the so-called effective scattering approach that is presented schematically in Fig. 2(a). In this approach, we treat the LDS layer as an effective homogeneous medium with the optical properties of the binder material. The effective amount of light scattering inside the layer is modelled by periodic scattering of the light ray as it propagates through the layer (the particles are assumed to be evenly dispersed in the binder material). The details of each scattering event and the distance (period) between two consecutive scattering events are defined by the optical properties of the materials and the structural parameters of the LDS layer (details in section 3.1). Additionally, photoluminescence of the phosphor particles is also taken into account in the model. According to the PL properties, new rays at longer wavelengths are generated during each scattering event, as shown schematically in Fig. 2(b). Each PL-generated ray continues to scatter as it propagates further through the LDS layer (details in section 3.2).
To perform complete optical simulations of LDS layers on glass (structure: air / LDS layer / glass / air) or solar cells with LDS layers (structure: air / LDS layer / solar cell / air), the developed optical model was integrated into the existing optical simulator CROWM (Combined Ray Optics / Wave Optics Model), developed at the University of Ljubljana . CROWM is based on three-dimensional ray tracing and transfer matrix methods used in conjunction to analyze light propagation in thick and thin layers, respectively. Its versatility has already been demonstrated for simulation of thin-film silicon , HIT , perovskite , and organic solar cells .
Finally, it should be noted that LDS layers deposited on top of glass substrates may exhibit surface roughness due to the variations in the fabrication process and/or due to large particles located closely beneath the front surface of the layer. In our study, we investigated the effects of surface roughness by directly importing the measured surface morphology of LDS layers into the optical simulator CROWM (standard feature of the simulator). Simulation results (not shown here) revealed, however, that surface scattering has negligible effects on the overall reflectance and transmittance of the analyzed layers. The reason is in pronounced scattering at the particles inside the LDS layers that greatly predominates. Therefore, surface roughness is not included in any of the following simulations (i.e. perfectly flat layers are assumed).
3.1 Description of scattering event modelling
In this section, we present in detail the so-called effective scattering approach that we introduced in our optical model. The description of individual scattering events is explained first, followed by the derivation of the scattering period (distance between two consecutive scattering events).
Each individual scattering event experienced by a light ray propagating through the LDS layer (small circles in Fig. 2) is modelled in two steps. First, the initial optical power carried by the ray before the scattering event is divided between the power that is absorbed by the particle and the power that is scattered by the particle. Then, new rays are generated to carry the scattered power further away from the particle. Although the scattered power in general propagates away from the particle in all directions (many rays), only a single direction (single ray) is chosen semi-randomly in our model (see further). Thus, the entire scattered part of the initial optical power is assumed to propagate forward in this new direction, as shown schematically in Fig. 2(a). With this approach we limit the number of newly generated rays significantly, reducing the computation time required by the simulations.
Both steps described above are characterized by the following four scattering parameters: the extinction efficiency Qext, the scattering efficiency Qsca, the absorption efficiency Qabs, and the angular intensity distribution of the scattered light AID. All these parameters are calculated using the equations from the Mie scattering theory  by assuming light scattering at a single perfectly spherical phosphor particle completely surrounded by the binder material. The scattering parameters depend on the refractive indices of the binder nb and the particle np, the diameter of the particle dp, and the wavelength of the incident illumination λ.
The efficiencies Qext, Qsca, and Qabs are defined as the ratios of the respective cross-sections (extinction Cext, scattering Csca, and absorption cross-section Cabs) to the geometric cross-section of the particles Cp. Qsca and Qabs are used in the model to determine the fraction of the initial optical power of the ray Pin that is either absorbed, Pabs, or scattered, Psca, by the particle during each scattering event. The relations are given in Eqs. (1) and (2). Note that since Qsca + Qabs = Qext, in the case of non-absorbing particles Qsca equals Qext and the entire optical power is retained after the scattering event, only the direction of propagation is changed (see below).
Qualitatively, the extinction efficiency Qext determines the amount of the incident plane-wave illumination that is extinguished from the specular direction by interaction with the particle. It depends strongly on the particle size and can become larger than 1, which means that even the incident illumination in an area larger than the cross-section of the particle is affected (diffraction). As an example, Qext as a function of the particle diameter for the case of a single spherical GAL particle surrounded by the LIM binder is plotted in Fig. 3(a) (full gray curve); results are calculated for the wavelength of 600 nm. The wavelength was selected so that there are no photoluminescence effects taking place. In addition, Qext as a function of the wavelength is plotted in Fig. 3(b) (full gray curve); results are calculated for the particle diameter of 15 μm. The pronounced oscillatory behavior that can be observed in Figs. 3(a) and 3(b) is directly related to the well-defined values of the wavelength and the particle diameter, respectively. If a fixed diameter is assumed, these oscillations also appear in simulation results (R and T). In measurements of realistic LDS layers, however, no such oscillatory behavior can be observed. This is due to the fact that in reality, a certain variation of the phosphor particle sizes is always present.
In our optical model, this realistic variation is taken into account by introducing averaging of the calculated scattering parameters over a range of different diameters. Averaging is carried out by weighting the individual contributions from different particle diameters according to the known particle size distribution (PSD). The bell curves of the three experimentally obtained GAL particle size distributions are plotted in Fig. 3(a) (right axis). In this case, averaging of Qext results according to the Normal PSD, Large PSD, and Small PSD yields constant Qext values of 2.10, 2.08, and 2.11, respectively. It can be concluded that smaller particles result in more pronounced scattering since a larger amount of incident illumination is intercepted by the particle (larger Qext values).
Finally, averaged Qext results as a function of the wavelength are shown in Fig. 3(b) for a broader wavelength range of 300 – 800 nm. Oscillations observed previously for a fixed dp value are efficiently suppressed when assuming realistic particle size variations. Averaging of scattering parameters is, therefore, crucial for obtaining realistic simulation results without oscillatory behavior.
The angular intensity distribution AID determines the relative amount of the (scattered) optical power that is propagating away from the particle in each direction defined by the combination of the zenith angle θ and azimuth angle φ. Although arbitrary AID's can be handled by the model, in the case of phosphor particles the AID is typically symmetric around the specular beam axis (θ = 0 °). Therefore, it is convenient to integrate it over the azimuth angles for each θ. The result AIDint contains the distribution of the scattered optical power among the solid zenith angles in the range from 0 ° (forward specular direction) to 180 °.
AIDint for the case of a single spherical GAL particle with the particle diameter of 15 μm surrounded by the LIM binder, as calculated by the Mie theory, is plotted in Fig. 4(a) (full gray curve); results are calculated for the wavelength of 600 nm and particle size of 15 μm. As before, pronounced oscillations observed in the results can be suppressed by averaging the AIDint results over different particle diameters according to the realistic particle size distribution; the averaged results for the case of Normal PSD are plotted by the full black curve in Fig. 4(a). The AIDint results for this particular case show that most of the light is scattered into the forward direction (0 ° ≤ θ ≤ 90 °), and only a small fraction (3%) is scattered into the backward direction (90 ° < θ ≤ 180 °). From the light scattered into the forward direction, about 50% is scattered into the near-specular direction (θ ≤ 5 °, the values of the near-specular part are out of range in the figure). The influences of different particle size distributions and different binder materials are presented in Figs. 4(b) and 4(c), respectively (averaging of the AIDint results assumed in all cases). It can be observed that smaller particles and the binder with a lower refractive index (LIM) generally result in somewhat broader AIDint curves, which means that more light is scattered into larger angles.
In the developed optical model, AIDint serves as the probability density function for selecting the random direction of propagation of the ray after each scattering event. Thus, as the ray is scattered away from the specular direction, it is more likely to scatter into the angles at which the AIDint values are higher. According to the results in Fig. 4(c) for the case of GAL particles immersed in LIM and HIM binders, it can be deduced that rays will most likely scatter in the forward (and especially near-specular) directions, and only a small probability of back scattering is expected.
Finally, the overall effective amount of volumetric light scattering taking place inside the LDS layer is determined in our model by the scattering period or distance between two consecutive scattering events Lsca. It presents the most important empirical parameter that we introduced within the scope of the effective scattering approach. Smaller Lsca values result in a larger number of scattering events experienced by a ray along its path, and consequently in a more pronounced effective scattering inside the layer.
The equation for Lsca was postulated as a product of three proportionality terms given in Eq. (5). The first term k1 in Eq. (3) is inverse-proportional to the extinction cross-section of the particles Cext, since higher values of Cext result in more pronounced effective scattering. The second term k2 in Eq. (4) is inverse-proportional to the number of particles per given volume Np/V, since more particles per volume result in a larger number of scattering events. The third term k3 in Eq. (5) is a proportionality factor.
By comparing the results of different types of LDS layers (not shown here), it was observed that the proportionality factor k3 does not depend on the binder material, the particle size distribution, the particle volume concentration, or the thickness of the layer. Instead, it only depends on the phosphor particles. This leads us to believe that this factor can take into account various irregularities of realistic layers, especially those introduced by the phosphor particles (e.g. errors in the specified particle sizes, effects caused by non-spherical shapes of the particles, agglomeration of the particles, etc.). Together with the free constants in Eqs. (3) and (4), the factor therefore presents the calibration parameter ksca of the optical model (ksca = 2/3·k3). An example of ksca determination for a particular type of LDS layer will be presented in section 4.1. The final equation for Lsca is presented in Eq. (5).
3.2 Description of photoluminescence event modelling
In our optical model, photoluminescence of the phosphor particles is assumed to take place during each scattering event, as presented schematically in Fig. 2(b). First, the optical power of the ray at the given wavelength (denoted in the following as excitation wavelength λexc) that is absorbed by the particle during the scattering event (Pabs in Eq. (1)) is expressed in terms of the total absorbed photon flux ϕabs. The measured photoluminescence quantum yield PLQY of the particles is then taken into account to calculate the total emission photon flux ϕem, as given in Eq. (6).
The total emission photon flux is distributed among different emission wavelengths according to the normalized measured emission PL spectrum SPL(λem) [Σi SPL(λemi) = 1]. A new ray is generated for each of the emission wavelengths in the emission PL spectrum, and the optical power of each ray is calculated from the distribution of the emission photon flux according to Eqs. (7) and (8). The PL generated rays at each wavelength propagate in random directions away from the scattering event, with the probability density function defined by the AID of the emission light (in general different than AID of the scattered light). In the case of GAL particles, spherical AID of the emission light was assumed (i.e. isotropic emission with equal probability of propagation in all directions).
4. Results and discussion
4.1 Calibration and verification
As noted previously, calibration of the developed optical model (i.e. determination of the calibration parameter ksca) is required prior to applying the model for simulation of realistic LDS layers. For the case of LDS layers based on GAL phosphor particles, the model was calibrated as follows: First, a single LDS layer from the batch of experimental samples was chosen (in our case LIM binder, d = 401 μm, PVC = 6%, Normal PSD) and the R and T data at the wavelength of 600 nm were extracted from the measurements. The R and T of the same LDS layer at the selected wavelength were then simulated using the developed optical model in CROWM, taking the entire sample structure (air / LDS layer / float glass substrate / air) into account. The value of ksca was varied iteratively until good agreement between the simulation and measurement results (both R and T) was achieved. Using this procedure, ksca = 0.4 was determined for the selected layer.
After calibration, the R and T of all LDS layers from the batch of experimental samples were simulated in a broader spectral range (300 – 800 nm), using the same value of the calibration parameter in all the simulations. The simulated T results for a number of selected LDS layers (different d, PVC, and particle size distributions) based on LIM and HIM binder materials are presented as full lines in Fig. 5, respectively. Note that in order to mimic the operation of the spectrophotometer with a monochromatic light source, all simulations were performed separately for each individual wavelength, i.e. T(λ) = PT(λ)/Pin(λ). This means that there is no coupling between different wavelength regions and, therefore, no PL contributions are present in the results (i.e. down-shifted light originating from short wavelengths does not contribute to the results at long wavelengths). If the wavelengths were coupled, however, an additional PL emission peak would be observed in the results due to the down-shifted light from short wavelengths. In Fig. 5(a), we show an example of this situation for one of the layers, assuming reference AM1.5 solar spectrum as the incident illumination (dashed line).
Measured T results for the selected LDS layers are also presented in Fig. 5 (symbols). In this case, however, it is important to note that there was no monochromator located at the detector of the spectrophotometer. This means that during the measurements in the short-wavelength range, the PL emission light also contributed to the detected signal. Comparison between the measurement and simulation results is therefore only valid in the spectral range from about 520 nm onward (outside the PL excitation range of GAL). As an example, measurement results below 520 nm are shown in Fig. 5 for the two most transparent LDS layers (small symbols). The measured T values in this range are unrealistically large due to the PL effects.
Taking the above into account, very good agreement between the simulation and measurement results can be observed for many different LDS layer variations (Fig. 5): using different binder materials, different d and PVC parameters, as well as different particle size distributions. This proves the validity of the developed optical model, especially the description of volumetric scattering at the phosphor particles that was introduced by the effective scattering approach. The comparison also confirms the assumption that the calibration parameter can be kept unchanged for the same type of phosphor particles.
Additionally, measurement and simulation results also illustrate how the total transmittance of the LDS layers is related to the various layer properties. As d or PVC increases, T is reduced due to the more pronounced scattering inside the layer. Smaller particles (at unchanged PVC) also reduce T due to the larger amount of scattering events and somewhat higher Qext values (see Fig. 3(b)). And finally, LDS layers based on HIM binder generally enable larger T values compared to layers based on LIM binder. This can be attributed to the combined effects of lower refractive index contrast between the binder and the particle materials, which results in a narrower AIDint (see Fig. 4(c)), and to the larger refractive index contrast between the binder material and air, which results in a narrower escape cone at the front air/binder interface (reduced R).
4.2 Application of LDS layers in organic solar cells
In the final part of our work, we employ the developed optical model to investigate the potential of LDS layers for enhanced solar spectrum harvesting in organic photovoltaics. For this purpose, the LDS layer can be located between the front glass sheet and the solar cell, or it can be applied directly on top of the PV module; in this study we focus on the latter case. As the device under test, we choose a basic organic solar cell structure with flat interfaces, see details in our previous work . The cell is based on 100 nm thick P3HT:PCBM active layer and is deposited on flat glass substrate. The entire device structure is as follows (top-down): air / glass (1 mm) / ITO (200 nm) / PEDOT:PSS (40 nm) / P3HT:PCBM (100 nm) / Al (100 nm) / air. Further details and complex refractive indices of the materials are given in .
We first employ CROWM to simulate the wavelength-dependent reflectance, transmittance, and absorptance within each layer of the organic solar cell without the LDS layer in the wavelength range of 300 – 700 nm. The absorptance within the active P3HT:PCBM layer is plotted in Fig. 6 (grey curve). As the figure of merit, we calculate the ideal short-circuit current density Jsc directly from the absorptance curve by applying the AM1.5 solar spectrum (neglecting any recombination losses and assuming perfect extraction of charge carriers). In the simulated wavelength range, the reference Jsc value of 9.99 mA/cm2 is obtained for the solar cell; the value is included in Table 1.
As the second step, we apply in simulations a pure 100 μm thick binder layer (LIM or HIM), without particles, on top of the front glass substrate. Results in Table 1 show that the inclusion of LIM binder slightly improves the performance of the solar cell, which can be attributed to lower parasitic absorption inside the binder material and lower refractive index compared to glass substrate (reduced total reflectance due to refractive index grading).
Then, the pure binder layer is replaced with a 100 μm thick LDS layer based on GAL particles (Large PSD) embedded in LIM or HIM binder (PVC of 10%). The developed optical model is used to simulate the LDS component of the device, however photoluminescence effects are not yet included at this point. Jsc results show that the overall performance of the solar cell drops for both types of binder materials. This is primarily due to the significant absorption taking place in GAL phosphor particles. However, by investigating the curve of absorptance in P3HT:PCBM shown e.g. for the LIM-based layer in Fig. 6 (blue curve), it can be observed that the absorptance is actually improved in the regions where GAL particles do not absorb (especially in the long-wavelength region). This improvement can be attributed to efficient light scattering within the LDS layer, which enables large angles of propagation and, thus, higher absorption and better light confinement within the device.
Simulations also reveal that LIM-based layers generally enable higher transmission of light into the solar cell compared to HIM-based layers, although an opposite behavior was observed previously in section 4.1 for transmission in air. The reason lies in the different optical situation at the bottom interface of the glass substrate. In the case of the solar cell, there are no total internal reflection effects taking place at this interface (glass/ITO instead of glass/air; nITO > nglass > nair), and, therefore, even the light scattered into large angles can be transmitted into the device.
Finally, photoluminescence effects of GAL phosphor particles are also included in the simulations, assuming measured excitation/emission spectra and a quantum yield of 98% . Besides the 100 μm thick LDS layers, 50 μm and 150 μm thick layers are also simulated. The Jsc results are summarized in Table 1, whereas the curve of absorptance in P3HT:PCBM for the case of 100 μm thick LIM-based layer is plotted in Fig. 6 (red curve). The absorptance curve clearly shows all three important effects contributing to the overall performance of the cell: the absorption in GAL particles (the reduction in absorptance at 345 nm and 450 nm), the contribution from PL emission (peak at 520 nm), and the improvement due to light scattering (a narrow region around 380 nm and the long-wavelength region). In addition, Jsc results reveal that the LDS layer thickness requires careful optimization. Among the analyzed cases, the organic solar cell with the 100 μm thick LIM-based LDS layer enabled the highest Jsc of 10.62 mA/cm2, which is 6.3% higher compared to the cell without the LDS layer.
An optical model was developed for simulation of phosphor-filled polymer layers. The model is based on the effective scattering approach applied to three-dimensional ray tracing. It is integrated into the optical simulator CROWM. The model was calibrated and verified for the case of fabricated LDS layers comprised of GAL phosphor particles embedded in two types of polymer binders. Very good agreement between the experimentally determined and simulated optical transmittance and reflectance was obtained for a wide range of layers with different parameters (different binder materials, layer thicknesses, particle volume concentrations, and particle size distributions).
The calibrated optical model was applied for simulation of complete organic solar cells with LDS layers deposited on top of the front glass substrate. Simulation results revealed that not only photoluminescence effects, but also efficient volumetric scattering improve the performance of the solar cell in the long-wavelength range. In the short-wavelength range, however, the performance is degraded due to the parasitic absorption in the phosphor particles. Precise balance between positive and negative effects therefore needs to be achieved by careful optimization of LDS layer properties. In the scope of our study, the calculated maximal short-circuit current improvement of 6.3% was achieved by coating the solar cell with the optimal LDS layer based on GAL phosphor particles embedded in a low-refractive-index polymer binder. This promising result confirms the feasibility of the LDS concept and paves the road for further optimization of phosphor-filled layers employed in photovoltaics.
The authors thank D. Riedel, J. Gast and T. Gall for experimental work. The authors acknowledge financial support from the Slovenian Research Agency (Research Programme P2-0197), the Bavarian Academic Center for Central, Eastern and Southeastern Europe (BAYHOST), Erlangen Graduate School in Advanced Optical Technologies, and the Bavarian Research Foundation (BFS) #1006-11. K. F. acknowledges use of the services and facilities of the Energie Campus Nürnberg (EnCN) and financial support through the “Aufbruch Bayern” initiative of the state of Bavaria and the EU-project SOLPROCEL (“Solution processed high performance transparent organic photovoltaic cells”, grant no. 604506).
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