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To enhance the performance of luminescent solar concentrator (LSC), there is an increased need to search novel emissive materials with broad absorption and large Stokes shifts. I-III-VI colloidal CuInS2 and CuInSe2 based nanocrystals, which exhibit strong photoluminescence emissions in the visible to near infrared region with large Stokes shifts, are expected to improve performance in luminescent solar concentrator applications. In this work, the performance of CuInS(Se)2 quantum dots in simple planar LSC is evaluated by applying Monte-Carlo ray-trace simulation. A systematic parameters study was conducted to optimize the performance. An optimized photon concentration ratio of 0.34 for CuInS2 nanocrystals and 1.25 for CuInSe2 nanocrystals doping LSC are obtained from the simulation. The results demonstrated that CuInSe2 based nanocrystals are particularly interesting for luminescent solar concentrator applications, especially to combine with low price Si solar cells.
© 2015 Optical Society of America
1. Introduction
Luminescent solar concentrator (LSC) [1] is a simple device employing a polymeric or glass waveguide doped with luminescent materials to generate electricity from sunlight when attached to a photovoltaic cell (PV) [2–4]. The LSC has the potential to find extended use in building integrated solar cells [5]. The primary challenge faced by the devices is to increase their photon-to-electron conversion efficiencies [1, 6]. One of the important ways is to explore advanced luminescent materials that absorb most of solar spectrum and reemit efficiently at longer wavelength with less self-absorption loss [7–9] In the past few years, organic fluorescent dyes and inorganic phosphors have been explored [10–13]. The performance has been limited by their less absorption ability and/or serious self-absorption problem. To enhance the LSC performance, there is an increased need to search novel emissive materials [14].
Recent development provides colloidal quantum dots (QDs) with tunable absorption and emission spectra for LSC applications [15–19]. According to the literature reports [20, 21], the concentrated optical efficiency of LSC doping with CdSe/ZnS is calculated to be 1.5% and 4.5% respectively when the quantum yield (QY) is 60% and 100% in the simulation. The efficiency of QDs based LSC can be significantly enhanced by using type II core shell structures and the optical design of device structure, yielding optical efficiencies > 10% and an effective concentration factor of 4.4 [22, 23]. The use of NIR emissive colloidal QDs can expand the absorption spectrum and reduce the self-absorption loss. For example, Ghosh’s group [24] and Aeberhard’s group [25] studied the performance of NIR emissive PbS QDs and theoretically achieved an optimized optical efficiency of 12.6% corresponding to the sample with QY of 100%. However, most of these materials are toxic compounds with heavy metallic ions. Very recently, it was shown that the Mn2+ doped ZnSe QDs with zero reabsorption can further enhanced the performance [26]. However the light absorption is limited due to their wide bandgaps(~2.7 eV). I-III-VI CuInS(Se)2 QDs exhibit strong photoluminescence (PL) emission in the visible to NIR region with large Stokes shifts [27–29]. In addition, the emission of CuInSe2 QDs can be tuned to match the bandgap of c-Si solar cells [30, 31]. It is expected that I-III-VI CuInS2 and CuInSe2 QDs have the potential to improve the LSC performance [27]. As we know, only a few works concern the use of I-III-VI QDs in LSC applications [32].
Recently, we developed a size-, composition- and surface- combined tuning strategy to synthesize highly luminescent I-III-VI QDs at gram scale [27]. This opens up the way to explore the use of I-III-VI QDs as functional luminescent materials in various applications [28]. In this work, we theoretically evaluated the performance of CuInS2 and CuInSe2 based QDs in LSC by using Monte-Carlo ray-trace simulation. In contrast to the previous works on thermodynamic modeling [32–34], the ray-trace modeling can give physical insights and reduce the experimental works for optimizing LSC design in terms of varying geometry, concentration and QDs types.
2. LSC model and input parameters
We take two conventional character parameters, optical efficiency (η opt) and photon concentration ratio (C ph) [35, 36], to quantify the performance of LSC devices.
(I) Optical efficiency is defined as the ratio of the total number of photons reached the PV cells (we ignored the photon loss between LSC plate and PV cells) to that of photons incident on the top surface of LSC. Particularly, we firstly calculate the external quantum efficiency (EQE) spectra of LSC, and then take a weighted integration method to derive optical efficiency [Eq. (1)]. EQE(λ) of LSC is defined the same as optical efficiency only it is under single-wavelength light illumination.
n(λ) is the normalized AM1.5 spectrum.(II) Photon concentration ratio C ph is defined as the product of G and η opt [Eq. (2)], where G, the geometric gain, is the ratio of the top surface aperture area to PV cells area. G equals the LSC length in our model as LSC thickness was assumed to be 1 cm (Changing LSC thickness is approximately equivalent to changing the QDs doping concentration. Because the critical thickness related events in LSC is QDs absorption whose probability is positively correlated to the product of LSC length and QDs concentration, according to the Beer-Lambert Law).
Since η opt strongly depends on LSC size, we present the η opt values of LSC sized 10*10*1 cm3 for reference, while investigate C ph as the main parameter to conduct LSC optimization.To simplify the calculation, we assume: (1) the waveguide of LSC is made of polymethyl methacrylate (PMMA) plate. The right side of PMMA plate is connected with PV cells, other three sides and bottom surface are covered with mirrors whose reflectivity is assumed as 0.8, while the top surface exposures to the air [Fig. 1(a) ]; (2) The PMMA plate has a constant refraction index of 1.5, while the air has that of 1; (3) Light scattering won’t occur in the plate, i.e., the scattering rates of QDs and PMMA are zero due to the small size of CuInS(Se)2 QDs; (4) The emission spectra of QDs keeps the same at different excitation wavelength. Because the PL spectra of CuInS(Se)2 QDs slightly varied with the excitation wavelength and excitation intensity. The above assumptions make limited difference in the statistic calculations. These assumptions are proposed from experiments, and are widely used in modeling. They’ve been proved reasonable by many successful simulations [32, 35–37].
Fig. 1 (a) The illustration of LSC device for our simulation. QDs were doped into the PMMA plate. The right surface of the plate is connected with photovoltaic cells, the top surface exposures to the air, and the other four surfaces are covered with mirrors. (b) The attenuation coefficient of PMMA. (c) The normalized PL and absorption spectra of typical CuInS(Se)2 QD samples used for the simulation.
The main input parameters for our simulation are:
- AM1.5 solar spectrum;
- Length and width of the LSC plate (the thickness is set to a constant, 1 cm);
- The PL spectrum, absorbance, quantum yield (QY), doping concentration of QDs;
- Attenuation coefficient of PMMA.
3. Measurements before simulation
To process the Monte-Carlo ray-trace simulations, we firstly figure out all the fate of incident photons and the probabilities of that. The probability of reflection or refraction for photons when they encounter an interface can be calculated via Fresnel equation. The probability of that, a photon is absorbed by QDs or PMMA, is positively correlated to the thickness and concentration of the material with an absorption coefficient, according to the Beer-Lambert Law. The wavelength of photons emitted from QDs can be determined from their PL spectra, while the ratio of emitted photons to absorbed photons depends on the QY of illuminant materials. Therefore, we need to measure the absorption and PL spectra of QDs, the attenuation coefficient of PMMA and the QY of QDs.
The measured QYs of our CuInS(Se)2 samples varied from 60% to 80% with batch to batch difference. In our simulation, a reasonable high QY value of 0.75 was chosen for the calculation of CuInS(Se)2 QD based LSC. This is arbitrary, but essential for our simulation.
It’s obvious that using PL/abs. spectra of QDs in PMMA may give more accurate simulation result than in toluene solution. However, the batch to batch difference in the experimental works may introduce obvious deviation to the measurements. To simplify the calculations, we employ the spectra of CuInS(Se)2 in toluene and considered the attenuation of PMMA in our modeling. This approach is widely used by both ray-trace and thermodynamic modeling [32, 33, 36, 37]. The attenuation coefficient of PMMA is measured by Perkin Elmer Lambda 900 UV/VIS/NIR Spectrometer [Fig. 1(b)]. CuInS2 QDs with PL emission peak at 530 nm, 615 nm, 650 nm and CuInSe2 QDs with emission peak at 900 nm in toluene solution were prepared according to our previous reports [27]. Their absorption and PL spectra were determined by using UV-6100 double beam spectrophotometer and FL-380 spectrofluorimeter [Fig. 1(c)].
4. Results and discussion
For a simple planar luminescent solar concentrator, the whole adjustable parameters are LSC size, luminescent material type and doping concentration. We took control variate method to optimize LSC size and QD doping concentration preliminarily and then a comprehensive consideration of these two parameters was conducted to determine the final LSC optimization results for these four kinds of QDs. We conduct the QY analysis, loss mechanism analysis and multi-layer stacked LSC design to further investigate the performance of CuInS(Se)2 QDs in LSC application.
4.1 The effect of QD doping concentration
To study the effect of QD doping concentrations, the QY of these samples was fixed to 0.75 and the size of LSC was assumed to be 10*10*1 cm3. The preparation concentrations of QDs are determined to be 1 mg/mL for CuInS2-530, 1mg/mL for CuInS2-615, 0.8 mg/mL for CuInS2-650 and 1 mg/mL for CuInSe2-900 QDs respectively. Figure 2(a) shows the EQE spectra of the four kinds of QD-LSCs with various doping concentrations. Generally, EQE is proportional to the absorption coefficient. With the QD concentration rising, EQE decreases in short-wavelength region (approximately 300~500 nm), while increases in the relatively long-wavelength region. This result can be easily explained from the aspect of thermodynamic modeling. Under a certain single-wavelength light illumination, higher QD concentration results in more notable reabsorption loss and lower QD concentration allows more photons go through the plate. So there should be an optimal QD concentration for a typical wavelength light incidence, and obviously higher QD absorption coefficient corresponding to lower optimal QD concentration. In CuInS(Se)2 case, QD concentration of 1 mg/mL is already higher than optimal values at short wavelengths, that results in EQE decrease with QD concentration while the opposite at long wavelengths.
Fig. 2 (a) The calculated EQE spectra of QD-LSC with a series of doping concentrations, these four subplots share the same EQE axis. (b) The QD doping concentration dependence of optical efficiency, which was derived from EQE spectra.
By integrating EQE along the whole solar spectrum, the plot between η opt and C doping can be derived [Fig. 2(b)]. We can easily find the optimal QD concentration from this plot. The optimal C doping corresponding to the maximal η opt were extracted for LSCs under precedent settings by polynomial fitting. And the optimization results were summarized in Table 1 . The maximal optical efficiency of CuInSe2-900 QD-LSC achieved 6.71%, which is better than most fluorescent dye based LSC. The optimal QD doping concentrations are 10~25 times the experimental concentrations. The loading of 25 mg/mL QDs into PMMA gives a volume proportion of QDs within 1%. It is reasonable to fabricate the PMMA composite samples with such high concentration of QDs.
Table 1. A summary of optimization results (QD doping concentration, LSC size) of CuInS(Se)2 QD-LSCs. The optical efficiency was calculated under condition of size 10*10*1 cm3 and QY 0.75.
4.2 The effect of LSC size
An effective solar concentrator must have high efficiency in a relatively large collecting region. Therefore, the size effect of LSC device is an important aspect to evaluate their application prospects. We set the QYs of all the sample QDs to be a constant of 0.75, and adopt the optimal doping concentrations to evaluate performance of CuInS(Se)2 QDs based LSCs with various sizes. The evolution of η opt and C ph along with the increasing of LSC size was studied and plotted in Fig. 3 (we only plotted the results of CuInS2-650 and CuInSe2-900 QD-LSCs for representative).
Fig. 3 Size dependence of η opt & C ph for CuInS2-650 (a, b) and CuInSe2-900 (c, d) QD-LSCs respectively. We set QY as 0.75 and QD doping concentration the optimal values as shown in Table 1 (9 mg/mL for CuInS2-650 and 11 mg/mL for CuInSe2-900 QDs).
It is observed that η opt decrease monotonously with the increasing of LSC length, while C ph exhibits an opposite tendency. For the LSC with a certain length, both η opt and C ph slightly are improved with the increasing of width. After the LSC size exceeds some certain value, η opt and C ph change gradually with LSC size. The theoretical calculation shows that the optimal LSC sizes corresponding to the maximal C ph are around 30*10*1 cm3 for CuInS2-650 and 140*80*1 cm3 for CuInSe2-900 QD-LSC respectively. The other sample QD-LSCs exhibit analogous results and these optimized size values were added to Table 1.
4.3 Comprehensive optimization of QD doping concentration and LSC size
It is noticed that the optimal doping concentration of QDs in the polymer matrix also changes with the LSC size. A comprehensive simulation was conducted to clarify the correlative influence on LSC performance by varying both the QD doping concentration and LSC length. After raised to some value, LSC width exhibits negligible effect on its performance as discussed in the LSC size effect study. Therefore, we set the width to a constant (for example, 40 cm for CuInSe2-900 QD-LSC) to only conduct the comprehensive optimization of QD doping concentration and LSC length. QY was set to be 0.75 again.
Figure 4(a) shows the result of typical CuInSe2-900 QD-LSC as a representative. It’s obvious that the optimal concentration of QDs showed a monotonous and gradually moderated decrease with the increasing length of plate. We took 8.5 mg/mL as the final optimal QD doping concentration for CuInSe2-900 QD-LSC and recalculated its photon concentration ratio. A value of 1.25 is achieved and this result was added to Table 1. The CuInS2 QD-LSCs showed similar but weaker variation tendency and their optimized length haven’t changed too much from 10 cm, so we didn't revise the optimization results for them. Knowles et al. reported a flux gain (a parameter used by thermodynamic modeling which is comparable to photon concentration ratio) exceeds 4 [32], which is much bigger than 1.25 because they used QY = 0.86 and didn’t take PMMA attenuation into consideration.
Fig. 4 (a) Optimal QD doping concentration at LSC length for CuInSe2-900 QD-LSC while width was set to a constant of 40 cm, QY is 0.75 again. (b) QY dependence of optical efficiency for four types of QD-LSCs.
4.4 The effect of QY
It has been known that QY of QDs has strong influence on LSC performance. In principle, high QY can lead to an increase of the photon collection efficiency. The effect of QY was studied to figure out the performance potential of CuInS(Se)2 QD-LSC. We set the LSC sizes as 30*12*1 cm3 for CuInS2 QD-LSCs and 140*80*1 cm3 for CuInSe2 QD-LSC. The optimized doping concentrations are showed in Table 1.
The LSC performance was evaluated by varying the QY from 0.5 to 1, and the QY dependence of optical efficiency for all the four types of QD-LSCs was plotted in Fig. 4(b). We can see that η opt increases monotonously and significantly as the QY becomes bigger. The measured QY of our CuInS(Se)2 samples is about 0.7. If it increases to 1, the optical efficiency and photon concentration ratio of these CuInS(Se)2 QD-LSCs will be expected to improve by a factor of 2. For example, the η opt of CuInS2-650 QD-LSC will increase from 1.06% to 2.22% when QY increases from 0.7 to 1. Also, it’s noticed that the LSC devices using QDs with emission peak at 650 nm has the highest optical efficiency of the three CuInS2 QDs. This can be understood by their absorption range of solar spectrum as CuInS2-650 has the widest absorption range and the results are similar to Manus Kennedy’s work [36].
The curve of CuInSe2-900 QD-LSC (colored black) is below that of CuInS2-650, which doesn’t mean its performance is worse for its bigger size setting than that of three CuInS2 QD-LSCs. Under the same size setting, the η opt of CuInSe2-900 QD-LSC will be more than 2 times bigger than that of CuInS2-650 QD-LSC [Fig. 2(b)]. CuInSe2-900 QD-LSC has the best performance from the perspective of photon concentration ratio (1.20 vs. 0.16~0.31, Table 1).
4.5 Analysis of loss mechanisms
To evaluate various loss mechanisms of LSC, we sum photons of different fate and calculate their proportions accounted for the incident photons. Figure 5 shows the result of CuInSe2-900 QD-LSC under the following settings: QD concentration is 13 mg/mL, width is 80 cm and QY is 0.75.
Fig. 5 Photon count proportions of different fates at length, typically the CuInSe2-900 QD-LSC. Line A,B,C,D,E represent proportions of photons reached PV cells, reflected by the top surface of LSC, absorbed by QDs without light emission (named self-absorption of QDs), absorbed by PMMA, travelled out of LSC while wave guiding. Line c1&c2 represent the light absorption of QDs. We use suffixes 1 and 2 to distinguish the first time photon absorption events from reabsorption events for QDs.
We can see that all the curves of photon number proportions for different fates become quite flat when the length of LSC exceeds 30 cm, but we must clarify that each of the line A, C2, D, E and c2 is not tend to a constant. (For example, one can still identify small increasing of curve C2 with the help of a horizontal reference line C1 when LSC length exceeds 100 cm). The proportions of photons reached PV cells (A), reflected by the top surface of LSC (B), absorbed by QDs without light emission (C, equals to C1 + C2), absorbed by PMMA (D), travelled out of LSC while light travelling (E), are about 1%, 4%, 35%, 16%, 44% at longer LSC length, respectively. At a certain LSC length, the sum of photon number proportion which marked capitals is 100%. Lines marked lowercase are not the final fate of photons and we plot them for reference. Suffixes 1 and 2 are used to distinguish the photon absorption from reabsorption. This made it possible to evaluate reabsorption loss (C2), which is a part of the nonrealistic QY loss or so called “self-absorption” loss (C).
The main photon loss is caused by self-absorption (35%) and travelling out of LSC (44%). Self-absorption loss is about 25 percent of QD absorbed photons (C1/c1 = C2/c2 = 25%) while we set the QY as 0.75. First time self-absorption loss C1 and reabsorption loss C2 each contribute half of the self-absorption loss at longer LSC length, approximately. The imperfect first time light absorption contribute about 33% (1-c1 = 100%-67% = 33%) among in the photon loss caused by travelling out of LSC. The left 11% (44%-33%) was caused by photons lost to the waveguide’s escape cones defined by Snell’s law.
These results suggest that the LSC performance has a great space to improve if we enhance QY and design better structure to expand the light absorption. It’s very important to control the size distribution with reduced reabsorption loss and to attach solar cells with matched spectral response. It is also worth to note that CuInSe2 QD-LSC has much better performance than CuInS2 QD-LSC due to its wider light absorption spectrum. This implies that the LSC performance can be significantly enhanced by enlarge the QD size which will reduce the band gap and extend the absorption range. To summarize, we can further enhance the CuInS(Se)2 QD-LSC performance by synthesizing larger size QDs with extended absorption range, enhancing QY and designing better LSC structure.
4.6 Multi-plate stacked LSC
To reduce the self-absorption of QDs, multi-plate stacked LSC [38, 39] has been proposed for the enhanced collection of solar spectrum. A schematic diagram of this LSC is shown in Fig. 6(a) . It can reduce self-absorption of high-energy photons effectively. We simulated the photon efficiency of multi-plate stacked LSC with two kinds of doping mode. In these two modes, CuInS2-650 QDs are used in the bottom plate while either CuInS2-530 or CuInS2-615 QDs is used in the top plate, respectively. The size of LSC was assumed to be 30*12*1 cm3 and 30*20*1 cm3 respectively and a QY of 0.75 was applied for the simulation.
Fig. 6 (a) A sketch map of dual-plate LSC. (b) The calculated EQE spectra. Line A and C represent the total EQE of CuInS2-530&650 QD doping dual-plate LSC and CuInS2-615&650 QD doping dual-plate LSC respectively. Line B is that of simple planner CuInS2-650 QD-LSC for comparison. Line a1, a2, c1 and c2 show the separate contribution of each plate (a1 + a2 = A; c1 + c2 = C).
After optimizing QD doping concentration of each plate (the results are 11, 20 mg/mL in the top and bottom plate for CuInS2-530&650 QD-LSC; 20, 15 mg/mL for CuInS2-615&650 QD-LSC), its EQE spectra was calculated and compared with that of single plate CuInS2-650 QD-LSC with the same size and QY. As Fig. 6(b) shows, EQE of the dual-plate LSC is generally larger than that of single plate LSC, especially in short-wavelength region. As discussed in section 4.1, the optimal QD doping concentrations under different wavelength illumination are different. A multi-layer design makes it possible to divide incident light into several spectral range and EQE enhancement could be achieved when one choose optimized QD doping concentration for each layer. EQE decrease would occur [as the case in Fig. 6(b), the intermediate range of line A] if photon loss between two adjacent plates dominate. A raise of η opt from 1.19% (line B) to 1.20%&1.24% (line A&C) was achieved, which demonstrated that multi-plate stacked LSC indeed enhance the LSC performance. However, further investigations like cost analysis are needed to determine whether it’s valuable or not to add these multi-plate production processes.
5. Conclusion
The simulation results suggest that LSCs using CuInS(Se)2 QDs with the QY of 0.75 are capable of yielding the photon concentration ratio C ph of nearly 1.25 for large plate size of 140*80*1 cm3. To improve CuInS(Se)2 QD-LSC efficiency, it is proposed that self-absorption loss can be reduced by enhancing QY of QDs. Simulation results for a perfect QY of CuInS(Se)2 QD-LSCs showed a potential >90% performance improvement in relative to the same LSC with a QY of 0.75. Based on Monte Carlo ray-trace simulation results, I-III-VI CuInS2 and CuInSe2 based nanocrystals, which exhibit strong PL emissions in the visible to NIR region with large Stokes shifts, could be very suitable candidates as the fluorescent material in LSCs. Further experiments will pay the attentions to the incorporation QDs into transparent matrix. In addition, the ray-trace simulation developed in this paper allows us to model LSCs in detail. It can be used to further investigate and optimize LSC systems.
Acknowledgments
The authors would like to thanks the funding support of The National Basic Research Program of China (No.2011CB933600), NSFC Research Grants (No. 51003005, 11004009,11474021) and Beijing Higher Education Young Elite Teacher Project (No. YETP1231).
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