- Email: [email protected]
Modeling Mathematical of the Behavior of Up Converter when Implemented in Bifacial Silicon Solar Cells
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 102 (2016) 80 – 86
E-MRS Spring Meeting 2016 Symposium T - Advanced materials and characterization techniques for solar cells III, 2-6 May 2016, Lille, France
Modeling Mathematical of the Behavior of Up Converter when Implemented in Bifacial Silicon Solar Cells Aline Cristiane Pan*1, Leandro Santos Grassi Cardoso2, Fernando Soares dos Reis2 12
Pontifical Catholic University of Rio Grande do Sul, Faculty of Physics1 and Faculty of Engineering2, Av. Ipiranga, 6681 - Partenon, Porto Alegre - RS, 90619-900 – Brasil. *Corresponding author: Tel.: +55 513320 3535 E-mail address: [email protected]
Abstract Up Converters implemented in solar cells have theoretical efficiencies of the conversion much higher than the actual and a much smaller production price. However, the experimental results in the present are not approaching the theoretical calculated values, because they have a small increase in photocurrent by incorporating the bifacial solar cell, for example. Hence, it is necessary dispose a quantitative tool for the characterization of candidate materials as up converter, which permits realize an influence sensibility analyzes of certain parameters and contrasts with the real values founded. Thus, the fundamental objective of this work is to develop a mathematical model to study the behavior of up converters, based on realistic parameters found in the literature, when implemented in silicon bifacial solar cells. Besides, exemplifies this model getting comparative results (I x V curve) for different materials used as an up converter when incorporated in silicon bifacial solar cells using the unidimensional software, PC1-D, in order to get the best candidates to be used. © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The European Materials Research Society (E-MRS). Peer-review under responsibility of The European Materials Research Society (E-MRS). Keywords: Mathematical modeling; Up converter; Solar cells.
1. Introduction In actuality, renewable sources of energies: wind, solar, biomass, geothermal, tidal and hydro, are situated in a prominent position due to the depletion of fossil resources and environmental problems. However, the designation of the hydroelectric facilities as "clean" is under discussion, since recent studies have shown the decomposition of organic matter in flooded areas for deposits of some of these facilities can generate and emit into the atmosphere significant amounts of methane and carbon dioxide, two of the gases involved in global warming [1].
1876-6102 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The European Materials Research Society (E-MRS). doi:10.1016/j.egypro.2016.11.321
Aline Cristiane Pan et al. / Energy Procedia 102 (2016) 80 – 86
Among renewable energy sources, solar energy shows up as great alternative because it can cover the needs of humanity with inexhaustible form and can serve as basis for sustainable development [2]. Instead, what happens with other renewable sources such as wind power, solar energy has a variety of resource fairly predictable and your magnitude is calculated from the place where the system is installed. Energy conversion occurs from photovoltaic effect, that being to make the conversion is necessary a photovoltaic cell. For their practical use, solar cells are usually associated electrically in series and encapsulated. The set of cells, connections and protection structure are called a photovoltaic module. Through these photovoltaic modules, solar energy stands out compared to other renewable sources to be simple and quick to install, be modular and not contaminate the environment [3]. In addition, the modularity allows to increase the capacity of the system gradually if high rise, and is also identified as ideal for isolated systems from the power supply, which can meet the needs of most people without electricity in developing countries. The primary problem that prevents a large expansion of this technology is economic, because it needs up an entire initial investment and the same is not subsidized, like other forms of energy. Consequently, one line of research follows is the deployment of solar cells with high efficiency and/or low cost. However, keep these two characteristics in a single device is not an easy task. Until now, no material or technology was able to completely achieve this goal, because of solar cells with high efficiency are too expensive and low cost does not achieve satisfactory performance [4]. Up Converter (UC) implemented in solar cells has theoretical electrical conversion efficiencies much higher than the current and a much smaller production target price [5]. Up conversion (UC) occurs when a material is photo-excited to high wavelengths (low energy) and emits photons at lower wavelengths (high energy). The absorption of photons (in two steps) below the width of the critical band in UC brings the excitement of carriers from its ground state to an intermediate level in UC, and from the intermediate level to a higher level excited. Some of these carriers excited recombines through radiative transitions that are accompanied by the emission of photons with energies above the width of the forbidden band [6]. When the energy of the photons generated by the UC process is greater than or equal to the solar cell absorption limit, the photons generated in the UC contribute to the generation of photocurrent on the device. The doped materials with trivalent ions of rare earths (TR3+) are the materials considered preferentially to be used at UC by the photovoltaic industry [7] and should be placed on the back of a bifacial solar cell for conversion of photons transmitted, and combined with a rear reflector to enable the highest energy photons converted to return the bifacial solar cell and to generate electron-hole pairs. For the association of the UC in solar cells is necessary to evaluate the parameters related to their luminescent properties. The energies transfer mechanisms (TE) between the TR3+ can enable conversion phenomena at low and high energies, and the detailed balance model is a very useful tool to calculate the thermodynamic limits of operation of the solar cell [8]. However, due to constructs in these analyzes, it becomes necessary to have other models to evaluate the potential improvement in the response of the solar cell with the photon converters. For other applications, such as lasers and optical fibers have been proposed mathematical models to simulate and / or compare the phenomena of photonic converters since the eighties [9] [10] [11] conducted a comprehensive study of the main parameters related to the TE mechanisms for UC processes. The increase in the number of absorbed photons due to the incorporation of UC, increasing the photocurrent and efficiency of the solar cell was calculated by Trupke [12]. In these theoretical calculations, it was considered a UC layer disposed on the back of bifacial solar cell and electronically isolated, this is, the coupling between UC and bifacial solar cell is produced purely radiative way. The efficiency limit contributed by this layer UC is 38.6 % for a low silicon cell non concentrated illumination (1 sun), reaching an increase of 63.2 % to a semiconductor material with energy gap of 1.955 eV and a lighting concentrated 46,200 suns (thermodynamic limit). These figures show a significant improvement over the limit efficiency of approximately 30 % calculated by Shockley and Queisser [13] for a silicon solar cell. However, the experimental results today [6] [14] [15] do not approach these calculated values, since they have small increases incorporate to UC at bifacial solar cell, for example. Therefore, one needs to have a quantitative tool for the characterization of candidate materials as UC, allowing perform sensitivity analyzes of the influence of certain parameters and contrast with the actual values found. Thus, the fundamental objective of this work is to develop a mathematical model to study the behavior of UC at higher energies, based on realistic parameters found in the literature, when implemented in bifacial silicon solar cell. In addition, it exemplifies this model obtaining comparative results (curves I x V) for different materials used as UC when incorporated in bifacial silicon solar cells using the unidimensional program PC1-D, in order to get the best candidates for use as UC.
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2.
Mathematical Model
2.1 Energy Transfer Mechanism A complete and detailed description of the physical processes occurring in the converter is very difficult to accomplish with complete accuracy. On the one hand, it would be necessary to know how it is distributed luminescent centers in different energy sublevels; and secondly, how does the propagation of light in the converter, and how to deal with this phenomenon [16]. Considering these factors, this study sought to find greed in the density of photons of a solar cell when incorporated into UC. UC consists generally of a non-absorbent matrix containing luminescent centers at a given concentration. The absorption and emission resulting from the luminescence were simplified considering the luminescent center as a series of three energy levels. Several TE takes place when employed to TR3+ in a solid medium. Most of these relate to the absorption and non-radioative transitions [17]. The minimum requirement for this to occur TE mechanisms is the presence of at least two metastable states. In addition to the UC phenomenon to be effective, these states must be large enough lifetimes, so that ions are able to participate in the luminescence process, or other photophysical processes most likely to occur compared with the non-radioactive relaxation [11]. The most important processes found in UC are: ground-state absorption (GSA), excited-state absorption (ESA), energy transfer up conversion (ETU), relaxation cross (CR), cooperative excitation (CE) and cooperative relaxation (CooR) [16]. These processes may be combined with each other making the most efficient UC effect [18] calls APTE (addition of photon by energy transfer) the most effective process for UC, where 3 ions are involved; two of these ions are excited by GSA and transfer their energy to the third ion by ETU. This process is also known as GSA / ETU [17]. The second process most probable is the absorption of the same ion in two steps, followed by the ESA for GSA (GSA / ESA) [11] and this is used in this paper that to realize the mathematical model. Other combined or individual processes have a low probability of occurrence, for example, CE probability is 5 orders of magnitude less than the APTE [18]. 2.2 Power Density Obtained for the UC To obtain the power density for each wavelength interval is calculated first the energy in this range by Eq. (1):
E = hv =
hc
λ
(1)
where h is Planck's constant, ν is the frequency, c is the speed of light and wavelength λ For the calculation of the photon density ( Φ ) on the average wavelength interval (Δλ), Eq. (2), it was using the energy value already calculated and irradiance values (F) for the solar spectrum tabulated AM1 .5G [19]. With the unit adjustments result was obtained at n/cm²s:
F § Δλ · . Φ = ( )*¨ ¸ E © 2 ¹
(2)
The next step was to calculate the power density in the same wavelength range, according to Eq. (3) W/cm²:
H = Φ*E .
(3)
With Eq. (4) there was the power density constant for all wavelength intervals by the sum of all irradiances of photons arranged:
CH = ¦ H .
(4)
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Considering the insertion of UC, was calculated again for the density of photons of wavelength ranges, but considering the radiation that is transmitted. That is, the optical transmittance was measured (T) for a bifacial silicon solar cell, and added to these values for Eq. (2), making it in Eq. (3):
F § Δλ · Φ = ( )*¨ ¸ *T . E © 2 ¹
(5)
There was also again the calculation of power density for each wavelength range, Eq. (3), considering the UC. According to Eq. (6):
H UC = Φ UC * E .
(6)
And finally, the constant of power density was obtained by the addition of UC according to Eq. (7):
CUC = ¦ H UC .
(7)
In the calculations can vary the conversion efficiency using a conversion factor of Eq. (7) and thus vary UC efficiencies. For all it considered that the emission of UC would be exactly half of its absorption. Because theoretically to occur UC phenomenon, it is necessary that two or more lower energy photons to recombine in a higher energy. So we used this relationship for this model, and it was considered UC of 1000 nm to 2200 nm. As, for example, for a UC who absorbs two photons of 1000 nm that will emit a photon of 500 nm to the sum of all densities from 1000 nm. This is just an initial simplification, it is known that the reality of each TR3+ and your host material will be another. 3.
Results and discussions
With the mathematical approaches developed, was obtained tables with photon density per unit (W/cm2) for all ranges of wavelengths, between 300 and 2100 nm, where those data were entered into the software which simulates dimensional solar cells [20]. The simulation was performed assuming a bifacial silicon solar cell already experimentally characterized and contrasted with theoretical data [21]. Forms of illuminations have been modified for this solar cell considering the information of UC, where changed the intensities constants (transmitted sunlight) and conversion efficiency. With these simulations were achieved important results, such as the current curves versus potential difference (I x V) for these cells when incorporated into the UC. For all the results the UC of 2000 nm, it is, that emits two photons in 1000 nm is what gives better responses when incorporated in the solar cell. Fig. 1 (a) shows a comparison of the curves I x V of UC of 2000 nm for different conversion efficiencies. Where maintaining the fixed power density of photons in 0.00208 W/cm², it is, considering that all solar radiation transmitted (non-absorbed) by the solar cell is absorbed and re-emitted by the UC again to the solar cell. This value was used considering the thermodynamic limits of a silicon solar cell [13], where 20.8 % of the solar radiation spectrum AM1,5G is transmitted. There is a variation of approximately 40 % on electrical current compared to concentrations of 25 and 100 %, and this response does not follow linearity. When the variation in the concentration of 25 % compared to 75 % is observed, senses a variation in current of approximately 32 %, and when compared to 50 % the difference is 22 %. To a 75 % concentration factor compared with 100 % and 50 % are obtained by this variation between 6 % and 10 %, respectively. Finally, comparing the concentrations of 100 %, and 50 % reaches 16 % of variation in electric current. In Fig. 1 (b) used the irradiance constant calculated for each converter. The worst results were for the UC 1000 nm. Electrical current for this converter decreases approximately by 50 % compared to 1800 nm. Between the UC 1800 nm and 2000 nm is observed little variation, about 1 % to their responses and are the best results obtained. The non-linearity is observed when UC 2200 nm it is analyzed their results are between UC 1000 nm and 2000 nm. In order to analyze the results of the emitted radiation found for UC and that calculated for AM 1.5G [13] obtained the comparative graph which is shown in Fig. 1 (c).
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Aline Cristiane Pan et al. / Energy Procedia 102 (2016) 80 – 86 UC2000 nm-25% UC2000 nm-50% UC2000 nm-75% UC2000 nm-100%
15 14 13 12 11
Current (mA)
10 9 8 7 6 5 4 3 2 1 0 0,0
0,1
0,2
0,3
0,4
0,5
Potential Difference (V)
(a) UC1000 nm UC1800 nm UC2000 nm UC2200 nm UC1500 nm UC1200 nm UC1700 nm UC2100 nm
6
5
Current (mA)
4
3
2
1
0 0,0
0,1
0,2
0,3
0,4
0,5
0,6
Potential Difference (V)
(b) AM1.5G + UC constant UC constant 20.8% AM 1.5G
11 10 9
Current (mA)
8 7 6 5 4 3 2 1 0 0,0
0,1
0,2
0,3
0,4
0,5
0,6
Potential Difference (V)
(c) Fig. 1. I x V curves obtained by PC1D using :(a) variations of concentrations of 2000 nm UC, (b) constants of irradiation calculated for different UC and (c) variations of irradiance for the 2000 nm UC.
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It used to the UC 2000 nm for this analysis, as this always has the best efficiencies. It is evident that when it is assumed that all the solar radiation which was transmitted by the solar cell is absorbed by the UC (20.8 %) the electric current increases excessively, more than 50 % compared with when it is considered AM 1.5G and the constant 0.0107 W/cm2 concerning of own UC of 2000 nm, which would be a more realistic comparison. Considering the configuration in which it used to constant calculated for the converter and the AM 1.5G with constant of converter note to an electric current difference of 14 %. The main electrical characteristics obtained by the graphics from Fig. 1 are shown in Tab. 1. Table – 1 Main generated electrical characteristics by Fig. 2.
25 % 50 % 75 % 100 % UC1000 UC1800 UC2000 UC2200 AM1.5G Constant+UC2000 0.0208+UC2000
Isc (mA) 8.279 10.50 11.50 12.10 0.7444 5.570 5.379 3.158 3.901 5.379 10.50
Pmax (W) 0.003220 0.004144 0.004576 0.004822 0.000224 0.002103 0.002025 0.001133 0.001425 0.002025 0.004144
Voc (V) 0.5212 0.5286 0.5316 0.5331 0.4357 0.5083 0.5074 0.4896 0.4965 0.5074 0.5286
FF (%) 74.62315 74.66263 74.84869 74.75378 69.06438 74.27864 74.19472 73.27847 73.57320 74.19472 74.66263
Ș (%) 0.161258 0.207532 0.229157 0.241486 0.016548 0.192160 0.197138 0.119213 0.138727 0.197138 0.207532
The simulations of I x V curves demonstrated that UCs which absorb at wavelengths between 1800 and 2000 nm have a better potential in relation to others, the efficiencies found (~20 %) for solar cells with UCs implemented are shown below the limit values calculated [12] (~36 %). However, approaches the values found in practice (~16 %) [22] and modeled [23]. 4.
Conclusions
The mathematical modeling of the behavior of photonic converters to higher energies, based on actual parameters found in the literature, when implemented in silicon bifacial solar cells was developed. Furthermore, it obtained results similar to other authors when analyzed using the electrical characteristics PC1D. For all variations of settings that was inserted into PC1D, the UCs that operate absorbing radiation transmitted by bifacial solar cell silicon in wavelength ranges between 1800 and 2000 nm are most suitable for this incorporation. Thus, for a future development and manufacture of converters for this purpose it is proposed to seek materials that are capable of absorbing the radiation in these wavelengths, and also have the ability to send back to the solar cell.
Acknowledgements This work was performed as part of the Universal Project 2014, nº 458145/2014-9, of the National Council for Scientific and Technological Development (CNPq). In same way, by Research Program for Students of PUCRS (BPA/2015). References [1] Kemenes, A., Forsberg, B., Melack, J., 2008. As hidrelétricas e o aquecimento global, Ciência Hoje, vol. 41, n. 245, pp. 20-25. [2] Moehlecke, A., 2002. Células Solares Eficientes e de Baixo Custo. Brasília: Prêmio Jovem Cientista e Prêmio Jovem Cientista do Futuro, pp.15-76. [3] Hohmeer, O., Ottinger, R. L., 1994. Social Costs of Energy, Springer-Verlang. [4] Pan, A. C., 2004. Processos de fabricação de células solares bifaciais em fornos de aquecimento rápido, Dissertação de Mestrado, PGETEMA, PUCRS, Porto Alegre. [5] Pan, A. C. et al., 2010. Enhancement of up-conversion efficiency by combining rare earth-doped phosphors with PbS quantum dots, Solar Energy Materials & Solar Cells, n. 94, pp.1923–1926.
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Aline Cristiane Pan et al. / Energy Procedia 102 (2016) 80 – 86 [6] Strümpel, C. et. al., 2007. Modifying the solar spectrum to enhance silicon solar cell efficiency—an overview of available materials, Solar Energy Materials and Solar Cells, vol. 91, n. 4, pp. 238-249. [7] Pan, A. C. et al., 2014. Análise Óptica da Implementação de Conversores Fotônicos e Pontos Quânticos em Células Solares Bifaciais de Silício, V Congresso Brasileiro de Energia Solar, Recife. [8] Luque, A., 2000. Third Generation Photovoltaics and Multiple Band Photovoltaic Conversion, Photovoltaic Oplympic Vision Workshop, Sydney, Austrália. [9] Pollack, S. A. et al., 1987. Upconversion use for viewing and recording infrared images, Applied Optics. Vol. 26, nº 20, pp. 4400-4406. [10] Xie, P., Rand, S. C., 1990. Continuous-wave, pair-pumped laser, Optics Letters, vol. 15, n. 15, pp. 848-850. [11] Gamelin, D. R., Güdel, G. U., 2001. Upconversion processes in transition metal and rare earth metal systems, Topics in Current Chemistry, vol. 214, pp. 1-56. [12] Trupke, T., Green, M., Würfel, P., 2002. Improving solar cell efficiencies by up-conversion of sub-band-gap light, Journal Applied Physics, vol. 92, n. 7, pp. 4117-4122. [13] Shockley, W., Queisser, H., 1961. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, vol. 32, n. 3, pp. 510-519. [14] Shalav, A., Richards, B., Green, M., 2007. Luminescent layers for enhanced silicon solar cell performance: up-conversion, Solar Energy Materials and Solar Cells, vol. 91, pp. 829-842. [15] Pan, A. C., Canizo, C., Luque, A., 2009. Characterization of up-converter layer on bifacial silicone solar cells, Materials Science and Engineering B, vol. 159-160, pp. 212-215. [16] Pan, A. C., 2009. Convertidores Fotónicos para Células Solares Bifaciales de Silicio, Tese de Doutorado, IES, UPM, Madri. [17] Suyer, J. F. et al., 2005. Novel materials doped with trivalent lanthanides and transition metal ions showing near-infrared to visible photon upconversion, Optical Material, vol. 27, pp. 1111-1130. [18] Auzel, F., 2004. Upconversion and anti-stokes processes with f and d ions in solids, Chemical Review, vol. 104, pp. 139-173. [19] Fraas, L. M., Partain, L. D., 2010. Solar Cells and Their Applications, Wiley, 2ª edition. [20] PC1D,. 2008. Software for modelling a solar cell, Download in: http://www.engineering.unsw.edu.au/energy-engineering/pc1d-software-formodelling-a-solar-cell. [21] Pan, A. C. Canizo, C., Luque, A., 2007. Thin Bifacial Silicon Solar Cell, 22nd European Photovoltaic Solar Energy Conference and Exhibition, Milão, pp. 1438-1442. [22] Fisher S., et al., 2015. Enhanced energy conversion of up-conversion solar cells by the integration of compound parabolic concentrating optics, Solar Energy Materials & Solar Cells, vol. 140, pp.217–223. [23] Gordon J., et al., 2005. Optical properties of perfluorocyclobutyl polymers. III. Spectroscopic characterization of rare-earth-doped perfluorocyclobutyl polymers, J. Opt. Soc. Am. B, pp. 1654–1659.
ScienceDirect Energy Procedia 102 (2016) 80 – 86
E-MRS Spring Meeting 2016 Symposium T - Advanced materials and characterization techniques for solar cells III, 2-6 May 2016, Lille, France
Modeling Mathematical of the Behavior of Up Converter when Implemented in Bifacial Silicon Solar Cells Aline Cristiane Pan*1, Leandro Santos Grassi Cardoso2, Fernando Soares dos Reis2 12
Pontifical Catholic University of Rio Grande do Sul, Faculty of Physics1 and Faculty of Engineering2, Av. Ipiranga, 6681 - Partenon, Porto Alegre - RS, 90619-900 – Brasil. *Corresponding author: Tel.: +55 513320 3535 E-mail address: [email protected]
Abstract Up Converters implemented in solar cells have theoretical efficiencies of the conversion much higher than the actual and a much smaller production price. However, the experimental results in the present are not approaching the theoretical calculated values, because they have a small increase in photocurrent by incorporating the bifacial solar cell, for example. Hence, it is necessary dispose a quantitative tool for the characterization of candidate materials as up converter, which permits realize an influence sensibility analyzes of certain parameters and contrasts with the real values founded. Thus, the fundamental objective of this work is to develop a mathematical model to study the behavior of up converters, based on realistic parameters found in the literature, when implemented in silicon bifacial solar cells. Besides, exemplifies this model getting comparative results (I x V curve) for different materials used as an up converter when incorporated in silicon bifacial solar cells using the unidimensional software, PC1-D, in order to get the best candidates to be used. © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The European Materials Research Society (E-MRS). Peer-review under responsibility of The European Materials Research Society (E-MRS). Keywords: Mathematical modeling; Up converter; Solar cells.
1. Introduction In actuality, renewable sources of energies: wind, solar, biomass, geothermal, tidal and hydro, are situated in a prominent position due to the depletion of fossil resources and environmental problems. However, the designation of the hydroelectric facilities as "clean" is under discussion, since recent studies have shown the decomposition of organic matter in flooded areas for deposits of some of these facilities can generate and emit into the atmosphere significant amounts of methane and carbon dioxide, two of the gases involved in global warming [1].
1876-6102 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The European Materials Research Society (E-MRS). doi:10.1016/j.egypro.2016.11.321
Aline Cristiane Pan et al. / Energy Procedia 102 (2016) 80 – 86
Among renewable energy sources, solar energy shows up as great alternative because it can cover the needs of humanity with inexhaustible form and can serve as basis for sustainable development [2]. Instead, what happens with other renewable sources such as wind power, solar energy has a variety of resource fairly predictable and your magnitude is calculated from the place where the system is installed. Energy conversion occurs from photovoltaic effect, that being to make the conversion is necessary a photovoltaic cell. For their practical use, solar cells are usually associated electrically in series and encapsulated. The set of cells, connections and protection structure are called a photovoltaic module. Through these photovoltaic modules, solar energy stands out compared to other renewable sources to be simple and quick to install, be modular and not contaminate the environment [3]. In addition, the modularity allows to increase the capacity of the system gradually if high rise, and is also identified as ideal for isolated systems from the power supply, which can meet the needs of most people without electricity in developing countries. The primary problem that prevents a large expansion of this technology is economic, because it needs up an entire initial investment and the same is not subsidized, like other forms of energy. Consequently, one line of research follows is the deployment of solar cells with high efficiency and/or low cost. However, keep these two characteristics in a single device is not an easy task. Until now, no material or technology was able to completely achieve this goal, because of solar cells with high efficiency are too expensive and low cost does not achieve satisfactory performance [4]. Up Converter (UC) implemented in solar cells has theoretical electrical conversion efficiencies much higher than the current and a much smaller production target price [5]. Up conversion (UC) occurs when a material is photo-excited to high wavelengths (low energy) and emits photons at lower wavelengths (high energy). The absorption of photons (in two steps) below the width of the critical band in UC brings the excitement of carriers from its ground state to an intermediate level in UC, and from the intermediate level to a higher level excited. Some of these carriers excited recombines through radiative transitions that are accompanied by the emission of photons with energies above the width of the forbidden band [6]. When the energy of the photons generated by the UC process is greater than or equal to the solar cell absorption limit, the photons generated in the UC contribute to the generation of photocurrent on the device. The doped materials with trivalent ions of rare earths (TR3+) are the materials considered preferentially to be used at UC by the photovoltaic industry [7] and should be placed on the back of a bifacial solar cell for conversion of photons transmitted, and combined with a rear reflector to enable the highest energy photons converted to return the bifacial solar cell and to generate electron-hole pairs. For the association of the UC in solar cells is necessary to evaluate the parameters related to their luminescent properties. The energies transfer mechanisms (TE) between the TR3+ can enable conversion phenomena at low and high energies, and the detailed balance model is a very useful tool to calculate the thermodynamic limits of operation of the solar cell [8]. However, due to constructs in these analyzes, it becomes necessary to have other models to evaluate the potential improvement in the response of the solar cell with the photon converters. For other applications, such as lasers and optical fibers have been proposed mathematical models to simulate and / or compare the phenomena of photonic converters since the eighties [9] [10] [11] conducted a comprehensive study of the main parameters related to the TE mechanisms for UC processes. The increase in the number of absorbed photons due to the incorporation of UC, increasing the photocurrent and efficiency of the solar cell was calculated by Trupke [12]. In these theoretical calculations, it was considered a UC layer disposed on the back of bifacial solar cell and electronically isolated, this is, the coupling between UC and bifacial solar cell is produced purely radiative way. The efficiency limit contributed by this layer UC is 38.6 % for a low silicon cell non concentrated illumination (1 sun), reaching an increase of 63.2 % to a semiconductor material with energy gap of 1.955 eV and a lighting concentrated 46,200 suns (thermodynamic limit). These figures show a significant improvement over the limit efficiency of approximately 30 % calculated by Shockley and Queisser [13] for a silicon solar cell. However, the experimental results today [6] [14] [15] do not approach these calculated values, since they have small increases incorporate to UC at bifacial solar cell, for example. Therefore, one needs to have a quantitative tool for the characterization of candidate materials as UC, allowing perform sensitivity analyzes of the influence of certain parameters and contrast with the actual values found. Thus, the fundamental objective of this work is to develop a mathematical model to study the behavior of UC at higher energies, based on realistic parameters found in the literature, when implemented in bifacial silicon solar cell. In addition, it exemplifies this model obtaining comparative results (curves I x V) for different materials used as UC when incorporated in bifacial silicon solar cells using the unidimensional program PC1-D, in order to get the best candidates for use as UC.
81
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Aline Cristiane Pan et al. / Energy Procedia 102 (2016) 80 – 86
2.
Mathematical Model
2.1 Energy Transfer Mechanism A complete and detailed description of the physical processes occurring in the converter is very difficult to accomplish with complete accuracy. On the one hand, it would be necessary to know how it is distributed luminescent centers in different energy sublevels; and secondly, how does the propagation of light in the converter, and how to deal with this phenomenon [16]. Considering these factors, this study sought to find greed in the density of photons of a solar cell when incorporated into UC. UC consists generally of a non-absorbent matrix containing luminescent centers at a given concentration. The absorption and emission resulting from the luminescence were simplified considering the luminescent center as a series of three energy levels. Several TE takes place when employed to TR3+ in a solid medium. Most of these relate to the absorption and non-radioative transitions [17]. The minimum requirement for this to occur TE mechanisms is the presence of at least two metastable states. In addition to the UC phenomenon to be effective, these states must be large enough lifetimes, so that ions are able to participate in the luminescence process, or other photophysical processes most likely to occur compared with the non-radioactive relaxation [11]. The most important processes found in UC are: ground-state absorption (GSA), excited-state absorption (ESA), energy transfer up conversion (ETU), relaxation cross (CR), cooperative excitation (CE) and cooperative relaxation (CooR) [16]. These processes may be combined with each other making the most efficient UC effect [18] calls APTE (addition of photon by energy transfer) the most effective process for UC, where 3 ions are involved; two of these ions are excited by GSA and transfer their energy to the third ion by ETU. This process is also known as GSA / ETU [17]. The second process most probable is the absorption of the same ion in two steps, followed by the ESA for GSA (GSA / ESA) [11] and this is used in this paper that to realize the mathematical model. Other combined or individual processes have a low probability of occurrence, for example, CE probability is 5 orders of magnitude less than the APTE [18]. 2.2 Power Density Obtained for the UC To obtain the power density for each wavelength interval is calculated first the energy in this range by Eq. (1):
E = hv =
hc
λ
(1)
where h is Planck's constant, ν is the frequency, c is the speed of light and wavelength λ For the calculation of the photon density ( Φ ) on the average wavelength interval (Δλ), Eq. (2), it was using the energy value already calculated and irradiance values (F) for the solar spectrum tabulated AM1 .5G [19]. With the unit adjustments result was obtained at n/cm²s:
F § Δλ · . Φ = ( )*¨ ¸ E © 2 ¹
(2)
The next step was to calculate the power density in the same wavelength range, according to Eq. (3) W/cm²:
H = Φ*E .
(3)
With Eq. (4) there was the power density constant for all wavelength intervals by the sum of all irradiances of photons arranged:
CH = ¦ H .
(4)
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Considering the insertion of UC, was calculated again for the density of photons of wavelength ranges, but considering the radiation that is transmitted. That is, the optical transmittance was measured (T) for a bifacial silicon solar cell, and added to these values for Eq. (2), making it in Eq. (3):
F § Δλ · Φ = ( )*¨ ¸ *T . E © 2 ¹
(5)
There was also again the calculation of power density for each wavelength range, Eq. (3), considering the UC. According to Eq. (6):
H UC = Φ UC * E .
(6)
And finally, the constant of power density was obtained by the addition of UC according to Eq. (7):
CUC = ¦ H UC .
(7)
In the calculations can vary the conversion efficiency using a conversion factor of Eq. (7) and thus vary UC efficiencies. For all it considered that the emission of UC would be exactly half of its absorption. Because theoretically to occur UC phenomenon, it is necessary that two or more lower energy photons to recombine in a higher energy. So we used this relationship for this model, and it was considered UC of 1000 nm to 2200 nm. As, for example, for a UC who absorbs two photons of 1000 nm that will emit a photon of 500 nm to the sum of all densities from 1000 nm. This is just an initial simplification, it is known that the reality of each TR3+ and your host material will be another. 3.
Results and discussions
With the mathematical approaches developed, was obtained tables with photon density per unit (W/cm2) for all ranges of wavelengths, between 300 and 2100 nm, where those data were entered into the software which simulates dimensional solar cells [20]. The simulation was performed assuming a bifacial silicon solar cell already experimentally characterized and contrasted with theoretical data [21]. Forms of illuminations have been modified for this solar cell considering the information of UC, where changed the intensities constants (transmitted sunlight) and conversion efficiency. With these simulations were achieved important results, such as the current curves versus potential difference (I x V) for these cells when incorporated into the UC. For all the results the UC of 2000 nm, it is, that emits two photons in 1000 nm is what gives better responses when incorporated in the solar cell. Fig. 1 (a) shows a comparison of the curves I x V of UC of 2000 nm for different conversion efficiencies. Where maintaining the fixed power density of photons in 0.00208 W/cm², it is, considering that all solar radiation transmitted (non-absorbed) by the solar cell is absorbed and re-emitted by the UC again to the solar cell. This value was used considering the thermodynamic limits of a silicon solar cell [13], where 20.8 % of the solar radiation spectrum AM1,5G is transmitted. There is a variation of approximately 40 % on electrical current compared to concentrations of 25 and 100 %, and this response does not follow linearity. When the variation in the concentration of 25 % compared to 75 % is observed, senses a variation in current of approximately 32 %, and when compared to 50 % the difference is 22 %. To a 75 % concentration factor compared with 100 % and 50 % are obtained by this variation between 6 % and 10 %, respectively. Finally, comparing the concentrations of 100 %, and 50 % reaches 16 % of variation in electric current. In Fig. 1 (b) used the irradiance constant calculated for each converter. The worst results were for the UC 1000 nm. Electrical current for this converter decreases approximately by 50 % compared to 1800 nm. Between the UC 1800 nm and 2000 nm is observed little variation, about 1 % to their responses and are the best results obtained. The non-linearity is observed when UC 2200 nm it is analyzed their results are between UC 1000 nm and 2000 nm. In order to analyze the results of the emitted radiation found for UC and that calculated for AM 1.5G [13] obtained the comparative graph which is shown in Fig. 1 (c).
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15 14 13 12 11
Current (mA)
10 9 8 7 6 5 4 3 2 1 0 0,0
0,1
0,2
0,3
0,4
0,5
Potential Difference (V)
(a) UC1000 nm UC1800 nm UC2000 nm UC2200 nm UC1500 nm UC1200 nm UC1700 nm UC2100 nm
6
5
Current (mA)
4
3
2
1
0 0,0
0,1
0,2
0,3
0,4
0,5
0,6
Potential Difference (V)
(b) AM1.5G + UC constant UC constant 20.8% AM 1.5G
11 10 9
Current (mA)
8 7 6 5 4 3 2 1 0 0,0
0,1
0,2
0,3
0,4
0,5
0,6
Potential Difference (V)
(c) Fig. 1. I x V curves obtained by PC1D using :(a) variations of concentrations of 2000 nm UC, (b) constants of irradiation calculated for different UC and (c) variations of irradiance for the 2000 nm UC.
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It used to the UC 2000 nm for this analysis, as this always has the best efficiencies. It is evident that when it is assumed that all the solar radiation which was transmitted by the solar cell is absorbed by the UC (20.8 %) the electric current increases excessively, more than 50 % compared with when it is considered AM 1.5G and the constant 0.0107 W/cm2 concerning of own UC of 2000 nm, which would be a more realistic comparison. Considering the configuration in which it used to constant calculated for the converter and the AM 1.5G with constant of converter note to an electric current difference of 14 %. The main electrical characteristics obtained by the graphics from Fig. 1 are shown in Tab. 1. Table – 1 Main generated electrical characteristics by Fig. 2.
25 % 50 % 75 % 100 % UC1000 UC1800 UC2000 UC2200 AM1.5G Constant+UC2000 0.0208+UC2000
Isc (mA) 8.279 10.50 11.50 12.10 0.7444 5.570 5.379 3.158 3.901 5.379 10.50
Pmax (W) 0.003220 0.004144 0.004576 0.004822 0.000224 0.002103 0.002025 0.001133 0.001425 0.002025 0.004144
Voc (V) 0.5212 0.5286 0.5316 0.5331 0.4357 0.5083 0.5074 0.4896 0.4965 0.5074 0.5286
FF (%) 74.62315 74.66263 74.84869 74.75378 69.06438 74.27864 74.19472 73.27847 73.57320 74.19472 74.66263
Ș (%) 0.161258 0.207532 0.229157 0.241486 0.016548 0.192160 0.197138 0.119213 0.138727 0.197138 0.207532
The simulations of I x V curves demonstrated that UCs which absorb at wavelengths between 1800 and 2000 nm have a better potential in relation to others, the efficiencies found (~20 %) for solar cells with UCs implemented are shown below the limit values calculated [12] (~36 %). However, approaches the values found in practice (~16 %) [22] and modeled [23]. 4.
Conclusions
The mathematical modeling of the behavior of photonic converters to higher energies, based on actual parameters found in the literature, when implemented in silicon bifacial solar cells was developed. Furthermore, it obtained results similar to other authors when analyzed using the electrical characteristics PC1D. For all variations of settings that was inserted into PC1D, the UCs that operate absorbing radiation transmitted by bifacial solar cell silicon in wavelength ranges between 1800 and 2000 nm are most suitable for this incorporation. Thus, for a future development and manufacture of converters for this purpose it is proposed to seek materials that are capable of absorbing the radiation in these wavelengths, and also have the ability to send back to the solar cell.
Acknowledgements This work was performed as part of the Universal Project 2014, nº 458145/2014-9, of the National Council for Scientific and Technological Development (CNPq). In same way, by Research Program for Students of PUCRS (BPA/2015). References [1] Kemenes, A., Forsberg, B., Melack, J., 2008. As hidrelétricas e o aquecimento global, Ciência Hoje, vol. 41, n. 245, pp. 20-25. [2] Moehlecke, A., 2002. Células Solares Eficientes e de Baixo Custo. Brasília: Prêmio Jovem Cientista e Prêmio Jovem Cientista do Futuro, pp.15-76. [3] Hohmeer, O., Ottinger, R. L., 1994. Social Costs of Energy, Springer-Verlang. [4] Pan, A. C., 2004. Processos de fabricação de células solares bifaciais em fornos de aquecimento rápido, Dissertação de Mestrado, PGETEMA, PUCRS, Porto Alegre. [5] Pan, A. C. et al., 2010. Enhancement of up-conversion efficiency by combining rare earth-doped phosphors with PbS quantum dots, Solar Energy Materials & Solar Cells, n. 94, pp.1923–1926.
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