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Two dimensional device simulation and performance optimization of n-type silicon solar cell structure using PC2D
Solar Energy 146 (2017) 119–124
Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
Two dimensional device simulation and performance optimization of n-type silicon solar cell structure using PC2D A. Mekemeche a,⇑, M. Beghdad a, M. Belarbi b, B. Semmache c, Y. Cuminal d a
Laboratory Signal-Systems and Department of Physics, Faculty of Exact Sciences and informatics, University Abdelhamid Ibn Badis, Mostaganem, Algeria Department of Technics Sciences, Faculty of Engineering Sciences, University Abdelhamid Ibn Badis, Mostaganem, Algeria c Semco Technologies, 625 rue de la Croix Verte-Euromedicine Park, 34196 Montpellier Cedex 5, France d Institut d’Electronique et des Systèmes (IES)-CC 05002, Campus St Priest-860 rue de St Priest-F, Université Montpellier-CNRS-UMR 5214, 34095 Montpellier Cedex 5, France b
a r t i c l e
i n f o
Article history: Received 6 May 2016 Received in revised form 3 February 2017 Accepted 9 February 2017
Keywords: Silicon solar cells n-Type Selective emitter (SE) PC2D
a b s t r a c t In this paper, we analyze the impact of various parameters on the performances of the n-type monocrystalline silicon solar cell experimented by Fraunhofer Institute for Solar Energy Systems (ISE) in Germany. We studied, especially the influence of the base parameters (lifetime, resistivity and thickness), the emitter sheet resistance and the back surface field (BSF) sheet resistance, on the solar cell performances. To optimize this cell we have used PC2D which is a solar cell device simulator that models twodimensional effects entirely within a Microsoft Excel spreadsheet. With an Al2O3/SiNx front side boron emitter passivation, the metallization parameters were optimized by the authors getting efficiency of 19.60%. If all the parameters have ideal values our optimization provided an efficiency of 20.05% for homogeneous emitter with sheet resistance of 75 X/h. Furthermore, the study of the emitter led to a new structure developed recently: the selective emitter of n-type solar cell achieving efficiency of 20.20% with sheet resistance of 50 X/h under the contacts and 100 X/h, between contacts. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The first silicon solar cells were made on n-type substrates in 1950s. This technology changed to p-type substrates because of their high resistance to space radiation, at a time when the only application for those cells was for space (Zhao et al., 2002). Up to a certain period, all commercialized silicon solar cells were realized on p-type silicon substrate because the technology of their production was easily industrialized and accessible. The photovoltaic industry of silicon was therefore developed around this idea and terrestrial market is still mainly supplied today by cells in p-type silicon (Wang and Wang, 2014). Another reason of the choice of p-type crystalline silicon is that the electrons mobility (minority carriers) is higher about three times than the holes, so they have a big diffusion length, and then it is easy to collect them (Sze and Ng, 2007). Nevertheless, in equivalent technology, the best results of efficiency are obtained with n-type crystalline silicon solar cells (20–25%) (Green et al., 2015). For example, Benick et al. (2008) obtained a maximum efficiency of 23.2% on 4 cm2 surface cells.
⇑ Corresponding author. E-mail address: [email protected] (A. Mekemeche). http://dx.doi.org/10.1016/j.solener.2017.02.018 0038-092X/Ó 2017 Elsevier Ltd. All rights reserved.
The main cause of this is the presence of very recombinant defects in the p-type crystalline silicon, particularly boronoxygen pairs which are generated under illumination and are responsible of the loss of cells efficiency during the first months of operation (Light-induced degradation: LID) (Schmidt et al., 2003; Bothe et al., 2005). Cells with n-type crystalline silicon doped with phosphorus are not affected to this type of defects and are much more stable over time (Lim et al., 2011). Furthermore, the n-type wafers may offer greater immunity to the effects of metal contaminants like iron, molybdenum, titanium and others (Macdonald and Geerligs, 2004), so these cells have a high lifetime exceeding 1 ms (Zhao et al., 2002; Cuevas et al., 2002). In this work, we would optimize the following layer parameters: base, emitter and BSF for n-type solar cells to improve their efficiency using PC2D (Basore and Cabanas-Holmen, 2011). 2. Simulated devices The design used is a two-busbars p+nn+ full square monocrystalline silicon cells of real surface 139.3 cm2 (125 mm 125 mm), homogenously boron doped front side emitter with a sheet resistance of 90 X/h corresponding to a surface doping concentration of 6 1019 cm–3 and a depth of about 0.25 lm calculated with PC1D (Clugston and Basore, 1997). The back side was doped by a
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A. Mekemeche et al. / Solar Energy 146 (2017) 119–124
phosphorous gaussian profile of 30 X/h corresponding to a surface doping concentration of 3 1019 cm–3 and a depth of 2 lm then contacted with evaporated aluminum on the whole cell area (Kalio et al., 2011; Richter et al., 2010). The front surface was textured with alkaline (KOH) in the purpose to have a surface pyramid structure with angle of 54.74° and depth of 3 lm, passivated with aluminum oxide (Al2O3) then covered with silicon nitride (SiNx) antireflective coating layer (Fig. 1) (Kalio et al., 2011; Richter et al., 2010). Using inkjet and aerosol jet printing with consequent silver electroplating, the metallization was optimized by Kalio et al. (2011) (Fraunhofer ISE) giving a contact resistance values of 3.8 X cm2, series resistance of 0.64 X cm2 (verified by calculation) and shunt resistance of 65 kX cm2. The most optical parameters for all simulated solar cells are taken from examples of Basore and Cabanas-Holmen (2014). 3. Simulation program The simulation is done with PC2D which is relatively a new solar device simulator (2011) that models two-dimensional effects of solar cells with the companionship of PC1D (Basore and Cabanas-Holmen, 2011). The region simulated by PC2D is the smallest elementary part, representative of the entire cell area of 1 cm2. The solution region is defined by X which is the width measured from the center of the contact to the midpoint situated between the center of two successive contacts, and Y which is the thickness of the cell. This region is divided into a grid of 20 20 identical rectangular elements bordered in two perpendicular directions by a mesh of 21 21 nodes (Fig. 2) in which the continuity equations and minority carriers current (n, p) are solved by the method of finite elements (Basore and Cabanas-Holmen, 2011):
dn=dt ¼ Gn Rn þ div J n =q dp=dt ¼ Gp Rp div J p =q J n ¼ q nln E þ Dn gradn J p ¼ q plp E Dp gradp The vectors J n ; J p (in bold type) are carrier currents, Gn and Gp: rates of carrier generation, Rn and Rp: rates of carrier recombina-
Fig. 2. Mesh of the simulated region.
tion, mn and mp: carrier mobilities, Dn and Dp: constants carrier diffusion (n for electrons and p for holes respectively), the vector E is the whole electric field across the structure and q, the electronic charge. The boundary conditions at the top and bottom surfaces represent the complex physics occurring in the very thin layers adjacent to each of these surfaces. The boundary conditions at the left and right side boundaries of the solution region can be either reflecting or repeating, according to the user’s specification (Basore and Cabanas-Holmen, 2011). The user defines the solar cell that he wishes to model in the ‘‘Device” and ‘‘Recombination” sheets with it solution region, typically selected to extend from the middle of a gridline to the midpoint between gridlines. In the ‘‘Device” sheet, we enter the structural, electrical and optical parameters. In ‘‘Recombination” sheet, we integrate recombination density currents J01 in doped emitter and at metal contacted surfaces of the cell, and the recombination density current J02 in the space charge region. J01 and J02 are determined by PC1D (Cabanas-holmen and Basore, 2012).
Fig. 1. Parameters used of simulated solar cells.
A. Mekemeche et al. / Solar Energy 146 (2017) 119–124 Table 1 Results of the two solar cells real/simulated. Cell
Jsc (mA/cm2)
Voc (mV)
FF (%)
g (%)
Real This work
38.00 37.46
651.6 649.5
79.00 80.92
19.60 19.68
121
The most important parameters of the base are lifetime, resistivity and thickness. These parameters have a very important role in the collection of the charge carriers and influence significantly on density current of the solar cell and therefore on its efficiency (Goetzberger et al., 1998). The sheet resistance of the emitter has a big effect on recombination density currents, so consequently on the open-circuit voltage (Goetzberger et al., 1998). The back surface field layer has an important effect on the performance of the solar cells; it creates a potential barrier tending to confine minority carriers (holes) in the more lightly doped region and helps to drive them toward the front improving the efficiency. 4.1. Effect of base parameters
Fig. 3. Simulated J–V curve.
4.1.1. Effect of the lifetime By varying the lifetime of the base minority carrier from 100 ms to 2.5 ms, all the graphs have the same allure, noting that all parameters of the cell increase quickly up to about 1 ms corresponding to: 649.5 mV of Voc, 37.46 mA/cm2 of Jsc, 80.92% of FF and 19.68% of Ƞ. The increase becomes slow beyond this value (Fig. 4). This result is expected since the increase in lifetime leads to a better collection of carriers.
There are no material files in PC2D as there are in PC1D; everything is in the spreadsheet itself. Once the solar cell is defined, we initiate the simulation in the ‘‘Excitation” sheet and can view the results and the graphs in the same sheet (Basore and CabanasHolmen, 2011; Cabanas-holmen and Basore, 2012). The simulation with our parameters gives the following results presented in Table 1. The results found (short-circuit density current Jsc, open-circuit voltage Voc, fill factor FF and efficiency g) are approximately the same as those of experience results of the solar cell (Kalio et al., 2011) (see Fig. 3). We note that the short-circuit density current value is slightly smaller than the experimental one (about 0.5 mA/cm2), same thing for the value of the open-circuit voltage (about 0.2 mV). The fill factor is weakly higher than the experimental one (less than 2%) (Table 1). This good accordance with experience permits us to use this program to study our cell and then optimize it by varying different parameters.
4.1.2. Effect of the resistivity When varying the base resistivity from 1 to 10 X cm (Fig. 5), it is found that the short-circuit density current increases up to 37.89 mA/cm2 corresponding to 6 X cm base resistivity, beyond this value the improvement is not too significant. This improvement is due to the decrease of recombination current due to reducing of the base doping (Sze and Ng, 2007). On the contrary, the open-circuit voltage decreases slightly with the base resistivity (variation of 1.5 mV in the range of 1–5 X cm), then it becomes almost invariable (Fig. 5). Theoretically, this result is expected because the reduction of base doping increases the saturation current which reduces the open-circuit voltage, this decrease is low because this voltage is also function of shortcircuit density current, exactly it is proportional to logarithm of rate of short-circuit density current to saturation density current as it indicates by the following equation (Goetzberger et al., 1998):
4. Results and discussions
V oc ðkT=qÞlnðJ sc =j0 Þ
Now, as we found approximately the same results (between real cell and the simulated one), we can optimize the parameters of this cell (base, emitter and BSF layer).
Likewise, the fill factor decreases with the resistivity due to the decrease of base resistance. Consequently, the result is an optimization of the efficiency (19.71%) shown on the graph in the range of 1.5–2 X cm (Fig. 5).
Fig. 4. Effect of lifetime on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
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4.1.3. Effect of the thickness It is clear that the increase in thickness of the substrate is an advantage to absorb more photons, but if the diffusion length L pffiffiffiffiffiffiffi (L ¼ Ds, D is the constant carrier diffusion and s is the lifetime) falls below the value of the base thickness, then the photocurrent will drop sharply (Goetzberger et al., 1998). So, for the shortcircuit density current and the efficiency there are some optimization of 37.86 mA/cm2 and 19.89% respectively around 400 lm (Fig. 6). The fill factor decreases from 80.98% at 100 lm to 80.64% at 600 lm because of the increase in base resistance. Note that a very large thickness substrate increases its cost.
4.2. Effect of emitter sheet resistance We remark that the short-circuit density current and the opencircuit voltage increase with the emitter sheet resistance (Fig. 7), since the reduction of emitter doping decreases recombination density current in the emitter from 143.53 fA/cm2 for 50 X/h to 44.3 fA/cm2 for 100 X/h (calculated with PC1D) (Cabanasholmen and Basore, 2012). Contrarily, the fill factor decreases because of the increase of the emitter resistance. Therefore, we remark an optimization of the efficiency at 75 X/h (average of the little range of 70–80 X/h) giving values of 19.70%, this is because high sheet resistance causes a low recombination density
Fig. 5. Effect of base resistivity on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
Fig. 6. Effect of base thickness on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
Fig. 7. Effect of emitter sheet resistance on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
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current. Beyond this range the efficiency decreases because the series resistance becomes predominant. Hence the choice of the selective emitter structure of n-type substrate (Poulain et al., 2012) which reduces the sheet resistance in the contacts to reduce the series resistance and increases it between the contacts to decrease recombination density current (Fig. 8) (Rahman, 2012).
4.3. Effect of the back surface field (BSF) The graphs show that the four parameters decrease with the increase of BSF sheet resistance (Fig. 9). In other words, the increase of BSF doping causes an improvement of the intensity back surface field in the high-low junction n+/n creating a potential barrier which tends to confine minority carriers (holes) in the more lightly doped region and helps to drive them toward the front. Therefore, the short-circuit current density will increase, the open-circuit voltage also will increase due to increased shortcircuit current. Consequently, the efficiency and the fill factor will noticeably increase. For example, the efficiency increases from 19.06% for the solar cell without BSF layer to 19.68% with 30 X/ h of BSF sheet resistance (real cell), improved to 19.82% with 20 X/h of BSF.
5. Performance of the optimized solar cell The optimized values: thick, resistivity, lifetime of substrate and BSF are respectively 250 mm, 1.75 X cm (average of 1.5–2 X cm), 1.5 ms and 20 X/h. With these parameters, the results of this optimization are shown in the following Table 2:
Table 2 Results of optimized solar cells (HE and example of SE). Cell
Jsc (mA/cm2)
Voc (mV)
FF (%)
g (%)
Optimized 75 X/h (HE) Example 50–100 X/h (SE)
38.07 38.14
651.50 654.56
80.86 80.90
20.05 20.20
The optimization of Kalio’s cell (HE90) leads to two structures: homogeneous emitter cell of 75 X/h (HE75) with an absolute gain of 0.37% in efficiency and selective emitter cell of 50 X/h under the contacts and 100 X/h between contacts (SE50-100) as example (Fig. 8) with an absolute gain of 0.52% in efficiency. This improvement is shown clearly on the graph of external quantum efficiency (EQE) in the infrared wavelength range due to the good collection of the charge carriers in the base of the optimized solar cells (optimization of the base and BSF parameters) (Fig. 10). We can also view the improvement of 0.15% in efficiency of (SE50-100) compared to (HE75) due to the selective emitter (Fig. 11). It is found that this structure permits an improvement of quantum efficiency in the ultra-violet wavelength range, due to a decrease in recombination density current from 73 fA/cm2 to 44.3 fA /cm2 (Section 4.2), resulting from a lower rate of different recombinations, mainly Auger type, due the highest sheet resistance of the emitter (between contacts). On the contrary, at highest wavelengths, the two cells give identical results, confirming that the structure of (SE) does not influence much the volume or the rear surface of these cells but the absorption is more superficial. This result can be improved by making a detailed study on this structure. 100% 90% 80% 70%
SE50-100
EQE
60% 50%
HE75
40%
HE90
30% 20% 10% 0% 300
Fig. 8. Part of selective emitter (SE) structure.
400
500
600
700
800 (nm)
900
1000
1100
1200
Fig. 10. Comparison of external quantum efficiency of SE50-100, HE75 and HE90.
Fig. 9. Effect of the back surface field on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
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95%
Conflict of interest
90%
None declared.
85%
EQE
80%
References
SE50-100 HE75
75% 70% 65% 60% 55% 300
350
400
450
500
(nm) Fig. 11. Comparison of external quantum efficiency of SE50-100 and HE75.
6. Conclusion Using PC2D simulation, we have optimized the most important parameters: base, emitter and BSF of n-type homogeneous solar cells experimented by Kalio et al. For the base parameters, we have noted that all parameters of the cell increase quickly up to 1 ms of lifetime, this increase becomes slow beyond this value. Likewise, the efficiency increases with the base thickness up to 400 lm then it decreases due to the increase of the resistance. The optimized base resistivity value is 1.75 X cm for a maximum efficiency. The analysis of the emitter solar cell shows that the efficiency increases up to the value of 75 X/h because high sheet resistance causes a low recombination density current. Beyond this value, the efficiency decreases because series resistance becomes predominant. Hence the choice of the selective emitter structure which reduces the sheet resistance in the contacts to reduce the series resistance and increases it between the contacts to decrease recombination density currents. The introduction of the BSF improved enormously the efficiency; with 20 X/h of BSF we obtained an improvement of 0.14% in relation to 30 X/h of BSF (experimental solar cell). Our optimization gives us an efficiency of 20.05% with sheet resistance of 75 X/h homogeneous emitter. This efficiency is improved to 20.20% with selective emitter of 50–100 X/h taken as example. A detailed study of this structure can give us higher efficiencies.
Basore, P.A., Cabanas-Holmen, K., 2011. PC2D: a circular-reference spreadsheet solar cell device simulator. IEEE J. Photovoltaics 1 (1), 72–77. Basore, P.A., Cabanas-Holmen, K., 2014. PC2D V2.4 examples, in, consulted on January 2016. Benick, J. et al., 2008. High efficiency n-type Si solar cells on Al2O3-passivated boron emitters. Appl. Phys. Lett. 92, 253504. Bothe, K., Sinton, R., Schmidt, J., 2005. Fundamental boron-oxygen-related carrier lifetime limit in mono- and multicrystalline silicon. Prog. Photovoltaics: Res. Appl. 13 (4), 287–296. Cabanas-holmen, K., Basore, P.A., 2012. PC2D: applied to a selective emitter cell. Energy Procedia (2011), 1–4. Clugston, D.A., Basore, P.A., 1997. PC1D version 5: 32-bit solar cell modeling on personal computers. Conference Record of the Twenty Sixth IEEE Photovoltaic Specialists Conference 1997, 207–210. Available at: http://ieeexplore.ieee.org/ lpdocs/epic03/wrapper.htm?arnumber=654065. Cuevas, A. et al., 2002. Millisecond minority carrier lifetimes in n-type multicrystalline silicon. Appl. Phys. Lett. 81 (26), 4952–4954. Goetzberger, A., Knobloch, J., Voss, B., 1998. Crystalline silicon solar cells. Available at: http://www.tf.uni-kiel.de/matwis/amat/semi_en/running_term/articles_ seminar/solar/general/overview_si_green.pdf. Green, M.A. et al., 2015. Solar cell efficiency tables (Version 45). Prog. Photovoltaics: Res. Appl. 23 (1), 1–9. Kalio, A. et al., 2011. Metallization of n-type silicon solar cells using fine line printing techniques. Energy Procedia 8, 571–576. http://dx.doi.org/10.1016/ j.egypro.2011.06.184. Lim, B. et al., 2011. Light-induced degradation of the carrier lifetime in n-type czochralski-grown silicon doped with boron and phosphorus. In: 26th European Photovoltaic Solar Energy Conference and Exhibition, pp. 944–948. Macdonald, D., Geerligs, L.J., 2004. Recombination activity of interstitial iron and other transition metal point defects in p- and n-type crystalline silicon. Appl. Phys. Lett. 85 (18), 4061–4063. Poulain, G. et al., 2012. Selective laser doping from boron silicate glass. Energy Procedia 27, 455–459. Rahman, M.Z., 2012. Status of selective emitters for p-type c-si solar cells. Opt. Photonics J. 2, 129–134. Richter, A. et al., 2010. Firing stable al2o3/sinx layer stack passivation for the front side boron emitter of n-type silicon solar cells. In: 25th European Photovoltaic Solar Energy Conference, pp. 1453–1459. Schmidt, J., Bothe, K., Hezel, R., 2003. Structure and transformation of the metastable centre in Cz-silicon solar cells. 3rd World Conference on Photovoltaic Energy Conversion, 2003. Proceedings of, vol. 3, pp. 2887–2892. Sze, S.M., Ng, K.K., 2007. Physics of Semiconductor Devices. John Wiley & Sons. Wang, X., Wang, Z.M. (Eds.), 2014. High-Efficiency Solar Cells: Physics Materials and Devices. Springer Series in Materials Science, vol. 190. Springer International Publishing, Switzerland. Zhao, J. et al., 2002. High efficiency PERT cells on n-type silicon substrates. In: 29th IEEE Photovoltaic Specialists Conference, pp. 218–221.
Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
Two dimensional device simulation and performance optimization of n-type silicon solar cell structure using PC2D A. Mekemeche a,⇑, M. Beghdad a, M. Belarbi b, B. Semmache c, Y. Cuminal d a
Laboratory Signal-Systems and Department of Physics, Faculty of Exact Sciences and informatics, University Abdelhamid Ibn Badis, Mostaganem, Algeria Department of Technics Sciences, Faculty of Engineering Sciences, University Abdelhamid Ibn Badis, Mostaganem, Algeria c Semco Technologies, 625 rue de la Croix Verte-Euromedicine Park, 34196 Montpellier Cedex 5, France d Institut d’Electronique et des Systèmes (IES)-CC 05002, Campus St Priest-860 rue de St Priest-F, Université Montpellier-CNRS-UMR 5214, 34095 Montpellier Cedex 5, France b
a r t i c l e
i n f o
Article history: Received 6 May 2016 Received in revised form 3 February 2017 Accepted 9 February 2017
Keywords: Silicon solar cells n-Type Selective emitter (SE) PC2D
a b s t r a c t In this paper, we analyze the impact of various parameters on the performances of the n-type monocrystalline silicon solar cell experimented by Fraunhofer Institute for Solar Energy Systems (ISE) in Germany. We studied, especially the influence of the base parameters (lifetime, resistivity and thickness), the emitter sheet resistance and the back surface field (BSF) sheet resistance, on the solar cell performances. To optimize this cell we have used PC2D which is a solar cell device simulator that models twodimensional effects entirely within a Microsoft Excel spreadsheet. With an Al2O3/SiNx front side boron emitter passivation, the metallization parameters were optimized by the authors getting efficiency of 19.60%. If all the parameters have ideal values our optimization provided an efficiency of 20.05% for homogeneous emitter with sheet resistance of 75 X/h. Furthermore, the study of the emitter led to a new structure developed recently: the selective emitter of n-type solar cell achieving efficiency of 20.20% with sheet resistance of 50 X/h under the contacts and 100 X/h, between contacts. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The first silicon solar cells were made on n-type substrates in 1950s. This technology changed to p-type substrates because of their high resistance to space radiation, at a time when the only application for those cells was for space (Zhao et al., 2002). Up to a certain period, all commercialized silicon solar cells were realized on p-type silicon substrate because the technology of their production was easily industrialized and accessible. The photovoltaic industry of silicon was therefore developed around this idea and terrestrial market is still mainly supplied today by cells in p-type silicon (Wang and Wang, 2014). Another reason of the choice of p-type crystalline silicon is that the electrons mobility (minority carriers) is higher about three times than the holes, so they have a big diffusion length, and then it is easy to collect them (Sze and Ng, 2007). Nevertheless, in equivalent technology, the best results of efficiency are obtained with n-type crystalline silicon solar cells (20–25%) (Green et al., 2015). For example, Benick et al. (2008) obtained a maximum efficiency of 23.2% on 4 cm2 surface cells.
⇑ Corresponding author. E-mail address: [email protected] (A. Mekemeche). http://dx.doi.org/10.1016/j.solener.2017.02.018 0038-092X/Ó 2017 Elsevier Ltd. All rights reserved.
The main cause of this is the presence of very recombinant defects in the p-type crystalline silicon, particularly boronoxygen pairs which are generated under illumination and are responsible of the loss of cells efficiency during the first months of operation (Light-induced degradation: LID) (Schmidt et al., 2003; Bothe et al., 2005). Cells with n-type crystalline silicon doped with phosphorus are not affected to this type of defects and are much more stable over time (Lim et al., 2011). Furthermore, the n-type wafers may offer greater immunity to the effects of metal contaminants like iron, molybdenum, titanium and others (Macdonald and Geerligs, 2004), so these cells have a high lifetime exceeding 1 ms (Zhao et al., 2002; Cuevas et al., 2002). In this work, we would optimize the following layer parameters: base, emitter and BSF for n-type solar cells to improve their efficiency using PC2D (Basore and Cabanas-Holmen, 2011). 2. Simulated devices The design used is a two-busbars p+nn+ full square monocrystalline silicon cells of real surface 139.3 cm2 (125 mm 125 mm), homogenously boron doped front side emitter with a sheet resistance of 90 X/h corresponding to a surface doping concentration of 6 1019 cm–3 and a depth of about 0.25 lm calculated with PC1D (Clugston and Basore, 1997). The back side was doped by a
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A. Mekemeche et al. / Solar Energy 146 (2017) 119–124
phosphorous gaussian profile of 30 X/h corresponding to a surface doping concentration of 3 1019 cm–3 and a depth of 2 lm then contacted with evaporated aluminum on the whole cell area (Kalio et al., 2011; Richter et al., 2010). The front surface was textured with alkaline (KOH) in the purpose to have a surface pyramid structure with angle of 54.74° and depth of 3 lm, passivated with aluminum oxide (Al2O3) then covered with silicon nitride (SiNx) antireflective coating layer (Fig. 1) (Kalio et al., 2011; Richter et al., 2010). Using inkjet and aerosol jet printing with consequent silver electroplating, the metallization was optimized by Kalio et al. (2011) (Fraunhofer ISE) giving a contact resistance values of 3.8 X cm2, series resistance of 0.64 X cm2 (verified by calculation) and shunt resistance of 65 kX cm2. The most optical parameters for all simulated solar cells are taken from examples of Basore and Cabanas-Holmen (2014). 3. Simulation program The simulation is done with PC2D which is relatively a new solar device simulator (2011) that models two-dimensional effects of solar cells with the companionship of PC1D (Basore and Cabanas-Holmen, 2011). The region simulated by PC2D is the smallest elementary part, representative of the entire cell area of 1 cm2. The solution region is defined by X which is the width measured from the center of the contact to the midpoint situated between the center of two successive contacts, and Y which is the thickness of the cell. This region is divided into a grid of 20 20 identical rectangular elements bordered in two perpendicular directions by a mesh of 21 21 nodes (Fig. 2) in which the continuity equations and minority carriers current (n, p) are solved by the method of finite elements (Basore and Cabanas-Holmen, 2011):
dn=dt ¼ Gn Rn þ div J n =q dp=dt ¼ Gp Rp div J p =q J n ¼ q nln E þ Dn gradn J p ¼ q plp E Dp gradp The vectors J n ; J p (in bold type) are carrier currents, Gn and Gp: rates of carrier generation, Rn and Rp: rates of carrier recombina-
Fig. 2. Mesh of the simulated region.
tion, mn and mp: carrier mobilities, Dn and Dp: constants carrier diffusion (n for electrons and p for holes respectively), the vector E is the whole electric field across the structure and q, the electronic charge. The boundary conditions at the top and bottom surfaces represent the complex physics occurring in the very thin layers adjacent to each of these surfaces. The boundary conditions at the left and right side boundaries of the solution region can be either reflecting or repeating, according to the user’s specification (Basore and Cabanas-Holmen, 2011). The user defines the solar cell that he wishes to model in the ‘‘Device” and ‘‘Recombination” sheets with it solution region, typically selected to extend from the middle of a gridline to the midpoint between gridlines. In the ‘‘Device” sheet, we enter the structural, electrical and optical parameters. In ‘‘Recombination” sheet, we integrate recombination density currents J01 in doped emitter and at metal contacted surfaces of the cell, and the recombination density current J02 in the space charge region. J01 and J02 are determined by PC1D (Cabanas-holmen and Basore, 2012).
Fig. 1. Parameters used of simulated solar cells.
A. Mekemeche et al. / Solar Energy 146 (2017) 119–124 Table 1 Results of the two solar cells real/simulated. Cell
Jsc (mA/cm2)
Voc (mV)
FF (%)
g (%)
Real This work
38.00 37.46
651.6 649.5
79.00 80.92
19.60 19.68
121
The most important parameters of the base are lifetime, resistivity and thickness. These parameters have a very important role in the collection of the charge carriers and influence significantly on density current of the solar cell and therefore on its efficiency (Goetzberger et al., 1998). The sheet resistance of the emitter has a big effect on recombination density currents, so consequently on the open-circuit voltage (Goetzberger et al., 1998). The back surface field layer has an important effect on the performance of the solar cells; it creates a potential barrier tending to confine minority carriers (holes) in the more lightly doped region and helps to drive them toward the front improving the efficiency. 4.1. Effect of base parameters
Fig. 3. Simulated J–V curve.
4.1.1. Effect of the lifetime By varying the lifetime of the base minority carrier from 100 ms to 2.5 ms, all the graphs have the same allure, noting that all parameters of the cell increase quickly up to about 1 ms corresponding to: 649.5 mV of Voc, 37.46 mA/cm2 of Jsc, 80.92% of FF and 19.68% of Ƞ. The increase becomes slow beyond this value (Fig. 4). This result is expected since the increase in lifetime leads to a better collection of carriers.
There are no material files in PC2D as there are in PC1D; everything is in the spreadsheet itself. Once the solar cell is defined, we initiate the simulation in the ‘‘Excitation” sheet and can view the results and the graphs in the same sheet (Basore and CabanasHolmen, 2011; Cabanas-holmen and Basore, 2012). The simulation with our parameters gives the following results presented in Table 1. The results found (short-circuit density current Jsc, open-circuit voltage Voc, fill factor FF and efficiency g) are approximately the same as those of experience results of the solar cell (Kalio et al., 2011) (see Fig. 3). We note that the short-circuit density current value is slightly smaller than the experimental one (about 0.5 mA/cm2), same thing for the value of the open-circuit voltage (about 0.2 mV). The fill factor is weakly higher than the experimental one (less than 2%) (Table 1). This good accordance with experience permits us to use this program to study our cell and then optimize it by varying different parameters.
4.1.2. Effect of the resistivity When varying the base resistivity from 1 to 10 X cm (Fig. 5), it is found that the short-circuit density current increases up to 37.89 mA/cm2 corresponding to 6 X cm base resistivity, beyond this value the improvement is not too significant. This improvement is due to the decrease of recombination current due to reducing of the base doping (Sze and Ng, 2007). On the contrary, the open-circuit voltage decreases slightly with the base resistivity (variation of 1.5 mV in the range of 1–5 X cm), then it becomes almost invariable (Fig. 5). Theoretically, this result is expected because the reduction of base doping increases the saturation current which reduces the open-circuit voltage, this decrease is low because this voltage is also function of shortcircuit density current, exactly it is proportional to logarithm of rate of short-circuit density current to saturation density current as it indicates by the following equation (Goetzberger et al., 1998):
4. Results and discussions
V oc ðkT=qÞlnðJ sc =j0 Þ
Now, as we found approximately the same results (between real cell and the simulated one), we can optimize the parameters of this cell (base, emitter and BSF layer).
Likewise, the fill factor decreases with the resistivity due to the decrease of base resistance. Consequently, the result is an optimization of the efficiency (19.71%) shown on the graph in the range of 1.5–2 X cm (Fig. 5).
Fig. 4. Effect of lifetime on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
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4.1.3. Effect of the thickness It is clear that the increase in thickness of the substrate is an advantage to absorb more photons, but if the diffusion length L pffiffiffiffiffiffiffi (L ¼ Ds, D is the constant carrier diffusion and s is the lifetime) falls below the value of the base thickness, then the photocurrent will drop sharply (Goetzberger et al., 1998). So, for the shortcircuit density current and the efficiency there are some optimization of 37.86 mA/cm2 and 19.89% respectively around 400 lm (Fig. 6). The fill factor decreases from 80.98% at 100 lm to 80.64% at 600 lm because of the increase in base resistance. Note that a very large thickness substrate increases its cost.
4.2. Effect of emitter sheet resistance We remark that the short-circuit density current and the opencircuit voltage increase with the emitter sheet resistance (Fig. 7), since the reduction of emitter doping decreases recombination density current in the emitter from 143.53 fA/cm2 for 50 X/h to 44.3 fA/cm2 for 100 X/h (calculated with PC1D) (Cabanasholmen and Basore, 2012). Contrarily, the fill factor decreases because of the increase of the emitter resistance. Therefore, we remark an optimization of the efficiency at 75 X/h (average of the little range of 70–80 X/h) giving values of 19.70%, this is because high sheet resistance causes a low recombination density
Fig. 5. Effect of base resistivity on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
Fig. 6. Effect of base thickness on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
Fig. 7. Effect of emitter sheet resistance on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
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current. Beyond this range the efficiency decreases because the series resistance becomes predominant. Hence the choice of the selective emitter structure of n-type substrate (Poulain et al., 2012) which reduces the sheet resistance in the contacts to reduce the series resistance and increases it between the contacts to decrease recombination density current (Fig. 8) (Rahman, 2012).
4.3. Effect of the back surface field (BSF) The graphs show that the four parameters decrease with the increase of BSF sheet resistance (Fig. 9). In other words, the increase of BSF doping causes an improvement of the intensity back surface field in the high-low junction n+/n creating a potential barrier which tends to confine minority carriers (holes) in the more lightly doped region and helps to drive them toward the front. Therefore, the short-circuit current density will increase, the open-circuit voltage also will increase due to increased shortcircuit current. Consequently, the efficiency and the fill factor will noticeably increase. For example, the efficiency increases from 19.06% for the solar cell without BSF layer to 19.68% with 30 X/ h of BSF sheet resistance (real cell), improved to 19.82% with 20 X/h of BSF.
5. Performance of the optimized solar cell The optimized values: thick, resistivity, lifetime of substrate and BSF are respectively 250 mm, 1.75 X cm (average of 1.5–2 X cm), 1.5 ms and 20 X/h. With these parameters, the results of this optimization are shown in the following Table 2:
Table 2 Results of optimized solar cells (HE and example of SE). Cell
Jsc (mA/cm2)
Voc (mV)
FF (%)
g (%)
Optimized 75 X/h (HE) Example 50–100 X/h (SE)
38.07 38.14
651.50 654.56
80.86 80.90
20.05 20.20
The optimization of Kalio’s cell (HE90) leads to two structures: homogeneous emitter cell of 75 X/h (HE75) with an absolute gain of 0.37% in efficiency and selective emitter cell of 50 X/h under the contacts and 100 X/h between contacts (SE50-100) as example (Fig. 8) with an absolute gain of 0.52% in efficiency. This improvement is shown clearly on the graph of external quantum efficiency (EQE) in the infrared wavelength range due to the good collection of the charge carriers in the base of the optimized solar cells (optimization of the base and BSF parameters) (Fig. 10). We can also view the improvement of 0.15% in efficiency of (SE50-100) compared to (HE75) due to the selective emitter (Fig. 11). It is found that this structure permits an improvement of quantum efficiency in the ultra-violet wavelength range, due to a decrease in recombination density current from 73 fA/cm2 to 44.3 fA /cm2 (Section 4.2), resulting from a lower rate of different recombinations, mainly Auger type, due the highest sheet resistance of the emitter (between contacts). On the contrary, at highest wavelengths, the two cells give identical results, confirming that the structure of (SE) does not influence much the volume or the rear surface of these cells but the absorption is more superficial. This result can be improved by making a detailed study on this structure. 100% 90% 80% 70%
SE50-100
EQE
60% 50%
HE75
40%
HE90
30% 20% 10% 0% 300
Fig. 8. Part of selective emitter (SE) structure.
400
500
600
700
800 (nm)
900
1000
1100
1200
Fig. 10. Comparison of external quantum efficiency of SE50-100, HE75 and HE90.
Fig. 9. Effect of the back surface field on the parameters of solar cell (Jsc, Voc, Ƞ and FF).
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95%
Conflict of interest
90%
None declared.
85%
EQE
80%
References
SE50-100 HE75
75% 70% 65% 60% 55% 300
350
400
450
500
(nm) Fig. 11. Comparison of external quantum efficiency of SE50-100 and HE75.
6. Conclusion Using PC2D simulation, we have optimized the most important parameters: base, emitter and BSF of n-type homogeneous solar cells experimented by Kalio et al. For the base parameters, we have noted that all parameters of the cell increase quickly up to 1 ms of lifetime, this increase becomes slow beyond this value. Likewise, the efficiency increases with the base thickness up to 400 lm then it decreases due to the increase of the resistance. The optimized base resistivity value is 1.75 X cm for a maximum efficiency. The analysis of the emitter solar cell shows that the efficiency increases up to the value of 75 X/h because high sheet resistance causes a low recombination density current. Beyond this value, the efficiency decreases because series resistance becomes predominant. Hence the choice of the selective emitter structure which reduces the sheet resistance in the contacts to reduce the series resistance and increases it between the contacts to decrease recombination density currents. The introduction of the BSF improved enormously the efficiency; with 20 X/h of BSF we obtained an improvement of 0.14% in relation to 30 X/h of BSF (experimental solar cell). Our optimization gives us an efficiency of 20.05% with sheet resistance of 75 X/h homogeneous emitter. This efficiency is improved to 20.20% with selective emitter of 50–100 X/h taken as example. A detailed study of this structure can give us higher efficiencies.
Basore, P.A., Cabanas-Holmen, K., 2011. PC2D: a circular-reference spreadsheet solar cell device simulator. IEEE J. Photovoltaics 1 (1), 72–77. Basore, P.A., Cabanas-Holmen, K., 2014. PC2D V2.4 examples, in