### MODELLING SOLAR CELL S-SHAPED I-V CHARACTERISTICS WITH DC LUMPED-PARAMETER EQUIVALENT CIRCUITS A REVIEW

**DOI Number**

**First page**

**Last page**

#### Abstract

This article reviews and appraises the dc lumped-parameter equivalent circuit models that have been proposed so far for representing some types of solar cells that can exhibit under certain circumstances a detrimental S-shaped concave deformation within the energy-producing fourth quadrant of their illuminated I–V characteristics. We first present a very succinct recollection of lumped-parameter equivalent circuits that are commonly used to model conventional solar cells in general. We then chronologically present and discuss lumped-parameter equivalent sub-circuits that, combined with conventional solar cell equivalent circuits, are used to specifically represent the undesired S-shaped behaviour. The mathematically descriptive equations of each complete equivalent circuit are also examined, and closed form solutions for the terminal current and voltage as explicit functions of each other are presented and discussed whenever available. While comparing the most salient features and explaining the practical advantages and disadvantages of such equivalent circuit models, we offer some comments on possible directions for further improvement.

#### Keywords

#### Full Text:

PDF#### References

A. Ortiz-Conde, F. J. García-Sánchez, J. Muci, A. Sucre-González, “A review of diode and solar cell equivalent circuit model lumped parameter extraction,” Facta Universitatis, Series: Electronics and Energetics, vol. 27, no 1, pp. 57-102, March 2014.

R. V. K. Chavali, J. V. Li, C. Battaglia, S. De Wolf, J. L. Gray, M. A. Alam, “A Generalized Theory Explains the Anomalous Suns–Voc Response of Si Heterojunction Solar Cells,” IEEE Journal of Photovoltaics, vol. 7, no. 1, pp. 169 - 176, Jan. 2017.

P. G. Kale, C. S. Solanki, "Silicon quantum dot solar cell using top-down approach." International Nano Letters, vol. 5, no. 2, pp. 61-65, Jun 2015.

S. van Reenen, M. Kemerink, H. J. Snaith, “Modeling Anomalous Hysteresis in Perovskite Solar Cells,” J. of Phys. Chem. Letters, vol. 6, pp. 3808−3814, 2015.

F. Xu, J. Zhu, R. Cao, S. Ge, W. Wang, H. Xu, R. Xu, Y. Wu, M. Gao, Z. Ma, F. Hong, Z. Jiang, “Elucidating the evolution of the current-voltage characteristics of planar organometal halide perovskite solar cells to an S-shape at low temperature,” Solar Energy Materials & Solar Cells, vol. 157, pp. 981–988, December 2016.

J. Liu, G. Wang, K. Luo, X. He, Q. Ye, C. Liao, J. Mei. “Understanding the role of electron transport layer in highly efficient planar perovskite solar cells.” ChemPhysChem. In Press, Jan 2017.

A. Wagenpfahl, D. Rauh, M. Binder, C. Deibel, V. Dyakonov, “S-shaped current-voltage characteristics of organic solar devices,” Physical Review B, vol. 82, no. 115306, September 2010.

A. Opitz, R. Banerjee, S. Grob, M. Gruber, A. Hinderhofer, U. Hörmann, J. Kraus, T. Linderl, C. Lorch, A. Steindamm, A. K Topczak, “Charge Separation at Nanostructured Molecular Donor–Acceptor Interfaces,” Chapter of Elementary Processes in Organic Photovoltaics , volume 272 of the series Advances in Polymer Science, pp. 77-108. Springer International Pub., 2017.

V. H. Tran, R. B. Ambade, S. B. Ambade, S. H. Lee, I. H. Lee. “Low-Temperature Solution-Processed SnO2 Nanoparticles as Cathode Buffer Layer for Inverted Organic Solar Cells.” ACS Applied Materials & Interfaces, Accepted paper in press, Jan 2017.

F. Araujo de Castro, J. Heier, F. Nüesch, R. Hany, “Origin of the Kink in Current-Density Versus Voltage Curves and Efficiency Enhancement of Polymer-C60 Heterojunction Solar Cells,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 16, no. 6, pp. 1690 – 1699, Nov/Dec 2010.

B. Qi, J. Wang, “Fill factor in organic solar cells,” Phys.Chem. Chem. Phys., vol.15, pp. 8972-8982, 2013.

W. Shockley, The theory of p-n junctions in semiconductors and p-n junction transistors, Bell System Technical Journal, vol. 28, no. 3, pp. 435−489, July 1949.

R. M. Corless, G. H. Gonnet , D.E.G. Hare, D. J. Jeffrey, D. E. Knuth, “On the lambert w function.” Adv. Comput. Math., vol. 5, no. 1, pp. 329–359, 1996.

Lambert W-Function (4.13), NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/4.13

S. R. Valluri, R. M. Corless and D. J. Jeffrey. “Some Applications of the Lambert W Function to Physics,” Canadian J. of Physics, vol. 78, no. 9, pp. 823-831, 2000.

D. Veberič, “Lambert W function for applications in physics,” Computer Physics Communications, vol. 183, pp. 2622–2628, 2012.

T. Banwell, A. Jayakumar, “Exact analytical solution for current flow through diode with series resistance.” Electronics Letters, vol. 36, no. 4, pp. 291–292, 17 Feb. 2000.

A. Ortiz-Conde, F. J. García-Sánchez, J. Muci, “Exact analytical solutions of the forward non-ideal diode equation with series and shunt parasitic resistances,” Solid-State Electronics, vol. 44, no. 10, pp. 1861–1864, October 2000.

A. Jain, A. Kapoor, “Exact analytical solutions of the parameters of real solar cells using Lambert W-function,” Solar Energy Materials & Solar Cells, vol. 81, no. 2, pp. 269-277, February 2004.

A. Jain, A. Kapoor, “A new approach to study organic solar cell using Lambert W-function,” Solar Energy Materials & Solar Cells, vol. 86, pp. 197–205, 2005.

D. C. Lugo-Muñoz, M. De Souza, M. A. Pavanello, D. Flandre, J. Muci, A. Ortiz-Conde, F. J. García-Sánchez, “Parameter Extraction in Quadratic Exponential Junction Model with Series Resistance using Global Lateral Fitting,” ECS Transactions, vol. 31, no. 1, pp. 369-376, 2010.

A. Ortiz-Conde, D. Lugo-Muñoz and F. J. García Sánchez, “An explicit multi-exponential model as an alternative to traditional solar cell models with series and shunt resistances,” IEEE Journal of Photovoltaics, vol. 2, no. 3, pp. 261-268, July 2012.

T. Ma, H. Yang, L. Lu, “Solar photovoltaic system modeling and performance prediction,” Renewable and Sustainable Energy Reviews, vol. 36, pp. 304-315, 2014.

V. J. Chin, Z. Salam, K. Ishaque, “Cell modelling and model parameters estimation techniques for photovoltaic simulator application: A review,” Applied Energy, 154, pp. 500–519, 2015.

A. M. Humada, M. Hojabri, S. Mekhilef, H. M. Hamada, “Solar cell parameters extraction based on single and double-diode models: A review,” Renewable and Sustainable Energy Reviews, vol. 56, pp. 494–509, 2016.

A. R. Jordehi, Parameter estimation of solar photovoltaic (PV) cells: A review,” Renewable and Sustainable Energy Reviews, vol. 61, pp. 354–371, 2016.

J. W. Jin, S. Jung, Y. Bonnassieux, G. Horowitz, A. Stamateri, C. Kapnopoulos, A. Laskarakis, S. Logothetidis, “Universal Compact Model for Organic Solar Cell,” IEEE Transactions on Electron Devices, vol. 63, no. 10, pp. 4053-4059, October 2016.

P. Kumar, A. Gaur, “Model for the J-V characteristics of degraded polymer solar cells,” Journal of Applied Physics, vol. 113, no. 094505, 2013.

A. Gaur, P. Kumar, “An improved circuit model for polymer solar cells,” Prog. Photovolt: Res. Appl., 2013.

A. Kumar, S. Sista, Y. Yang, “Dipole induced anomalous S-shape I-V curves in polymer solar cells,” Journal of Applied Physics, vol. 105, no. 094512, 2009.

J. Wagner, M. Gruber, A. Wilke, Y. Tanaka, K. Topczak, et al, “Identification of different origins for s-shaped current voltage characteristics in planar heterojunction organic solar cells,” Journal of Applied Physics, vol. 111, no. 054509, March 2012.

R. Saive, C. Mueller, J. Schinke, R. Lovrincic, W. Kowalsky, “Understanding S-shaped current-voltage characteristics of organic solar cells: Direct measurement of potential distributions by scanning Kelvin probe,” Applied Physics Letters, vol. 103, no. 243303, 2013.

O. J. Sandberg, M. Nyman, R. Österback, “Effect of Contacts in Organic Bulk Heterojunction Solar Cells,” Phys. Rev. Applied, vol. 1, 024003, 27 March 2014.

W. Tress, O. Inganäs, “Simple experimental test to distinguish extraction and injection barriers at the electrodes of (organic) solar cells with S-shaped current–voltage characteristics,” Solar Energy Materials & Solar Cells, vol. 117, pp. 599–603, 2013.

M. M. Furchi, A. A. Zechmeister, F. Hoeller, S. Wachter, A. Pospischil, T. Mueller, “Photovoltaics in Van der Waals Heterostructures,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 23, no. 1, pp. 4100111, Jan/Feb 2017.

L. Zuo, J. Yao, H. Li, H. Chen, “Assessing the origin of the S-shaped I–V curve in organic solar cells: An improved equivalent circuit model,” Solar Energy Materials & Solar Cells, vol. 122, pp. 88–93, 2014.

A. Cheknane, H. S. Hilal, F. Djeffal, B. Benyoucef, J.-P. Charles, “An equivalent circuit approach to organic solar cell modeling,” Microelectronics Journal, vol. 39, pp. 1173–1180, 2008.

B. Mazhari, “An improved solar cell circuit model for organic solar cells,” Solar Energy Materials & Solar Cells, vol. 90, no. 7, pp. 1021-1033, May 2006.

B. Romero, G. del Pozo, B. Arredondo, “Exact analytical solution of a two diode circuit model for organic solar cells showing S-shape using Lambert W-functions,” Solar Energy, vol. 86, pp. 3026–3029, 2012.

K, Roberts, S. R. Valluri. "On Calculating the Current-Voltage Characteristic of Multi-Diode Models for Organic Solar Cells." arXiv preprint arXiv:1601.02679 , 2015.

F. A. De Castro, A. Laudani, F. Riganti Fulginei, A. Salvini, “An in-depth analysis of the modelling of organic solar cells using multiple-diode circuits,” Solar Energy, vol. 135, pp. 590–597, 2016.

A. Ortiz-Conde, Y. Ma, J. Thomson, E. Santos, J. J. Liou, F. J. García-Sánchez, M. Lei, J. Finol, P. Layman, “Direct extraction of semiconductor diode parameters using lateral optimization method,” Solid-State Electronics, vol. 43, no. 4, pp. 845–848, 1999.

G. del Pozo, B. Romero, B. Arredondo, “Evolution with annealing of solar cell parameters modeling the S-shape of the current–voltage characteristic,” Solar Energy Materials & Solar Cells, vol. 104, pp. 81–86, 2012.

G. Del Pozo, B. Romero, B. Arredondo, “Extraction of circuital parameters of organic solar cells using the exact solution based on Lambert W-function,” Proceedings of the Int. Society for Optical Engineering (SPIE), Brussels, Belgium, vol. 8435, Organic Photonics V, 84351Z, June 2012.

K. Tada, “Validation of opposed two-diode equivalent-circuit model for S shaped characteristic in polymer photocell by low-light characterization,” Organic Electronics, vol. 40, pp. 8-12, 2017.

B. Romero, G. Del Pozo, E. Destouesse, S. Chambon, B. Arredondo, “Circuital modelling of S-shape removal in the current–voltage characteristic of TiOx inverted organic solar cells through white-light soaking,” Organic Electronics, vol. 15, pp. 3546–3551, 2014.

B. Romero, G. del Pozo, B. Arredondo, J. P. Reinhardt, M. Sessler, and U. Würfel, “Circuital Model Validation for S-Shaped Organic Solar Cells by Means of Impedance Spectroscopy,” IEEE Journal of Photovoltaics, vol. 5, no. 1, pp. 234-237, January 2015.

F. J. García-Sánchez, D. Lugo-Muñoz, J. Muci, A. Ortiz-Conde, “Lumped Parameter Modeling of Organic Solar Cells’ S-Shaped I-V Characteristics,” IEEE Journal of Photovoltaics, vol. 3, no. 1, pp. 330-335, January 2013.

Ortiz-Conde, A., Estrada, M., Cerdeira, A., García Sánchez, F.J., De Mercato, G. , “Modeling real junctions by a series combination of two ideal diodes with parallel resistance and its parameter extraction,” Solid-State Electronics, vol. 45, no. 2, pp. 223-228, 2001.

P. J. Roland, K. P. Bhandari, R. J. Ellingson, “Electronic Circuit Model for Evaluating S-Kink Distorted Current-Voltage Curves,” Proc. IEEE 43rd Photovoltaic Specialists Conf. (PVSC), 2016.

### Refbacks

- There are currently no refbacks.

ISSN: 0353-3670 (Print)

ISSN: 2217-5997 (Online)

COBISS.SR-ID 12826626