Exact Analytical Solution for Organic Solar Cells Showing S-Shaped J-V Characteristics Using Special Trans Function Theory (STFT)

Abstract

Many organic solar cells exhibit anomalous kinks showing S-shaped J-V behaviour. This atypical behaviour may be electrically modelled by including a second diode (D2) with opposite current characteristics together with a shunt resistance to that of the conventional solar cell diode (D1). In this communication, we present an exact analytical expression for the cell’s output voltage as an explicit function of its terminal current by the application of special trans function theory (STFT) for the S-shaped J-V characteristics model. The explicit nature of the proposed solution avoids approximations and numerical iterations. The differentiability of the trans function in STFT facilitates the analytical analysis of the problem. The evolution of the S-shaped J-V characteristics and the fill factor (FF) is also deliberated by varying different parameters to validate the proposed analytical solution.

Keywords

• Organic Solar Cells (OSC); S-shaped kinks; Solar Cell Model; STFT

References

1. N. Nang, J. Yu, Y. Zheng, Z. Guan, Y. Jiang, “Organic photovoltaic cells based on a phosphorescent material and C60”, J. Phys. Chem. C 116 (2012) 5887-5891. medium-bandgap
2. G. Li, L. Liu, F. Wei, S. Xia, X. Qian, “Recent progress in modeling, simulation, and optimization of polymer solar cells”, IEEE J. Photovoltaics, 2 (2012) 320-340.
3. H. Jin, M. Tuomikoski, J. Hiltunen, P. Kopola, A. Maaninen, F. Pino, “Polymer−Electrode Interfacial Effect on hexylthiophene):Phenyl-C61-butyric Acid Methyl Ester Based Solar Cells”, J. Phys. Chem. C 113 (2009) 16807- in Poly (3
4. H. Mori, E. Miyazaki, I. Osaka, K. Takimiya, “Organic photovoltaics porphyrazines”, Organic Electron. 13 (2012) 1975-1980. on hexylthiophene-fused
5. A. Wagenpfahl, D. Rauh, M. Binder, C. Deibel, V. Dyakonov, “S-shaped current-voltage characteristics of organic solar devices”, Phys. Rev. B 82 (2010) 115306.
6. F.A. de Castro, J. Heier, F. Nuesch, 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, 16(4) (2010) 1690-1699.
7. W. Tress, K. Leo, M. Riede, “Influence of hole transport layers and donor materials on open circuit voltage and shape of IV curves of organic solar cells”, Adv. Funct. Mater., 21 (2011) 2140-2149.
8. J. Wagner, M. Gruber, A. Wilke, Y. Tanaka, K. Topczak, A. Steindamm, U. Hormann, A. Opitz, Y. Nakayama, H. Ishii, J. pflaum, N. Koch, W. Brutting, “Identification of different characteristics in planar heterojunction organic solar cells”, J. Appl. Phys. 111 (5) (2012) 054509(1-12).

9. W. Tress, A. Petrich, M. Hummert, M. Hein, K. Leo, M. Reide, “Imbalanced mobilities causing S-shaped I-V curves in planar heterojunction organic solar cells”, Applied Physics Letters 98 (2011) 063301.
10. G. del Pozo, B. Romero, B. Arredendo, “Evolution with annealing of solar cell parameters modeling the S- shape of the current-voltage characteristic”, Sol. Energy Mater. Sol. Cells 104 (2012) 81-86.
11. 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 86 (10) (2012) 3026-3029.
12. S.M. Perovich, S.K. Simic, D.V. Tosic, S.I. Bauk, “On the analytical solution of some families of transcendental equations”, Appl. Math. Lett. 20 (2007) 498.
13. N.S. Singh, A. Jain, A. Kapoor, “Determination of the solar cell junction ideality factor using special trans function theory (STFT)”, Sol. Energy Mater. Sol. Cells (2009) 269-277.
14. N.S. Singh, A. Jain, A. Kapoor, “An exact analytical method for calculating the parameters of a real solar cell using special trans function theory (STFT)”, Inter. Jour. of Renewable Energy Research 3(1) (2013) 201-206.
15. N.S. Singh, A. Jain, A. Kapoor, “A new method to determine the optimum load of a real solar cell using special trans function theory (STFT)”, accepted for publication in Inter. Jour. of Renewable Energy Research.