Extraction of circuital parameters of organic solar cells using the exact solution based on Lambert W-function

The electrical behavior of organic solar cell (OSC) has been analyzed using a simple circuital model consisting on an ideal diode together with a series and parallel resistances (R-S and R-P respectively). Applying Kirchhoff's Laws to the circuit leads to a transcendental equation that can be solved numerically without approximations using the Lambert W function. Theoretical expression has been fitted to experimental current-voltage (I-V) curves under forward bias, obtaining fairly accurate values for the electrical parameters. This model has been validated comparing the extracted parameters for dark and illumination conditions of different devices. Results show good agreement for R-S, and ideality factor eta. Electrical parameters obtained in this work are also compared to those ones extracted using an approximated method often employed by other authors (1). We conclude that approximated method leads to reasonable good values for R-S, R-P and. However, in the case of Rp the voltage range chosen to fit the data with the exact method must be constrained to the fourth quadrant, where the role of parallel resistance is more critical. To validate the model, a bunch of organic solar cells with structure ITO/ poly(3,4-ethylenedioxythiophene)-poly (4-styrene sulfonate (PEDOT:PSS)/ poly(3-hexylthiophene) (P3HT): 1-(3-methoxycarbonyl)-propyl-1-1-phenyl-(6,6) C61 (PCBM)/Al has been fabricated in inert atmosphere. Different active layers were deposited varying the P3HT: PCBM ratio (1:0.64, 1:1, 1:1.55) and the active layer thickness ( ranging from 100 to 280 nm). Devices are encapsulated inside the glove-box prior its characterization outside the glove-box. Electro optical characterization has been performed with a halogen lamp. Values extracted for RS range from 142 Omega to 273 Omega, values for R-P range from 25 k Omega to 331 k Omega. Ideality factor ranges from 5 to 17. [1] Yang Shen, Kejia Li, Nabanita Majumdar, Joe C. Campbell, Mool C. Gupta, "Bulk and contact resistance in P3HT:PCBM heterojunction solar cells", Solar Energy Materials and Solar Cells 95, 1-4 (2011).