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A free-carrier-to-free-carrier recombination pathway is also included in the model. However, most organic solar cells have a great deal of trap states and an ideality factor greater than 1.0 suggesting that free to free recombination is not the dominant mechanism. It is also worth noting that since I included this recombination pathway in the model I have not found it useful to reproduce experimental results.
Free-to-free recombination is described using equation 20
The above set of non linear equations are placed into a single sparse matrix, and solved using the umfpack solver. The drift diffusion are cast into a Scharfetter-Gummel form, to ensure stability.