Publication date: 17th February 2025
The Gaussian Disorder Model has been shown to be effective in describing the disordered energy structure of organic solar cells, and used in conjunction with kinetic Monte Carlo approaches, has been successful in deriving experimentally reproducible results for key charge transport quantities. It has also been successful in describing organic solar cell processes in analytical work. We present here our efforts in extending the Gaussian Disorder Model to a full analytical model for key processes, including photoexcitation, spontaneous emission, stimulated emission, trap assisted recombination and charge transport, to produce an energy dependent analogue of the drift diffusion equations for organic solar cells. This has been achieved by deriving differential equations using continuum limits of discrete master equations, with Miller-Abrahams, Marcus and Fermi’s Golden Rule rates to describe transitions between states. Finally, we have applied the method of lines approach to determine numerical solutions for the electron occupation, which in contrast to the typical drift diffusion equations are energy dependent.
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