Connection between two models of organic solar cells
Sebastian Müller a
a School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
Proceedings of International Conference on Hybrid and Organic Photovoltaics (HOPV19)
Roma, Italy, 2019 May 12th - 15th
Organizers: Prashant Kamat, Filippo De Angelis and Aldo Di Carlo
Poster, Sebastian Müller, 269
Publication date: 11th February 2019

We present theoretical work linking two models of organic solar cells, the Gaussian disorder model as well as differential equations describing the drift, diffusion, generation and recombination of charge carriers. In the Gaussian disorder model, the charge carriers are localised at randomly distributed sites, with possible energies following a Gaussian distribution. The hopping rates between any two sites depend on their distance as well as on the corresponding energies and can be taken as Marcus rates. We show that in a continuum limit, the Gaussian disorder model can be mapped first to master equations for electrons and holes and then after Taylor expansion of the integrand to differential equations. This approach establishes relations between the free parameters of both models and yields corrections to the differential equations. In particular it allows to study the dependence of the electron and hole concentration on energy, and investigate the energies for which states contribute most strongly to the transport of charge carriers.

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