Proceedings of International Conference on Hybrid and Organic Photovoltaics (HOPV18)
DOI: https://doi.org/10.29363/nanoge.hopv.2018.172
Publication date: 21st February 2018
We present theoretical work connecting two models of organic solar cells (and other organic semiconductors). One of these is the Gaussian disorder model [1]. In this model, the possible states of the charge carriers are localized on randomly distributed sites. The energies of these states follow a Gaussian distribution, and jumps from site i to j follow Miller-Abrahams jump rates [2]. These rates are proportional to exp(-2 gamma dij) where gamma is a constant and dij is the distance between i and j. If the site j has a larger energy (Ej>Ei) there is also a further factor exp(-(Ej-Ei)/(kBT)). A related model involves differential equations for the concentration of carriers involving drift, diffusion, generation, and recombination. We show how in a continuum limit the Gaussian disorder model gives rise to differential equations of this type. This approach establishes relations between the parameters of both models. It also allows to incorporate further effects into the differential equations, for instance related to the energy dependence of the concentration and to inhomogeneities in the distribution of states.
[1] H. Bässler, Phys. Status Solidi B 174, 15 (1993)
[2] A. Miller and E. Abrahams, Phys. Rev. 257 (1960)
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