Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 81, Issue 4, Pages 1767-1780Publisher
SIAM PUBLICATIONS
DOI: 10.1137/20M131758X
Keywords
perturbations; transport processes; random media; organic semiconductors
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The study investigates the effectiveness of the drift-diffusion model in random materials, showing that the key assumption for its validity is that the correlation lengths of randomly perturbed coefficients are much smaller than any other characteristic length of the problem. Additionally, the research examines how the effective drift and diffusion coefficients depend on randomness.
Organic semiconductors are intrinsic randomly inhomogeneous materials where charge transport occurs by hopping of the carriers between localized sites having a distribution of energy levels. However, the average carrier density seems to be accurately described by a simple drift-diffusion equation. We investigate the reasons for the effectiveness of the drift-diffusion model in a random material and show that the key assumption for its validity is that the correlation lengths of the randomly perturbed coefficients are much smaller than any other characteristic length of the problem. As a byproduct, we find how the effective drift and diffusion coefficients depend on the randomness.
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