Potential-Dependent Generalized Einstein Relation in Disordered Organic Semiconductors

The generalized Einstein relation (GER) is extended to consider the potential energy of carriers in an electric field (PDGER). It can be equivalently seen as the GER having position-dependent Fermi energy, and implies the organic semiconductor is in non-equilibrium under an electric field. The distribution of the carrier density with position is solved for two polymer layers. The numerical results are used to evaluate the PDGER. It is shown that the ratio of diffusion coefficient to mobility, μ/D, increases with Fermi energy and decreases with carrier density. The PDGER gives non-traditional values for the two polymer layers; the value of μ/D is small near the surface, and slightly increases as the position departs from the surface.