Validity of the Einstein Relation in Disordered Organic Semiconductors

It is controversial whether energetic disorder in semiconductors is already sufficient to violate the classical Einstein relation, even in the case of thermal equilibrium. We demonstrate that the Einstein relation is violated only under nonequilibrium conditions due to deeply trapped carriers, as in diffusion-driven current measurements on organic single-carrier diodes. Removal of these deeply trapped carriers by recombination unambiguously proves the validity of the Einstein relation in disordered semiconductors in thermal (quasi) equilibrium.