Generalization of Einstein relation for organic semiconductor thin films

Under the basis of Gaussian energy distributions of the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), analytical expressions of generalized Einstein relation for electron and hole transport in organic semiconductor thin films are developed. Numerical calculations show that, although traditional Einstein relation is still valid for low carrier concentrations, when the carrier concentration is high, the diffusion coefficient-mobility ratio increases rapidly with the carrier concentration. A relative turning carrier concentration, characterizing the upper limit of the validity of traditional Einstein relation is defined. The dependences of the relative turning concentration on the variance of LUMO or HOMO energy distributions as well as the sample temperature, and the applications of the generalized Einstein relation in the analysis of organic light-emitting device are discussed.