General Einstein relation model in disordered organic semiconductors under quasiequilibrium

In this work, the Einstein relation between the diffusivity and mobility of charge carriers for disordered organic semiconductors is analyzed. We formulate an analytic theory that allows predicting the Einstein relation for charge carrier hopping in disordered organic semiconductors with Gaussian density of states distribution as a function of disorder, temperature, bias field, and Fermi level, i.e., concentration of occupied states of the DOS under the condition of quasiequilibrium. By scanning the Fermi across the DOS, we calculate the charge carrier mobility and diffusivity as well the qD/mu k(B)T ratio. We are thus able to identify the role of mobile and localized states on the interplay of diffusion and drift and can determine under which condition Einstein relation is valid or not.