On the qualitative difference between phonon-assisted transition rates of electrons and holes in organic disordered semiconductors

We suggest universal expressions for the rates of charge transition between molecules in organic disordered semiconductors, which differ between electrons and holes. The donor and acceptor molecules (monomers) are represented in terms of their frontier orbitals, with asymptotic tails reflecting the different asymptotic potential wells which bind different charge carriers. This model predicts an asymmetry of the tunnel factors and the interaction with phonon field with respect to electrons and holes, leading to different formulas for the transition rates and the thermal mobility of the different charge carriers. This is demonstrated explicitly for transitions between organic molecules initiated by fluctuations of the inter-molecular distance due to deformation of by the phonon field, but the asymmetry between the carriers is universal and should be essential for quantitative analysis of charge transport in any disordered material. In particular, in the framework of classical Mott considerations our result predict an unusual temperature dependence of holes mobility, $\sim (T_0/T)^r \exp -( T_0/T)^{1/4}$, where $r = ( E_F^h)^{-1/2}$, and $E_F^h$ is the energy of hole at the Fermi level in atomic units.