Time-consistent hopping transport with vibration-mode-resolved electron-phonon couplings

Abstract

Charge transport in organic semiconductors is affected by the complex interaction between charge carriers and molecular vibrations. A common way to treat the molecular vibrations in hopping approaches is by condensing them into a single analytical parameter, the reorganization energy. In contrast, here we present a nonadiabatic hopping transport approach that avoids this approximation by dividing the vibrational spectrum of organic molecules into three distinct analytical classes, namely the quasistatic, low-frequency dynamic, and high-frequency dynamic modes. The quasistatic and dynamic regimes are separated time consistently with respect to the timescale of the hopping events, which results in charge transfer events driven by a set of strongly coupling driving modes. Using these time-consistent hopping rates, we compute the charge carrier mobilities for a set of hopping transport materials and a control set of band-transport materials and compare them to experimental values. The resulting mobilities are consistent for both sets by showing similar values for the hopping transport materials and lower values for the control set of band-transport materials due to the absence of coherent transport contributions. We further study other popular hopping approaches such as the Marcus theory and the Levich-Jortner theory and observe substantial inconsistencies for them.