Transport energy concept as a unifying framework for hopping conductivity in disordered organic semiconductors

Abstract

Charge transport in disordered organic semiconductors has been studied using a variety of theoretical and computational approaches. Among these, the concept of a transport energy (TE) level provides a particularly useful framework: it acts as an analog of a mobility edge, reducing the complex problem of hopping transport to the simpler picture of the multiple-trapping model. In this work, we demonstrate that for a given system, the existence and position of the TE are universal: for any transition rate that satisfies detailed balance, regardless of its specific form, the TE is uniquely determined and governs charge-carrier dynamics. This universality establishes a coherent framework that unifies diverse hopping models and simplifies the description of transport in spatially and energetically disordered systems. To support this result, we introduce an optimized kinetic Monte Carlo approach and employ it to show that model-specific rate parameters do not affect the TE. The framework is validated across a wide range of hopping models, energetic disorders, and localization lengths, and its practical utility is demonstrated through the interpretation of experimental mobility data.