Simulation of Hopping Transport Based on Charge Carrier Localization Times Derived for a Two-Level System

Incoherent hopping models are commonly used to describe charge transport in many classes of electrically conducting materials. An important parameter in these models is the charge carrier hopping rate or its inverse, the charge carrier lifetime at a localization site. Among the most common approaches to calculating the charge hopping rate are those based on the hydrogen molecular ion (H-2(+)) theory and on the Marcus theory of electron transfer reactions. The former is typically used when describing doped inorganic crystalline semiconductors, while the latter is commonly employed for organic systems. In the present paper the limitations of these approaches are examined and a generalized expression for the charge carrier lifetime at a localization site is proposed, which includes the expressions found from H-2(+) theory and Marcus theory as limiting cases. Charge transport simulations based on all three expressions are compared.