Effective-medium theory of hopping charge-carrier transport in weakly disordered organic solids

Abstract

An effective-medium theory describing the temperature and electric-field dependence of the drift charge-carrier mobility for the nondispersive transport regime in weakly disordered organic systems is elaborated. Only the energetic disorder effects are taken into consideration, and polaronic effects are neglected. Both the exact (approach I) and approximate (approach II) Miller-Abrahams expressions were used to describe the carrier jump rates. In previous studies mainly approach II, which ignores phonon emission, was used. We show that only approach I provides correct results for temperature and electric-field dependences of mobility in solids with particularly low energetic disorder. Further, we show that in the case of a small degree of disorder, $\ensuremath{\sigma}{/k}_{B}T,$ the temperature and field dependences of the charge mobility are much weaker than for larger disorder. Theoretical predictions are in quantitative agreement with the experimental observation in a \ensuremath{\pi}-conjugated polymer with weak energetic disorder.