One-dimensional hopping transport in disordered organic solids. I. Analytic calculations

Analytic calculations are carried out for temperature and field dependences of the hopping drift mobility of charge carriers in strongly anisotropic disordered solids where transport can be treated as one dimensional. The solutions obtained are exact fur hopping processes with noninteracting carriers and carrier transitions to the nearest sites in a one-dimensional chain. Only such transitions are essential in systems with strongly correlated space-energy distributions of localized states [see K. Kohary et nl., following paper, Phys. Rev. B 63, 094202 (2001)]. Comparison is given for results obtained with symmetrical and asymmetrical transition rates. It is shown that mesoscopic effects play an essential role even for rather long chains with hundreds of localization sites. Moreover, not only the magnitude of the drift mobility, but also its temperature dependence is influenced by the chain length. A suggested theoretical description provides a general basis for the treatment of transport processes in one-dimensional disordered organic solids, such as columnar discotic liquid-crystalline glasses.