Weak-field carrier hopping in disordered organic semiconductors: the effects of deep traps and partly filled density-of-states distribution

Abstract

An analytic model of the weak-field carrier transport in an energetically disordered and positionally random hopping system is formulated. Within the framework of this model, the carrier mobility can be calculated by either direct averaging of carrier hopping rates or by the use of the effective transport energy concept. It is shown that multiple carrier jumps within pairs of occasionally close hopping sites affect the position of the effective transport level on the energy scale. In good quantitative agreement with experimental data and results of Monte Carlo simulation, the temperature and concentration dependences of the mobility can be almost perfectly factorized, i.e. represented as a product of two functions one of which depends solely upon the temperature while the other governs the dependence upon the density of localized states. The model is also used for the calculation of trap-controlled hopping mobility and for the analysis of hopping transport at high charge-carrier densities.