A competitive hopping model for carrier transport in disordered organic semiconductors.

Here, we formulate a theoretical transport model for disordered organic semiconductors based on the concept of competitive hopping. We demonstrate theoretically that carriers occupying states with higher energy levels have higher probabilities and higher rates of hopping to the transport energy. This model suggests a temperature (T) dependence of mobility (μ) given by lg(μ) ∝ T-n, where the low carrier density and small energetic disorder limitation of the competitive hopping model gives the non-Arrhenius lg(μ) ∝ T-2 relation, and the high carrier density and large energetic disorder limitation gives the Arrhenius type lg(μ) ∝ T-1 relation. The carrier density dependence of carrier mobility is steeper at high carrier density than at low carrier density. These results are well explained by the relative positions of the Fermi level and the equilibrium level as the initial hopping levels. The competitive hopping model successfully explains the trap energy dependence of the carrier mobility for systems with deep traps. The mobility enhancement with increasing trap energy at deep trapping situations can be explained by the increasing contribution to the carrier transport of the hopping between the intrinsic states.