Unified Mobility Model for Disordered Organic Semiconductors

The influence of temperature, carrier density, and electric field on hopping transport in disordered organic semiconductors is discussed, and an accurate mobility model that accounts for all those effects in a single analytical expression is derived. The model is based on the concept of percolation in a variable range hopping system, and the calculations are worked out by exploiting the effective temperature approach. At room temperature, the dependence on carrier density plays a major role, whereas at low temperatures or high fields, the influence of electric field becomes relevant. Neglecting only one of them leads to an evident underestimation of hopping mobility. The model accurately reproduces experiments and numerical simulations and provides, by means of a single mathematical expression, a clear picture of several physical effects as the Poole-Frenkel dependence of the mobility on the electric field or the Arrhenius behavior on temperature.