EXPLANATION FOR THE ROOT-E-DEPENDENT MOBILITIES OF CHARGE-TRANSPORT IN MOLECULARLY DOPED POLYMERS

Although disorder is widely believed to be the primary distinguishing feature governing the transport of photoinjected charges in molecularly doped polymers, disorder theory has yet to convincingly explain why the linearity of the log of the mobility with the square root of the applied field persists over such a wide range. In this article a theory for high-field hopping transport in strongly disordered materials is developed which combines the elements of a continuous time random walk with existing variable-range hopping techniques. A self-consistent integral equation is derived from which the distribution of site energies for those sites which characterize the percolation pathways is determined. The theory is applied to an energetically disordered system and the mobility is calculated for the Miller-Abrahams form of the jump rate. It is shown that if the site energies belong to a Gaussian distribution, the logarithm of the mobility rises nearly linearly with root E for electric fields spanning almost two decades. The slope is temperature dependent, and agrees with the Poole-Frenkel law.