Theory of the Pre-exponential Factor in Organic Semiconductors

Tunneling through intermolecular barriers from activated energy levels of molecules is postulated to be the conduction mechanism in some organic semiconductors. The compensation rule follows immediately from this model. The relationship between the characteristic temperature on one hand, and the barrier shape, height, width, and the effective mass of the electrons on the other, is established. It is shown that the triangular barrier assumption gives a qualitative but not quantitative agreement with experiment. Estimates of the barrier height, width, and effective mass are given. Activated state effective masses of ${\text{∼\hspace{0.17em}100m}}_e$ result. The experimentally found correlation between ${\sigma }_0\prime$ and the characteristic temperature acquires a physical basis.