Hopping transport in prototypical organic glasses

Abstract

Recent computer simulations have shown that the temperature dependence of the charge-carrier mobility in an amorphous organic hopping system, where the profile of the energy distribution of the hopping sites is a Gaussian, should follow $\ensuremath{\mu}(T)={\ensuremath{\mu}}_{0}\mathrm{exp}[\ensuremath{-}{(\frac{{T}_{0}}{T})}^{2}]$. ${T}_{0}$ is proportional to the Gaussian width $\ensuremath{\sigma}$. Experimental data obtained for the hole mobility in a variety of organic glasses confirm this relationship and yield $\ensuremath{\sigma}$ values on the order 0.1 eV and ${\ensuremath{\mu}}_{0}$ values on the order ${10}^{\ensuremath{-}2}$ ${\mathrm{cm}}^{2}$/V s. Changes of the $\ensuremath{\mu}(T)$ dependence observed near the glass transition temperature are attributed to an increase of $\ensuremath{\sigma}$ above ${T}_{g}$ as a result of dynamic disorder superimposed on the static fluctuations of site energies. The model predicts a field dependence of $\ensuremath{\mu}$ of the form $\ensuremath{\mu}(E)=\ensuremath{\mu}(E=0)\mathrm{exp}(\frac{E}{{E}_{0}})$ which is observed. Agreement between simulation results and experiment is excellent. It demonstrates that the field dependence of $\ensuremath{\mu}$ is an inherent consequence of hopping transport in a system subject to a Gaussian type of diagonal disorder. No charged trap states have to be invoked.