Hopping transport in prototypical organic glasses

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 $\mu \mathrm{}\left(T\right)={\mu }_0\exp [-{\left(\frac{T_0}{T}\right)}^2]$. $T_0$ is proportional to the Gaussian width $\sigma$. Experimental data obtained for the hole mobility in a variety of organic glasses confirm this relationship and yield $\sigma$ values on the order 0.1 eV and ${\mu }_0$ values on the order ${10}^{-2\mathrm{}}$ ${\mathrm{cm}}^2$/V s. Changes of the $\mu \mathrm{}\left(T\right)\mathrm{}$ dependence observed near the glass transition temperature are attributed to an increase of $\sigma$ above $T_g$ as a result of dynamic disorder superimposed on the static fluctuations of site energies. The model predicts a field dependence of $\mu$ of the form $\mu \mathrm{}\left(E\right)=\mu \mathrm{}(E=0\mathrm{})\mathrm{}\exp \left(\frac{E}{E_0}\right)$ which is observed. Agreement between simulation results and experiment is excellent. It demonstrates that the field dependence of $\mu$ 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.