Variable range hopping as possible origin of a universal relation between conductivity and mobility in disordered organic semiconductors

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Analyzing current characteristics of organic field effect transistors with doped amorphous organic active layers, Brown et al. [Synthetic Metals 68 (1994) 65] found the measured field effect mobility to increase strongly with the conductivity. Comparing with further data from literature, they proposed that these quantities may be linked by a universal empirical relationship of the form μ (cm 2/V s) ≈ σ 0.76 (S/cm). In this paper, it is shown that Mott’s variable range hopping (VRH) yields a dependence between mobility and conductivity with the density of states of the hopping transport levels as parameter. Considering the simple model with a constant density of states near the Fermi energy, for three- and two-dimensional (3D and 2D) systems and for realistic parameters (phonon energy, Bohr radius of the hopping states) this dependence is close to the empirical relationship in the relevant range of the conductivity below 0.1 S/cm. Comparison between the corresponding dependence of the conductivity on the density of states with the measured dependence on the doping level, which is empirically described by a power law, suggests a proportional increase of the density of states of the hopping transport with the doping level. Considering both dependencies, the overall description of the experimental data is a little better for the 3D system. The large scattering of the experimental values from both empirical dependencies for the various materials finds a natural explanation in a variation of the hopping parameters and can be caused also by a non-constant density of states. Finally, it is demonstrated that there is also a connection with the thermal velocity which has rarely been considered in hopping transport but which is important for carrier trapping by deep states.