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Using analytical arguments and computer simulations we show that the dependence of the hopping carrier mobility on the electric field $\mu(F)/\mu(0)$ in a system of random sites is determined by the localization length $\alpha$ and not by the concentration of sites $N$. This result is in drastic contrast to what is usually assumed in the literature for theoretical description of experimental data and for device modeling, where $N^-1/3$ is considered as the decisive length scale for $\mu(F)$. We show that although the limiting value $\mu(F \rightarrow 0)$ is determined by the ratio $N^-1/3/\alpha$, the dependence $\mu(F)/\mu(0)$ is sensitive to the magnitude of $\alpha$ and not to $N^-1/3$. Furthermore, our numerical and analytical results prove that the effective temperature responsible for the combined effect of the electric field $F$ and the real temperature $T$ on the hopping transport via spatially random sites can contain the electric field only in the combination $eF\alpha$.

@article{ title = {Fundamental characteristic length scale for the field dependence of hopping charge transport in disordered organic semiconductors}, type = {article}, year = {2017}, identifiers = {[object Object]}, pages = {035204}, volume = {96}, websites = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.035204}, id = {df883676-b1a6-3356-8519-8d991cd05e6d}, created = {2017-07-27T09:36:55.016Z}, file_attached = {true}, profile_id = {f593ffaf-f5ef-31db-ab88-e023f3a82e91}, last_modified = {2018-02-02T10:37:01.616Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {true}, hidden = {false}, citation_key = {Nenashev2017}, folder_uuids = {fdb5e0cd-09c7-45b3-9244-098e0449f800}, private_publication = {false}, abstract = {Using analytical arguments and computer simulations we show that the dependence of the hopping carrier mobility on the electric field $\mu(F)/\mu(0)$ in a system of random sites is determined by the localization length $\alpha$ and not by the concentration of sites $N$. This result is in drastic contrast to what is usually assumed in the literature for theoretical description of experimental data and for device modeling, where $N^-1/3$ is considered as the decisive length scale for $\mu(F)$. We show that although the limiting value $\mu(F \rightarrow 0)$ is determined by the ratio $N^-1/3/\alpha$, the dependence $\mu(F)/\mu(0)$ is sensitive to the magnitude of $\alpha$ and not to $N^-1/3$. Furthermore, our numerical and analytical results prove that the effective temperature responsible for the combined effect of the electric field $F$ and the real temperature $T$ on the hopping transport via spatially random sites can contain the electric field only in the combination $eF\alpha$.}, bibtype = {article}, author = {Nenashev, A. V. and Oelerich, J. O. and Dvurechenskii, A. V. and Gebhard, F. and Baranovskii, S. D.}, journal = {Physical Review B}, number = {3} }

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