Charge transport at low electric fields inπ-conjugated polymers

In low-mobility materials the charge carrier mobility is usually measured using time-of-flight (TOF) methods. However, the use of TOF methods calls for a necessary condition to be fulfilled: viz., that the dielectric relaxation time must be bigger than the charge carrier transit time, ${\tau }_{\sigma }\gg t_{\mathrm{tr}},$ through the interelectrode distance d. If this condition is not fulfilled, then the equilibrium charge carrier concentration $p_0$ is sufficient to redistribute the electric field inside the sample during a time interval shorter than the small-charge drift time. Consequently, in the low-field region, the apparent charge carrier mobility estimated by the TOF method increases when the electric field decreases, while in reality the mobility does not increase. We show how to estimate the real mobility values, using extraction current transients [G. Juška et al., Phys. Rev. Lett. 84, 4946 (2000)] for which the fulfillment of the ${\tau }_{\sigma }>t_{\mathrm{tr}}$ condition is unnecessary. We demonstrate this effect in regioregular poly(3-octyl thiophene) using both the TOF and carrier extraction by a linearly increasing voltage methods and show that the true mobility does not increase as a function of decreasing field.