Charge transport perpendicular to the high mobility plane in organic crystals: Bandlike temperature dependence maintained despite hundredfold anisotropy

Abstract

Charge carrier mobility in van der Waals bonded organic crystals is strongly dependent on the transfer integral between neighboring molecules, and therefore the anisotropy of charge transport is determined by the molecular arrangement within the crystal lattice. Here we report on temperature dependent transport measurements along all three principal crystal directions of the same rubrene single crystals of high purity. Hole mobilities are obtained from the carrier transit time measured with high-frequency admittance spectroscopy perpendicular to the molecular layers $({\ensuremath{\mu}}_{c})$ and from the transfer characteristics of two field-effect transistor (FET) structures oriented perpendicularly to each other in the layers $({\ensuremath{\mu}}_{a}$ and ${\ensuremath{\mu}}_{b})$. While the measurements of the field-effect channels confirm the previously reported high mobility and anisotropy within the $ab$ plane, we find the mobility perpendicular to the molecular layers in the same crystals to be lower by about two orders of magnitude $({\ensuremath{\mu}}_{c}\ensuremath{\sim}0.2\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$ at $300\phantom{\rule{0.16em}{0ex}}\mathrm{K})$. Although the bandwidth is vanishingly small along the $c$ direction and the transport cannot be coherent, we find ${\ensuremath{\mu}}_{c}$ to increase upon cooling. We show that the delocalization within the high mobility $ab$ plane prevents the formation of small polarons and leads to the observed ``bandlike'' temperature dependence also in the direction perpendicular to the molecular layers, despite the incoherent transport mechanism.