Theory of Charge Carrier Transport in Aromatic Hydrocarbon Crystals

Abstract

Evidence is presented that the dominant electron–phonon coupling in aromatic hydrocarbons is quadratic in molecular out‐of‐plane vibrational coordinates. A linear‐chain model based on this interaction, previously treated in the hopping transport limit, is extended to the coherent transport limit. Both limits are also studied for a model with two oscillators per lattice site. Hopping transport varies little with the number of oscillators, but coherent transport decreases approximately as the square of this number. Carrier mobilities in three‐dimensional lattices comprise contributions from mobilities along nearest‐neighbor directions. The model calculations and literature values of intermolecular electronic couplings are used to determine the dominant contributions to carrier drift mobilities in anthracene self‐consistently from the experimental data. Transport of electrons in the $\mathrm{c\prime }$ direction by hopping accounts for the observed magnitude, temperature dependence, and deuterium effect. The other diagonal mobility components for electrons and holes can be attributed to transport which is either coherent or intermediate between coherent and hopping transport in the slow‐phonon limit. The off‐diagonal mobility components ${\mu }_{\mathrm{ac}}\prime$ at 300°K are predicted to be 0.2 cm²V⁻¹·sec⁻¹ for both electrons and holes. By allowing different modes of transport to contribute to the same mobilities the model proves superior to previous ones, which fail to account for the anisotropy and the temperature dependence of all the carrier mobility components in anthracene.