Abstract
This work focuses on the intrinsic electron transport in stoichiometric . Electron hopping is described by a polaron model, whereby a negative polaron is localized at a site and hops to an adjacent site. Polaron hopping is described via Marcus theory formulated for polaronic systems and quasiequivalent to the Emin-Holstein-Austin-Mott theory. We obtain the relevant parameters in the theory (namely, the activation energy , the reorganization energy , and the electronic coupling matrix elements ) for selected crystallographic directions in rutile and anatase, using periodic density functional theory and Hartree-Fock cluster calculations. The method was required to correct the well-known electron self-interaction error in DFT for the calculation of polaronic wave functions. Our results give nonadiabatic activation energies of similar magnitude in rutile and anatase, all near . The electronic coupling matrix element was determined to be largest for polaron hopping parallel to the direction in rutile and indicative of adiabatic transfer (thermal hopping mechanism) with a value of , while the other directions investigated in both rutile and anatase gave values of about one order of magnitude smaller and indicative of diabatic transfer (tunneling mechanism) in anatase.
5 More- Received 20 October 2006
DOI:https://doi.org/10.1103/PhysRevB.75.195212
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