This work focuses on the intrinsic electron transport in stoichiometric Ti O2. Electron hopping is described by a polaron model, whereby a negative polaron is localized at a Ti3+ site and hops to an adjacent Ti4+ 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 Δ G*, the reorganization energy λ, and the electronic coupling matrix elements VAB) for selected crystallographic directions in rutile and anatase, using periodic density functional theory (DFT) +U and Hartree-Fock cluster calculations. The DFT+U 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 ∼0.3 eV. The electronic coupling matrix element VAB was determined to be largest for polaron hopping parallel to the c direction in rutile and indicative of adiabatic transfer (thermal hopping mechanism) with a value of 0.20 eV, while the other directions investigated in both rutile and anatase gave VAB values of about one order of magnitude smaller and indicative of diabatic transfer (tunneling mechanism) in anatase.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - May 22 2007|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics