Grain Boundary Controlled Electron Mobility in Polycrystalline Titanium Dioxide

• DOI: 10.1002/admi.201400078
• Publication Date: 2014-05-03T08:51:20Z
• Authors: Suzanne K. Wallace; Keith P. McKenna
• Keywords: Nanocrystalline material; Electron Mobility

Grain boundaries are shown to play a critical role in controlling electron mobility nanocrystalline titanium dioxide affecting material performance for applications such as solar energy generation and catalysis. Theoretical modelling demonstrates that can be reduced by several orders of magnitude result enhanced trapping at grain improved high current densities highly nonlinear trap filling effect. The electrons oxide materials underpins diverse range areas generation, catalysis, gas sensing nanoelectronics.1-5 boundaries, one the most pervasive defects these materials, widely believed but probing their effects directly has proved extremely challenging. Here, we provide atomistic insight into this important issue through first principles based modeling interaction with TiO2. We show perturbations electrostatic potential responsible concentrations strong sites which hamper transport between grains. However, effect is partially ameliorated (>0.01 mAcm−2) pointing ways help improve dye-sensitized cells photocatalysts.1-6 Nanocrystalline oxides, encompassing both porous powders dense ceramic ubiquitous form technological material. TiO2 perhaps exceptional incredibly wide it finds, including photocatalysts self-cleaning glass water splitting,3 (DSSCs) generation,1-6 Li-ion battery storage7 resistive switching memories low power non-volatile data storage.5 Key varied may introduced optical excitation, electrical injection or doping. For example, catalytic polaronic surfaces produces reactive Ti3+ facilitate chemical reactions. In DSSCs, injected network from photo-excited dye molecules must percolate order reach charge collection electrode. It been suggested interfaces nanocrystals present deep traps hindering diffusion.1, 8-10 On other hand, diffusion along extended memory devices proposed essential mechanism.5 Despite its importance numerous definitive information on properties still lacking. First theoretical calculations invaluable materials.11-13 Many investigations performed within framework density functional theory (DFT) have studied TiO2, bulk crystals (both rutile anatase polymorphs), point defects.11, 12, 14 These challenging accurate prediction achieved using methods hybrid-DFT DFT+U correct self-interaction (SI) error lead artificial delocalization (e.g. see ref. 15). become self-trapped Ti ions crystal forming small polarons consistent experimental evidence.12, 16 At near oxygen vacancies multiple configurations trapped similar stability dynamic hopping predicted.17 much weaker explaining higher mobility. Surprisingly there no studies intrinsic interfacial always combine kinetic Monte Carlo (KMC) simulation investigate consider model Σ5 (210)[001] tilt boundary rutile18 focus without impurities something very difficult do experimentally. Grain-boundary models obtained systematic screening different atomic classical interatomic approach19 followed refinement DFT level. formalism corrects SI sufficiently allow localization described while remaining computationally feasible complex systems containing more than 300 atoms (full details available Methods section Supporting Information). Figure 1a shows predicted structure previous transmission microscopy studies18 calculations.20 exhibits degree only few undercoordinated O close plane. also varies significantly an stabilizing electrons. 5 Å ±0.35 V potential. While considered here represents specific case shares common features observed general namely undercoordination, topological disruption strain.21-23 To defect attempted localize polaron all inequivalent 1 nm This involved creating precursor well displacing nearest neighbor anions away particular site 0.1 full self-consistent optimization structure. Bader analysis optimized structures indicates about 0.4 single ion distributed over neighbouring ions.24 Far plane total nearly independent corresponding bulk-like polaron. Therefore, following energies, Et, defined relative take equidistant two planes (indicated black square 1a). find correlation calculated difference on-site respect (Figure 1b). almost linear found except circle 1a) considerably stable should expected given discrepancy understood because coordinated atoms. greater freedom distortion affords stabilizes despite A fit points yields slope −1.1 ± 0.1, unity would simple model. fully assess simulate correlated flux across bicrystal KMC approach used hematite.7, 25 rate Marcus, Emin, Holstein, Austin Mott26 gives transfer terms diabatic activation energies above electronic coupling matrix elements Hab (see Information details). Two approximate dimensions 21 × 20 50 adjoined center 3. Periodic conditions employed directions parallel left side fixed photogenerated current). probability jump unoccupied adjacent (in directions) removed once they right boundary. calculation rates adiabatic approximation (i.e. κel = 1) frequency characteristic longitudinal phonon mode ν (24 THz). taken results above. modified electron-electron term depends locations nearby sites. was numerical DFT+U. Consistent dielectric constant screened Coulomb essentially negligible beyond third Calculation since requires simultaneously elimination description band gap. employ 0.2 eV value study rutile.12 series simulations room temperature densities. After initial transient period system reaches steady state where time average number net particle constant. characterize efficiency calculate transit (τ) travel function density. 4 τ cell equivalent crystallographic orientation crystal) reference. less 10−2 mAcm−2 presence 7.0 ms temperature. compared distance 71 ns, five faster. long a4 equivalent) face barrier escape. occupation deepest (<0.01 per site) interactions not influence transport. starts increase. already filled follow alternate path b 2) lower energy. Such decreases residence boundary, reducing 102 mAcm−2. Beyond saturation (limited short e-e repulsion) e inverse proportion up maximum sustainable 106 summarize results, favorably eV. As consequence increased 50% increase 10 ns 7 temperature, magnitude. whereby states under steady-state resulting greatly time. predictions line earlier observations so-called DSSCs coefficients increasing light intensity.8 possible origin understand experiment alone. example many i.e. strain, coordination perturbation. control associated correlations reported gap oxides MgO, HfO2 ZrO2 suggesting general.13, 27 equally decisive determining (See main challenge quantitative exchange large systems. semi-quantitative absolute however trends reliable. choices parameters like ΔEbulk change values times overall qualitatively unchanged. With gained suggest photocatalysts. Since will introduce one-dimensional nanowire minimize cross.28 Alternatively advantage operate densities, although negative consequences device durability. Another n-type dopants additional carriers fill boundaries. some affinity towards beneficial. prospective electrode Li could important, aiding separation ions.7 often attractive due ultrahigh surface area usually contain interfaces. speculation clear evidence obtain. technologically More generally, superconductivity magnetism.29 nano- poly-crystalline. presented deepen our fundamental understanding effects. implemented METADISE code.19, 30 converted three-dimensionally periodic supercell below. Spin polarized projector augmented wave (PAW) method Vienna ab initio package.31 use Perdew-Burke-Ernzerhof employing approach. Hubbard U parameter 3d-states work fitted spectroscopic (UTi 4.2 eV).11 valence wavefunctions expanded basis 500 structural until forces 0.01 eV/Å. Full Information. K.P.M. acknowledges support EPSRC (EP/K003151) COST Action CM1104. made facilities HECToR, UK's national high-performance computing service, via membership UK HPC Materials Chemistry Consortium, funded (EP/F067496 EP/L000202). acknowledge Nuffield Foundation Institute Physics supporting summer student (S.W.). Note: license changed after publication. service authors readers, journal provides supplied authors. peer reviewed re-organized online delivery, copy-edited typeset. Technical issues arising (other missing files) addressed Please note: publisher content functionality any Any queries content) directed author article.