First-Principles Modeling of Oxygen-Deficient Anatase TiO₂ Nanoparticles

Abstract

First-principles calculations of the electronic structure of reduced anatase TiO 2 nanoparticles are performed using a hybrid density functional theory approach for an accurate description of charge trapping. It is found that, in the bulk and at extended surfaces, electrons introduced by oxygen vacancies delocalize but, in reduced nanoparticles, electrons preferentially localize (forming Ti 3+ species) at low-coordinated sites on the surface of the particle. It is favorable for nanoparticles to be oxygendeficient in oxygen-poor conditions with the Ti 33 O 66 nanoparticle being significantly easier to reduce than the larger Ti 151 O 302 nanoparticle. Since low-coordinated sites are more prevalent in smaller nanoparticles, this suggests that there is a delicate balance between the number of carriers introduced by vacancies and the number of trapped electrons.

Unveiling the Electronic Structure of Grain Boundaries in Anatase with Electron Microscopy and First-Principles Modeling

“…In contrast, the oxygen-deficient Σ5{103}-AS and Σ5{103}-AS-r GBs would be far more pathological for device performance; the structure inherently contains large numbers of oxygen vacancies and under-coordinated Ti sites. We find that the excess electrons trap on under-coordinated Ti sites, which is consistent with a previous theoretical study using the same functional investigating the properties of highly oxygen-deficient anatase nanoparticles . Vacancies that strongly trap electrons at the GB would reduce the number of mobile carriers introduced by each vacancy, reduce electron mobility, and could lead to increased carrier recombination, leading to reduced conductivity in photovoltaic applications.…”

“…We find that the excess electrons trap on under-coordinated Ti sites, which is consistent with a previous theoretical study using the same functional investigating the properties of highly oxygen-deficient anatase nanoparticles. 37 Vacancies that strongly trap electrons at the GB would reduce the number of mobile carriers introduced by each vacancy, reduce electron mobility, and could lead to increased carrier recombination, leading to reduced conductivity in photovoltaic applications. On the other hand, these trap states appear at ∼0.5−1.0 eV below the conduction band minimum and would increase visible-light absorption.…”

Hole Polaron Migration in Bulk Phases of TiO2 Using Hybrid Density Functional Theory

“… 39 This approach has been employed to predict the properties of stable electrons and hole polarons in all known phases of TiO 2 , where the use of large supercells (>500 atoms) also minimizes finite size effects as well as at surfaces, twin boundaries, and nanocrystals. 14 , 31 , 40 − 42 …”

“…In principle, the generalized Koopmans condition (a known property of the exact functional) provides a means to constrain the choice of parameters in the functional, ensuring a more complete cancellation of the SIE − It has been recently shown for model systems in 1D (for which the many-body problem can be solved exactly) that hybrid functionals parameterized in this way provide ionization energies and electron densities in excellent agreement with exact solutions . This approach has been employed to predict the properties of stable electrons and hole polarons in all known phases of TiO 2 , where the use of large supercells (>500 atoms) also minimizes finite size effects as well as at surfaces, twin boundaries, and nanocrystals. ,,− …”

Near-Surface Composition, Structure, and Energetics of TiO2 Thin Films: Characterization of Stress-Induced Defect States in Oxides Prepared via Chemical Vapor Deposition versus Solution Deposition from Sol–Gel Precursors

“…We are also guided by the substantial body of work describing near-surface defects for both single crystal (anatase and rutile) TiO 2 surfaces and more recently on studies of the types of defects formed in nanoparticle versions of these oxides, which help to rationalize defect formation and loss in both amorphous CVD and SG oxide films. ,,,,,,− Figure provides a schematic view of a range of defect states that have been postulated for the surface of TiO 2 ; in this case we show the (001) termination of the anatase unit cell, which guides our understanding of interactions with perovskite precursors. ,,,,,,,− , Both 5- and 6-coordinate (Ti 4+ 6c and Ti 4+ 5c ) are present in such surfaces along with an undercoordinated electron-rich Lewis acidic defect (Ti 3+ 4c ) associated with oxygen vacancies (V O prominent in the studies discussed below) and an interstitial form (Ti i ). ,,,,− These electron-rich states are important in n-doping the oxide film, providing adequate electrical conductivity for its use in efficient device platforms with low series resistance and have even been shown recently to provide for two-dimensional metallic and “plasmonic” states when the defect concentrations are sufficiently high in the near-surface region. − …”