The formations of intrinsic n-type defects, that is, oxygen vacancies and titanium interstitials, in rutile and anatase TiO2 have been compared using GGA+U calculations. In both crystal structures, these defects give rise to states in the band gap, corresponding to electrons localized at Ti3+ centers. O vacancy formation in rutile results in two excess electrons occupying 3d orbitals on Ti atoms neighboring the vacancy. Similarly, for anatase, two Ti 3d orbitals are occupied by the excess electrons, with one of these Ti sites neighboring the vacancy, and the second at a next-nearest Ti position. This localization is accompanied by one oxygen moving toward the vacancy site to give a “split vacancy” geometry. A second fully localized solution is also found for anatase, with both occupied Ti sites neighboring the vacancy site. This minimum is 0.05 eV less stable than the split vacancy and is thus expected to be present in experimental samples. A partially delocalized solution corresponding to the split vacancy geometry, with one electron occupying the bottom of the conduction band, is also identified as 0.28 eV less stable. Formation of titanium interstitials donates four electrons to the Ti lattice. In anatase, one of these electrons is located at the interstitial Ti site, and three occupied defect states are hybridized between three nearest neighbor Ti sites. In rutile, these excess electrons are mostly localized at four nearest neighbor Ti sites, with only a small amount of excess charge found on the interstitial Ti atom. This difference in the charge on the interstitial atom is a consequence of the differing interstitial geometries in the two polymorphs. Calculated optical absorption spectra for all defects show significant decreases of the optical band gap, with a larger red shift predicted for titanium interstitials in anatase than in rutile. Defect formation energies have been calculated under oxygen-rich and oxygen-poor conditions for both polymorphs. Under all conditions, O vacancy formation is slightly more favorable in anatase than in rutile, while Ti interstitials form more easily in rutile than anatase. Under O-rich conditions, O vacancies are the favored defect type, but both defect types have high formation energies. Under O-poor conditions, both defect types are stabilized, with Ti interstitials predicted to become the favored defect in rutile samples, particularly at elevated temperatures.

Oxygen vacancy formation at the (110), (100), (001), and (101) surfaces of rutile TiO2 has been investigated using density functional theory with an on-site correction for strongly correlated systems (DFT + U). In agreement with experimental data, the reduced (110) surface shows an occupied defect state 0.7 eV below the bottom of the conduction band. The other reduced surfaces also show defect states in the band gap, with the defect state energies being strongly dependent on the choice of surface, and following the trend expected from crystal field arguments. For all the reduced surfaces, the excess charge associated with the defect states is primarily localized on two Ti sites neighboring the vacancy, formally reducing these to TiIII. For the (101) and (001) surfaces these Ti sites are geometrically inequivalent, and the corresponding gap states are separated in energy. Vacancy formation energies vary as ΔEvac(100) > ΔEvac(110) > ΔEvac(001) > ΔEvac(101). The variation in vacancy formation energy and gap state energies suggests potential differences between the surfaces in catalytic behavior for adsorbed reactant molecules.

LaMnO3-based perovskites, which have been extensively studied as cathodes for high temperature solid oxide fuel cells (SOFCs), are also of interest for intermediate temperature SOFCs (T = 600–1000 K). Oxygen vacancy formation is required in LaMnO3 for oxygen diffusion, therefore a low vacancy formation energy is preferable. The stability of the low index surfaces of orthorhombic LaMnO3 has been investigated, with the {010} surface found to be the most stable. Surface stability was found to be affected by the La and Mn coordination, and the Mn–O bonds cleaved on surface formation. The crystal morphology has been predicted, in order to determine the most likely terminations to be present. The formation of oxygen vacancies in bulk LaMnO3 and at all of its low index surfaces has been examined, and it has been found that formation of vacancies in the bulk has a high energy, while there is a large variation in formation energies at the low index surfaces, which is likely to lead to segregation of vacancies to the surface of orthorhombic LaMnO3.

The doping of CeO2 with trivalent cations is a common technique for enhancing ionic conductivity in electrolytes for solid oxide fuel cell applications. However, the local defect structure in these materials is yet to be fully explored. Furthermore, many studies have overlooked the effect of the dopants on the reducibility of CeO2, which is important as electronic conductivity can short-circuit the fuel cell. Density functional theory (DFT)+U calculations have been performed on a series of CeO2 systems doped with trivalent cations. The most stable configuration and the relative attraction between dopant cations and oxygen vacancies were determined, and it was found that the defect structure is principally dependent on the ionic radius of the dopant cations. The reduction energy was found to be dependent on the structure around the dopants but did not vary significantly between dopants of similar ionic radii. From these results, it is possible to suggest which trivalent cations would be most suitable to enhance ionic conductivity without increasing electronic conductivity in solid oxide fuel cell electrolytes.

The electronic structure of a family of ternary copper chalcogenide systems Cu3MCh4 (M = V, Nb, Ta; Ch = S, Se, Te) has been explored to ascertain the compounds' potential for optoelectronic device applications. The lattice parameters, density of states, band gap, optical absorption, and effective mass of each of the nine systems were determined with PBEsol+U, and a valence band alignment was performed to assess the doping limits of the series. The calculated optical band gaps of the materials range from 1.19 eV for Cu3VTe4 to 2.60 eV for Cu3TaS4, with the former also predicted to have the highest valence band maximum and the lowest hole effective mass of the series, indicative of a p-type material with photovoltaic potential. The wide range of band gap energies predicted in this series of isostructural materials evidences how selective combination of elements in ternary systems can be used to tune electronic properties through alloying and thus target ideal values for specific applications. Five materials in the series are predicted to have optical band gaps suitable for solar cell absorbers, with Cu3NbTe4 and Cu3TaTe4 being of particular interest due not only to their respective band gaps of 1.46 eV and 1.69 eV but also their potential to be alloyed based on their similar lattice constants and valence band energies.

The failure to develop a degenerate, wide band gap, p-type oxide material has been a stumbling block for the optoelectronics industry for decades. Mg-doped LaCuOSe has recently emerged as a very promising p-type anode layer for optoelectronic devices, displaying high conductivities and low hole injection barriers. Despite these promising results, many questions regarding the defect chemistry of this system remain unanswered, namely (i) why does this degenerate semiconductor not display a Moss–Burnstein shift?, (ii) what is the origin of conductivity in doped and un-doped samples?, and (iii) why is Mg reported to be the best dopant, despite the large cation size mismatch between Mg and La? In this article we use screened hybrid density functional theory to study both intrinsic and extrinsic defects in LaCuOSe, and identify for the first time the source of charge carriers in this system. We successfully explain why LaCuOSe does not exhibit a Moss–Burstein shift, and we identify the source of the subgap optical absorption reported in experiments. Lastly we demonstrate that Mg doping is not the most efficient mechanism for p-type doping LaCuOSe, and propose an experimental reinvestigation of this system.

Ceria (CeO2) co-doping has been suggested as a means to achieve ionic conductivities that are significantly higher than those in singly doped systems. Rekindled interest in this topic over the last decade has given rise to claims of much improved performance. The present study makes use of computer simulations to investigate the bulk ionic conductivity of rare earth (RE) doped ceria, where RE = Sc, Gd, Sm, Nd and La. The results from the singly doped systems are compared to those from ceria co-doped with Nd/Sm and Sc/La. The pattern that emerges from the conductivity data is consistent with the dominance of local lattice strains from individual defects, rather than the synergistic co-doping effect reported recently, and as a result, no enhancement in the conductivity of co-doped samples is observed.

The use of a density functional theory methodology with on-site corrections (DFT + U) has been repeatedly shown to give an improved description of localised d and f states over those predicted with a standard DFT approach. However, the localisation of electrons also carries with it the problem of metastability, due to the possible occupation of different orbitals and different locations. This study details the use of an occupation matrix control methodology for simulating localised d and f states with a plane-wave DFT + U approach which allows the user to control both the site and orbital localisation. This approach is tested for orbital occupation using octahedral and tetrahedral Ti(III) and Ce(III) carbonyl clusters and for orbital and site location using the periodic systems anatase-TiO2 and CeO2. The periodic cells are tested by the addition of an electron and through the formation of a neutral oxygen vacancy (leaving two electrons to localise). These test systems allow the successful study of orbital degeneracies, the presence of metastable states and the importance of controlling the site of localisation within the cell, and it highlights the use an occupation matrix control methodology can have in electronic structure calculations.

In this paper we report a computational study of the effects of strain on the conductivity of Y-doped ceria (YDC). This material was chosen as it is of technological interest in the field of Solid Oxide Fuel Cells (SOFCs). The simulations were performed under realistic operational temperatures and strain (𝜖) levels. For bulk and thin film YDC, the results show that tensile strain leads to conductivity enhancements of up to 3.5 × and 1.44 × , respectively. The magnitude of these enhancements is in agreement with recent experimental and computational evidence. In addition, the methods presented herein allowed us to identify enhanced ionic conductivity in the surface regions of YDC slabs and its anisotropic character.

Ce is one of the few lanthanide elements to exhibit well-defined (III) and (IV) oxidation states in solid-state environments, and there is therefore ambiguity as to whether CeVO4 should be formulated as Ce(III)V(V)O4 or Ce(IV)V(IV)O4. To address this question, CeVO4 and Ce0.5Bi0.5VO4 have been studied by density functional theory calculations and X-ray photoemission spectroscopy. A peak above the main O 2p valence band in photoemission is attributed to localized Ce 4f states, in agreement with the calculations which show occupation of Ce 4f states. The Ce 3d core level spectrum is diagnostic of Ce(III) with no sign of a peak associated with 4f0 final states that are characteristic of Ce(IV) compounds. The experimental and theoretical results thus confirm that both compounds contain Ce(III) and V(V), rather than Ce(IV) and V(IV). In agreement with experiment, the calculations also show that the tetragonal zircon phase adopted by CeVO4 is more stable for Ce0.5Bi0.5VO4 than the monoclinic clinobisvanite phase adopted by BiVO4, so that the formation of the stereochemically active Bi(III) lone pairs is suppressed by Ce doping.

Tin monoxide has garnered a great deal attention in the recent literature, primarily as a transparent p-type conductor. However, due to its layered structure (dictated by non-bonding dispersion forces) simulation via density functional theory often fails to accurately model the unit cell. This study applies a PBE0-vdW methodology to accurately predict both the atomic and electronic structure of SnO. Empirical van der Waals corrections improve the structure, with the calculated c/a ratio matching experiment, while the PBE0 hybrid-DFT method gives accurate band gaps (0.67 and 2.76 eV for the indirect and direct band gaps) and density of states which are in agreement with experimental spectra. This methodology has been applied to the simulation of the native intrinsic defects of SnO, to further understand the conductivity. The results indicate that n-type conductivity will not arise from intrinsic defects and that donor doping would be necessary. For p-type conduction, the Sn vacancy is seen to be the source, with the 0/−1 transition level found 0.39 eV above the valence band maximum. By considering the formation energies and transition levels of the defects at different chemical potentials, it is found that the p-type conductivity is sensitive to the O chemical potential. When the chemical potential is close to its lowest value (−2.65 eV here), the oxygen vacancy is stabilized which, whilst not leading to n-type conduction, could reduce p-type conduction by limiting the formation of hole states.

Lead dioxide has been studied for over 150 years as a component of the lead-acid battery. Based on first-principles calculations, we predict that by tuning the concentration of electrons in the material, through control of the defect chemistry, PbO2 can be rendered from black to optically transparent, thus opening up applications in the field of optoelectronics.

As the thin film photovoltaic sector continues to expand, there is an emerging need to base these technologies on abundant, low cost materials in place of the expensive, rare, or toxic elements such as Te, In, or Cd that currently constitute the industry standards. To this end, the geometric and electronic structure of four materials comprising low cost, earth abundant elements (Cu3SbS3, Cu3SbSe3, Cu3BiS3, and Cu3BiSe3) are investigated with the screened hybrid exchange–correlation functional HSE06 and their candidacy for use as absorber materials assessed. The materials are shown to exhibit low VBM effective masses, due partially to the presence of lone pairs that originate from the Sb and Bi states. Although all four materials possess indirect fundamental band gaps, calculated optical absorbance shows direct transitions close in energy. Optical band gaps within the visible-light spectrum are also predicted for three of the systems, (Cu3SbSe3, Cu3BiS3 and Cu3BiSe3) making them promising candidates for PV applications.

This study details density functional theory calculations on all the polymorphs of the binary oxides of antimony (Sb2O3, Sb2O4, and Sb2O5) to assess the electronic structures and differences in bonding between SbIII and SbV ions with oxygen. The results show that lone-pair formation is via a similar mechanism to other main group elements which exhibit an oxidation state of two less than the group valence, through direct interaction of Sb 5s and O 2p states, with the antibonding interaction stabilized by Sb 5p states. Furthermore, structural distortion of the Sb site directly affects the strength of the resulting lone pair. In addition to the analysis of the density of states and charge density, band structures and optical absorption spectra are also detailed. The results indicate that all materials are indirect band gap materials, with the exception of the β-polymorphs of Sb2O3 and Sb2O4. In addition, the fundamental and optical band gaps of the materials are found to decrease from Sb2O3 to Sb2O4 to Sb2O5. Calculated band-edge effective masses suggest that β-Sb2O3 may exhibit reasonable p-type properties. Furthermore, β-Sb2O3, γ-Sb2O3, and Sb2O5 possess low electron effective masses which are conducive with strong n-type conduction.

The defect structure and ionic diffusion processes within the anion-deficient, fluorite structured system Ce1–xYxO2–x/2 have been investigated at high temperatures (873 K–1073 K) as a function of dopant concentration, x, using a combination of neutron diffraction studies, impedance spectroscopy measurements, and molecular dynamics (MD) simulations using interionic potentials developed from ab initio calculations. Particular attention is paid to the short-range ion–ion correlations, with no strong evidence that the anion vacancies prefer, at high temperature, to reside in the vicinity of either cationic species. However, the vacancy–vacancy interactions play a more important role, with preferential ordering of vacancy pairs along the ⟨111⟩ directions, driven by their strong repulsion at closer distances, becoming dominant at high values of x. This effect explains the presence of a maximum in the ionic conductivity in the intermediate temperature range as a function of increasing x. The wider implications of these conclusions for understanding the structure–property relationships within anion-deficient fluorite structured oxides are briefly discussed, with reference to complementary studies of yttria and/or scandia doped zirconia published previously.Keywords: cation interactions; doped ceria (CeO2); molecular dynamics (MD); oxygen vacancy ordering; reverse Monte Carlo (RMC); SOFC electrolytes;

SnO2 is an abundant, low cost, natively n-type, wide band gap oxide, which can achieve high conductivities due to facile donor doping. Realization of a p-type SnO2 would, however, open up many new avenues in device applications, and has become a major research goal. Previous experimental and theoretical studies have proved inconclusive, with the p-type ability of SnO2 being both supported and questioned in equal measure. In this study we use state of the art hybrid density functional theory to investigate the nature of intrinsic and extrinsic p-type defects in SnO2. We demonstrate that all the p-type defects considered in SnO2 produce localized hole polarons centered on anion sites. We calculate the thermodynamic ionization energies of these defects, and demonstrate that an efficient p-type SnO2 is not achievable.

Cu-based I–III–VI2 materials have enjoyed much attention as candidate solar cell adsorbers. While the vast majority of studies has centered on materials with group 13 (In, Ga) as the trivalent metal, the scarcity and expense of In has motivated a research drive to discover alternative Cu-based absorber materials. In this study, we use screened hybrid density functional theory (DFT) to investigate the electronic structure and bonding in some novel I–III–VI2 materials, namely, CuMCh2 (M = Sb, Bi; Ch = S, Se). We demonstrate that these materials possess fundamental band gaps that are indirect in nature, which is at variance with previous experimental results. We analyze the crystal structures and rationalize the structural differences between these and typical chalcopyrite materials. The band structure features and bonding of these materials are then discussed in relation to their utility as solar cell absorbers.

We have investigated the formation of intrinsic defects in CeO2 using density functional theory with the generalized gradient approximation (GGA) corrected for on-site Coulombic interactions (GGA+U). We employed an ab initio fitting procedure to determine a U{O2p} value that satisfies a Koopmans-like condition and obtained a value of U{O2p} = 5.5 eV. We subsequently demonstrated that by applying GGA+U to the O2p states, in addition to the Ce4f states, we were able to model localized holes in addition to localized electrons, thus improving the description of p-type defects in CeO2. Our results show that under oxygen-poor conditions the defects with the lowest formation energy are oxygen vacancies, while oxygen interstitials, which form peroxide ions, will be more favorable under oxygen-rich conditions. We carried out temperature and pressure dependence analyses to determine the relative abundance of intrinsic defects under real-world conditions and determined that oxygen vacancies will always be the dominant defect. Furthermore, we determined that at the dilute limit none of the defects studied can account for the intrinsic ferromagnetism that has been observed in nanosized CeO2.

CdO has been studied for decades as a prototypical wide band gap transparent conducting oxide with excellent n-type ability. Despite this, uncertainty remains over the source of conductivity in CdO and over the lack of p-type CdO, despite its valence band maximum (VBM) being high with respect to other wide band gap oxides. In this article, we use screened hybrid DFT to study intrinsic defects and hydrogen impurities in CdO and identify for the first time the source of charge carriers in this system. We explain why the oxygen vacancy in CdO acts as a shallow donor and does not display negative-U behavior similar to all other wide band gap n-type oxides. We also demonstrate that p-type CdO is not achievable, as n-type defects dominate under all growth conditions. Lastly, we estimate theoretical doping limits and explain why CdO can be made transparent by a large Moss–Burstein shift caused by suitable n-type doping.

The doping of ceria (CeO2) with divalent noble metal ions has been shown to improve the reducibility and enhance the oxygen storage capacity (OSC), although the reasons for this are not well understood. We have examined the interaction of a range of divalent dopants with CeO2 using density functional theory, and found that the dopant preferentially adopts the coordination of its own oxide, instead of the cubic coordination of Ce(IV) in ceria. Depending on the electronic structure of the dopants, the different coordinations can create weakly- or under-coordinated oxygen ions that are more easily removed than in pure CeO2. We have used these insights to identify dopants which will increase the reducability of CeO2, while being economically more viable than the presently used noble metals, and we outline guidelines for the design of improved oxide catalysts.Keywords: catalysis; CeO2; ceria; defects; doping; vacancy;

CuCrO2 is the most promising Cu-based delafossite for p-type optoelectronic devices. Despite this, little is known about the p-type conduction mechanism of this material, with both CuI/CuII and CrIII/CrIV hole mechanisms being proposed. In this article we examine the electronic structure, thermodynamic stability and the p-type defect chemistry of this ternary compound using density functional theory with three different approaches to the exchange and correlation; the generalized-gradient-approximation of Perdew, Burke and Ernzerhof (PBE), PBE with an additional correction for on-site Coulombic interactions (PBE + U) and the nonlocal, screened-exchange hybrid functional HSE06. The fundamental band gap of CuCrO2 is demonstrated to be indirect in nature. Under all growth conditions, the dominant intrinsic p-type defect will be the Cu vacancy, with hole formation centered solely on the Cu sublattice. Mg doping is found to be significantly lower in energy than intrinsic defect formation, explaining the large increases in conductivity seen experimentally. Cu-rich/Cr-poor growth conditions are found to be optimal for both intrinsic and extrinsic (Mg doping) defect formation, and should be adopted to maximize performance.

Doping CeO2 with Pd or Pt increases the oxygen storage capacity (OSC) and catalytic activity of this environmentally important material. To date, however, an understanding of the mechanism underlying this improvement has been lacking. We present a density functional theory analysis of Pd- and Pt-doped CeO2, and demonstrate that the increased OSC is due to a large displacement of the dopant ions from the Ce lattice site. Pd(II)/Pt(II) (in a d8 configuration) moves by ∼1.2 Å to adopt a square-planar coordination due to crystal field effects. This leaves three three-coordinate oxygen atoms that are easier to remove, and which are the source of the increased OSC. These results highlight the importance of rationalizing the preferred coordination environments of both dopants and host cations when choosing suitable dopants for next generation catalysts.

Development of high figure-of-merit p-type transparent conducting oxides has become a global research goal. ZnM2IIIO4 (MIII = Co, Rh, Ir) spinels have been identified as potential p-type materials, with ZnIr2O4 reported to be a transparent conducting oxide. In this article the geometry and electronic structure of ZnM2IIIO4 are studied using the Perdew-Purke-Ernzerhof generalized gradient approximation (PBE-GGA) to density functional theory and a hybrid density functional, HSE06. The valence band features of all the spinels indicate that they are not conducive to high p-type ability, as there is insufficient dispersion at the valence band maxima. The trend of increasing band-gap as the atomic number of the MIII cation increases, as postulated from ligand field theory, is not reproduced by either level of theory, and indeed is not seen experimentally in the literature. GGA underestimates the band-gaps of these materials, while HSE06 severely overestimates the band-gaps. The underestimation (overestimation) of the band-gaps by GGA (HSE06) and the reported transparency of ZnIr2O4 is discussed.

The mechanism of the tetragonal ↔ orthorhombic phase separation of Li-intercalated anatase TiO2 has previously been proposed to be a cooperative Jahn–Teller distortion due to occupation of low-lying Ti 3dxz,yz orbitals. Using density functional calculations, we show that the orthorhombic distortion of Li0.5TiO2 is not a purely electronic phenomenon and that intercalated Li plays a critical role. For a 2 × 1 × 1 expanded supercell for 0 ≤ x(Li) ≤ 1, the intercalation voltage is minimized for x(Li) = 0.5. The low-energy structures display a common structural motif of edge-sharing pairs of LiO6 octahedra, which allows all Li to adopt favorable oxygen coordination. Long-ranged disorder of these subunits explains the apparent random Li distribution seen in experimental diffraction data.Keywords: anatase TiO2; GGA; Jahn−Teller distortion; orthorhombic distortion; supercell;

Tin monoxide is a technologically important p-type material which has a layered structure dictated by nonbonded dispersion forces. As standard density functional theory (DFT) approaches are unable to account for dispersion forces properly, they routinely give rise to a poor description of the unit cell structure. This study therefore applies two forms of empirical dispersion corrections, using either atomic- or ionic-based parameters for the dispersion coefficients, to assess their ability to correctly model the atomic structure and the formation energies of the important p-type defects. Although both approaches show an improvement in the predicted unit cell structure over that with no dispersion corrections, the ionic-based parameter set shows significantly better results, with lattice vectors reproduced within 0.2% of experiment. The atomic-based parameters still predict a distorted cell though, which is carried through to the defective system. On the introduction of defects, a similar degree of structural relaxation is observed regardless of the approach. The defect formation energies, however, are seen to differ more substantially, with the atomic-based set giving an overestimation of the energies due to excessive Sn–Sn interactions. Overall, this study shows that empirical van der Waals corrections utilizing an ionic-based parameter set can be used to model SnO.

Density functional theory calculations have been performed on stoichiometric and intrinsically defective p-type transparent conducting oxide SrCu2O2, using GGA corrected for on-site Coulombic interactions (GGA + U). Analysis of the absorption spectrum of SrCu2O2 indicates that the fundamental direct band gap could be as much as ∼0.5 eV smaller than the optical band gap. Our results indicate that the defects that cause p-type conductivity are favoured under all conditions, with defects that cause n-type conductivity having significantly higher formation energies. We show conclusively that the most stable defects are copper and strontium vacancies. Copper vacancies introduce a distinct acceptor single particle level above the valence band maximum, consistent with the experimentally known activated hopping mechanism.

Cuprous oxide is widely known to be a native p-type semiconductor. Despite this, reports of electrodeposited films of n-type Cu2O continue to appear in the literature, with oxygen vacancies commonly implicated as the electron-donating defect. Through first-principles calculations, we demonstrate conclusively that intrinsic n-type defects or defect complexes in Cu2O cannot be the source of any n-type behavior displayed by electrodeposited samples. In light of these results, we discuss the experimental findings.Keywords: cuprous oxide; defect complexes; electrodeposited film; first-principles calculations; oxygen vacancies; semiconductor;

The geometric and electronic structures of MoO3 and MoO2 have been calculated using the generalized gradient approximation to density functional theory. The calculated cross-section weighted densities of states are compared with high-resolution X-ray photoemission spectra. There is very good agreement between the calculated structures and those determined previously by X-ray diffraction and between the computed densities of states and the present photoemission measurements. MoO2 is shown to be a metallic material, as is found experimentally, but the Fermi level sits in a distinct trough in the density of states. Satellite peaks found in core photoemission spectra of MoO2 are shown to derive from final state screening effects in this narrow band metallic material.

CuAlO2 is a prototypical delafossite p-type transparent conducting oxide (TCO). Despite this, many fundamental questions about its band structure and conductivity remain unanswered. We utilize the screened hybrid exchange functional (HSE06) to investigate defects in CuAlO2 and find that copper vacancies and copper on aluminum antisites will dominate under Cu-poor/Al-poor conditions. Our calculated transitions levels are deep in the band gap, consistent with experimental findings, and we identify the likely defect levels that are often mistaken as indirect band gaps. Finally, we critically discuss delafossite oxides as TCO materials.Keywords: conductivity; defects; transparent conducting oxide;

Discovering new candidate p-type transparent conducting oxides has become a major goal for material scientists. Recently delafossite CuBO2 has been proposed as a promising candidate, showing good room temperature electrical conductivity and excellent transparency [Appl. Phys. Lett. 2007, 91, 092123]. In this article we report a density functional theory investigation of CuBO2, examining the geometry and electronic structure using GGA corrected for on-site Coulomb interactions (GGA + U) and a hybrid density functional (HSE06). From analysis of the calculated band structure, density of states, and optical absorption, we predict an indirect fundamental band gap of ∼3.1 eV and a direct optical band gap of ∼3.6 eV. The hole effective mass at the valence band maximum indicates the potential for good p-type conductivity, consistent with the reported experimental results. These results are discussed in relation to other delafossite oxides.

Development of a p-type TCO to rival the high-performance n-type TCOs presently utilized in many applications is one of the grand challenges for materials scientists. However, most of the p-type TCOs fabricated to date have suffered from limited hole mobilities, low conductivities, and indirect band gaps. Recently, [Cu2S2][Sr3Sc2O5] has been identified as a possible p-type TCO material, with improved hole mobility. In this article, we study the geometry and electronic structure of [Cu2S2][Sr3Sc2O5] using both GGA + U and HSE06 . We show conclusively that [Cu2S2][Sr3Sc2O5] is a direct band gap material, with a hole effective mass at the valence band maximum that indicates the potential for good p-type conductivity, consistent with the reported experimental results. These results are discussed in relation to other p-type TCO materials.

Experimental studies of thin-film Nb- and Ta-doped TiO2 have reported that doped anatase is highly conductive, yet doped rutile is semiconducting. Standard DFT functionals (LDA, GGA) predict that for doped anatase TiO2 the excess charge occupies the bottom of the conduction band, and is delocalised over all the Ti atoms. This has previously been proposed as the source of the experimentally observed high conductivity. GGA predicts a similar metallic system for Nb-doped rutile, however, in contradiction with experimental data that characterise doped rutile as a semiconductor with a localised gap state. This demonstrates that standard DFT functionals cannot explain the difference in experimental behaviour between polymorphs. Supplementing GGA with a “+ U” on-site Coulomb correction recovers an electronic structure for Nb-doped rutile TiO2 that is in agreement with the experimental data; a localised gap state is seen, corresponding to a small polaron on a single Ti site. GGA + U also predicts a small-polaronic Ti3+ gap state within a semiconducting system for {Nb,Ta}-doped anatase. On this basis we suggest the experimental variance between polymorphs in doped thin films is not an inherent property of the bulk crystals, but is due to other factors, e.g. additional defects or sample morphology, dependent on the synthesis history. For both anatase and rutile the defect feature is found to be insensitive to the identity of the dopant, and similar Ti3+ polarons are expected generally for doping where electrons are donated to the Ti lattice.

The geometries and electronic structures resulting from surface reduction, CO adsorption, and NO2 adsorption at the (110) surface of CeO2 have been calculated using density functional theory corrected for on-site Coulomb interactions, GGA+U. We report a novel electronic structure for the reduced surface, denoted the split vacancy, which is more stable than the previously reported simple vacancy with subsurface CeIII. Analysis of CO adsorption modes highlights the importance of the geometry of the CO molecule when in contact with the surface, with a tilted adsorption mode being most energetically favorable with the formation of a carbonate anion coupled with surface reduction. A new bidentate adsorption mode is observed for NO2 adsorption, accompanied by partial surface oxidation. These novel structures observed on reduction, CO adsorption, and NO2 adsorption are all energetically more stable than the previously reported structures. In all of the systems, it was found that the location of the CeIII ions did not have a strong effect on the energetics, although they were coupled to strong local distortions of the structure.

Empirically, intrinsic defects in SnO2 are known to give rise to a net oxygen substoichiometry and n-type conductivity; however, the atomistic nature of the defects is unclear. Through first-principles density functional theory calculations, we present detailed analysis of both the formation energies and electronic properties of the most probable isolated defects and their clustered pairs. While stoichiometric Frenkel and Schottky defects are found to have a high energetic cost, oxygen vacancies, compensated through Sn reduction, are predicted to be the most abundant intrinsic defect under oxygen-poor conditions. These are likely to lead to conductivity through the mobility of electrons from Sn(II) to Sn(IV) sites. The formation of Sn interstitials is found to be higher in energy, under all charge states and chemical environments. Although oxygen interstitials have low formation energies under extreme oxygen-rich conditions, they relax to form peroxide ions (O22−) with no possible mechanism for p-type conductivity.

Two methods of reduction of V2O5 have been investigated: oxygen vacancy formation and lithium intercalation. The electronic structure, geometry, and energetics of these reduced systems are examined. Oxygen vacancies in bulk α-V2O5 have been investigated by using gradient-corrected density functional theory (GGA) and density functional theory corrected for on-site Coulomb interactions in strongly correlated systems (GGA+U). The GGA calculation predicts a delocalized defect electronic state. This disagrees with experimental evidence, which indicates that oxygen vacancies produce a localized reduced vanadium state in the band gap. The DFT+U results for U = 4.0 eV are consistent with available UPS and XPS data, indicating strong localization on the vanadium atoms nearest the vacancy, and showing reduced V(IV) species. Intercalation of Li in V2O5, which has important potential applications in energy storage devices, is also reported at the GGA+U level, using the value of U obtained from the oxygen-deficient calculation, and localized reduction is demonstrated. These results are again in agreement with available UPS data and crystallographic data, indicating good transferability of this value of U among the systems of interest. Calculated lithium intercalation energies for both the α- and γ-V2O5 phases are reported, and the structure and relative stability of the deintercalated γ-V2O5 phase are also examined.

Experimental observations indicate that removing bridging oxygen atoms from the TiO2 rutile (1 1 0) surface produces a localised state approximately 0.7 eV below the conduction band. The corresponding excess electron density is thought to localise on the pair of Ti atoms neighbouring the vacancy; formally giving two Ti3+ sites. We consider the electronic structure and geometry of the oxygen deficient TiO2 rutile (1 1 0) surface using both gradient-corrected density functional theory (GGA DFT) and DFT corrected for on-site Coulomb interactions (GGA + U) to allow a direct comparison of the two methods. We show that GGA fails to predict the experimentally observed electronic structure, in agreement with previous uncorrected DFT calculations on this system. Introducing the +U term encourages localisation of the excess electronic charge, with the qualitative distribution depending on the value of U. For low values of U (⩽4.0 eV) the charge localises in the sub-surface layers occupied in the GGA solution at arbitrary Ti sites, whereas higher values of U (⩾4.2 eV) predict strong localisation with the excess electronic charge mainly on the two Ti atoms neighbouring the vacancy. The precise charge distribution for these larger U values is found to differ from that predicted by previous hybrid-DFT calculations.

The pyrochlore based bismuth stannate, Bi2Sn2O7, is a material with important applications in catalysis and gas sensing. The thermodynamically stable α phase has 352 atoms in the unit cell and is one of the most complex oxide crystal structures to have been solved by powder diffraction. We have performed a full atomic relaxation and calculated the electronic structure, using gradient corrected density functional theory, with the resulting structure in very good agreement with the previous experimentally determined unit cell. The computed density of states is in excellent agreement with our valence band X-ray photoelectron spectra. The combined results shed new light on the bonding and lone pair activity in this material. A mixture of Bi 6s and O 2p states are found to dominate the top of the valence band while Sn 5s, O 2p and Bi 6p states dominate the bottom of the conduction band. The differing contributions of Sn 5s and Bi 6s states to the valence and conduction bands reflect both differences in atomic binding energies and differences in the strength of the metal s interactions with O 2p. The preference of this material for a distorted structure and its unique catalytic and gas sensing activity are discussed.

PtSn {111} forms two ordered surface alloys namely p(2 × 2) and (√3 × √3R30°) and such bimetallic catalysts are often used in industrially catalysed reactions, such as hydrogenations, to improve performance although the reasons behind the improvements are generally not well understood. In this study density functional theory calculations have been performed for hydrogen adsorption at various sites on Pt {111} and the ordered PtSn {111} surfaces in order to characterise the differences between the pure and doped surfaces. The structural, bonding, electronic and vibrational characteristics of each system are presented indicating that there are no significant bonding differences when adsorption occurs at platinum sites on the surface. Where adsorption occurs at a tin site on the doped surface the adsorption energy is negative or the adsorption site changes to one involving only platinum atoms. Nudged elastic band calculations were used to determine the barrier to diffusion of the hydrogen atoms on the surface. The diffusion calculations show significant differences in the mobility of hydrogen providing a possible explanation for the changes in catalytic action on tin doping of platinum.

First principles calculations using density functional theory with corrections for on-site Coulomb interactions (DFT + U) are presented in which we compute the energy for the conversion of CO to CO2, NO2 to NO and NO to N2 over ceria surfaces. The surface sensitivity is discussed on the basis of the vacancy formation energies.

Applications of ceria, CeO2 in catalysis and solid oxide fuel cells arise from the relative ease with which oxygen vacancies are formed, producing reactive sites or facilitating ionic diffusion. In this paper, we consider modelling oxygen vacancies in bulk ceria and on the low index surfaces, as well as oxygen vacancy migration in bulk. We apply density functional theory (DFT), corrected for on-site Coulomb interactions, DFT + U, since DFT is unable to describe correctly the electronic structure of defective ceria. We obtain a description of oxygen vacancies consistent with experiment, with localisation of charge on the Ce ions neighbouring the vacancy site. Confirming classical interatomic potential results, the oxygen vacancy formation energy in reduced on surfaces compared to bulk. An elastic band approach is applied to the study of vacancy migration in bulk ceria, yielding a diffusion path and energy barrier which are compared with previous studies.

Ceria, CeO2, plays an important role in catalysis, participating directly in the conversion of environmentally sensitive molecules. This arises from the ability of ceria to store and release oxygen depending upon the conditions present in the exhaust gas. Obtaining a basic understanding of oxygen vacancy defects in ceria and the interaction of defective structures with such molecules is central to our understanding of the role of ceria in catalysis. In this work we examine using first principles density functional theory (DFT), with the inclusion of on site electronic correlations (DFT + U), the geometry and electronic structure of (1 1 1), (1 1 0) and (1 0 0) ceria surfaces that include oxygen vacancies. We find for all surfaces that the surface (atomistic) structure is strongly perturbed and the extraction of an oxygen vacancy is associated with a reduction of two neighbouring Ce(IV) species to Ce(III) rather than partial reduction of all Ce ions in the simulation cell. In the electronic density of states a new gap state appears between the top of the valence band and the bottom of the unoccupied Ce 4f states. Localisation of charge due to the gap state and excess spin density on Ce3+ sites neighbouring the vacancy is observed for all three surfaces. These DFT + U results are validated by recent experimental results regarding the electronic structure of reduced ceria surfaces, in contrast to previous DFT results. We observe an interesting result that the vacancy formation energies do not follow the same order as the stabilities of the pure surfaces, as measured by the surface energy; thus, the (1 1 0) surface has the lowest vacancy formation energy. The impact of this for the study of catalytic reactions on ceria surfaces is discussed.

We present periodic density functional theory (DFT) calculations of bulk ceria and its low index surfaces (1 1 1), (1 1 0) and (1 0 0). We find that the surface energies increase in the order (1 1 1) > (1 1 0) > (1 0 0), while the magnitude of the surface relaxations follows the inverse order. The electronic properties of the bulk and surfaces are analysed by means of the electronic density of states and the electron density. We demonstrate that the bonding in pure ceria is partially covalent and analysis of the resulting electronic states confirms the presence of localised Ce 4f states above the Fermi level. The surface atoms show only a small change in the charge distribution in comparison to the bulk and from the DOS the main differences are due to the changes in the oxygen 2p and cerium 5 d states. Investigation of the atomic and electronic structure of an oxygen vacancy on the (1 0 0) surface shows the problems DFT can have with the description of strongly localised systems, wrongly predicting electron delocalisation over all of the cerium atoms in the simulation cell. We demonstrate an improvement in the description of the strongly correlated cerium 4f states in partially reduced ceria by applying the DFT+U methodology, which leads to the appearance of a new gap state between the valence band and the empty Ce 4f band. Analysis of the partial charge density shows that these states are localised on the CeIII ions neighbouring the oxygen vacancy. In terms of classical defect chemistry, the vacancy is bound by two neighbouring CeIII ions, which have been reduced from CeIV, i.e. VO··+2CeCe′. The remaining Ce ions are in the CeIV oxidation state. The localisation of Ce 4f electrons modifies the predicted structure of the defective surface.

Although density functional theory (DFT) is the method of choice for computational studies of the properties of metal oxides, there are a number of important systems where it fails to give a proper description of the atomic and electronic structure. These are structures which are doped or have anion vacancies and are experimentally determined to have strongly localised (hole) states, which are coupled to strong structural distortions. We have investigated the problem of oxygen hole states at the (1 0 0) surface of lithium doped MgO and show that the generalised gradient approximation of DFT results in delocalisation of the electronic states and an incorrect description of the geometry. This occurs because of the failure of DFT to cancel the electron self-interaction. The GGA + U method is one way of correcting for this problem and is applied in the present work. We consider a dopant atom in the surface layer and in a subsurface layer. For both dopant atom positions, we find a strongly distorted geometry, with the surface doped structure in best agreement with experiment, while the calculated formation energies also demonstrate that the surface dopant position is most stable. Additionally, we find strong localisation of the hole density on the oxygen atom and the excess spin density. As part of the catalytic process, we consider the energetics of hydrogen abstraction from methane with Li-doped MgO.

The concept of a chemically inert but stereochemically active 6s2 lone pair is commonly associated with Pb(II). We have performed density functional theory calculations on PbO and PbS in both the rocksalt and litharge structures which show anion dependence of the stereochemically active lone pair. PbO is more stable in litharge while PbS is not, and adopts the symmetric rocksalt structure showing no lone pair activity. Analysis of the electron density, density of states and crystal orbital overlap populations shows that the asymmetric electron density formed by Pb(II) is a direct result of anion–cation interactions. The formation has a strong dependence on the electronic states of the anion and while oxygen has the states required for interaction with Pb 6s, sulphur does not. This explains for the first time why PbO forms distorted structures and possesses an asymmetric density and PbS forms symmetric structures with no lone pair activity. This analysis shows that distorted Pb(II) structures are not the result of chemically inert, sterically active lone pairs, but instead result from asymmetric electron densities that rely on direct electronic interaction with the coordinated anions.Antibonding states responsible for the lone pair activity in solid state Pb(II) materials: (a) strong lone pair activity in litharge PbO and (b) weak lone pair activity in hypothetical litharge PbS.

Density functional theory calculations have been performed on ethene adsorption on the Pd{1 1 1} surface. The results indicate that adsorption in the di-σ mode (to two metal atoms) is more stable than π adsorption (to one metal atom) by 17 kJ mol−1. This result is in variance to the interpretation of most of the experimental data for this system but the calculations gives rise to structure, electronic structure and vibrational frequencies that are consistent with this experiment data. The study concludes that the experimental data is more consistent with a di-σ adsorption mode indicating that a re-evaluation of the adsorption mode is required.

We have performed the first atomistic simulations on the termination of screw dislocations at the surfaces of oxides. We have examined the structure and stability of the a〈100〉 and screw dislocations and the a〈100〉 dislocation terminating at the {100} surface of MgO. These simulations show that the is highly mobile leading to dislocation annihilation. Simulations where additional MgO units are attached to a surface dominated by screw dislocations have been performed to learn more about their behaviour at the atomic scale during crystal growth. The initial binding is at the dislocation core with a second unit binding to the first. The atoms rearrange as more molecules are added to give rise to growth of the step.

A recently defined charge set, to be used in conjunction with the all-atom CHARMM27r force field, has been validated for a series of phosphatidylcholine lipids. The work of Sonne et al. successfully replicated experimental bulk membrane behaviour for dipalmitoylphosphatidylcholine (DPPC) under the isothermal-isobaric (NPT) ensemble. Previous studies using the defined CHARMM27r charge set have resulted in lateral membrane contraction when used in the tensionless NPT ensemble, forcing the lipids to adopt a more ordered conformation than predicted experimentally. The current study has extended the newly defined charge set to 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) and 1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphatidylcholine (PDPC). Molecular dynamics simulations were run for each of the lipids (including DPPC) using both the CHARMM27r charge set and the newly defined modified charge set. In all three cases a significant improvement was seen in both bulk membrane properties and individual atomistic effects. Membrane width, area per lipid and the depth of water penetration were all seen to converge to experimental values. Deuterium order parameters generated with the new charge set showed increased disorder across the width of the bilayer and reflected both results from experiment and similar simulations run with united atom models. These newly validated models can now find use in mixed biological simulations under the tensionless ensemble without concern for lateral contraction.

Density functional theory calculations have been performed on stoichiometric and intrinsically defective p-type transparent conducting oxide SrCu2O2, using GGA corrected for on-site Coulombic interactions (GGA + U). Analysis of the absorption spectrum of SrCu2O2 indicates that the fundamental direct band gap could be as much as ∼0.5 eV smaller than the optical band gap. Our results indicate that the defects that cause p-type conductivity are favoured under all conditions, with defects that cause n-type conductivity having significantly higher formation energies. We show conclusively that the most stable defects are copper and strontium vacancies. Copper vacancies introduce a distinct acceptor single particle level above the valence band maximum, consistent with the experimentally known activated hopping mechanism.

The electronic structure of a family of ternary copper chalcogenide systems Cu3MCh4 (M = V, Nb, Ta; Ch = S, Se, Te) has been explored to ascertain the compounds' potential for optoelectronic device applications. The lattice parameters, density of states, band gap, optical absorption, and effective mass of each of the nine systems were determined with PBEsol+U, and a valence band alignment was performed to assess the doping limits of the series. The calculated optical band gaps of the materials range from 1.19 eV for Cu3VTe4 to 2.60 eV for Cu3TaS4, with the former also predicted to have the highest valence band maximum and the lowest hole effective mass of the series, indicative of a p-type material with photovoltaic potential. The wide range of band gap energies predicted in this series of isostructural materials evidences how selective combination of elements in ternary systems can be used to tune electronic properties through alloying and thus target ideal values for specific applications. Five materials in the series are predicted to have optical band gaps suitable for solar cell absorbers, with Cu3NbTe4 and Cu3TaTe4 being of particular interest due not only to their respective band gaps of 1.46 eV and 1.69 eV but also their potential to be alloyed based on their similar lattice constants and valence band energies.

The failure to develop a degenerate, wide band gap, p-type oxide material has been a stumbling block for the optoelectronics industry for decades. Mg-doped LaCuOSe has recently emerged as a very promising p-type anode layer for optoelectronic devices, displaying high conductivities and low hole injection barriers. Despite these promising results, many questions regarding the defect chemistry of this system remain unanswered, namely (i) why does this degenerate semiconductor not display a Moss–Burnstein shift?, (ii) what is the origin of conductivity in doped and un-doped samples?, and (iii) why is Mg reported to be the best dopant, despite the large cation size mismatch between Mg and La? In this article we use screened hybrid density functional theory to study both intrinsic and extrinsic defects in LaCuOSe, and identify for the first time the source of charge carriers in this system. We successfully explain why LaCuOSe does not exhibit a Moss–Burstein shift, and we identify the source of the subgap optical absorption reported in experiments. Lastly we demonstrate that Mg doping is not the most efficient mechanism for p-type doping LaCuOSe, and propose an experimental reinvestigation of this system.

SnO2 is an abundant, low cost, natively n-type, wide band gap oxide, which can achieve high conductivities due to facile donor doping. Realization of a p-type SnO2 would, however, open up many new avenues in device applications, and has become a major research goal. Previous experimental and theoretical studies have proved inconclusive, with the p-type ability of SnO2 being both supported and questioned in equal measure. In this study we use state of the art hybrid density functional theory to investigate the nature of intrinsic and extrinsic p-type defects in SnO2. We demonstrate that all the p-type defects considered in SnO2 produce localized hole polarons centered on anion sites. We calculate the thermodynamic ionization energies of these defects, and demonstrate that an efficient p-type SnO2 is not achievable.

Ceria (CeO2) co-doping has been suggested as a means to achieve ionic conductivities that are significantly higher than those in singly doped systems. Rekindled interest in this topic over the last decade has given rise to claims of much improved performance. The present study makes use of computer simulations to investigate the bulk ionic conductivity of rare earth (RE) doped ceria, where RE = Sc, Gd, Sm, Nd and La. The results from the singly doped systems are compared to those from ceria co-doped with Nd/Sm and Sc/La. The pattern that emerges from the conductivity data is consistent with the dominance of local lattice strains from individual defects, rather than the synergistic co-doping effect reported recently, and as a result, no enhancement in the conductivity of co-doped samples is observed.

Development of high figure-of-merit p-type transparent conducting oxides has become a global research goal. ZnM2IIIO4 (MIII = Co, Rh, Ir) spinels have been identified as potential p-type materials, with ZnIr2O4 reported to be a transparent conducting oxide. In this article the geometry and electronic structure of ZnM2IIIO4 are studied using the Perdew-Purke-Ernzerhof generalized gradient approximation (PBE-GGA) to density functional theory and a hybrid density functional, HSE06. The valence band features of all the spinels indicate that they are not conducive to high p-type ability, as there is insufficient dispersion at the valence band maxima. The trend of increasing band-gap as the atomic number of the MIII cation increases, as postulated from ligand field theory, is not reproduced by either level of theory, and indeed is not seen experimentally in the literature. GGA underestimates the band-gaps of these materials, while HSE06 severely overestimates the band-gaps. The underestimation (overestimation) of the band-gaps by GGA (HSE06) and the reported transparency of ZnIr2O4 is discussed.

Doping CeO2 with Pd or Pt increases the oxygen storage capacity (OSC) and catalytic activity of this environmentally important material. To date, however, an understanding of the mechanism underlying this improvement has been lacking. We present a density functional theory analysis of Pd- and Pt-doped CeO2, and demonstrate that the increased OSC is due to a large displacement of the dopant ions from the Ce lattice site. Pd(II)/Pt(II) (in a d8 configuration) moves by ∼1.2 Å to adopt a square-planar coordination due to crystal field effects. This leaves three three-coordinate oxygen atoms that are easier to remove, and which are the source of the increased OSC. These results highlight the importance of rationalizing the preferred coordination environments of both dopants and host cations when choosing suitable dopants for next generation catalysts.

As the thin film photovoltaic sector continues to expand, there is an emerging need to base these technologies on abundant, low cost materials in place of the expensive, rare, or toxic elements such as Te, In, or Cd that currently constitute the industry standards. To this end, the geometric and electronic structure of four materials comprising low cost, earth abundant elements (Cu3SbS3, Cu3SbSe3, Cu3BiS3, and Cu3BiSe3) are investigated with the screened hybrid exchange–correlation functional HSE06 and their candidacy for use as absorber materials assessed. The materials are shown to exhibit low VBM effective masses, due partially to the presence of lone pairs that originate from the Sb and Bi states. Although all four materials possess indirect fundamental band gaps, calculated optical absorbance shows direct transitions close in energy. Optical band gaps within the visible-light spectrum are also predicted for three of the systems, (Cu3SbSe3, Cu3BiS3 and Cu3BiSe3) making them promising candidates for PV applications.

The use of a density functional theory methodology with on-site corrections (DFT + U) has been repeatedly shown to give an improved description of localised d and f states over those predicted with a standard DFT approach. However, the localisation of electrons also carries with it the problem of metastability, due to the possible occupation of different orbitals and different locations. This study details the use of an occupation matrix control methodology for simulating localised d and f states with a plane-wave DFT + U approach which allows the user to control both the site and orbital localisation. This approach is tested for orbital occupation using octahedral and tetrahedral Ti(III) and Ce(III) carbonyl clusters and for orbital and site location using the periodic systems anatase-TiO2 and CeO2. The periodic cells are tested by the addition of an electron and through the formation of a neutral oxygen vacancy (leaving two electrons to localise). These test systems allow the successful study of orbital degeneracies, the presence of metastable states and the importance of controlling the site of localisation within the cell, and it highlights the use an occupation matrix control methodology can have in electronic structure calculations.

Experimental studies of thin-film Nb- and Ta-doped TiO2 have reported that doped anatase is highly conductive, yet doped rutile is semiconducting. Standard DFT functionals (LDA, GGA) predict that for doped anatase TiO2 the excess charge occupies the bottom of the conduction band, and is delocalised over all the Ti atoms. This has previously been proposed as the source of the experimentally observed high conductivity. GGA predicts a similar metallic system for Nb-doped rutile, however, in contradiction with experimental data that characterise doped rutile as a semiconductor with a localised gap state. This demonstrates that standard DFT functionals cannot explain the difference in experimental behaviour between polymorphs. Supplementing GGA with a “+ U” on-site Coulomb correction recovers an electronic structure for Nb-doped rutile TiO2 that is in agreement with the experimental data; a localised gap state is seen, corresponding to a small polaron on a single Ti site. GGA + U also predicts a small-polaronic Ti3+ gap state within a semiconducting system for {Nb,Ta}-doped anatase. On this basis we suggest the experimental variance between polymorphs in doped thin films is not an inherent property of the bulk crystals, but is due to other factors, e.g. additional defects or sample morphology, dependent on the synthesis history. For both anatase and rutile the defect feature is found to be insensitive to the identity of the dopant, and similar Ti3+ polarons are expected generally for doping where electrons are donated to the Ti lattice.

CuCrO2 is the most promising Cu-based delafossite for p-type optoelectronic devices. Despite this, little is known about the p-type conduction mechanism of this material, with both CuI/CuII and CrIII/CrIV hole mechanisms being proposed. In this article we examine the electronic structure, thermodynamic stability and the p-type defect chemistry of this ternary compound using density functional theory with three different approaches to the exchange and correlation; the generalized-gradient-approximation of Perdew, Burke and Ernzerhof (PBE), PBE with an additional correction for on-site Coulombic interactions (PBE + U) and the nonlocal, screened-exchange hybrid functional HSE06. The fundamental band gap of CuCrO2 is demonstrated to be indirect in nature. Under all growth conditions, the dominant intrinsic p-type defect will be the Cu vacancy, with hole formation centered solely on the Cu sublattice. Mg doping is found to be significantly lower in energy than intrinsic defect formation, explaining the large increases in conductivity seen experimentally. Cu-rich/Cr-poor growth conditions are found to be optimal for both intrinsic and extrinsic (Mg doping) defect formation, and should be adopted to maximize performance.

Lead dioxide has been studied for over 150 years as a component of the lead-acid battery. Based on first-principles calculations, we predict that by tuning the concentration of electrons in the material, through control of the defect chemistry, PbO2 can be rendered from black to optically transparent, thus opening up applications in the field of optoelectronics.