Intrinsic Oxygen Vacancy and Extrinsic Aluminium Dopant Interplay: A Route to the Restoration of Defective TiO2_2

Density functional theory (DFT) and DFT corrected for on-site Coulomb interactions (DFT+U) calculations are presented on Aluminium doping in bulk TiO$_2$ and the anatase (101) surface. Particular attention is paid to the mobility of oxygen vacancies throughout the doped TiO$_2$ lattice, as a means by which charge compensation of trivalent dopants can occur. The effect that Al doping of TiO$_2$ electrodes has in dye sensitised solar cells is explained as a result of this mobility and charge compensation. Substitutional defects in which one Al3+ replaces one Ti4+ are found to introduce valence band holes, while intrinsic oxygen vacancies are found to introduce states in the band-gap. Coupling two of these substitutional defects with an oxygen vacancy results in exothermic defect formation which maintain charge neutrality. Nudged elastic band calculations have been performed to investigate the formation of these clustered defects in the (101) surface by oxygen vacancy diffusion, with the resulting potential energy surface suggesting energetic gains with small diffusion barriers. Efficiency in- creases observed in dye sensitised solar cells as a result of aluminium doping of TiO$_2$ electrodes are investigated by adsorbing the tetrahydroquinoline C2-1 chromophore on the defective surfaces. Adsorption on the clustered extrinsic Al3+ and intrinsic oxygen vacancy defects are found to behave as if adsorbed on a clean surface, with vacancy states not present, while adsorption on the oxygen vacancy results in a down shift of the dye localised states within the band-gap and defect states being present below the conduction band edge. Aluminium doping therefore acts as a benign dopant for 'cleaning' TiO$_2$ through oxygen vacancy diffusion.Comment: 32 pages, 15 figures, accepted for publication by J. Phys. Chem.

DSSC Anchoring Groups: A Surface Dependent Decision

Electrodes in dye sensitised solar cells (DSSCs) are typically nanocrystalline anatase TiO2 with a majority (101) surface exposed. Generally the sensitising dye employs a carboxylic anchoring moiety through which it adheres to the TiO2 surface. Recent interest in exploiting the properties of differing TiO2 electrode morphologies, such as rutile nanorods exposing the (110) surface and anatase electrodes with high percentages of the (001) surface exposed, begs the question of whether this anchoring strategy is best, irrespective of the majority surface exposed. Here we address this question by presenting density functional theory calculations contrasting the binding properties of two promising anchoring groups, phosphonic acid and boronic acid, to that of carboxylic acid. Anchor-electrode interactions are studied for the pro- totypical anatase (101) surface, along with the anatase (001) and rutile (110) surfaces. Finally the effect of using these alternative anchoring groups to bind a typical coumarin dye (NKX- 2311) to these TiO2 substrates is examined. Significant differences in the binding properties are found depending on both the anchor and surface, illustrating that the choice of anchor is necessarily dependent upon the surface exposed in the electrode. In particular the boronic acid is found to show the potential to be an excellent anchor choice for electrodes exposing the anatase (001) surface.Comment: 44 pages, 15 figures, accepted by J. Phys.:Condens. Matter. Coordinates for structures available via figshar

Linear Scaling Density Matrix Real Time TDDFT: Propagator Unitarity \& Matrix Truncation

Real time, density matrix based, time dependent density functional theory proceeds through the propagation of the density matrix, as opposed to the Kohn-Sham orbitals. It is possible to reduce the computational workload by imposing spatial cut-off radii on sparse matrices, and the propagation of the density matrix in this manner provides direct access to the optical response of very large systems, which would be otherwise impractical to obtain using the standard formulations of TDDFT. Following a brief summary of our implementation, along with several benchmark tests illustrating the validity of the method, we present an exploration of the factors affecting the accuracy of the approach. In particular we investigate the effect of basis set size and matrix truncation, the key approximation used in achieving linear scaling, on the propagator unitarity and optical spectra. Finally we illustrate that, with an appropriate density matrix truncation range applied, the computational load scales linearly with the system size and discuss the limitations of the approach.Comment: Accepted for publication in J. Chem. Phy

Reaction paths of alane dissociation on the Si(001) surface

Building on our earlier study, we examine the kinetic barriers to decomposition of alane, AlH$_3$, on the Si(001) surface, using the nudged elastic band (NEB) approach within DFT. We find that the initial decomposition to AlH with two H atoms on the surface proceeds without a significant barrier. There are several pathways available to lose the final hydrogen, though these present barriers of up to 1 eV. Incorporation is more challenging, with the initial structures less stable in several cases than the starting structures, just as was found for phosphorus. We identify a stable route for Al incorporation following selective surface hydrogen desorption (e.g. by STM tip). The overall process parallels PH$_3$, and indicates that atomically precise acceptor doping should be possible.Comment: 19 pages, 8 figures, submitted to J. Physics.: Condens. Matte

Alane adsorption and dissociation on the Si(001) surface

We used DFT to study the energetics of the decomposition of alane, AlH3, on the Si(001) surface, as the acceptor complement to PH3. Alane forms a dative bond with the raised atoms of silicon surface dimers, via the Si atom lone pair. We calculated the energies of various structures along the pathway of successive dehydrogenation events following adsorption: AlH2, AlH and Al, finding a gradual, significant decrease in energy. For each stage, we analyse the structure and bonding, and present simulated STM images of the lowest energy structures. Finally, we find that the energy of Al atoms incorporated into the surface, ejecting a Si atom, is comparable to Al adatoms. These findings show that Al incorporation is likely to be as precisely controlled as P incorporation, if slightly less easy to achieve.Comment: Submitted to J. Phys.: Condens. Matte

Stable and Efficient Linear Scaling First-Principles Molecular Dynamics for 10,000+ atoms

The recent progress of linear-scaling or O(N) methods in the density functional theory (DFT) is remarkable. We expect that first-principles molecular dynamics (FPMD) simulations based on DFT can now treat more realistic and complex systems using the O(N) technique. However, very few examples of O(N) FPMD simulations exist so far and the information for the accuracy or reliability of the simulations is very limited. In this paper, we show that efficient and robust O(N) FPMD simulations are now possible by the combination of the extended Lagrangian Born-Oppenheimer molecular dynamics method, which was recently proposed by Niklasson et al (Phys. Rev. Lett. 100, 123004 (2008)), and the density matrix method as an O(N) technique. Using our linear-scaling DFT code Conquest, we investigate the reliable calculation conditions for the accurate O(N) FPMD and demonstrate that we are now able to do actual and reliable self-consistent FPMD simulation of a very large system containing 32,768 atoms.Comment: 26 pages, 10 figures, accepted by J. Chem. Theory Compu

Hydrogen adsorption and diffusion around Si(001)/Si(110) corners in nanostructures

While the diffusion of hydrogen on silicon surfaces has been relatively well characterised both experimentally and theoretically, the diffusion around corners between surfaces, as will be found on nanowires and nanostructures, has not been studied. Motivated by nanostructure fabrication by Patterned Atomic Layer Epitaxy (PALE), we present a density functional theory (DFT) study of the diffusion of hydrogen around the edge formed by the orthogonal (001) and (110) surfaces in silicon. We find that the barrier from (001) to (110) is approximately 0.3 eV lower than from (110) to (001), and that it is comparable to diffusion between rows on the clean surface, with no significant effect on the hydrogen patterns at the growth temperatures used.Comment: 11 pages, 4 figure