Managing the supercell approximation for charged defects in semiconductors: finite size scaling, charge correction factors, the bandgap problem and the ab initio dielectric constant

The errors arising in ab initio density functional theory studies of semiconductor point defects using the supercell approximation are analyzed. It is demonstrated that a) the leading finite size errors are inverse linear and inverse cubic in the supercell size, and b) finite size scaling over a series of supercells gives reliable isolated charged defect formation energies to around +-0.05 eV. The scaled results are used to test three correction methods. The Makov-Payne method is insufficient, but combined with the scaling parameters yields an ab initio dielectric constant of 11.6+-4.1 for InP. Gamma point corrections for defect level dispersion are completely incorrect, even for shallow levels, but re-aligning the total potential in real-space between defect and bulk cells actually corrects the electrostatic defect-defect interaction errors as well. Isolated defect energies to +-0.1 eV are then obtained using a 64 atom supercell, though this does not improve for larger cells. Finally, finite size scaling of known dopant levels shows how to treat the band gap problem: in less than about 200 atom supercells with no corrections, continuing to consider levels into the theoretical conduction band (extended gap) comes closest to experiment. However, for larger cells or when supercell approximation errors are removed, a scissors scheme stretching the theoretical band gap onto the experimental one is in fact correct.Comment: 11 pages, 3 figures (6 figure files). Accepted for Phys Rev

Structure and apparent topography of TiO2 (110) surfaces

We present self-consistent ab-initio total-energy and electronic-structure calculations on stoichiometric and non-stoichiometric TiO2 (110) surfaces. Scanning tunneling microscopy (STM) topographs are simulated by calculating the local electronic density of states over an energy window appropriate for the experimental positive-bias conditions. We find that under these conditions the STM tends to image the undercoordinated Ti atoms, in spite of the physical protrusion of the O atoms, giving an apparent reversal of topographic contrast on the stoichiometric 1x1 or missing-row 2x1 surface. We also show that both the interpretation of STM images and the direct comparison of surface energies favor an added-row structure over the missing-row structure for the oxygen-deficient 2x1 surface.Comment: 6 pages, two-column style with 5 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#ng_tio

Variational finite-difference representation of the kinetic energy operator

A potential disadvantage of real-space-grid electronic structure methods is the lack of a variational principle and the concomitant increase of total energy with grid refinement. We show that the origin of this feature is the systematic underestimation of the kinetic energy by the finite difference representation of the Laplacian operator. We present an alternative representation that provides a rigorous upper bound estimate of the true kinetic energy and we illustrate its properties with a harmonic oscillator potential. For a more realistic application, we study the convergence of the total energy of bulk silicon using a real-space-grid density-functional code and employing both the conventional and the alternative representations of the kinetic energy operator.Comment: 3 pages, 3 figures, 1 table. To appear in Phys. Rev. B. Contribution for the 10th anniversary of the eprint serve

First-principles study of spontaneous polarization in multiferroic BiFeO3_3

The ground-state structural and electronic properties of ferroelectric BiFeO$_3$ are calculated using density functional theory within the local spin-density approximation and the LSDA+U method. The crystal structure is computed to be rhombohedral with space group $R3c$, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90-100 $\mu$C/cm$^2$ is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differing by an order of magnitude from early experiments. One possible explanation is that the latter may have suffered from large leakage currents. However both past and contemporary measurements are shown to be consistent with the modern theory of polarization, suggesting that the range of reported polarizations may instead correspond to distinct switching paths in structural space. Modern measurements on well-characterized bulk samples are required to confirm this interpretation.Comment: (9 pages, 5 figures, 5 tables

Heterovalent and A-atom effects in A(B'B'')O3 perovskite alloys

Using first-principles supercell calculations, we have investigated energetic, structural and dielectric properties of three different A(B'B'')O_3 perovskite alloys: Ba(Zn_{1/3}Nb_{2/3})O_3 (BZN), Pb(Zn_{1/3}Nb_{2/3})O_3 (PZN), and Pb(Zr_{1/3}Ti_{2/3})O_3 (PZT). In the homovalent alloy PZT, the energetics are found to be mainly driven by atomic relaxations. In the heterovalent alloys BZN and PZN, however, electrostatic interactions among B' and B'' atoms are found to be very important. These electrostatic interactions are responsible for the stabilization of the observed compositional long-range order in BZN. On the other hand, cell relaxations and the formation of short Pb--O bonds could lead to a destabilization of the same ordered structure in PZN. Finally, comparing the dielectric properties of homovalent and heterovalent alloys, the most dramatic difference arises in connection with the effective charges of the B' atom. We find that the effective charge of Zr in PZT is anomalous, while in BZN and PZN the effective charge of Zn is close to its nominal ionic value.Comment: 7 pages, two-column style with 2 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#lb_he

Energetics of hydrogen impurities in aluminum and their effect on mechanical properties

The effects of hydrogen impurities in the bulk and on the surface of aluminum are theoretically investigated. Within the framework of density functional theory, we have obtained the dependence on H concentration of the stacking fault energy, the cleavage energy, the Al/H surface energy and the Al/H/Al interface formation energy. The results indicate a strong dependence of the slip energy barrier in the $[\bar 211]$ direction the cleavage energy in the [111] direction and the Al/H/Al interface formation energy, on H concentration and on tension. The dependence of the Al/H surface energy on H coverage is less pronounced, while the optimal H coverage is $\leq 0.25$ monolayer. The calculated activation energy for diffusion between high symmetry sites in the bulk and on the surface is practically the same, 0.167 eV. From these results, we draw conclusions about the possible effect of H impurities on mechanical properties, and in particular on their role in embrittlement of Al.Comment: 9 pages, 5 figure

Relative concentration and structure of native defects in GaP

The native defects in the compound semiconductor GaP have been studied using a pseudopotential density functional theory method in order to determine their relative concentrations and the most stable charge states. The electronic and atomic structures are presented and the defect concentrations are estimated using calculated formation energies. Relaxation effects are taken into account fully and produce negative-U charge transfer levels for VP and PGa. The concentration of VGa is in good agreement with the results of positron annihilation experiments. The charge transfer levels presented compare qualitatively well with experiments where available. The effect of stoichiometry on the defect concentrations is also described and is shown to be considerable. The lowest formation energies are found for PGa +2 in p-type and VGa −3 in n-type GaP under P-rich conditions, and for GaP −2 in n-type GaP under Ga-rich conditions. Finally, the finite size errors arising from the use of supercells with periodic boundary conditions are examined

First-principles study of the structural energetics of PdTi and PtTi

The structural energetics of PdTi and PtTi have been studied using first-principles density-functional theory with pseudopotentials and a plane-wave basis. We predict that in both materials, the experimentally reported orthorhombic $B19$ phase will undergo a low-temperature phase transition to a monoclinic $B19'$ ground state. Within a soft-mode framework, we relate the $B19$ structure to the cubic $B2$ structure, observed at high temperature, and the $B19'$ structure to $B19$ via phonon modes strongly coupled to strain. In contrast to NiTi, the $B19$ structure is extremely close to hcp. We draw on the analogy to the bcc-hcp transition to suggest likely transition mechanisms in the present case.Comment: 8 pages 5 figure