Effect of improved band-gap description in density functional theory on defect energy levels in alpha-quartz

We compare defect energy levels of point defects in alpha-quartz using density functionals of different accuracy: a standard generalized-gradient-approximation functional and a hybrid functional. The latter is known to improve the description of band gaps through the incorporation of a fraction of Hartree-Fock exchange. The separations between the defect levels are found to be preserved when going from the standard to the more accurate hybrid functional, indicating that they are already well described with the standard functional. We also find that the defect wave functions obtained with the two functionals are very similar. Consequently, the defect energy levels pertaining to the hybrid functional can be obtained through the perturbational method. (C) 2007 Elsevier B.V. All rights reserved.

Adjustable potential probes for band-gap predictions of extended systems through nonempirical hybrid functionals

Thomas Bischoff, Alfredo Pasquarello, Igor Reshetnyak

We describe a nonempirical procedure for achieving accurate band gaps of extended systems through the insertion of suitably defined potential probes. By enforcing Koopmans' condition on the resulting localized electronic states, we determine the optimal fraction of Fock exchange to be used in the adopted hybrid functional. As potential probes, we consider point defects, the hydrogen interstitial, and various adjustable potentials that allow us to vary the energy level of the localized state in the band gap. By monitoring the delocalized screening charge, we achieve a measure of the degree of hybridization with the band states, which can be used to improve the band-gap estimate. Application of this methodology to AlP, C, and MgO yields band gaps differing by less than 0.2 eV from experiment.

2019

Structural and electronic properties of an abrupt 4H-SiC(0001)/SiO2 interface model: Classical molecular dynamics simulations and density functional calculations

Peter Broqvist, Fabien Devynck, Alfredo Pasquarello

Using a density functional approach, we study structural and electronic properties of the 4H(0001)-SiC/SiO2 interface. Through the sequential use of classical and ab initio simulation methods, we generate an abrupt model structure which describes the transition between crystalline SiC and amorphous SiO2 without showing any coordination defect. The first step in our generation procedure consists in identifying suitable interfacial bonding patterns which account for the bond density reduction across the interface. In the second step, the connection to amorphous SiO2 is achieved through classical molecular dynamics. The atomic positions are then relaxed within a generalized gradient approximation of density functional theory. The final model structure shows good structural parameters and an oxide density typical of amorphous SiO2. We investigate the electronic structure of the generated model interface through the local density of states obtained with hybrid density functionals. In our atomically abrupt interface model, the full oxide band gap is recovered at a distance of similar to 5 A from the interface. This extent is in good agreement with estimates derived from internal photoemission measurements and provides support for the abrupt nature of the interface. We obtained band offsets through two different procedures: by evaluating the local density of states and by aligning the band extrema through the local electrostatic potential. Band offsets calculated with various functionals are compared to experimental values. The best agreement is achieved for a hybrid functional in which a screened Coulomb potential is used in the Hartree-Fock exchange term. For this case, the calculated band offsets underestimate the experimental values by similar to 25%, but agree with experiment within a few percent when expressed with respect to the oxide band gap.

2007

Hybrid-functional calculations with plane-wave basis sets: Effect of singularity correction on total energies, energy eigenvalues, and defect energy levels

Audrius Alkauskas, Peter Broqvist, Alfredo Pasquarello

When described through a plane-wave basis set, the inclusion of exact nonlocal exchange in hybrid functionals gives rise to a singularity, which slows down the convergence with the density of sampled k points in reciprocal space. In this work, we investigate to what extent the treatment of the singularity through the use of an auxiliary function is effective for k-point samplings of limited density, in comparison to analogous calculations performed with semilocal density functionals. Our analysis applies, for instance, to calculations in which the Brillouin zone is sampled at the sole Gamma point, as often occurs in the study of surfaces, interfaces, and defects or in molecular-dynamics simulations. In the adopted formulation, the treatment of the singularity results in the addition of a correction term to the total energy. The energy eigenvalue spectrum is affected by a downwards shift in the energy eigenvalues of the occupied states, while those of the unoccupied states remain unaffected. Analogous corrections also speed up the convergence of screened exchange interactions despite the absence of a proper singularity. Focusing first on neutral systems, both finite and extended, we show that the account of the singularity corrections bears convergence properties which are quantitatively similar to those observed with semilocal density functionals. We emphasize that this is not the case for uncorrected energies, particularly for elongated simulation cells for which qualitatively different trends are found. We then consider differences between total energies of systems differing by their charge state. For systems involving localized electron states, such as ionization potentials and electron affinities of molecular systems or charge transition levels of point defects, the proper account of the singularity correction yields convergence properties which are similar to those of neutral systems. In the case of extended systems, such energy differences provide an alternative way to determine the band edges, but are found to converge more slowly with simulation cells than in corresponding semilocal functionals because of the exchange self-interaction associated to the extra charge.