Hybrid Functional Scheme Research Articles

First-principles study of a pressure-induced spin transition in multiferroic Bi2FeCrO6

We report on a first-principles study of the structural, electronic, and magnetic properties of multiferroic double perovskite Bi${}_{2}$FeCrO${}_{6}$, using density functional theory within the local spin-density approximation (LSDA), the LSDA+U approximation as well as a hybrid functional scheme. We show that Bi${}_{2}$FeCrO${}_{6}$ presents two competing ferrimagnetic phases, sharing the same total magnetic moment of 2${\ensuremath{\mu}}_{B}$ per unit cell but with a different electronic configuration for the Fe${}^{3+}$ species. The phase with high-spin iron is the ground state at ambient conditions, but we predict that low-spin iron gets stabilized under compression. We also investigate the corresponding ferromagnetic phases, and show that the magnetic couplings sharply decrease when moving form high- to low-spin Fe${}^{3+}$.

Germanium core-level shifts at Ge/GeO2interfaces through hybrid functionals

The Ge core-level shift across the Ge/GeO${}_{2}$ interface is determined within semilocal and hybrid density functional schemes. We first assess the accuracy achieved within these theoretical frameworks by comparing calculated and measured core-level shifts for a set of Ge-based molecules. The comparison with experimental data results in rms deviations of 0.19 and 0.09 eV for core-level shifts calculated with semilocal and hybrid density functionals, respectively. We also compare calculated core-level shifts at the Ge(001)-$c(4\ifmmode\times\else\texttimes\fi{}2)$ surface with high-resolution x-ray photoemission spectra finding similar agreement. We then turn to the Ge/GeO${}_{2}$ interface, which we describe with atomistic superlattice models showing alternating layers of Ge and GeO${}_{2}$. The adopted models include a substoichiometric transition region in which all Ge atoms are fourfold coordinated and all O atoms are twofold coordinated, as inferred for Si/SiO${}_{2}$ interfaces. Since the calculation of core-level shifts involves charged systems subject to finite-size effects, we use two different methods to ascertain the core-level shift $\ensuremath{\Delta}{E}_{\mathrm{XPS}}$ between the oxidation state Ge${}^{0}$ and Ge${}^{+4}$ across the interface. In the first method, core-hole relaxations are first evaluated in bulk models of the interface components and then complemented by the initial-state shift calculated across the interface, while the second method consists of direct interface calculations corrected through classical electrostatics. Using the more accurate hybrid functional scheme, we obtain a shift $\ensuremath{\Delta}{E}_{\mathrm{XPS}}$ of $2.7\ifmmode\pm\else\textpm\fi{}0.1$ eV. This value is significantly lower than experimental data, which typically fall around 3.3 eV or higher, but the underestimation is consistent with that found for the valence band offset of the same model. This leads to the conclusion that the adopted model structures yield an incorrect description of the interface dipole and emphasizes that Ge/GeO${}_{2}$ interfaces possess different structural properties than their silicon counterparts.

Hybrid functional study of band structures of GaAs1−xNxand GaSb1−xNxalloys

Band structures of GaAs${}_{1\ensuremath{-}x}$N${}_{x}$ and GaSb${}_{1\ensuremath{-}x}$N${}_{x}$ alloys are studied in the framework of the density functional theory within the hybrid functional scheme (HSE06). We find that the scheme gives a clear improvement over the traditional (semi)local functionals in describing, in a qualitative agreement with experiments, the bowing of electron energy band gap in GaAs${}_{1\ensuremath{-}x}$N${}_{x}$ alloys. In the case of GaSb${}_{1\ensuremath{-}x}$N${}_{x}$ alloys, the hybrid functional used makes the study of band structures possible ab initio without any empirical parameter fitting. We explain the trends in the band gap reductions in the two materials that result mainly from the positions of the nitrogen-induced states with respect to the bottoms of the bulk conduction bands.

The performance and relationship among range-separated schemes for density functional theory

The performance and relationship among different range-separated (RS) hybrid functional schemes are examined using the Coulomb-attenuating method (CAM) with different values for the fractions of exact Hartree-Fock (HF) exchange (α), long-range HF (β), and a range-separation parameter (μ), where the cases of α + β = 1 and α + β = 0 were designated as CA and CA0, respectively. Attenuated PBE exchange-correlation functionals with α = 0.20 and μ = 0.20 (CA-PBE) and α = 0.25 and μ = 0.11 (CA0-PBE) are closely related to the LRC-ωPBEh and HSE functionals, respectively. Time-dependent density functional theory calculations were carried out for a number of classes of molecules with varying degrees of charge-transfer (CT) character to provide an assessment of the accuracy of excitation energies from the CA functionals and a number of other functionals with different exchange hole models. Functionals that provided reasonable estimates for local and short-range CT transitions were found to give large errors for long-range CT excitations. In contrast, functionals that afforded accurate long-range CT excitation energies significantly overestimated energies for short-range CT and local transitions. The effects of exchange hole models and parameters developed for RS functionals for CT excitations were analyzed in detail. The comparative analysis across compound classes provides a useful benchmark for CT excitations.

Defect levels through hybrid density functionals: Insights and applications

AbstractHybrid density functional calculations applied to defect charge transition levels are explored in the attempt to overcome the band‐gap problem of semilocal density functionals. Charge transition levels of a large set of point defects calculated with semilocal and hybrid density functionals are found to correspond closely when aligned with respect to the average electrostatic potential. This strongly suggests that the defect levels defined in this way are already accurately described at these levels of theory. In particular, this then also applies to the energy separation between different defect levels, which is directly accessible experimentally. At variance, within the same alignment scheme, the band edges obtained with hybrid functionals are found to undergo significant shifts with respect to those obtained with semilocal functionals. While these shifts systematically give larger band gaps, the agreement with experiment is not always satisfactory when a fixed fraction of exact exchange is admixed. This describes a current limitation of hybrid functional schemes. In the attempt of identifying a viable theoretical description within the class of one‐parameter hybrid functionals based on bare exchange, we explore the validity of the empirical procedure which consists in tuning the fraction of nonlocal exchange to a value which gives a theoretical band gap reproducing the experimental one. Comparisons with experiment for band offsets and specific defect levels record very encouraging results. Despite its inherent limitations, such an empirical scheme based on hybrid functionals represents a definite improvement with respect to semilocal functionals.

Alignment of defect levels and band edges through hybrid functionals: Effect of screening in the exchange term

We investigate how various treatments of exact exchange affect defect charge transition levels and band edges in hybrid functional schemes for a variety of systems. We distinguish the effects of long-range vs short-range exchange and of local vs nonlocal exchange. This is achieved by the consideration of a set of four functionals, which comprise the semilocal Perdew-Burke-Ernzerhof (PBE) functional, the PBE hybrid (PBE0), the Heyd-Scuseria-Ernzerhof (HSE) functional, and a hybrid derived from PBE0 in which the Coulomb kernel in the exact exchange term is screened as in the HSE functional but which, unlike HSE, does not include a local expression compensating for the loss of the long-range exchange. We find that defect levels in PBE0 and in HSE almost coincide when aligned with respect to a common reference potential, due to the close total-energy differences in the two schemes. At variance, the HSE band edges determined within the same alignment scheme are found to shift significantly with respect to the PBE0 ones: the occupied and the unoccupied states undergo shifts of about +0.4 eV and -0.4 eV, respectively. These shifts are found to vary little among the materials considered. Through a rationale based on the behavior of local and nonlocal long-range exchange, this conclusion is generalized beyond the class of materials used in this study. Finally, we explicitly address the practice of tuning the band gap by adapting the fraction of exact exchange incorporated in the functional. When PBE0-like and HSE-like functionals are tuned to yield identical band gaps, their respective results for the positions of defect levels within the band gap and for the band alignments at interfaces are found to be very close.

A hybrid functional scheme for defect levels and band alignments at semiconductor–oxide interfaces

AbstractWe introduce a theoretical scheme to study defect energy levels and band alignments at semiconductor–oxide interfaces. The scheme relies on hybrid functionals to overcome the band gap underestimation typically achieved with semilocal density functionals. For atomically localized defects, the more accurate description achieved with hybrid functionals does not lead to significant shifts of the charge transition levels, provided these levels are referred to a common reference potential. This result effectively decouples the shifts of the band edges with respect to the defect levels. We also show that relative shifts of conduction and valence band edges as determined by exact nonlocal exchange lead to band offsets in excellent agreement with experimental values for several semiconductor–oxide interfaces. The proposed scheme is illustrated through a series of applications, including the dangling bond defects in silicon and germanium, the charge state of the O2 molecule during silicon oxidation, and the oxygen vacancy in Si–SiO2–HfO2 stacks.