Quasiparticle Energy Calculations Research Articles

Simple Approximate Physical Orbitals forGWQuasiparticle Calculations

Generating unoccupied orbitals within density functional theory (DFT) for use in GW calculations of quasiparticle energies becomes prohibitive for large systems. We show that, without any loss of accuracy, the unoccupied orbitals may be replaced by a set of simple approximate physical orbitals made from appropriately prepared plane waves and localized basis DFT orbitals that represent the continuum and resonant states of the system, respectively. This approach allows for accurate quasiparticle calculations using only a very small number of unoccupied DFT orbitals, resulting in an order of magnitude gain in speed.

Electronic Structure of O-vacancy in High-kDielectrics and Oxide Semiconductors

ABSTRACTFirst-principles density functional calculations are performed to investigate the electronic properties of O-vacancy defects in high-kHfO2, Si/HfO2interface, and amorphous oxide semiconductors. The role of O-vacancy in device performance is discussed by comparing the results of the GGA, hybrid density functional, and quasiparticle energy calculations.

Band parameters and strain effects in ZnO and group-III nitrides

We present consistent sets of band parameters (including band gaps, crystal-field splittings, effective masses, Luttinger and EP parameters) for AlN, GaN, InN and ZnO in the wurtzite phase. For band-energy differences we observe a pronounced nonlinear dependence on strain. Consistent and complete sets of deformation potentials are then derived for realistic strain conditions in the linear regime around the experimental equilibrium volume. To overcome the limitations of density-functional theory in the local-density and generalized-gradient approximations we employ the Heyd–Scuseria–Ernzerhof hybrid functional as well as exact exchange (OEPx)-based quasi-particle energy calculations in the G0W0 approach.

Enhanced static approximation to the electron self-energy operator for efficient calculation of quasiparticle energies

An enhanced static approximation for the electron self-energy operator is proposed for efficient calculation of quasiparticle energies. Analysis of the static Coulomb-hole screened-exchange (COHSEX) approximation originally proposed by Hedin shows that most of the error derives from the short-wavelength contributions of the assumed adiabatic accumulation of the Coulomb hole. A wave-vector-dependent correction factor can be incorporated as the basis for a new static approximation. This factor can be approximated by a single scaling function, determined from the homogeneous electron-gas model. The local field effect in real materials is captured by a simple ansatz based on symmetry consideration. As inherited from the COHSEX approximation, the new approximation presents a Hermitian self-energy operator and the summation over empty states is eliminated from the evaluation of the self-energy operator. Tests were conducted comparing the new approximation to GW calculations for diverse materials ranging from crystals, molecules, atoms and a carbon nanotube. The accuracy for the minimum gap is about 10% or better. Like in the COHSEX approximation, the occupied bandwidth is overestimated.

Charged Oxygen Defects inSiO2: Going beyond Local and Semilocal Approximations to Density Functional Theory

The long-standing problem of the oxygen self-diffusion mechanism in silicon dioxide, a prototypical oxide, both in the crystalline and in the amorphous phase, is studied from first principles. We demonstrate that the widely used local-density approximation to density functional theory (DFT) predicts a kinetic behavior of oxygen in strong disagreement with available experiments. Applying a recently developed scheme that combines DFT with quasiparticle energy calculations in the G0W0 approximation considerably improves defect energetics and gives gratifying agreement with experiment.

Controlling Polarization at Insulating Surfaces: Quasiparticle Calculations for Molecules Adsorbed on Insulator Films

By means of quasiparticle-energy calculations in the G0W0 approach, we show for the prototypical insulator-semiconductor system NaCl/Ge(001) that polarization effects at the interfaces noticeably affect the excitation spectrum of molecules adsorbed on the surface of the NaCl films. The magnitude of the effect can be controlled by varying the thickness of the film, offering new opportunities for tuning electronic excitations in, e.g., molecular electronics or quantum transport. Polarization effects are visible even for the excitation spectrum of the NaCl films themselves, which has important implications for the interpretation of surface science experiments for the characterization of insulator surfaces.

Charge-transition levels of oxygen vacancy as the origin of device instability in HfO2 gate stacks through quasiparticle energy calculations

We perform quasiparticle energy calculations to study the charge-transition levels of oxygen vacancy (VO) in HfO2. The negative-U property of VO can explain flat band voltage shifts and threshold voltage (Vth) instability in hafnium based devices. In p+ Si gate electrode, the Fermi level pinning varies by up to 0.55 eV, in good agreement with the measured values. Depending on gate bias, VO traps electrons or holes from the Si channel, causing the Vth instability. It is suggested that short time-scale charge trapping/detrapping is due to metastable VO−1 centers, whereas stable VO−2 centers dominate long time-scale instability.

Defect Formation Energies without the Band-Gap Problem: Combining Density-Functional Theory and theGWApproach for the Silicon Self-Interstitial

We present an improved method to calculate defect formation energies that overcomes the band-gap problem of Kohn-Sham density-functional theory (DFT) and reduces the self-interaction error of the local-density approximation (LDA) to DFT. We demonstrate for the silicon self-interstitial that combining LDA with quasiparticle energy calculations in the G0W0 approach increases the defect formation energy of the neutral charge state by approximately 1.1 eV, which is in good agreement with diffusion Monte Carlo calculations (E. R. Batista, Phys. Rev. B 74, 121102(R) (2006)10.1103/PhysRevB.74.121102; W.-K. Leung Phys. Rev. Lett. 83, 2351 (1999)10.1103/PhysRevLett.83.2351). Moreover, the G0W0-corrected charge transition levels agree well with recent measurements.

Calculation of Quasi-Particle Energies of Aromatic Self-Assembled Monolayers on Au(111)

We present many-body perturbation theory calculations of the electronic properties of phenylene diisocyanide self-assembled monolayers (SAMs) on a gold surface. Using structural models obtained within density functional theory (DFT), we have investigated how the SAM molecular energies are modified by self-energy corrections and how they are affected by the presence of the surface. We have employed a combination of GW (G = Green's function; W = screened Coulomb interaction) calculations of the SAM quasi-particle energies and a semiclassical image potential model to account for surface polarization effects. We find that it is essential to include both quasi-particle corrections and surface screening in order to provide a reasonable estimate of the energy level alignment at a SAM-metal interface. In particular, our results show that within the GW approximation the energy distance between phenylene diisocyanide SAM energy levels and the gold surface Fermi level is much larger than that found within DFT, e.g., more than double in the case of low packing densities of the SAM.

Back Cover: phys. stat. sol. (b) 245/5

AbstractThe authors of this issue's Editor's Choice (pp. 929–945) present the combination of quasiparticle energy calculations in the G0W0 approximation with DFT calculations in the exact‐exchange (OEPx(cLDA)) approach. Using OEPx(cLDA) instead of LDA or GGA removes the inherent self‐interaction of the latter from the ground state calculation. For ScN (the illustration on the back cover shows the charge density difference (OEPx(cLDA)–LDA)) this gives rise to a more attractive exchange potential and a higher charge density around the nitrogen sites. OEPx(cLDA) thus constitutes a better starting point for band structure calculations in first order perturbation theory using the G0W0 approximation. Combined, OEPx(cLDA) and G0W0 provide a description of the electronic structure that overcomes the deficiencies of LDA based approaches. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Exciting prospects for solids: Exact‐exchange based functionals meet quasiparticle energy calculations

AbstractFocussing on spectroscopic aspects of semiconductors and insulators we will illustrate how quasiparticle energy calculations in the G0W0 approximation can be successfully combined with density‐functional theory calculations in the exact‐ exchange optimised effective potential approach (OEPx) to achieve a first principles description of the electronic structure that overcomes the limitations of local‐ or gradient‐corrected DFT functionals (LDA and GGA). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dielectric Properties of Ice and Liquid Water from First-Principles Calculations

We present a first-principles study of the static dielectric properties of ice and liquid water. The eigenmodes of the dielectric matrix E are analyzed in terms of maximally localized dielectric functions similar, in their definition, to maximally localized Wannier orbitals obtained from Bloch eigenstates of the electronic Hamiltonian. We show that the lowest eigenmodes of E (-1) are localized in real space and can be separated into groups related to the screening of lone pairs, intra-, and intermolecular bonds, respectively. The local properties of the dielectric matrix can be conveniently exploited to build approximate dielectric matrices for efficient, yet accurate calculations of quasiparticle energies.

Vertex corrections in localized and extended systems

Within many-body perturbation theory, we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a Kohn-Sham Green's function constructed from density-functional theory in the local-density approximation. The vertex appears in two places---in the screened Coulomb interaction $W$ and in the self-energy $\ensuremath{\Sigma}$---and we obtain a systematic discrimination of these two effects by turning the vertex in $\ensuremath{\Sigma}$ on and off. We also make comparisons to standard $GW$ results within the usual random-phase approximation, which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate little improvement over standard $GW$. For jellium, we observe marked improvement in the quasiparticle bandwidth when the vertex is included only in $W$, whereas turning on the vertex in $\ensuremath{\Sigma}$ leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in $W$ is a valid way to improve quasiparticle energy calculations, while the vertex in $\ensuremath{\Sigma}$ is unphysical, and points the way to the development of improved vertices for ab initio electronic structure calculations.

Exact-exchange-based quasiparticle energy calculations for the band gap, effective masses, and deformation potentials of ScN

The band gaps, longitudinal and transverse effective masses, and deformation potentials of ScN in the rock-salt structure have been calculated employing G0W0-quasiparticle calculations using exact-exchange Kohn-Sham density functional theory one-particle wavefunctions and energies as input. Our quasiparticle gaps support recent experimental observations that ScN has a much lower indirect band gap than previously thought. The results are analyzed in terms of the influence of different approximations for exchange and correlation taken in the computational approach on the electronic structure of ScN.

Band gap and band parameters of InN and GaN from quasiparticle energy calculations based on exact-exchange density-functional theory

The authors have studied the electronic structure of InN and GaN employing G0W0 calculations based on exact-exchange density-functional theory. For InN their approach predicts a gap of 0.7eV. Taking the Burnstein-Moss effect into account, the increase of the apparent quasiparticle gap with increasing electron concentration is in good agreement with the observed blueshift of the experimental optical absorption edge. Moreover, the concentration dependence of the effective mass, which results from the nonparabolicity of the conduction band, agrees well with recent experimental findings. Based on the quasiparticle band structure the parameter set for a 4×4k∙p Hamiltonian has been derived.

Implementation and performance of the frequency-dependentGWmethod within the PAW framework

Algorithmic details and results of fully frequency-dependent ${G}_{0}{W}_{0}$ calculations are presented. The implementation relies on the spectral representation of the involved matrices and their Hilbert or Kramers-Kronig transforms to obtain the polarizability and self-energy matrices at each frequency. Using this approach, the computational time for the calculation of polarizability matrices and quasiparticle energies is twice as that for a single frequency, plus Hilbert transforms. In addition, the implementation relies on the PAW method, which allows to treat $d$-states with relatively modest effort and permits the reevaluation of the core-valence interaction on the level of the Hartree-Fock approximation. Tests performed on an $sp$ material (Si) and materials with $d$ electrons (GaAs and CdS) yield quasiparticle energies that are very close to previous all-electron pseudopotential and all-electron full-potential linear muffin-tin-orbital calculations.

Quasiparticle energy bands of NiO in theGWapproximation

We present a first-principles study of the quasiparticle excitations spectrum of NiO. The calculations are performed using the spin-polarized GW approximation in a plane-wave basis set with ab initio pseudopotentials. We find a feature in the band structure which can explain both an absorption edge of 3.1 eV in optical measurements and an energy gap of 4.3 eV found in XPS/BIS measurements. The calculated quasiparticle density of states shows that the oxygen 2p peaks overlap with the satellite structure at similar to 8 eV below the Fermi level. Finally, we discuss the difference between this work and two previous quasiparticle energy calculations.

Combining GW calculations with exact-exchange density-functional theory: an analysis of valence-band photoemission for compound semiconductors

We report quasi-particle energy calculations of the electronic bandstructure as measured by valence-band photoemission for selected II–VI compounds and group III nitrides. By applying GW as perturbation to the ground state of the fictitious, non-interacting Kohn–Sham electrons of density-functional theory (DFT), we systematically study the electronic structure of zinc-blende GaN, ZnO, ZnS and CdS. Special emphasis is put on analysing the role played by the cation semicore d-electrons that are explicitly included as valence electrons in our pseudo-potential approach. Unlike in the majority of previous GW studies, which are almost exclusively based on ground state calculations in the local-density approximation (LDA), we combine GW with exact-exchange DFT calculations in the optimized-effective potential approach (OEPx). This is a much more elaborate and computationally expensive approach. However, we show that applying the OEPx approach leads to an improved description of the d-electron hybridization compared to the LDA. Moreover, we find that it is essential to use OEPx pseudo-potentials in order to treat core–valence exchange consistently. Our OEPx-based quasi-particle valence bandstructures are in good agreement with available photoemission data in contrast to the ones based on the LDA. We therefore conclude that for these materials, OEPx constitutes the better starting point for subsequent GW calculations.

Band gaps and quasiparticle energy calculations on ZnO, ZnS, and ZnSe in the zinc-blende structure by theGWapproximation

We have calculated the quasiparticle band gaps of ZnO, ZnS, and ZnSe in zinc-blende structure within the GW approximation using a full random-phase approximation dielectric matrix. The linear muffin-tin orbital basis was used for this calculation and the $3d$ orbitals of the Zn atom were treated as valence band in every case. The calculated band gaps are 3.59, 3.97, and 3.10 eV for ZnO, ZnS, and ZnSe, respectively. The gaps of ZnS and ZnSe are in good agreement with the experimental values and so is the gap of ZnO if we compare it with the experimental optical gap of wurtzite ZnO.

Multi-quasiparticle potential-energy surfaces

Diabatic-blocking calculations, with inclusion of γ-deformation, are performed for the first time. Significant configuration dependence is found for multi-quasiparticle potential-energy surfaces. The calculations of quasiparticle energies require a renormalised pairing strength which includes shape and blocking effects in reproducing experimental odd-even mass differences. The detailed excitation energies known in 178W are well reproduced. For the 182Os K π =25 + isomer, the calculation shows | γ|≈10° and the obtained quadrupole moment agrees with the measured value.