Band-edge problem in the theoretical determination of defect energy levels: The O vacancy in ZnO as a benchmark case

Calculations of formation energies and charge transition levels of defects routinely rely on density functional theory (DFT) for describing the electronic structure. Since bulk band gaps of semiconductors and insulators are not well described in semilocal approximations to DFT, band-gap correction schemes or advanced theoretical models, which properly describe band gaps, need to be employed. However, it has become apparent that different methods that reproduce the experimental band gap can yield substantially different results regarding charge transition levels of point defects. We investigate this problem in the case of the (+2/0) charge transition level of the O vacancy in ZnO, which has attracted considerable attention as a benchmark case. For this purpose, we first perform calculations based on nonscreened hybrid density functionals, and then compare our results with those of other methods. While our results agree very well with those obtained with screened hybrid functionals, they are strikingly different compared to those obtained with other band-gap-corrected schemes. Nevertheless, we show that all the different methods agree well with each other and with our calculations when a suitable alignment procedure is adopted. The proposed procedure consists in aligning the electron band structure through an external potential, such as the vacuum level. When the electron densities are well reproduced, this procedure is equivalent to an alignment through the average electrostatic potential in a calculation subject to periodic boundary conditions. We stress that, in order to give accurate defect levels, a theoretical scheme is required to yield not only band gaps in agreement with experiment, but also band edges correctly positioned with respect to such a reference potential.

First-principles determination of defect energy levels through hybrid density functionals and GW

Wei Chen, Alfredo Pasquarello

In this topical review, we discuss recent progress in electronic-structure methods for calculating defect energy levels in semiconductors and insulators. We concentrate mainly on two advanced electronic-structure schemes, namely hybrid density functional theory and many-body perturbation theory in the GW approximation. These two schemes go beyond standard density functional theory in the semilocal approximation providing a more realistic description of band gaps. In particular, we address important aspects underlying the GW scheme and highlight the correspondence between the defect levels as obtained in the various schemes. We further assess the quality of the band-edge positions determined with hybrid functionals and GW through the calculation of band-offsets at semiconductor heterojunctions and of ionization potentials at semiconductor surfaces.

Institute of Physics2015

Crystalline and correlated phases in two-dimensional transition metal dichalcogenides

Diego José Pasquier

This thesis is dedicated to the study of various aspects of the electronic structure of two-dimensional transition metal dichalcogenides (TMDs) of chemical composition MX

_2

(where M is a transition metal atom and X= S, Se, Te), using a combination of \textit{ab inito} density-functional methods. We first address the relative stability of the

1T

and

1H

phases of two-dimensional TMDs as a function of the column of the transition metal atom in the periodic table. Using a Wannier-function approach, we calculate crystal field and ligand field parameters for a broad range of members of this family of materials. Taking TaS

_2

as an example, we show how the splitting of the

d

electron states arises from an interplay of electrostatic effects and hybridization with the ligands'

s

p

and

d

states. We show that the ligand field alone cannot explain the stabilization of the

1H

polymorph for

d^1

and

d^2

TMDs, and that band structure effects are dominant. We present trends of the calculated parameters across the periodic table, and argue that these allow developing simple chemical intuition. Secondly, we study the occurrence of charge density wave phases and periodic lattice distortion in metallic

1T

transition metal dichalcogenides. The phonon dispersion and fermiology of representative examples with different

d

electron counts are studied as a function of doping. Two qualitatively different behaviours are found as a function of the filling of the

t_{2g}

subshell. We argue that away from half-filling, weak-coupling nesting arguments are a useful starting point for understanding, whereas closer to half-filling a strong-coupling real-space picture is more correct. Using Wannier functions, it is shown that strong metal-metal bonds are formed and that simple bond-counting arguments apply. Thirdly, the recently synthesized

1T

phase of NbSe

_2

, in monolayer form, is investigated from first principles. We find that

1T

-NbSe

_2

is unstable towards the formation of an incommensurate charge density wave phase, whose periodicity can be understood from the Fermi surface topology. We investigate different scenarios for the experimentally observed superlattice and insulating behaviour, and conclude that the star-of-David phase is the most stable commensurate charge density wave phase. We study the electronic properties of the star-of-David phase at various levels of theory and confirm its Mott insulating character, as speculated and in analogy with TaS

_2

. The Heisenberg exchange couplings are found to be ferromagnetic, which suggests a parallel with the so-called flat-band ferromagnetism in certain multiband Hubbard models. Finally, we address the possibility of the occurrence of the excitonic insulator phase in single-layer TiSe

_2

. The relative role of electron-electron and electron-phonon interactions in driving the charge density wave in layered and two-dimensional TiSe

_2

has been disputed and is still unresolved. We calculate the electronic structure and finite-momentum exciton spectrum from hybrid density functional theory. We find that in a certain range of parameters, excitonic effects are strong and the material is close to a pure excitonic insulator instability. A possible necessary condition for the physical realization of a pure excitonic insulator is proposed.

EPFL2019

Alignment of energy levels in amorphous oxides and at semiconductor-water interfaces

Zhendong Guo

We conduct a detailed investigation of defects in two representative amorphous oxides: amorphous Al2O3 (am-Al2O3) and TiO2 (am-TiO2), by combining ab initio molecular dynamics (MD) simulations and hybrid functional calculations. Our results indicate that oxygen vacancies and interstitials occur neither in am-Al2O3 nor in am-TiO2 due to structural rearrangements which assimilate the defect structure, and that the injection of extra holes can lead to the formation of O-O peroxy linkages. In am-Al2O3, hydrogen is found to be amphoteric. Based on localized Wannier functions, we identify the nominal charge state and the composition of the defect core units related to C and N impurities in am-Al2O3, which are found to depend on the total charge set in the simulation cell. Through the adopted electron counting rule, we assess that carbon and nitrogen impurities are only found in neutral and in singly positive charge states, respectively, indicating that none of them gives charge transition levels in am-Al2O3. In addition, those defect core units are shown to incorporate a varying number of oxygen atoms, by which their formation energy is dependent on the oxygen chemical potential. In addition, we propose an exchange mechanism for hole transport in am-TiO2 that relies on the simultaneous breaking and forming of O-O peroxy linkages that share one O atom. Through the use of nudged-elastic-band calculations, a hopping path as long as 1.2 nm with barriers of 0.3-0.5 eV is demonstrated, suggesting that hole diffusion through O-O peroxy linkages is viable in am-TiO2. In this work, we also determine the band alignment between various semiconductors and liquid water by combining MD simulations of atomistic interface models, electronic-structure calculations at the hybrid-functional and GW levels, and a computational standard hydrogen electrode (SHE). Our study comprises GaAs, GaP, GaN, CdS, ZnO, SnO2, rutile and anatase TiO2. For each semiconductor, we generate atomistic interface models with liquid water at the pH corresponding to the point of zero charge. The MD simulations are started from initial configurations, in which the water molecules are either molecularly (m) or dissociatively (d) adsorbed on the semiconductor surface. The calculated band offsets are found to be strongly influenced by the adsorption mode at the semiconductor-water interface, leading to differences larger than 1 eV between m and d models of the same semiconductor. We then assess the accuracy of various ab initio electronic-structure schemes in determining the band alignment. In the last part, we try to evaluate photocatalysts for water-splitting by considering the surface coverage and the energy alignment. We determine surface concentrations of water molecules, protons, and hydroxyl ions adsorbed at the semiconductor-water interfaces mentioned above as a function of pH. This is achieved through the calculation of the acidity constants at the surface sites, which are derived from ab initio MD simulations and a grand-canonical formulation of adsorbates. It is finally shown how the potential of a semiconductor material as photocatalysts for water splitting can be inferred by combining the nature of the surface coverage and the alignment of the band edges to the relevant redox levels.

EPFL2019

Alignment of energy levels in amorphous oxides and at semiconductor-water interfaces

Zhendong Guo

EPFL2019

Crystalline and correlated phases in two-dimensional transition metal dichalcogenides

Diego José Pasquier

This thesis is dedicated to the study of various aspects of the electronic structure of two-dimensional transition metal dichalcogenides (TMDs) of chemical composition MX

_2

(where M is a transition metal atom and X= S, Se, Te), using a combination of \textit{ab inito} density-functional methods. We first address the relative stability of the

1T

and

1H

_2

as an example, we show how the splitting of the

d

electron states arises from an interplay of electrostatic effects and hybridization with the ligands'

s

p

and

d

states. We show that the ligand field alone cannot explain the stabilization of the

1H

polymorph for

d^1

and

d^2

1T

transition metal dichalcogenides. The phonon dispersion and fermiology of representative examples with different

d

electron counts are studied as a function of doping. Two qualitatively different behaviours are found as a function of the filling of the

t_{2g}

1T

phase of NbSe

_2

, in monolayer form, is investigated from first principles. We find that

1T

-NbSe

_2

_2

_2

. The relative role of electron-electron and electron-phonon interactions in driving the charge density wave in layered and two-dimensional TiSe

_2

EPFL2019