Nonempirical hybrid functionals for advanced electronic-structure calculations

Electronic-structure calculations based on hybrid functionals have emerged as a standard technique used in physics, chemistry, and material science. Despite this success, hybrid functionals have the drawback of containing undetermined parameters. To overcome this deficiency, two different nonempirical determination schemes are being investigated at present, namely dielectric-dependent hybrid (DDH) functionals and hybrid functionals that satisfy Koopmans' condition. This thesis is dedicated to the examination and further development of these approaches. In particular, we show that a precise description of band gaps in condensed-matter systems can be achieved with these functionals. Moreover, we demonstrate that their accuracy is comparable to state-of-the-art $GW$ methods while requiring substantially lower computational cost.

First, we focus on the development of hybrid functionals satisfying Koopmans' condition. We show that the construction of those functionals can be optimized through suitably defined potential probes. 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. We show that the application of this methodology to common semiconducting and insulating materials yields band gaps differing by less than 0.2 eV from experiment. These conceptual developments are an important step towards establishing hybrid functionals satisfying Koopmans' condition as a robust approach for band-gap predictions.

Second, we examine DDH functionals and hybrid functionals satisfying Koopmans' condition for band gaps of more sophisticated materials. In particular, we focus on inorganic metal-halide perovskites which have recently drawn great scientific attention. For this class of materials, we show that both nonempirical hybrid-functional schemes yield band gaps of comparable accuracy ( $\sim$ 0.2 eV) with respect to $GW$ reference calculations. Furthermore, we discuss the suitability of nonempirical hybrid-functional schemes for the application to the screening of large sets of perovskite materials.

Third, we investigate the fundamental band gap of liquid water and hexagonal ice. These materials are particularly challenging since experimental studies have not reached a consensus on the band gap yet. Therefore, we first deduce robust benchmarks on the basis of a critical review of various experimental studies in the literature. Then, we compute the band gap through state-of-the-art $GW$ methods as well as nonempirical hybrid functionals. We show that theoretical calculations and experimental references are in good agreement with each other and we discuss critical aspects which are essential to ensure a consistent description of the band gap.

Finally, we investigate band-edge levels as obtained with hybrid-functional calculations. The CaF $_2$ /Si(111) interface serves thereby as an ideal test case to examine the accuracy of different theoretical schemes. The comparison with experiment reveals that global hybrid functionals and self-consistent $GW$ methods provide the most accurate description of the interfacial band alignment.

Effect of metal cation replacement on the electronic structure of metalorganic halide perovskites: Replacement of lead with alkaline-earth metals

Ulf Anders Hagfeldt, Tor Jesper Jacobsson

Organic and inorganic lead halogen perovskites, and in particular, CH3NH3PbI3, have during the last years emerged as a class of highly efficient solar cell materials. Herein we introduce metalorganic halogen perovskite materials for energy-relevant applications based on alkaline-earth metals. Based on the classical notion of Goldschmidt's rules and quantum mechanical considerations, the three alkaline-earth metals, Ca, Sr, and Ba, are shown to be able to exchange lead in the perovskite structure. The three alkaline-earth perovskites, CH3NH3CaI3, CH3NH3SrI3, and CH3NH3BaI3, as well as the reference compound, CH3NH3PbI3, are in this paper investigated with density functional theory (DFT) calculations, which predict these compounds to exist as stable perovskite materials, and their electronic properties are explored. A detailed analysis of the projected molecular orbital density of states and electronic band structure from DFT calculations were used for interpretation of the band-gap variations in these materials and for estimation of the effective masses of the electrons and holes. Neglecting spin-orbit effects, the band gap of MACaI(3), MASrI(3), and MABaI(3) were estimated to be 2.95, 3.6, and 3.3 eV, respectively, showing the relative change expected for metal cation exchange. The shifts in the conduction band (CB) edges for the alkaline-earth perovskites were quantified using scalar relativistic DFT calculations and tight-binding analysis, and were compared to the situation in the more extensively studied lead halide perovskite, CH3NH3PbI3, where the change in the work function of the metal is the single most important factor in tuning the CB edge and band gap. The results show that alkaline-earth-based organometallic perovskites will not work as an efficient light absorber in photovoltaic applications but instead could be applicable as charge-selective contact materials. The rather high CB edge and the wide band gap together with the large difference of the electron and hole effective masses make them good candidates for n-type selective layers in hot carrier injection solar cell devices together with some light absorber candidates. The fact that they have similar lattice constants as the lead perovskite and suitable positions of the valence band edges open up the possibility to use them also as thin epitaxial p-type hole selective contacts in combination with the lead halogen perovskite materials. This can lead to both charge selectivity as well as to superior crystal growth of lead perovskite with less contact stress, which is interesting for further investigations.

Amer Physical Soc2016

Electronic Transport in 2D Materials with Strong Spin-orbit Coupling

Artem Pulkin

The thesis describes the computational study of structural, electonic and transport properties of monolayer transition metal dichalcogenides (TMDs) in the stable 2H and the metastable 1T' phases. Several aspects have been covered by the study including the electronic properties of the topological quantum spin Hall (QSH) state in the 1T' monolayer phase as well as the effects of strain, periodic line defects, interfaces and edges of monolayer TMDs. The electronic properties of the bulk monolayer phases were described by the ab-initio density functional theory framework while the electronic and transport properties of 1D defects were calculated using the non-equilibrium Green's function formalism. A specific focus was made on the transport of spin-polarized charge carriers across line defects in the monolayer 2H phase. Subject to energy, pseudomomentum and spin conservation, the size of the transport gap is governed by both bulk properties of a material and symmetries of a line defect. Outside the transport gap energy region, the charge carriers are discriminated with respect to their spin resulting in the spin polarization of the transmitted current. Next, the properties of the metastable monolayer 1T' phase were studied. The presence of a sufficiently large band gap is crucial to observe the QSH phase in the family of materials by probing the topological boundary states. The meV-order band gaps of the 1T' phase of monolayer TMDs were found to be sensitive to materials' lattice constants suggesting the control of the band gap size by strain. In particular, the electronic band structure and the size of the band gap in monolayer 1T'-WSe2 were found to be in agreement with spectroscopy studies. The topologically protected states at the edges of the monolayer 1T' phase as well as at the boundaries between the topological 1T' phase and the trivial 2H phase of monolayer TMDs were studied. Specific atomic structure configurations were suggested to observe experimentally the topological protection of the charge carrier transport against back-scattering. Finally, in the context of lateral semiconducting device engineering, the electronic and transverse transport properties of 2H-1T' phase boundaries as well as the dimerization defects in the 1T' phase were investigated. Both kinds of defects considered exhibit a relatively large transmission probability for the charge carriers crossing the defects. However, the differences between the shapes of bulk bands of the two phases open a sizeable transport gap for charge carriers crossing periodic domain boundaries between the monolayer 2H and 1T' phases. The calculated formation energies of dimerization defects were found to be relatively low suggesting their high concentration in real samples of monolayer 1T'-TMDs. Additionally, the thesis includes studies of magnetic dopants on the surface of Bi2Te3 and atomic vacancies in monolayer 2H-MoSe2 where the electronic properties of point defects were calculated and compared to experimental results. The two possible adsorption sites of Fe on the surface of Bi2Te3 both show a large out-of-plane magnetic anisotropy in agreement with experiments. The calculated local electronic properties of Se vacancies in monolayer 2H-MoSe2 show the presence of in-gap states which are not observed in experiment. Nevertheless, the combination of theoretical and experimental scanning tunneling microscopy images allowed the unambiguous identification of the vacancy defect.

EPFL2017

Band alignment at the CaF2/Si(111) interface through advanced electronic structure calculations

Thomas Bischoff, Alfredo Pasquarello, Igor Reshetnyak

We determine the band alignment at the CaF2/Si(111) interface through various advanced electronic structure methods. This interface is experimentally well studied and serves as an ideal test case to examine the accuracy of theoretical schemes. We use both global and range-separated hybrid functionals as well as GW calculations including self-consistency and vertex corrections. Our calculation procedure accounts for residual strain resulting from the small mismatch in the lateral lattice constants at the interface to minimize the systematic error in the comparison with experiment. Both the hybrid functional and the GW schemes give band alignments in overall good agreement with the experimental characterization. However, the considered methods yield sizable variations in the calculated band offsets, which do not originate from incorrect evaluations of the band gaps but rather from different inherent relative positions of the band edges. The comparison with experiment reveals that the global hybrid functional and the quasiparticle self-consistent GW with vertex corrections give the most accurate description of the band alignment. We then determine the variation of the band offsets as a function of the amount of excess fluorine at the interface and attribute the experimental spread in the measured offsets to uncontrolled fluorine contamination.