Band offsets at the Si/SiO2 interface from many-body perturbation theory

Many-Body Effects at Heterogeneous Interfaces from First-Principles: Progress, Challenges, and Opportunities

Heterogeneous interfaces are pivotal in numerous nanoscale devices and applications. First-principles approaches based on quantum mechanics and atomistic structures provide critical insights into structure-property relationships, enabling the informed design of materials and devices. Accurate first-principles methods must reliably capture many-body effects, i.e., electron-electron interactions, which significantly influence system properties compared to the predictions from models using free or noninteracting electrons. In this Perspective, we survey a few computational tools in this context and attempt to be forward looking by discussing the current challenges and emerging research opportunities. We examine diverse manifestations of many-body effects across several domains: geometries and reaction barriers (total-energy properties), orbital energy levels and band alignments (one-particle properties), and optical excited states (two-particle properties).

Role of Interfacial Morphology in Cu2O/TiO2 and Band Bending: Insights from Density Functional Theory

Photocatalysis, a promising solution to environmental challenges, relies on the generation and utilization of photogenerated charge carriers within photocatalysts. However, the recombination of these carriers often limits efficiency. Heterostructures, especially Cu2O/TiO2, have emerged as effective solutions to enhance charge separation. This study systematically explores the effect of interfacial morphologies on the band bending within Cu2O/TiO2 anatase heterostructures by employing density functional theory. Through this study, eight distinct interfaces are identified and analyzed, revealing a consistent staggered-type band alignment. Despite variations in band edge positions, systematic charge transfer from Cu2O to TiO2 is observed across all interfaces. The proposed band bending configurations would suggest enhanced charge separation and photocatalytic activity under ultraviolet illumination due to a Z-scheme configuration. This theoretical investigation provides valuable insights into the interplay between interfacial morphology, band bending, and charge transfer for advancing the understanding of fundamental electronic mechanisms in heterostructures.

First-Principles Band Alignments at the Si:Anatase TiO2 Interface

TiO₂ has been identified as a promising electron transport layer in Si solar cells. Experiments have revealed that the Si:TiO₂ interface undergoes structural changes depending on how it was fabricated. However, less is understood about the sensitivity of electronic properties, such as band alignments, to these changes. Here, we present first-principles calculations of band alignments between Si and anatase TiO₂, investigating different surface orientations and terminations. By calculating vacuum-level alignments, we observe a large band offset reduction of 2.5 eV for the O-terminated Si slab compared to other terminations. Furthermore, a 0.5 eV increase is found for the anatase (101) surface compared to (001). We compare the band offsets obtained through vacuum alignment with four different heterostructure models. Even though the heterostructure models contain an excess of oxygen, their offsets agree well with vacuum-level alignments using stoichiometric or H-terminated slabs, and the reduction in band offsets seen for the O-terminated Si slab is not observed. Additionally, we have investigated different exchange-correlation treatments including PBE + U, postprocessing GW corrections, and the meta-GGA rSCAN functional. We find that rSCAN provides more accurate band offsets than PBE, but further corrections are still required to achieve <0.5 eV accuracy. Overall, our study quantifies the importance of surface termination and orientation for this interface.

Electronic Properties of Functionalized Diamanes for Field-Emission Displays

Ultrathin diamond films, or diamanes, are promising quasi-2D materials that are characterized by high stiffness, extreme wear resistance, high thermal conductivity, and chemical stability. Surface functionalization of multilayer graphene with different stackings of layers could be an interesting opportunity to induce proper electronic properties into diamanes. Combination of these electronic properties together with extraordinary mechanical ones will lead to their applications as field-emission displays substituting original devices with light-emitting diodes or organic light-emitting diodes. In the present study, we focus on the electronic properties of fluorinated and hydrogenated diamanes with (111), (110), (0001), (101̅0), and (2̅110) crystallographic orientations of surfaces of various thicknesses by using first-principles calculations and Bader analysis of electron density. We see that fluorine induces an occupied surface electronic state, while hydrogen modifies the occupied bulk state and also induces unoccupied surface states. Furthermore, a lower number of layers is necessary for hydrogenated diamanes to achieve the convergence of the work function in comparison with fluorinated diamanes, with the exception of fluorinated (110) and (2̅110) films that achieve rapid convergence and have the same behavior as other hydrogenated surfaces. This induces a modification of the work function with an increase of the number of layers that makes hydrogenated (2̅110) diamanes the most suitable surface for field-emission displays, better than the fluorinated counterparts. In addition, a quasi-quantitative descriptor of surface dipole moment based on the Tantardini-Oganov electronegativity scale is introduced as the average of bond dipole moments between the surface atoms. This new fundamental descriptor is capable of predicting a priori the bond dipole moment and may be considered as a new useful feature for crystal structure prediction based on artificial intelligence.

DFT-1/2 and shell DFT-1/2 methods: electronic structure calculation for semiconductors at LDA complexity

It is known that the Kohn-Sham eigenvalues do not characterize experimental excitation energies directly, and the band gap of a semiconductor is typically underestimated by local density approximation (LDA) of density functional theory (DFT). An embarrassing situation is that one usually uses LDA+Ufor strongly correlated materials with rectified band gaps, but for non-strongly-correlated semiconductors one has to resort to expensive methods like hybrid functionals orGW. In spite of the state-of-the-art meta-generalized gradient approximation functionals like TB-mBJ and SCAN, methods with LDA-level complexity to rectify the semiconductor band gaps are in high demand. DFT-1/2 stands as a feasible approach and has been more widely used in recent years. In this work we give a detailed derivation of the Slater half occupation technique, and review the assumptions made by DFT-1/2 in semiconductor band structure calculations. In particular, the self-energy potential approach is verified through mathematical derivations. The aims, features and principles of shell DFT-1/2 for covalent semiconductors are also accounted for in great detail. Other developments of DFT-1/2 including conduction band correction, DFT+A-1/2, empirical formula for the self-energy potential cutoff radius, etc, are further reviewed. The relations of DFT-1/2 to hybrid functional, sX-LDA,GW, self-interaction correction, scissor's operator as well as DFT+Uare explained. Applications, issues and limitations of DFT-1/2 are comprehensively included in this review.

GPU Acceleration of Large-Scale Full-Frequency GW Calculations

Many-body perturbation theory is a powerful method to simulate electronic excitations in molecules and materials starting from the output of density functional theory calculations. By implementing the theory efficiently so as to run at scale on the latest leadership high-performance computing systems it is possible to extend the scope of GW calculations. We present a GPU acceleration study of the full-frequency GW method as implemented in the WEST code. Excellent performance is achieved through the use of (i) optimized GPU libraries, e.g., cuFFT and cuBLAS, (ii) a hierarchical parallelization strategy that minimizes CPU-CPU, CPU-GPU, and GPU-GPU data transfer operations, (iii) nonblocking MPI communications that overlap with GPU computations, and (iv) mixed precision in selected portions of the code. A series of performance benchmarks has been carried out on leadership high-performance computing systems, showing a substantial speedup of the GPU-accelerated version of WEST with respect to its CPU version. Good strong and weak scaling is demonstrated using up to 25 920 GPUs. Finally, we showcase the capability of the GPU version of WEST for large-scale, full-frequency GW calculations of realistic systems, e.g., a nanostructure, an interface, and a defect, comprising up to 10 368 valence electrons.

Do HOMO-LUMO Energy Levels and Band Gaps Provide Sufficient Understanding of Dye-Sensitizer Activity Trends for Water Purification?

A dye-sensitized solar cell assembly can be used to harvest solar energy, while suitable dye sensitizers can be used to purify water. Here, we characterized the activity trends of four dye sensitizers, namely, PORPC-1, PORPC-2, PORPC-3, and PORPC-4, for water purification applications using density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE), B3LYP, and PBE0 functionals, ΔSCF, time-dependent DFT (TD-DFT), and quasiparticle Green's function (GW) methods. The energy levels of the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) were calculated using gas-phase and aqueous-phase methods in order to understand charge-injection abilities and the dye regeneration processes. PBE, B3LYP, PBE0, and TD-DFT methods failed to predict PORPC-4 to be the best sensitizer, while PORPC-2 and PORPC-4 were predicted to be the best sensitizers using ΔSCF coupled with the implicit solvation method, and HOMO-LUMO energies were corrected for the aqueous environment in the GW calculations. However, none of these methods accurately predicted the performance trend of all four dye sensitizers. Consequently, we used the aggregation assembly patterns of the dye molecules in an aqueous environment to further probe the activity trends and found that PORPC-3 and PORPC-4 prefer J-aggregated assembly patterns, whereas PROPC-1 and PORPC-2 prefer to be H-aggregated. Therefore, the performance of these dye molecules can be determined by combining HOMO-LUMO energy levels with aggregate-assembly patterns, with the activity trend predicted to be PORPC-4 > PORPC-2 > PORPC-3 > PORPC-1, which is in good agreement with experimental findings.

Local Modified Becke-Johnson Exchange-Correlation Potential for Interfaces, Surfaces, and Two-Dimensional Materials

The modified Becke-Johnson meta-GGA potential of density functional theory has been shown to be the best exchange-correlation potential to determine band gaps of crystalline solids. However, it cannot be consistently used for the electronic structure of nonperiodic or nanostructured systems. We propose an extension of this potential that enables its use to study heterogeneous, finite, and low-dimensional systems. This is achieved by using a coordinate-dependent expression for the parameter c that weights the Becke-Russel exchange, in contrast to the original global formulation, where c is just a fitted number. Our potential takes advantage of the excellent description of band gaps provided by the modified Becke-Johnson potential and preserves its modest computational effort. Furthermore, it yields with one single calculation band diagrams and band offsets of heterostructures and surfaces. We exemplify the usefulness and efficiency of our local meta-GGA potential by testing it for a series of interfaces (Si/SiO₂, AlAs/GaAs, AlP/GaP, and GaP/Si), a Si surface, and boron nitride monolayer.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

Absolute Energy Levels of Liquid Water

We determine the ionization potential (IP) and the electron affinity (EA) of liquid water together with the absolute redox level of the standard hydrogen electrode (SHE) by combining advanced electronic-structure calculations, ab initio molecular dynamics simulations, thermodynamic integration, and potential alignment at the water-vacuum interface. The calculated SHE level lies at 4.56 eV below the vacuum level, close to the experimental reference of 4.44 eV inferred by Trasatti. The band edges are determined through a hybrid functional designed to reproduce the band gap achieved with highly accurate GW calculations. Our analysis yields IP = 9.7 eV and EA = 0.8 eV, consistent with both photoemission spectra of liquid water and thermodynamical data for the hydrated electron.

The organic-2D transition metal dichalcogenide heterointerface

Since the first isolation of graphene, new classes of two-dimensional (2D) materials have offered fascinating platforms for fundamental science and technology explorations at the nanometer scale. In particular, 2D transition metal dichalcogenides (TMD) such as MoS2 and WSe2 have been intensely investigated due to their unique electronic and optical properties, including tunable optical bandgaps, direct-indirect bandgap crossover, strong spin-orbit coupling, etc., for next-generation flexible nanoelectronics and nanophotonics applications. On the other hand, organics have always been excellent materials for flexible electronics. A plethora of organic molecules, including donors, acceptors, and photosensitive molecules, can be synthesized using low cost and scalable procedures. Marrying the fields of organics and 2D TMDs will bring benefits that are not present in either material alone, enabling even better, multifunctional flexible devices. Central to the realization of such devices is a fundamental understanding of the organic-2D TMD interface. Here, we review the organic-2D TMD interface from both chemical and physical perspectives. We discuss the current understanding of the interfacial interactions between the organic layers and the TMDs, as well as the energy level alignment at the interface, focusing in particular on surface charge transfer and electronic screening effects. Applications from the literature are discussed, especially in optoelectronics and p-n hetero- and homo-junctions. We conclude with an outlook on future scientific and device developments based on organic-2D TMD heterointerfaces.

GW100: Comparison of Methods and Accuracy of Results Obtained with the WEST Code

The reproducibility of calculations carried out within many-body perturbation theory at the G₀ W₀ level is assessed for 100 closed shell molecules and compared to that of density functional theory. We consider vertical ionization potentials (VIP) and electron affinities (VEA) obtained with five different codes: BerkeleyGW, FHI-aims, TURBOMOLE, VASP, and WEST. We review the approximations and parameters that control the accuracy of G₀ W₀ results in each code, and we discuss in detail the effect of extrapolation techniques for the parameters entering the WEST code. Differences between the VIP and VEA computed with the various codes are within ∼60 and ∼120 meV, respectively, which is up to four times larger than in the case of the best results obtained with DFT codes. Vertical ionization potentials are validated against experiment and CCSD(T) quantum chemistry results showing a mean absolute relative error of ∼4% for data obtained with WEST. Our analysis of the differences between localized orbitals and plane-wave implementations points out molecules containing Cu, I, Ga, and Xe as major sources of discrepancies, which call for a re-evaluation of the pseudopotentials used for these systems in G₀ W₀ calculations.

Computational Predictions for Single Chain Chalcogenide-Based One-Dimensional Materials

Exfoliation of multilayered materials has led to an abundance of new two-dimensional (2D) materials and to their fabrication by other means. These materials have shown exceptional promise for many applications. In a similar fashion, we can envision starting with crystalline polymeric (multichain) materials and exfoliate single-chain, one-dimensional (1D) materials that may also prove useful. We use electronic structure methods to elucidate the properties of such 1D materials: individual chains of chalcogens, of silicon dichalcogenides and of sulfur nitrides. The results indicate reasonable exfoliation energies in the case of polymeric three-dimensional (3D) materials. Quantum confinement effects lead to large band gaps and large exciton binding energies. The effects of strain are quantified and heterojunction band offsets are determined. Possible applications would entail 1D materials on 3D or 2D substrates.

Predicting point defect equilibria across oxide hetero-interfaces: model system of ZrO2/Cr2O3

We present a multi-scale model to predict defect redistribution both in interface core and space charge layer across oxide/oxide hetero-interfaces.

Synergistic effect of N-decorated and Mn(2+) doped ZnO nanofibers with enhanced photocatalytic activity

Here we report a high efficiency photocatalyst, i.e., Mn²⁺-doped and N-decorated ZnO nanofibers (NFs) enriched with vacancy defects, fabricated via electrospinning and a subsequent controlled annealing process. This nanocatalyst exhibits excellent visible-light photocatalytic activity and an apparent quantum efficiency up to 12.77%, which is 50 times higher than that of pure ZnO. It also demonstrates good stability and durability in repeated photocatalytic degradation experiments. A comprehensive structural analysis shows that high density of oxygen vacancies and nitrogen are introduced into the nanofibers surface. Hence, the significant enhanced visible photocatalytic properties for Mn-ZnO NFs are due to the synergetic effects of both Mn²⁺ doping and N decorated. Further investigations exhibit that the Mn²⁺-doping facilitates the formation of N-decorated and surface defects when annealing in N₂ atmosphere. N doping induce the huge band gap decrease and thus significantly enhance the absorption of ZnO nanofibers in the range of visible-light. Overall, this paper provides a new approach to fabricate visible-light nanocatalysts using both doping and annealing under anoxic ambient.

All-electron GW quasiparticle band structures of group 14 nitride compounds

We have investigated the group 14 nitrides (M3N4) in the spinel phase (γ-M3N4 with M = C, Si, Ge, and Sn) and β phase (β-M3N4 with M = Si, Ge, and Sn) using density functional theory with the local density approximation and the GW approximation. The Kohn-Sham energies of these systems have been first calculated within the framework of full-potential linearized augmented plane waves (LAPW) and then corrected using single-shot G0W0 calculations, which we have implemented in the modified version of the Elk full-potential LAPW code. Direct band gaps at the Γ point have been found for spinel-type nitrides γ-M3N4 with M = Si, Ge, and Sn. The corresponding GW-corrected band gaps agree with experiment. We have also found that the GW calculations with and without the plasmon-pole approximation give very similar results, even when the system contains semi-core d electrons. These spinel-type nitrides are novel materials for potential optoelectronic applications because of their direct and tunable band gaps.

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

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.

Computational Screening of 2D Materials for Photocatalysis

Two-dimensional (2D) materials exhibit a range of extraordinary electronic, optical, and mechanical properties different from their bulk counterparts with potential applications for 2D materials emerging in energy storage and conversion technologies. In this Perspective, we summarize the recent developments in the field of solar water splitting using 2D materials and review a computational screening approach to rapidly and efficiently discover more 2D materials that possess properties suitable for solar water splitting. Computational tools based on density-functional theory can predict the intrinsic properties of potential photocatalyst such as their electronic properties, optical absorbance, and solubility in aqueous solutions. Computational tools enable the exploration of possible routes to enhance the photocatalytic activity of 2D materials by use of mechanical strain, bias potential, doping, and pH. We discuss future research directions and needed method developments for the computational design and optimization of 2D materials for photocatalysis.

First-principles approach to calculating energy level alignment at aqueous semiconductor interfaces

A first-principles approach is demonstrated for calculating the relationship between an aqueous semiconductor interface structure and energy level alignment. The physical interface structure is sampled using density functional theory based molecular dynamics, yielding the interface electrostatic dipole. The  GW approach from many-body perturbation theory is used to place the electronic band edge energies of the semiconductor relative to the occupied 1b1 energy level in water. The application to the specific cases of nonpolar (101¯0) facets of GaN and ZnO reveals a significant role for the structural motifs at the interface, including the degree of interface water dissociation and the dynamical fluctuations in the interface Zn-O and O-H bond orientations. These effects contribute up to 0.5 eV.

Electronic structure calculations of mercury mobilization from mineral phases and photocatalytic removal from water and the atmosphere

Mercury is a hazardous environmental pollutant mobilized from natural sources, and anthropogenically contaminated and disturbed areas. Current methods to assess mobility and environmental impact are mainly based on field measurements, soil monitoring, and kinetic modelling. In order to understand in detail the extent to which different mineral sources can give rise to mercury release it is necessary to investigate the complexity at the microscopic level and the possible degradation/dissolution processes. In this work, we investigated the potential for mobilization of mercury structurally trapped in three relevant minerals occurring in hot spring environments and mining areas, namely, cinnabar (α-HgS), corderoite (α-Hg3S2Cl2), and mercuric chloride (HgCl2). Quantum chemical methods based on density functional theory as well as more sophisticated approaches are used to assess the possibility of a) direct photoreduction and formation of elemental Hg at the surface of the minerals, providing a path for ready release in the environment; and b) reductive dissolution of the minerals in the presence of solutions containing halogens. Furthermore, we study the use of TiO2 as a potential photocatalyst for decontamination of polluted waters (mainly Hg(2+)-containing species) and air (atmospheric Hg(0)). Our results partially explain the observed pathways of Hg mobilization from relevant minerals and the microscopic mechanisms behind photocatalytic removal of Hg-based pollutants. Possible sources of disagreement with observations are discussed and further improvements to our approach are suggested.

Understanding quantum confinement of charge carriers in layered 2D hybrid perovskites

Layered hybrid organic perovskites (HOPs) structures are a class of low-cost two-dimensional materials that exhibit outstanding optical properties, related to dielectric and quantum confinement effects. Whereas modeling and understanding of quantum confinement are well developed for conventional semiconductors, such knowledge is still lacking for 2D HOPs. In this work, concepts of effective mass and quantum well are carefully investigated and their applicability to 2D HOPs is discussed. For ultrathin layers, the effective-mass model fails. Absence of superlattice coupling and importance of non-parabolicity effects prevents the use of simple empirical models based on effective masses and envelope function approximations. An alternative method is suggested in which 2D HOPs are treated as composite materials, and a first-principles approach to the calculation of band offsets is introduced. These findings might also be relevant for other classes of layered 2D functional materials.

Ionization potentials of solids: the importance of vertex corrections

The ionization potential is a fundamental key quantity with great relevance to diverse material properties. We find that state of the art methods based on density functional theory and simple diagrammatic approaches as commonly taken in the GW approximation predict the ionization potentials of semiconductors and insulators unsatisfactorily. Good agreement between theory and experiment is obtained only when diagrams resulting from the antisymmetry of the many-electron wave function are taken into account via vertex corrections in the self-energy. The present approach describes both localized and delocalized states accurately, making it ideally suited for a wide class of materials and processes.

A computational investigation of nickel (silicides) as potential contact layers for silicon photovoltaic cells

Nickel has been proposed as a low-cost alternative to silver for contacting in high-performance solar cells. Nickel at a crystalline silicon surface can form a number of silicide phases, depending on fabrication conditions. Using density functional theory calculations we calculate the Schottky barrier height (SBH) at the different possible interfaces. Depending on the silicide phase, crystallographic orientation and doping the SBH at the interface with Si can range from 0.39 to 0.70 eV. These calculations demonstrate which of the nickel (silicide) phases have potential use as contacting materials for silicon based solar cells. Furthermore, we explain the origin of the SBH tuning effect of P dopant atoms as being due to a dipole formed at the interface, demonstrating the linear relationship between the charge transfer at the interface upon doping and the concomitant modulation of the SBH.

Shallow impurity level calculations in semiconductors using ab initio methods

An ab initio method is presented to calculate shallow impurity levels in bulk semiconductors. This method combines the GW calculation for the treatment of the central-cell potential with a potential patching method for large systems (with 64,000 atoms) to describe the impurity state wave functions. The calculated acceptor levels in Si, GaAs, and an isovalent bound state of GaP are in excellent agreement with experiments with a root-mean-square error of 8.4 meV.

Quantitative analysis of valence photoemission spectra and quasiparticle excitations at chromophore-semiconductor interfaces

Investigating quasiparticle excitations of molecules on surfaces through photoemission spectroscopy forms a major part of nanotechnology research. Resolving spectral features at these interfaces requires a comprehensive theory of electron removal and addition processes in molecules and solids which captures the complex interplay of image charges, thermal effects, and configurational disorder. Here, we develop such a theory and calculate the quasiparticle energy-level alignment and the valence photoemission spectrum for the prototype biomimetic solar cell interface between anatase TiO(2) and the N3 chromophore. By directly matching our calculated photoemission spectrum to experimental data, we clarify the atomistic origin of the chromophore peak at low binding energy. This case study sets a new standard in the interpretation of photoemission spectroscopy at complex chromophore-semiconductor interfaces.

First-principles study of Cu2ZnSnS4 and the related band offsets for photovoltaic applications

First-principles calculations of the band offsets between Cu(2)ZnSnS(4) (CZTS) and XS (X = Cd, Zn) are performed. While the interface dipole contribution for the band offsets is calculated using the Perdew-Burke-Ernzerhof functional, the Heyd-Scuseria-Ernzerhof hybrid functional is employed to introduce the quasiparticle corrections to the band offsets. The calculated conduction band offset between CZTS and CdS is 0.2 eV, validating CdS for the buffer layer of the CZTS solar cell. The small conduction band offset stems from the band gap narrowing of CdS under the interface strain caused by the lattice misfit with CZTS. A large valence band offset over 0.9 eV between CZTS and ZnS indicates that precipitated ZnS is regarded as an inactive insulator phase in CZTS absorbers.

Hybrid functional investigations of band gaps and band alignments for AlN, GaN, InN, and InGaN

Band gaps and band alignments for AlN, GaN, InN, and InGaN alloys are investigated using density functional theory with the with the Heyd-Scuseria-Ernzerhof {HSE06 [J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 134, 8207 (2003); 124, 219906 (2006)]} XC functional. The band gap of InGaN alloys as a function of In content is calculated and a strong bowing at low In content is found, described by bowing parameters 2.29 eV at 6.25% and 1.79 eV at 12.5%, indicating the band gap cannot be described by a single composition-independent bowing parameter. Valence-band maxima (VBM) and conduction-band minima (CBM) are aligned by combining bulk calculations with surface calculations for nonpolar surfaces. The influence of surface termination [(1100) m-plane or (1120) a-plane] is thoroughly investigated. We find that for the relaxed surfaces of the binary nitrides the difference in electron affinities between m- and a-plane is less than 0.1 eV. The absolute electron affinities are found to strongly depend on the choice of XC functional. However, we find that relative alignments are less sensitive to the choice of XC functional. In particular, we find that relative alignments may be calculated based on Perdew-Becke-Ernzerhof [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 134, 3865 (1996)] surface calculations with the HSE06 lattice parameters. For InGaN we find that the VBM is a linear function of In content and that the majority of the band-gap bowing is located in the CBM. Based on the calculated electron affinities we predict that InGaN will be suited for water splitting up to 50% In content.

Band offsets at semiconductor-oxide interfaces from hybrid density-functional calculations

Band offsets at semiconductor-oxide interfaces are determined through a scheme based on hybrid density functionals, which incorporate a fraction alpha of Hartree-Fock exchange. For each bulk component, the fraction alpha is tuned to reproduce the experimental band gap, and the conduction and valence band edges are then located with respect to a reference level. The lineup of the bulk reference levels is determined through an interface calculation, and shown to be almost independent of the fraction alpha. Application of this scheme to the Si-SiO2, SiC-SiO2, and Si-HfO2 interfaces yields excellent agreement with experiment.

Defect energy levels in density functional calculations: alignment and band gap problem

For materials of varying band gap, we compare energy levels of atomically localized defects calculated within a semilocal and a hybrid density-functional scheme. Since the latter scheme partially relieves the band gap problem, our study describes how calculated defect levels shift when the band gap approaches the experimental value. When suitably aligned, defect levels obtained from total-energy differences correspond closely, showing average shifts of at most 0.2 eV irrespective of band gap. Systematic deviations from ideal alignment increase with the extent of the defect wave function. A guideline for comparing calculated and experimental defect levels is provided.