Finite-size supercell correction for charged defects at surfaces and interfaces

Fukui Function and Fukui Potential for Solid-State Chemistry: Application to Surface Reactivity

The Fukui function and its associated potential serve as essential descriptors of chemical reactivity within the framework of conceptual density functional theory (c-DFT). While c-DFT is well-established for molecular systems, it encounters formal and technical challenges when applied to extended systems. This comprehensive study addresses the complexities involved in calculating the Fukui function and its potential in systems with periodic boundary conditions (PBC). We specifically investigate the introduction of a fictitious potential associated with a compensating background of charge (CBC) in these calculations, examining its implications for the reliability of these reactivity descriptors. To explore this issue, we analyze a diverse range of metallic and semiconductor surfaces, including elemental metals such as Ti and Pt, metal oxides like TiO2, SnO2, and MgO, and transition metal carbides such as TiC and ZrC. By encompassing this varied selection, this work aims to uncover both the limitations and advantages of various computational approaches in accurately capturing the intrinsic chemical reactivity of extended systems. Our findings indicate that while certain methods yield reliable results, others introduce artifacts that can significantly distort interpretations of surface reactivity. We advocate for the calculation of the Fukui function and potential using finite differences with self-consistent potential correction whenever feasible. Interpolation methods may also be employed if delocalization errors are manageable. Furthermore, we demonstrate that a reliable method for computing the Fukui potential, in combination with perturbation theory, can predict the interaction energies of reducing agents such as sodium and oxidants like chlorine with TiO2 surfaces, thus supporting the application of c-DFT in heterogeneous catalysis. This research contributes critical insights to the field, offering practical methodologies to address the inherent challenges in predicting surface reactivity. By elucidating the complexities of the Fukui function under PBC, we not only enhance theoretical frameworks but also equip researchers with robust tools for advancing materials science and surface chemistry.

Synergy Between Dynamic Behavior of Hydrogen Defects and Non-Radiative Recombination in Metal-Halide Perovskites

In organic-inorganic hybrid perovskite solar cells (PSCs), hydrogen defects introduce deep-level trap states, significantly influencing non-radiative recombination processes. Those defects are primarily observed in MA-PSCs rather than FA-PSCs. As a result, MA-PSCs demonstrated a lower efficiency of 23.6% compared to 26.1% of FA-PSCs. In this work, both hydrogen vacancy (VH -) and hydrogen interstitial (Hi -) defects in MAPbI3 bulk and on surfaces, respectively are investigated. i) Bulk VH - defects have dramatic impact on non-radiative recombination, with lifetime varying from 67 to 8 ns, depending on whether deprotonated MA0 are ion-bonded or not. ii) Surface H-defects exhibited an inherent self-healing mechanism through a chemical bond between MA0 and Pb2+, indicating a self-passivation effect. iii) Both VH - and Hi - defects can be mitigated by alkali cation passivation; while large cations are preferable for VH - passivation, given strong binding energy of cation/perovskite, as well as, weak band edge non-adiabatic couplings; and small cations are suited for Hi - passivation, considering the steric hindrance effect. The dual passivation strategy addressed diverse experimental outcomes, particularly in enhancing performance associated with cation selections. The dynamic connection between hydrogen defects and non-radiative recombination is elucidated, providing insights into hydrogen defect passivation essential for high-performance PSCs fabrication.

The Defects Genome of Janus Transition Metal Dichalcogenides

2D Janus Transition Metal Dichalcogenides (TMDs) have attracted much interest due to their exciting quantum properties arising from their unique two-faced structure, broken-mirror symmetry, and consequent colossal polarization field within the monolayer. While efforts are made to achieve high-quality Janus monolayers, the existing methods rely on highly energetic processes that introduce unwanted grain-boundary and point defects with still unexplored effects on the material's structural and excitonic properties Through high-resolution scanning transmission electron microscopy (HRSTEM), density functional theory (DFT), and optical spectroscopy measurements; this work introduces the most encountered and energetically stable point defects. It establishes their impact on the material's optical properties. HRSTEM studies show that the most energetically stable point defects are single (VS and VSe) and double chalcogen vacancy (VS -VSe), interstitial defects (Mi), and metal impurities (MW) and establish their structural characteristics. DFT further establishes their formation energies and related localized bands within the forbidden band. Cryogenic excitonic studies on h-BN-encapsulated Janus monolayers offer a clear correlation between these structural defects and observed emission features, which closely align with the results of the theory. The overall results introduce the defect genome of Janus TMDs as an essential guideline for assessing their structural quality and device properties.

Physics of band-filling correction in defect calculations of solid-state materials

In solid-state physics/chemistry, a precise understanding of defect formation and its impact on the electronic properties of wide-bandgap insulators is a cornerstone of modern semiconductor technology. However, complexities arise in the electronic structure theory of defect formation when the latter triggers partial occupation of the conduction/valence band, necessitating accurate post-process correction to the energy calculations. Herein, we dissect these complexities, focusing specifically on the post-process band-filling corrections, a crucial element that often demands thorough treatment in defect formation studies. We recognize the importance of these corrections in maintaining the accuracy of electronic properties predictions in wide-bandgap insulators and their role in reinforcing the importance of a reliable common reference state for defect formation energy calculations. We explored solutions such as aligning deep states and electrostatic potentials, both of which have been used in previous works, showing the effect of band alignment on defect formation energy. Our findings demonstrate that the impact of defect formation on electronic structure (even deep states) can be significantly dependent on the supercell size. We also show that within band-filling calculations, one needs to account for the possible change of electronic structure induced by defect formation, which requires sufficient convergence of electronic structure with supercell size. Thus, this work emphasizes the critical steps to accurately predict defect formation energy and paves the way for future research to overcome these challenges and advance the field with more efficient and reliable predictive models.

A substitutional quantum defect in WS2 discovered by high-throughput computational screening and fabricated by site-selective STM manipulation

Point defects in two-dimensional materials are of key interest for quantum information science. However, the parameter space of possible defects is immense, making the identification of high-performance quantum defects very challenging. Here, we perform high-throughput (HT) first-principles computational screening to search for promising quantum defects within WS2, which present localized levels in the band gap that can lead to bright optical transitions in the visible or telecom regime. Our computed database spans more than 700 charged defects formed through substitution on the tungsten or sulfur site. We found that sulfur substitutions enable the most promising quantum defects. We computationally identify the neutral cobalt substitution to sulfur (CoS 0 ) and fabricate it with scanning tunneling microscopy (STM). The CoS 0 electronic structure measured by STM agrees with first principles and showcases an attractive quantum defect. Our work shows how HT computational screening and nanoscale synthesis routes can be combined to design promising quantum defects.

The Case for a Defect Genome Initiative

The Materials Genome Initiative (MGI) has streamlined the materials discovery effort by leveraging generic traits of materials, with focus largely on perfect solids. Defects such as impurities and perturbations, however, drive many attractive functional properties of materials. The rich tapestry of charge, spin, and bonding states hosted by defects are not accessible to elements and perfect crystals, and defects can thus be viewed as another class of "elements" that lie beyond the periodic table. Accordingly, a Defect Genome Initiative (DGI) to accelerate functional defect discovery for energy, quantum information, and other applications is proposed. First, major advances made under the MGI are highlighted, followed by a delineation of pathways for accelerating the discovery and design of functional defects under the DGI. Near-term goals for the DGI are suggested. The construction of open defect platforms and design of data-driven functional defects, along with approaches for fabrication and characterization of defects, are discussed. The associated challenges and opportunities are considered and recent advances towards controlled introduction of functional defects at the atomic scale are reviewed. It is hoped this perspective will spur a community-wide interest in undertaking a DGI effort in recognition of the importance of defects in enabling unique functionalities in materials.

First-principles theory of the nitrogen interstitial in hBN: a plausible model for the blue emitter

Color centers in hexagonal boron nitride (hBN) have attracted considerable attention due to their remarkable optical properties enabling robust room temperature photonics and quantum optics applications in the visible spectral range. On the other hand, identification of the microscopic origin of color centers in hBN has turned out to be a great challenge that hinders the in-depth theoretical characterization, on-demand fabrication, and development of integrated photonic devices. This is also true for the blue emitter, which is a result of irradiation damage in hBN, emitting at 436 nm wavelength with desirable properties. Here, we propose the negatively charged nitrogen split interstitial defect in hBN as a plausible microscopic model for the blue emitter. To this end, we carried out a comprehensive first-principles theoretical study of the nitrogen interstitial. We carefully analyzed the accuracy of first-principles methods and showed that the commonly used HSE hybrid exchange-correlation functional fails to describe the electronic structure of this defect. Using the generalized Koopman's theorem, we fine-tuned the functional and obtained a zero-phonon photoluminescence (ZPL) energy in the blue spectral range. We showed that the defect exhibits a high emission rate in the ZPL line and features a characteristic phonon side band that resembles the blue emitter's spectrum. Furthermore, we studied the electric field dependence of the ZPL and numerically showed that the defect exhibits a quadratic Stark shift that is perpendicular to plane electric fields, making the emitter insensitive to electric field fluctuations in the first order. Our work emphasizes the need for assessing the accuracy of common first-principles methods in hBN and exemplifies a workaround methodology. Furthermore, our work is a step towards understanding the structure of the blue emitter and utilizing it in photonics applications.

Electrochemical hydrogen evolution on Pt-based catalysts from a theoretical perspective

Hydrogen evolution reaction (HER) by splitting water is a key technology toward a clean energy society, where Pt-based catalysts were long known to have the highest activity under acidic electrochemical conditions but suffer from high cost and poor stability. Here, we overview the current status of Pt-catalyzed HER from a theoretical perspective, focusing on the methodology development of electrochemistry simulation, catalytic mechanism, and catalyst stability. Recent developments in theoretical methods for studying electrochemistry are introduced, elaborating on how they describe solid-liquid interface reactions under electrochemical potentials. The HER mechanism, the reaction kinetics, and the reaction sites on Pt are then summarized, which provides an atomic-level picture of Pt catalyst surface dynamics under reaction conditions. Finally, state-of-the-art experimental solutions to improve catalyst stability are also introduced, which illustrates the significance of fundamental understandings in the new catalyst design.

Electronic and magnetic properties of charged point defects in monolayer CrI3

The two-dimensional magnetic material CrI₃ has gained considerable attention owing to its promising applications in photoelectric and spin-related devices. Recently, various structural defects in CrI₃ have been identified; however, the charge states of these defects have been mainly ignored. Here, we report on an investigation of the charged defects in monolayer CrI₃, focused on the electronic and magnetic properties of the five most stable point defects using first-principles calculations. For positively charged I vacancies and negatively charged Cr vacancies, a blue- and red-shift of defect states near the Fermi level can be observed because of the atom relaxation. Our results also indicate that, among the five defects, the Cr interstitial defect has the smallest ionization energy of 0.34 eV, which makes its ionization easiest. Furthermore, a 0.2 μ_B enhancement of the magnetic moment on the nearest Cr atom can be found for the I vacancy and Cr interstitial defect. The investigation contributes to the atomic-scale comparison and understanding of the charged defects of monolayer CrI₃.

Defect modeling and control in structurally and compositionally complex materials

Conventional computational approaches for modeling defects face difficulties when applied to complex materials, mainly due to the vast configurational space of defects. In this Perspective, we discuss the challenges in calculating defect properties in complex materials, review recent advances in computational techniques and showcase new mechanistic insights developed from these methods. We further discuss the remaining challenges in improving the accuracy and efficiency of defect modeling in complex materials, and provide an outlook on potential research directions.

Fundamental Limit of Selectivity in Photocatalytic Denitrification over Titania

Although photocatalytic decomposition of NO (deNO) into N₂ and O₂ is low-cost and non-polluting, it has a low NO conversion efficiency. Establishing the activity and selectivity trend among active sites is an important base to explore and improve the deNO processes. Because the experimental performances are determined by the reaction rate, it is worthwhile to investigate the kinetic limiting steps calculated by comparative microkinetic modeling. We found that, without illumination, N₂ production is inactive over various TiO₂ surfaces/sites, but photogenerated holes can break the scaling relation of the dark condition by weakening O₂* adsorption, leading to a significant increase in deNO activity on defective titania surfaces. However, the low N₂ selectivity can be attributed to the small strength of N₂O adsorption. In contrast, the N₂ selectivity is enhanced in Ti-modified zeolite because of a stronger N₂O* adsorption. We demonstrate here that the reaction phase diagram analysis can clearly establish a global picture of reaction activity and selectivity over various catalytic sites. In combination with microkinetic modeling, it can effectively determine the kinetic limits, providing insights to improve the design of photocatalysts.

Obtaining Consistent Free Energies for Ion Binding at Surfaces from Solution: Pathways versus Alchemy for Determining Kink Site Stability

Ion incorporation or removal from a solid at the interface with solution is a fundamental part of crystal growth. Despite this, there have been few quantitative determinations of the thermodynamics for such processes from atomistic molecular dynamics due to the associated technical challenges. In this study, we compute the free energies for ion removal from kink sites at the interface between NaCl and water as an illustrative example. To examine the influence of the free energy technique used, we compare methods that follow an explicit pathway for dissolution with those that focus on the thermodynamics of the initial and final states using metadynamics and free energy perturbation, respectively. While the initial results of the two approaches are found to be completely different, it is demonstrated that the thermodynamics can be reconciled with appropriate corrections for the standard states, thus illustrating the need for caution in interpreting raw free energy curves for ion binding as widely found in the literature. In addition, a new efficient approach is introduced to correct for the system size dependence of kink site energies both due to the periodic interaction of charges in an inhomogeneous dielectric system and due to the dipolar interactions between pairs of kinks along a row. Ultimately, it is shown that with suitable care, both classes of free energy techniques are capable of producing kink site stabilities that are consistent with the solubility of the underlying bulk solid. However, the precise values for individual kink sites exhibit a small systematic offset, which can be ascribed to the contribution of the interfacial potential to the pathway-based results. For the case of NaCl, the free energies of the kink sites relative to a 1 M aqueous solution for Na⁺ and Cl^- are found to be surprisingly different and of opposite sign, despite the ions having very similar hydration free energies.

Computational design of quantum defects in two-dimensional materials

Missing atoms or atom substitutions (point defects) in crystal lattices in two-dimensional (2D) materials are potential hosts for emerging quantum technologies, such as single-photon emitters and spin quantum bits (qubits). First-principles-guided design of quantum defects in 2D materials is paving the way for rational spin qubit discovery. Here we discuss the frontier of first-principles theory development and the challenges in predicting the critical physical properties of point defects in 2D materials for quantum information technology, in particular for optoelectronic and spin-optotronic properties. Strong many-body interactions at reduced dimensionality require advanced electronic structure methods beyond mean-field theory. The great challenges for developing theoretical methods that are appropriate for strongly correlated defect states, as well as general approaches for predicting spin relaxation and the decoherence time of spin defects, are yet to be addressed.

Oxygen chemistry of halogen-doped CeO2(111)

We study substitutional fluorine, chlorine and bromine impurities at CeO₂(111), and their effects on the oxygen chemistry of the surface, using density functional theory. We find that impurity formation results in a halide ion and one Ce³⁺ ion for all three halogens, although the formation energy depends strongly on the identity of the halogen; however, once formed, all three halogens exhibit a similar propensity to form impurity-impurity pairs. Furthermore, while the effects of halogen impurities on oxygen vacancy formation are marginal, they are more significant for oxygen molecule adsorption, due to electron transfer from the Ce³⁺ ion which results in an adsorbed superoxide molecule. We also consider the displacement of a halide ion on to the surface by half of an oxygen molecule, and find that the energy required to do so depends strongly not only on the identity of the halogen, but also on whether or not a second halogen impurity, with its associated Ce³⁺ ion, is present; if it is, then the process is greatly facilitated. Overall, our results demonstrate the existence of a rich variety of ways in which the oxygen chemistry of CeO₂(111) may be modified by the presence of halogen dopants.

Activity and Mechanism Mapping of Photocatalytic NO2 Conversion on the Anatase TiO2(101) Surface

NO_x emission heavily affects our environment and human health. Photocatalytic denitrification (deNO_x) attracted much attention because it is low-cost and nonpolluting, but undesired nitrite and nitrate were produced in reality, instead of harmless N₂. Unveiling the active sites and the photocatalytic mechanism is very important to improve the process. Herein, we have employed a combinational scenario to investigate the reaction mechanism of NO₂ and H₂O on anatase TiO₂(101). On the one hand, a polaron-corrected GGA functional (GGA + Lany-Zunger) was applied to improve the description of electronic states in photoassisted processes. On the other hand, a reaction phase diagram (RPD) was established to understand the (quasi) activity trend over both perfect and defective surfaces. It was found that a perfect surface is more active via the Eley-Rideal mechanism without NO₂ adsorption, while the activity on defective surfaces is limited by the sluggish recombinative desorption. A photogenerated hole can weaken the OH* adsorption energies and circumvents the scaling relation of the dark reaction, eventually enhancing the deNO_x activity significantly. The insights gained from our work indicate that tuning the reactivity by illumination-induced localized charge and diverse reaction pathways are two methods for improving adsorption, dissociation, and desorption processes to go beyond the conventional activity volcano plot limit of dark conditions.

Dimensionality-Inhibited Chemical Doping in Two-Dimensional Semiconductors: The Phosphorene and MoS2 from Charge-Correction Method

Despite the great appeal of two-dimensional semiconductors for electronics and optoelectronics, to achieve the required charge carrier concentrations by means of chemical doping remains a challenge due to large defect ionization energies (IEs). Here, by decomposing the defect IEs into three parts based on ionization process, we propose a conceptual picture that the large defect IEs are caused by two effects of reduced dimensionality. While the quantum confinement effect makes the neutral single-electron point defect levels deep, the reduced screening effect leads to high energy cost for the electronic relaxation. The first-principles calculations for black phosphorus and MoS₂ do demonstrate the general trend. Using BP monolayer either embedded into dielectric continuum or encapsulated between two hBN layers, we demonstrate the feasibility of increasing the screening to reduce the defect IEs. Our analysis is expected to help achieve effective carrier doping and open ways toward more extensive applications of 2D semiconductors.

Chemistry of Oxygen Ionosorption on SnO2 Surfaces

Ionosorbed oxygen is the key player in reactions on metal-oxide surfaces. This is particularly evident for chemiresistive gas sensors, which operate by modulating the conductivity of active materials through the formation/removal of surface O-related acceptors. Strikingly though, the exact type of species behind the sensing response remains obscure even for the most common material systems. The paradigm for ab initio modeling to date has been centered around charge-neutral surface species, ignoring the fact that molecular adsorbates are required to ionize to induce the sensing response. Herein, we resolve this inconsistency by carrying out a careful analysis of all charged O-related species on three naturally occurring surfaces of SnO₂. We reveal that two types of surface acceptors can form spontaneously upon the adsorption of atmospheric oxygen: (i) superoxide O₂^- on the (110) and the (101) surfaces and (ii) doubly ionized O^2- on the (100) facet, with the previous experimental evidence pointing to the latter as the source of sensing response. This species has a unique geometry involving a large displacement of surface Sn, forcing it to attain the coordination resembling that of Sn²⁺ in SnO, which seems necessary to stabilize O^2- and activate metal-oxide surfaces for gas sensing.

Chemistry of Oxygen Ionosorption on SnO2 Surfaces

Ionosorbed oxygen is the key player in reactions on metal-oxide surfaces. This is particularly evident for chemiresistive gas sensors, which operate by modulating the conductivity of active materials through the formation/removal of surface O-related acceptors. Strikingly though, the exact type of species behind the sensing response remains obscure even for the most common material systems. The paradigm for ab initio modeling to date has been centered around charge-neutral surface species, ignoring the fact that molecular adsorbates are required to ionize to induce the sensing response. Herein, we resolve this inconsistency by carrying out a careful analysis of all charged O-related species on three naturally occurring surfaces of SnO₂. We reveal that two types of surface acceptors can form spontaneously upon the adsorption of atmospheric oxygen: (i) superoxide O₂^- on the (110) and the (101) surfaces and (ii) doubly ionized O^2- on the (100) facet, with the previous experimental evidence pointing to the latter as the source of sensing response. This species has a unique geometry involving a large displacement of surface Sn, forcing it to attain the coordination resembling that of Sn²⁺ in SnO, which seems necessary to stabilize O^2- and activate metal-oxide surfaces for gas sensing.

First-principles calculations of hybrid inorganic-organic interfaces: from state-of-the-art to best practice

The computational characterization of inorganic-organic hybrid interfaces is arguably one of the technically most challenging applications of density functional theory. Due to the fundamentally different electronic properties of the inorganic and the organic components of a hybrid interface, the proper choice of the electronic structure method, of the algorithms to solve these methods, and of the parameters that enter these algorithms is highly non-trivial. In fact, computational choices that work well for one of the components often perform poorly for the other. As a consequence, default settings for one materials class are typically inadequate for the hybrid system, which makes calculations employing such settings inefficient and sometimes even prone to erroneous results. To address this issue, we discuss how to choose appropriate atomistic representations for the system under investigation, we highlight the role of the exchange-correlation functional and the van der Waals correction employed in the calculation and we provide tips and tricks how to efficiently converge the self-consistent field cycle and to obtain accurate geometries. We particularly focus on potentially unexpected pitfalls and the errors they incur. As a summary, we provide a list of best practice rules for interface simulations that should especially serve as a useful starting point for less experienced users and newcomers to the field.

Self-Consistent Potential Correction for Charged Periodic Systems

Supercell models are often used to calculate the electronic structure of local deviations from the ideal periodicity in the bulk or on the surface of a crystal or in wires. When the defect or adsorbent is charged, a jellium counter charge is applied to maintain overall neutrality, but the interaction of the artificially repeated charges has to be corrected, both in the total energy and in the one-electron eigenvalues and eigenstates. This becomes paramount in slab or wire calculations, where the jellium counter charge may induce spurious states in the vacuum. We present here a self-consistent potential correction scheme and provide successful tests of it for bulk and slab calculations.

First-Principles Atomistic Thermodynamics and Configurational Entropy

In most applications, functional materials operate at finite temperatures and are in contact with a reservoir of atoms or molecules (gas, liquid, or solid). In order to understand the properties of materials at realistic conditions, statistical effects associated with configurational sampling and particle exchange at finite temperatures must consequently be taken into account. In this contribution, we discuss the main concepts behind equilibrium statistical mechanics. We demonstrate how these concepts can be used to predict the behavior of materials at realistic temperatures and pressures within the framework of atomistic thermodynamics. We also introduce and discuss methods for calculating phase diagrams of bulk materials and surfaces as well as point defect concentrations. In particular, we describe approaches for calculating the configurational density of states, which requires the evaluation of the energies of a large number of configurations. The cluster expansion method is therefore also discussed as a numerically efficient approach for evaluating these energies.

Iron and oxygen vacancies at the hematite surface: pristine case and with a chlorine adatom

Defect complexes play critical roles in the dynamics of water molecules in photoelectrochemical cell devices. For the specific case of hematite (α-Fe₂O₃), iron and oxygen vacancies are said to mediate the water splitting process through the localization of optically-derived charges. Using first-principles methods based on density-functional theory we show that both iron and oxygen vacancies can be observed at the surface. For an oxygen-rich environment, usually under wet conditions, the charged iron vacancies should be more frequent. As sea water would be an ideal electrolyte for this kind of device, we have also analyzed the effect of additional chlorine adsorption on this surface. While the chlorine adatom kills the charged oxygen vacancies, entering the void sites, it will not react with the iron vacancies, keeping them active during water splitting processes.

Fermi level dependence of gas-solid oxygen defect exchange mechanism on TiO2 (110) by first-principles calculations

In the same way that gases interact with oxide semiconductor surfaces from above, point defects interact from below. Previous experiments have described defect-surface reactions for TiO₂(110), but an atomistic picture of the mechanism remains unknown. The present work employs computations by density functional theory of the thermodynamic stabilities of metastable states to elucidate possible reaction pathways for oxygen interstitial atoms at TiO₂(110). The simulations uncover unexpected metastable states including dumbbell and split configurations in the surface plane that resemble analogous interstitial species in the deep bulk. Comparison of the energy landscapes involving neutral (unionized) and charged intermediates shows that the Fermi energy E_F exerts a strong influence on the identity of the most likely pathway. The largest elementary-step thermodynamic barrier for interstitial injection trends mostly downward by 2.1 eV as E_F increases between the valence and conduction band edges, while that for annihilation trends upward by 2.1 eV. Several charged intermediates become stabilized for most values of E_F upon receiving conduction band electrons from TiO₂, and the behavior of these species governs much of the overall energy landscape.

The first-principles study of nH-VSn complex: impurity effects on p-type SnO monolayer

As a rare typical p-channel layered oxide semiconductor, two-dimensional tin monoxide has attracted great attention due to its wide promising applications in nano-electronics. Using the first-principles calculation, we studied the effects of multi-hydrogen-tin/oxygen vacancy complex impurities on the electronic properties of the p-type monolayer SnO. The calculation results indicated that O vacancy (V_O) is a donor and Sn vacancy (V_Sn) acts as a double acceptor. V_Sn should be the source of p-type in undoped SnO in an O-rich environment. When hydrogen is introduced, the more stable nH-V_Sn (n = 1, 2, and 3) complex defects can be formed. These complex impurities can affect the p-type SnO monolayer in the following three main ways: (i) the p-type H-V_Sn compensates the deeper acceptor level of V_Sn and enhances the majority carrier mobility. (ii) The more stable 2H-V_Sn neutralizes the p-type dopant nature of V_Sn and H-V_Sn. (iii) The 3H-V_Sn converts the defect to be an n-type dopant. Our results indicated that limitation of hydrogen is necessary for the preparation of high-quality p-type two-dimensional SnO, as a small amount of hydrogen produces positive effect on p-type SnO; however, the higher concentration of hydrogen is destructive to the p-type character of monolayer SnO.

Intrinsic defects of GaSe

GaSe is a layered semiconductor with an optical band gap tunable by the number of layers in a thin film. This is promising for application in micro/optoelectronics and photovoltaics. However, for that, knowledge about the intrinsic defects are needed, since they may influence device behavior. Here we present a comprehensive study of intrinsic point defects in both bulk and monolayer (ML) GaSe, using an optimized hybrid functional which reproduces the band gap and is Koopmans' compliant. Formation energies and charge transition levels are calculated, the latter in good agreement with available experimental data. We find that the only intrinsic donor is the interlayer gallium interstitial, which is absent in the case of the ML. The vacancies are acceptors, the selenium interstitial is electrically inactive, and small intrinsic defect complexes have formation energies too high to play a role in the electronic properties of samples grown under quasi-equilibrium conditions. Bulk GaSe is well compensated by the intrinsic defects, and is an ideal substrate. The ML is intrinsically p-type, and p-type doping cannot be compensated either. The opening of the band gap changes the defect physics considerably with respect to the bulk.

Extrapolated Defect Transition Level in Two-Dimensional Materials: The Case of Charged Native Point Defects in Monolayer Hexagonal Boron Nitride

Defect formation energy as well as the charge transition level (CTL) plays a vital role in understanding the underlying mechanism of the effect of defects on material properties. However, the accurate calculation of charged defects, especially for two-dimensional materials, is still a challenging topic. In this paper, we proposed a simplified scheme to rescale the CTLs from the semilocal to the hybrid functional level, which is time-saving during the charged defect calculations. Based on this method, we systematically calculated the formation energy of four kinds of intrinsic point defects in two-dimensional hexagonal boron nitride (2D h-BN) by uniformly scaling the supercells by which we found a time-saving method to obtain the "special vacuum size" (Komsa, H.-P.; Berseneva, N.; Krasheninnikov, A. V.; Nieminen, R. M. Phys. Rev. X, 2014, 4, 031044). Native defects including nitrogen vacancy (V_N), boron vacancy (V_B), nitrogen atom anti-sited on boron position (N_B), and boron atom anti-sited on nitrogen position (B_N) were calculated. The reliability of our scheme was verified by taking V_N as a probe to conduct the hybrid functional calculation, and the rescaled CTL is within the acceptable error range with the pure HSE results. Based on the results of CTLs, all the native point defects in the h-BN monolayer act as hole or electron trap centers under certain conditions and would suppress the p- or n-type electrical conduction of h-BN-based devices. Our rescale method is also suitable for other materials for defect charge transition level calculations.

Strong Hole Trapping Due to Oxygen Dimers in BiVO4: Effect on the Water Oxidation Reaction

We present a study of hole bipolarons in BiVO₄. We show that in the presence of two holes O-O dimers are formed, leading to strong charge trapping. While the formation of bipolarons in bulk BiVO₄ requires overcoming a kinetic barrier, we find that these defects should be spontaneously formed at the surface of the material and its interface with water. Through molecular dynamics simulations, we study the effect of bipolarons on the water-splitting reaction and show that their presence may be especially beneficial in alkaline conditions.

Electron and Hole Polarons at the BiVO4-Water Interface

We determine the transition levels of electron and hole polarons at the BiVO₄-water interface through thermodynamic integration within a hybrid functional scheme, thereby accounting for the liquid nature of the water component. The electron polaron is found to be less stable at the interface than in the bulk by 0.18 eV, while for the hole polaron the binding energy increases by 0.20 eV when the charge localizes in the surface layer of BiVO₄. These results indicate that interfacial effects on the polaron binding energy and charge distribution are sizeable and cannot trivially be inferred from bulk calculations.

Fermi Level Determination for Charged Systems via Recursive Density of States Integration

Determining the Fermi level position for a given material is important to understand many of its electronic and chemical properties. Ab initio methods are effective in computing Fermi levels when using charge-neutral supercells. However, in the case where charges are explicitly included, the compensating homogeneous background charge, which is necessary to maintain charge neutrality in periodic models, causes the vacuum potential to be ill-defined - which would otherwise have been a reliable reference potential. Here, we develop a method based on recursively integrating the density of states to determine shifts in the Fermi level upon charging. By introducing incremental charges, one can compute the density of states profile and determine the shift in the Fermi level that corresponds to adding or removing a given increment of charge δq, which allows the evaluation of the Fermi level for any arbitrary charge q. We test this method for a range of materials (graphene, h-BN, C₃N₄, Cu, and MoS₂) and demonstrate that this method can produce a reasonable agreement with models that rely on localized compensating background charges.

pH-Dependent Surface Chemistry from First Principles: Application to the BiVO4(010)-Water Interface

We present a theoretical formulation for studying the pH-dependent interfacial coverage of semiconductor-water interfaces through ab initio electronic structure calculations, molecular dynamics simulations, and the thermodynamic integration method. This general methodology allows one to calculate the acidity of the individual adsorption sites on the surface and consequently the pH at the point of zero charge, pH_PZC, and the preferential adsorption mode of water molecules, either molecular or dissociative, at the semiconductor-water interface. The proposed method is applied to study the BiVO₄(010)-water interface, yields a pH_PZC in excellent agreement with the experimental characterization. Furthermore, from the calculated p K_a values of the individual adsorption sites, we construct an ab initio concentration diagram of all adsorbed species at the interface as a function of the pH of the aqueous solution. The diagram clearly illustrates the pH-dependent coverage of the surface and indicates that protons are found to be significantly adsorbed (∼1% of available sites) only in highly acidic conditions. The surface is found to be mostly covered by molecularly adsorbed water molecules in a wide interval of pH values ranging from 2 to 8. Hydroxyl ions are identified as the dominant adsorbed species at pH larger than 8.2.

Modelling molecular adsorption on charged or polarized surfaces: a critical flaw in common approaches

A number of recent computational material design studies based on density functional theory (DFT) calculations have put forward a new class of materials with electrically switchable chemical characteristics that can be exploited in the development of tunable gas storage and electrocatalytic applications. We find systematic flaws in almost every computational study of gas adsorption on polarized or charged surfaces, stemming from an improper and unreproducible treatment of periodicity, leading to very large errors of up to 3 eV in some cases. Two simple corrective procedures that lead to consistent results are proposed, constituting a crucial course correction to the research in the field.

Application of the Lany-Zunger polaron correction for calculating surface charge trapping

Defect calculations, using density functional theory in a local or semi-local approximation, in transition metal oxides are severely handicapped by the electron self-interaction error. The underestimation of the band gap may cause incorrect occupation of defect states and wrong formation energies, and the underestimated localization of the states disfavors the formation of small polarons. These problems can be avoided by using higher level approximations (GW or a correctly chosen hybrid functional), but those methods are computationally too expensive to be used for calculating surface defects in a periodic slab model. Lany and Zunger have suggested a convenient (low-cost) solution for solving the band-gap and charge delocalization problem, by applying a correction scheme to the standard local or semi-local approximations. Most importantly, the linearity of the total energy as a function of the fractional occupation numbers, is restored, leading to the fulfillment of the generalized Koopmans' theorem. The method works well in the bulk but, as we show here, it is not accurate on the surface due to the different screening environment. We also show that by making the atom- and angular-momentum dependent parameters of the Lany-Zunger polaron-correction also coordination dependent, it is possible to correctly describe charge trapping in small polaron states on the anatase (1 0 1) and rutile (1 1 0) surfaces at a low computational cost.

Native defects and substitutional impurities in two-dimensional monolayer InSe

As a burgeoning two-dimensional (2D) semiconductor, InSe holds unique electronic properties and great promise for novel 2D electronic devices. To advance the development of 2D InSe devices, the exploration of n-type and p-type conductivities of InSe is indispensable. With first-principles calculations, we investigate the properties of native defects and substitutional impurities in monolayer InSe, including formation energies and ionization energies. As the traditional jellium scheme encounters an energy divergence for charged defects in 2D materials, an extrapolation approach is adopted here to obtain convergent energies. We find that In vacancy is a deep acceptor and Se vacancy is an electrically neutral defect. All the studied substitutional dopants at In or Se sites have high ionization energies in the range of 0.41-0.84 eV. However, electrons may transport through the defect-bound band edge states in X_Se (X = Cl, Br, and I) as a potential source of n-type conductivity.

Atomistic Corrective Scheme for Supercell Density Functional Theory Calculations of Charged Defects

A new method to correct formation energies of charged defects obtained by supercell density-functional calculations is presented and applied to bulk, surface, and low-dimensional systems. The method relies on atomistic models and a polarizable force field to describe a material system and its dielectric properties. The polarizable force field is based on a minimal set of fitting parameters, it accounts for the dielectric screening arising from ions and electrons separately, and it can be easily implemented in any software for atomistic molecular dynamics simulations. This work illustrates both technical aspects and applications of the new corrective scheme. The method is tested on systems in vacuo to validate the energy scheme. It is applied to charged defects in the bulk and at the surface of realistic materials to achieve comparison with published results obtained by using available corrective schemes based on continuum electrostatics treatments. Moreover, to demonstrate its generality, the method is used to correct the formation energy obtained by DFT of a singly negatively charged S vacancy in monolayer, bilayer, trilayer and bulk MoS₂.

Atomic Structure and Spectroscopy of Single Metal (Cr, V) Substitutional Dopants in Monolayer MoS2

Dopants in two-dimensional dichalcogenides have a significant role in affecting electronic, mechanical, and interfacial properties. Controllable doping is desired for the intentional modification of such properties to enhance performance; however, unwanted defects and impurity dopants also have a detrimental impact, as often found for chemical vapor deposition (CVD) grown films. The reliable identification, and subsequent characterization, of dopants is therefore of significant importance. Here, we show that Cr and V impurity atoms are found in CVD grown MoS₂ monolayer 2D crystals as single atom substitutional dopants in place of Mo. We attribute these impurities to trace elements present in the MoO₃ CVD precursor. Simultaneous annular dark field scanning transmission electron microscopy (ADF-STEM) and electron energy loss spectroscopy (EELS) is used to map the location of metal atom substitutions of Cr and V in MoS₂ monolayers with single atom precision. The Cr and V are stable under electron irradiation at 60 to 80 kV, when incorporated into line defects, and when heated to elevated temperatures. The combined ADF-STEM and EELS differentiates these Cr and V dopants from other similar contrast defect structures, such as 2S self-interstitials at the Mo site, preventing misidentification. Density functional theory calculations reveal that the presence of Cr or V causes changes to the density of states, indicating doping of the MoS₂ material. These transferred impurities could help explain the presence of trapped charges in CVD prepared MoS₂.

A mechanism of Cu work function reduction in CsBr/Cu photocathodes

Thin films of CsBr deposited on Cu(100) have been proposed as next-generation photocathode materials for applications in particle accelerators and free-electron lasers. However, the mechanisms underlying an improved photocathode performance as well as their long-term stability remain poorly understood. We present Density Functional Theory (DFT) calculations of the work function reduction following the application of CsBr thin film coatings to Cu photocathodes. The effects of both flat and rough interface and van der Waals forces are examined. Calculations suggest that CsBr films can reduce the Cu(100) work function by about 1.5 eV, which would explain the observed increase in quantum efficiency (QE) of coated vs. uncoated photocathodes. A model explaining the experimentally observed laser activation of photocathodes is provided whereby the photo-induced creation of Br vacancies and Cs-Br di-vacancies and their subsequent diffusion to the Cu/CsBr interface lead to a further increase in QE after a period of laser irradiation.

Determination of formation and ionization energies of charged defects in two-dimensional materials

We present a simple and efficient approach to evaluate the formation energy and, in particular, the ionization energy (IE) of charged defects in two-dimensional (2D) systems using the supercell approximation. So far, first-principles results for such systems can scatter widely due to the divergence of the Coulomb energy with vacuum dimension, denoted here as L_{z}. Numerous attempts have been made in the past to fix the problem under various approximations. Here, we show that the problem can be resolved without any such assumption, and a converged IE can be obtained by an extrapolation of the asymptotic IE expression at large L_{z} (with a fixed lateral area S) back to the value at L_{z}=0. Application to defects in monolayer boron nitride reveal that defects in 2D systems can be unexpectedly deep, much deeper than the bulk.

Origin of Fermi-level pinning at GaAs surfaces and interfaces

Through first-principles simulation methods, we assign the origin of Fermi-level pinning at GaAs surfaces and interfaces to the bistability between the As-As dimer and two As dangling bonds, which transform into each other upon charge trapping. This defect is shown to be naturally formed both at GaAs surfaces upon oxygen deposition and in the near-interface substoichiometric oxide. Using electron-counting arguments, we infer that the identified defect occurs in opposite charge states. The Fermi-level pinning then results from the amphoteric nature of this defect which drives the Fermi level to its defect level. These results account for the experimental characterization at both GaAs surfaces and interfaces within a unified picture, wherein the role of As antisites is elucidated.

Adsorption and reactions of O2 on anatase TiO2

CONSPECTUS: The interaction of molecular oxygen with titanium dioxide (TiO2) surfaces plays a key role in many technologically important processes such as catalytic oxidation reactions, chemical sensing, and photocatalysis. While O2 interacts weakly with fully oxidized TiO2, excess electrons are often present in TiO2 samples. These excess electrons originate from intrinsic reducing defects (oxygen vacancies and titanium interstitials), doping, or photoexcitation and form polaronic Ti(3+) states in the band gap near the bottom of the conduction band. Oxygen adsorption involves the transfer of one or more of these excess electrons to an O2 molecule at the TiO2 surface. This results in an adsorbed superoxo (O2(-)) or peroxo (O2(2-)) species or in molecular dissociation and formation of two oxygen adatoms (2 × O(2-)). Oxygen adsorption is also the first step toward oxygen incorporation, a fundamental reaction that strongly affects the chemical properties and charge-carrier densities; for instance, it can transform the material from an n-type semiconductor to a poor electronic conductor. In this Account, we present an overview of recent theoretical work on O2 adsorption and reactions on the reduced anatase (101) surface. Anatase is the TiO2 polymorph that is generally considered most active in photocatalysis. Experiments on anatase powders have shown that the properties of photoexcited electrons are similar to those of excess electrons from reducing defects, and therefore, oxygen on reduced anatase is also a model system for studying the role of O2 in photocatalysis. Experimentally, the characteristic Ti(3+) defect states disappear after adsorption of molecular oxygen, which indicates that the excess electrons are indeed trapped by O2. Moreover, superoxide surface species associated with two different cation surface sites, possibly a regular cation site and a cation close to an anion vacancy, were identified by electron paramagnetic resonance spectroscopy. On the theoretical side, however, density functional theory studies have consistently found that it is energetically more favorable for O2 to adsorb in the peroxo form rather than the superoxo form. As a result, obtaining a detailed understanding of the nature of the observed superoxide species has proven difficult for many years. On reduced anatase (101), both oxygen vacancies and Ti interstitials have been shown to reside exclusively in the susbsurface. We discuss how reaction of O2 with a subsurface O vacancy heals the vacancy while leading to the formation of a surface bridging dimer defect. Similarly, the interaction of O2 with a Ti interstitial causes migration of this defect to the surface and the formation of a surface TiO2 cluster. Finally, we analyze the peroxo and superoxo states of the adsorbed molecule. On the basis of periodic hybrid functional calculations of interfacial electron transfer between reduced anatase and O2, we show that the peroxide form, while energetically more stable, is kinetically less favorable than the superoxide form. The existence of a kinetic barrier between the superoxo and peroxo states is essential for explaining a variety of experimental observations.

Concentration of vacancies at metal-oxide surfaces: case study of MgO(100)

We investigate the effects of doping on the formation energy and concentration of oxygen vacancies at a metal-oxide surface, using MgO(100) as an example. Our approach employs density-functional theory, where the performance of the exchange-correlation functional is carefully analyzed, and the functional is chosen according to a condition on density-functional theory ionization energies. The approach is further validated by coupled-cluster calculations, including single, double, and perturbative triple substitutions, for embedded clusters. We demonstrate that the concentration of oxygen vacancies at a doped oxide surface is largely determined by the formation of a macroscopically extended space-charge region.