Defect Charge Transition Levels Research Articles

Case of the Bromine Vacancy in Cs4PbBr6.

Typically defect tolerance is equated with a lack of deleterious defects or with abundant defects creating only shallow levels. Here, we address the idea that deep defects, when unavoidable, do not guarantee harmful consequences. Using halogen vacancy as a common defect among halides, we explore its behavior in Cs4PbBr6. It is a large gap material (band gap of ∼4 eV) known for its green emission at ∼520 nm. We show that its Br-vacancy is indeed a deep defect as obtained from hybrid density functional calculations. An analysis of the configuration coordinate diagram corresponding to the defect's charge transition levels enables us to conclude that the nonradiative recombination cycle will be hampered by an extremely slow hole capture process. Therefore, Br-vacancy will not suppress light emission in Cs4PbBr6. Although this finding does not signal that all deep defects will behave similarly, it indicates that defect tolerance may be achievable despite their occurrence.

Experimental and theoretical studies of native deep-level defects in transition metal dichalcogenides

Transition metal dichalcogenides (TMDs), especially in two-dimensional (2D) form, exhibit many properties desirable for device applications. However, device performance can be hindered by the presence of defects. Here, we combine state of the art experimental and computational approaches to determine formation energies and charge transition levels of defects in bulk and 2D MX2 (M = Mo or W; X = S, Se, or Te). We perform deep level transient spectroscopy (DLTS) measurements of bulk TMDs. Simultaneously, we calculate formation energies and defect levels of all native point defects, which enable identification of levels observed in DLTS and extend our calculations to vacancies in 2D TMDs, for which DLTS is challenging. We find that reduction of dimensionality of TMDs to 2D has a significant impact on defect properties. This finding may explain differences in optical properties of 2D TMDs synthesized with different methods and lays foundation for future developments of more efficient TMD-based devices.

Spinney: Post-processing of first-principles calculations of point defects in semiconductors with Python

Understanding and predicting the thermodynamic properties of point defects in semiconductors and insulators would greatly aid in the design of novel materials and allow tuning the properties of existing ones. As a matter of fact, first-principles calculations based on density functional theory (DFT) and the supercell approach have become a standard tool for the study of point defects in solids. However, in the dilute limit, of most interest for the design of novel semiconductor materials, the “raw“ DFT calculations require an extensive post-processing. Spinney is an open-source Python package developed with the aim of processing first-principles calculations to obtain several quantities of interest, such as the chemical potential limits that assure the thermodynamic stability of the defect-laden system, defect charge transition levels, defect formation energies, including electrostatic corrections for finite-size effects, and defect and carrier concentrations. In this paper we demonstrate the capabilities of the Spinney code using c-BN, GaN:Mg, TiO2 and ZnO as examples. Program summaryProgram Title:SpinneyCPC Library link to program files:https://doi.org/10.17632/2xp4ddwmgx.1Developer’s repository link:https://gitlab.com/Marrigoni/spinneyCode Ocean capsule:https://codeocean.com/capsule/4970623Licensing provisions: MITProgramming language: Python 3External libraries: NumPy [1], SciPy [2], Pandas [3], Matplotlib [4], ASE [5]Nature of problem: Post-processing of first-principles calculations in order to obtain important properties of defect laden systems in the dilute-limit: chemical potential values ensuring thermodynamic stability, thermodynamic charge transition levels, defect formation energies and corrections thereof using state-of-the-art corrections schemes for electrostatic finite-size effects, equilibrium defect and carriers concentrations.Solution method: Flexible low-level interface for allowing the post-processing of the raw fist-principles data provided by any computer code. High-level interface for parsing and post-processing the first-principles data produced by the popular computer codes VASP and WIEN2k.Additional comments including restrictions and unusual features: An extensive documentation is available at: https://spinney.readthedocs.io

Layer dependence of defect charge transition levels in two-dimensional materials

Point defects in two-dimensional (2D) materials hold great promise for optoelectronic and quantum technologies. Their properties depend sensitively on the dielectric environment and number of 2D layers, but this has remained a challenge to include in first-principles calculations on account of the high computational cost. Recent first-principles techniques facilitate efficient prediction of substrate effects on defect charge transition levels in 2D materials, replacing the substrate by a continuum dielectric model. Here, we show that analogous continuum treatment of defect-free layers in multilayer 2D materials accurately predicts defect energies compared to explicit multilayer calculations, but at a small fraction of the computational cost. Applications of this technique to one- to five-layer and bulk hexagonal boron nitride reveal that defect ionization energies systematically decrease with an increasing number of layers and for defects in inner layers due to increased dielectric screening. Our results highlight the dominant role of electrostatic screening in the effect of the environment and the feasibility of tuning defect levels in 2D materials using material thickness and defect location within the material.

Properties of intrinsic point defects and dimers in hexagonal boron nitride

Hexagonal boron nitride (hBN) is a wide gap 2D layered material with good insulating properties. Intrinsic point defects in hBN play an important role in its applications as a dielectric in 2D electronic devices. However, the electronic properties of these defects are still poorly understood. We have calculated the structure and properties of a wide range of intrinsic point defects in the bulk of hBN using hybrid density functional theory (DFT). These include vacancies and interstitial states of B and N as well as di- and tri-vacancies. For each isolated defect, multiple charge states are calculated, and for each charge state multiple spin states are investigated. Positions of defect charge transition levels in the band gap of hBN are calculated. In particular, we predict that B vacancies are likely to be negatively charged in contact with graphene and other metals. Calculations of the interaction between vacancies predict that divacancies in both B and N sublattices are strongly binding. Moreover, the interaction of single B and N vacancies in adjacent layers induces the creation of -N–N- and -B–B- molecular bridges, which greatly distort the local structure, leading to local bond weakening. These results provide further insight into the properties of defects which can be responsible for degradation of hBN based devices.

Fundamental principles for calculating charged defect ionization energies in ultrathin two-dimensional materials

Defects in 2D materials are becoming prominent candidates for quantum emitters and scalable optoelectronic applications. However, several physical properties that characterize their behavior, such as charged defect ionization energies, are difficult to simulate with conventional first-principles methods, mainly because of the weak and anisotropic dielectric screening caused by the reduced dimensionality. We establish fundamental principles for accurate and efficient calculations of charged defect ionization energies and electronic structure in ultrathin 2D materials. We propose to use the vacuum level as the reference for defect charge transition levels (CTLs) because it gives robust results insensitive to the level of theory, unlike commonly used band edge positions. Furthermore, we determine the fraction of Fock exchange in hybrid functionals for accurate band gaps and band edge positions of 2D materials by enforcing the generalized Koopmans' condition of localized defect states. We found the obtained fractions of Fock exchange vary significantly from 0.2 for bulk $h$-BN to 0.4 for monolayer $h$-BN, whose band gaps are also in good agreement with experimental results and calculated GW results. The combination of these methods allows for reliable and efficient prediction of defect ionization energies (difference between CTLs and band edge positions). We motivate and generalize these findings with several examples including different defects in monolayer to few-layer hexagonal boron nitride ($h$-BN), monolayer MoS$_2$ and graphane. Finally, we show that increasing the number of layers of $h$-BN systematically lowers defect ionization energies, mainly through CTLs shifting towards vacuum, with conduction band minima kept almost unchanged.

Theoretical confirmation of the polaron model for the Mg acceptor in β-Ga2O3

β-Ga2O3 has recently been considered for power electronics applications but p-type doping is an issue, especially since small hole polarons were predicted and observed in this material. Recently, by using a gap-optimized, Koopmans-compliant hybrid functional, we were able to reproduce the observed charge transition levels of defects, including the hole polaron in the intrinsic material. In this study, the same hybrid functional is used to confirm the assignment of the electron paramagnetic resonance (EPR) spectrum observed in Mg-doped β-Ga2O3 samples. The Mg impurity introduces a deep acceptor level in β-Ga2O3 corresponding to a small polaron, localized at an oxygen site adjacent to the substitutional Mg. The so-called O1 site is energetically favored and the superhyperfine interactions with the neighboring tetrahedrally coordinated Ga atom are 1.9 times stronger than with the neighboring octahedrally coordinated Ga. The calculated hyperfine tensor agrees well with the EPR measurement. These results confirm that Mg cannot act as a shallow acceptor in β-Ga2O3.

Substrate screening effects on the quasiparticle band gap and defect charge transition levels in MoS2

Monolayer MoS$_2$ has emerged as an interesting material for nanoelectronic and optoelectronic devices. The effect of substrate screening and defects on the electronic structure of MoS$_2$ are important considerations in the design of such devices. Here, we present ab initio density functional theory (DFT) and GW calculations to study the effect of substrate screening on the quasiparticle band gap and defect charge transition levels (CTLs) in monolayer MoS$_2$. We find a giant renormalization to the free-standing quasiparticle band gap by 350 meV and 530 meV in the presence of graphene and graphite as substrates, respectively. Our results are corroborated by recent experimental measurements on these systems using scanning tunneling spectroscopy and photoluminescence excitation spectroscopy. Sulfur vacancies are the most abundant native defects found in MoS$_2$. We study the CTLs of these vacancies in MoS$_2$ using the DFT+GW formalism. We find (+1/0) and (0/-1) CTLs appear in the pristine band gap of MoS$_2$. Substrate screening results in renormalization of the (0/-1) level, with respect to the valence band maximum (VBM), by the same amount as the gap. This results in the pinning of the (0/-1) level about $\sim$500 meV below the conduction band minimum for the free-standing case as well as in the presence of substrates. The (+1/0) level, on the other hand, lies less than 100 meV above the VBM for all the cases.

First-principles engineering of charged defects for two-dimensional quantum technologies

Charged defects in 2D materials have emerging applications in quantum technologies such as quantum emitters and quantum computation. Advancement of these technologies requires rational design of ideal defect centers, demanding reliable computation methods for quantitatively accurate prediction of defect properties. We present an accurate, parameter-free and efficient procedure to evaluate quasiparticle defect states and thermodynamic charge transition levels of defects in 2D materials. Importantly, we solve critical issues that stem from the strongly anisotropic screening in 2D materials, that have so far precluded accurate prediction of charge transition levels in these materials. Using this procedure, we investigate various defects in monolayer hexagonal boron nitride (h-BN) for their charge transition levels, stable spin states and optical excitations. We identify $C_BN_V$ (nitrogen vacancy adjacent to carbon substitution of boron) to be the most promising defect candidate for scalable quantum bit and emitter applications.

Electron trap states at InGaAs/oxide interfaces under inversion through constant Fermi-level ab initio molecular dynamics

We employ constant-Fermi-level ab initio molecular dynamics to investigate defects at the InGaAs/oxide interface upon inversion. We adopt a substoichiometric amorphous model for modelling the structure at the interface and investigate the formation of defect structures upon setting the Fermi-level above the conduction band minimum. The defect formation is detected through both an analysis of the atomic structure and a Wannier-decomposition of the electronic structure. This computer driven approach is able to retrieve In and Ga lone-pair defects and As–As dimer/dangling bond defects, in agreement with previous studies based on physical intuition. In addition, the present simulation reveals hitherto unidentified defect structures consisting of metallic In–In, In–Ga, and Ga–Ga bonds. The defect charge transition levels of such metallic bonds in Al2O3 are then determined through a hybrid functional scheme and found to be consistent with the defect density measured at InGaAs/Al2O3 interfaces. Hence, we conclude that both In and Ga lone pairs dangling bonds and metallic In–In bonds are valid candidate defects for charge trapping at InGaAs/oxide interfaces upon charge carier inversion. This study demonstrates the effectiveness of constant-Fermi-level ab initio molecular dynamics in revealing and identifying defects at InGaAs/oxide interfaces.

Electronic structure of substitutionally doped diamond: Spin-polarized, hybrid density functional theory analysis

Individual substitutional defects in diamond have been theoretically investigated using spin-polarized, hybrid density functional theory method. The revised Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE06) was applied for the total energy calculation. We analyzed the equilibrium geometry, formation energy as a function of charge state and defect charge transition levels, in order to predict the relative stability and doping nature of each defect. Calculations revealed that the crystal radius cannot be solely used to anticipate trend in the volume relaxation and subsequently defect formation energy. A thorough analysis of formation energy vs Fermi level diagrams indicate that none of the investigated elements can individually generate a shallow acceptor or donor level, competitive with substitutional B and P.

Electronic Structure and N-Type Doping in Diamond from First Principles

An investigation of the electronic structure of charged vacancies and X(C), X=(As, Sb, P) substitutional centers in diamond has been carried out by means of ab initio density functional theory. The revised Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE06) was utilized for the total energy calculation. The equilibrium geometry, defect charge transition levels and energetics of the vacancies and substitutional centers were determined. It is found that substitutional As and Sb introduce a donor level into the band gap about 0.5 eV with respect to the conduction band minimum (CBM), therefore, these elements may be a good choice for achieving n-type diamond. From a technological point of view, however, fabrication of As and Sb doped diamond would be challenging due to its high, positive formation energy.

Redox levels in aqueous solution: Effect of van der Waals interactions and hybrid functionals.

We investigate redox levels in aqueous solution using a combination of ab initio molecular dynamics (MD) simulations and thermodynamic integration methods. The molecular dynamics are performed with both the semilocal Perdew-Burke-Ernzerhof functional and a nonlocal functional (rVV10) accounting for van der Waals (vdW) interactions. The band edges are determined through three different schemes, namely, from the energy of the highest occupied and of the lowest unoccupied Kohn-Sham states, from total-energy differences, and from a linear extrapolation of the density of states. It is shown that the latter does not depend on the system size while the former two are subject to significant finite-size effects. For the redox levels, we provide a formulation in analogy to the definition of charge transition levels for defects in crystalline materials. We consider the H(+)/H2 level defining the standard hydrogen electrode, the OH(-)/OH(∗) level corresponding to the oxidation of the hydroxyl ion, and the H2O/OH(∗) level for the dehydrogenation of water. In spite of the large structural modifications induced in liquid water, vdW interactions do not lead to any significant structural effect on the calculated band gap and band edges. The effect on the redox levels is also small since the solvation properties of ionic species are little affected by vdW interactions. Since the electronic properties are not significantly affected by the underlying structural properties, it is justified to perform hybrid functional calculations on the configurations of our MD simulations. The redox levels calculated as a function of the fraction α of Fock exchange are found to remain constant, reproducing a general behavior previously observed for charge transition levels of defects. Comparison with experimental values shows very good agreement. At variance, the band edges and the band gap evolve linearly with α. For α ≃ 0.40, we achieve a band gap, band-edge positions, and redox levels in overall good agreement with experiment.

An amorphous SiO2/4H-SiC(0001) interface: Band offsets and accurate charge transition levels of typical defects

A defect-free structural model of the amorphous SiO2/4H-SiC(0001) interface is presented through first-principle calculations. Following the potential lineup method, we first calculate the valence- and conduction-band offsets of this interface, which are in good agreement with the experimental values. Based on this interface model, we create several typical interface defects and estimate the accurate charge transition levels of these defects within the HSE06 hybrid functional scheme. The results indicate that the silicon interstitial in SiO2 and carbon dimers in both SiC and SiO2 are the possible candidates for the large interface states experimentally observed near the conduction band of 4H-SiC.

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

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

Defect levels through hybrid density functionals: Insights and applications

AbstractHybrid density functional calculations applied to defect charge transition levels are explored in the attempt to overcome the band‐gap problem of semilocal density functionals. Charge transition levels of a large set of point defects calculated with semilocal and hybrid density functionals are found to correspond closely when aligned with respect to the average electrostatic potential. This strongly suggests that the defect levels defined in this way are already accurately described at these levels of theory. In particular, this then also applies to the energy separation between different defect levels, which is directly accessible experimentally. At variance, within the same alignment scheme, the band edges obtained with hybrid functionals are found to undergo significant shifts with respect to those obtained with semilocal functionals. While these shifts systematically give larger band gaps, the agreement with experiment is not always satisfactory when a fixed fraction of exact exchange is admixed. This describes a current limitation of hybrid functional schemes. In the attempt of identifying a viable theoretical description within the class of one‐parameter hybrid functionals based on bare exchange, we explore the validity of the empirical procedure which consists in tuning the fraction of nonlocal exchange to a value which gives a theoretical band gap reproducing the experimental one. Comparisons with experiment for band offsets and specific defect levels record very encouraging results. Despite its inherent limitations, such an empirical scheme based on hybrid functionals represents a definite improvement with respect to semilocal functionals.

Alignment of defect levels and band edges through hybrid functionals: Effect of screening in the exchange term

We investigate how various treatments of exact exchange affect defect charge transition levels and band edges in hybrid functional schemes for a variety of systems. We distinguish the effects of long-range vs short-range exchange and of local vs nonlocal exchange. This is achieved by the consideration of a set of four functionals, which comprise the semilocal Perdew-Burke-Ernzerhof (PBE) functional, the PBE hybrid (PBE0), the Heyd-Scuseria-Ernzerhof (HSE) functional, and a hybrid derived from PBE0 in which the Coulomb kernel in the exact exchange term is screened as in the HSE functional but which, unlike HSE, does not include a local expression compensating for the loss of the long-range exchange. We find that defect levels in PBE0 and in HSE almost coincide when aligned with respect to a common reference potential, due to the close total-energy differences in the two schemes. At variance, the HSE band edges determined within the same alignment scheme are found to shift significantly with respect to the PBE0 ones: the occupied and the unoccupied states undergo shifts of about +0.4 eV and -0.4 eV, respectively. These shifts are found to vary little among the materials considered. Through a rationale based on the behavior of local and nonlocal long-range exchange, this conclusion is generalized beyond the class of materials used in this study. Finally, we explicitly address the practice of tuning the band gap by adapting the fraction of exact exchange incorporated in the functional. When PBE0-like and HSE-like functionals are tuned to yield identical band gaps, their respective results for the positions of defect levels within the band gap and for the band alignments at interfaces are found to be very close.