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

Charge state of the O2_{2} molecule during silicon oxidation through hybrid functional calculations

We study the charge state of the diffusing O$_2$ molecule during silicon oxidation through hybrid functional calculations. We calculate charge transition levels of O$_2$ in bulk SiO$_2$ and use theoretical band offsets to align these levels with respect to the Si band edges. To overcome the band-gap problem of semilocal density fuctionals, we employ hybrid functionals with both predefined and empirically adjusted mixing coefficients. We find that the charge transition level $\epsilon^{0/-}$ in bulk SiO$_2$ occurs at $\sim$1.1 eV above the silicon conduction band edge, implying that the O$_2$ molecule diffuses through the oxide in the neutral charge state. While interfacial effects concur to lower the charge transition level, our estimates suggest that the neutral charge state persists until silicon oxidation.Comment: 4 pages, 3 figure

First-principles theory of the luminescence lineshape for the triplet transition in diamond NV centre

In this work we present theoretical calculations and analysis of the vibronic structure of the spin-triplet optical transition in diamond nitrogen-vacancy centres. The electronic structure of the defect is described using accurate first-principles methods based on hybrid functionals. We devise a computational methodology to determine the coupling between electrons and phonons during an optical transition in the dilute limit. As a result, our approach yields a smooth spectral function of electron-phonon coupling and includes both quasi-localized and bulk phonons on equal footings. The luminescence lineshape is determined via the generating function approach. We obtain a highly accurate description of the luminescence band, including all key parameters such as the Huang-Rhys factor, the Debye-Waller factor, and the frequency of the dominant phonon mode. More importantly, our work provides insight into the vibrational structure of nitrogen vacancy centres, in particular the role of local modes and vibrational resonances. In particular, we find that the pronounced mode at 65 meV is a vibrational resonance, and we quantify localization properties of this mode. These excellent results for the benchmark diamond nitrogen-vacancy centre provide confidence that the procedure can be applied to other defects, including alternative systems that are being considered for applications in quantum information processing

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.Comment: 4 pages, 3 figure

Optical Signatures of Quantum Emitters in Suspended Hexagonal Boron Nitride

Hexagonal boron nitride (h-BN) is a tantalizing material for solid-state quantum engineering. Analogously to three-dimensional wide-bandgap semiconductors like diamond, h-BN hosts isolated defects exhibiting visible fluorescence, and the ability to position such quantum emitters within a two-dimensional material promises breakthrough advances in quantum sensing, photonics, and other quantum technologies. Critical to such applications, however, is an understanding of the physics underlying h-BN's quantum emission. We report the creation and characterization of visible single-photon sources in suspended, single-crystal, h-BN films. The emitters are bright and stable over timescales of several months in ambient conditions. With substrate interactions eliminated, we study the spectral, temporal, and spatial characteristics of the defects' optical emission, which offer several clues about their electronic and chemical structure. Analysis of the defects' spectra reveals similarities in vibronic coupling despite widely-varying fluorescence wavelengths, and a statistical analysis of their polarized emission patterns indicates a correlation between the optical dipole orientations of some defects and the primitive crystallographic axes of the single-crystal h-BN film. These measurements constrain possible defect models, and, moreover, suggest that several classes of emitters can exist simultaneously in free-standing h-BN, whether they be different defects, different charge states of the same defect, or the result of strong local perturbations

Dangling Bonds in Hexagonal Boron Nitride as Single-Photon Emitters.

Hexagonal boron nitride has been found to host color centers that exhibit single-photon emission, but the microscopic origin of these emitters is unknown. We propose boron dangling bonds as the likely source of the observed single-photon emission around 2 eV. An optical transition where an electron is excited from a doubly occupied boron dangling bond to a localized B p_{z} state gives rise to a zero-phonon line of 2.06 eV and emission with a Huang-Rhys factor of 2.3. This transition is linearly polarized with the absorptive and emissive dipole aligned. Because of the energetic position of the states within the band gap, indirect excitation through the conduction band will occur for sufficiently large excitation energies, leading to the misalignment of the absorptive and emissive dipoles seen in experiment. Our calculations predict a singlet ground state and the existence of a metastable triplet state, in agreement with experiment