Audrius Alkauskas

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.

Measurement and Control of Single Nitrogen-Vacancy Center Spins above 600 K

We study the spin and orbital dynamics of single nitrogen-vacancy (NV) centers in diamond between room temperature and 700 K. We find that the ability to optically address and coherently control single spins above room temperature is limited by nonradiative processes that quench the NV centers fluorescence-based spin readout between 550 and 700 K. Combined with electronic structure calculations, our measurements indicate that the energy difference between the 3E and 1A1 electronic states is approximately 0.8 eV. We also demonstrate that the inhomogeneous spin lifetime (T2*) is temperature independent up to at least 625 K, suggesting that single NV centers could be applied as nanoscale thermometers over a broad temperature range.

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 nonscreened 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.

First-principles theory of nonradiative carrier capture via multiphonon emission

We develop a practical first-principles methodology to determine nonradiative carrier capture coefficients at defects in semiconductors. We consider transitions that occur via multiphonon emission. Parameters in the theory, including electron-phonon coupling matrix elements, are computed consistently using state-of-the-art electronic structure techniques based on hybrid density functional theory. These provide a significantly improved description of bulk band structures, as well as defect geometries and wavefunctions. In order to properly describe carrier capture processes at charged centers, we put forward an approach to treat the effect of long-range Coulomb interactions on scattering states in the framework of supercell calculations. We also discuss the choice of initial conditions for a perturbative treatment of carrier capture. As a benchmark, we apply our theory to several hole-capturing centers in GaN and ZnO, materials of high technological importance in which the role of defects is being actively investigated. Calculated hole capture coefficients are in good agreement with experimental data. We discuss the insights gained into the physics of defects in wide-band-gap semiconductors, such as the strength of electron-phonon coupling and the role of different phonon modes.

Hybrid-functional calculations with plane-wave basis sets: Effect of singularity correction on total energies, energy eigenvalues, and defect energy levels

When described through a plane-wave basis set, the inclusion of exact nonlocal exchange in hybrid functionals gives rise to a singularity, which slows down the convergence with the density of sampled k points in reciprocal space. In this work, we investigate to what extent the treatment of the singularity through the use of an auxiliary function is effective for k-point samplings of limited density, in comparison to analogous calculations performed with semilocal density functionals. Our analysis applies, for instance, to calculations in which the Brillouin zone is sampled at the sole Gamma point, as often occurs in the study of surfaces, interfaces, and defects or in molecular-dynamics simulations. In the adopted formulation, the treatment of the singularity results in the addition of a correction term to the total energy. The energy eigenvalue spectrum is affected by a downwards shift in the energy eigenvalues of the occupied states, while those of the unoccupied states remain unaffected. Analogous corrections also speed up the convergence of screened exchange interactions despite the absence of a proper singularity. Focusing first on neutral systems, both finite and extended, we show that the account of the singularity corrections bears convergence properties which are quantitatively similar to those observed with semilocal density functionals. We emphasize that this is not the case for uncorrected energies, particularly for elongated simulation cells for which qualitatively different trends are found. We then consider differences between total energies of systems differing by their charge state. For systems involving localized electron states, such as ionization potentials and electron affinities of molecular systems or charge transition levels of point defects, the proper account of the singularity correction yields convergence properties which are similar to those of neutral systems. In the case of extended systems, such energy differences provide an alternative way to determine the band edges, but are found to converge more slowly with simulation cells than in corresponding semilocal functionals because of the exchange self-interaction associated to the extra charge.

First-Principles Calculations of Luminescence Spectrum Line Shapes for Defects in Semiconductors: The Example of GaN and ZnO

We present a theoretical study of the broadening of defect luminescence bands due to vibronic coupling. Numerical proof is provided for the commonly used assumption that a multidimensional vibrational problem can be mapped onto an effective one-dimensional configuration coordinate diagram. Our approach is implemented based on density functional theory with a hybrid functional, resulting in luminescence line shapes for important defects in GaN and ZnO that show unprecedented agreement with experiment. We find clear trends concerning effective parameters that characterize luminescence bands of donor- and acceptor-type defects, thus facilitating their identification.

Band alignments and defect levels in Si–HfO2 gate stacks: Oxygen vacancy and Fermi-level pinning

The determination of band alignments and defect levels is demonstrated for the technologically relevant Si–SiO2–HfO2 gate stack. The proposed scheme, which combines first-principles molecular dynamics for model generation and hybrid density functionals for electronic-structure calculations, yields band offsets in close agreement with experiment. Charge transition and pinning levels associated with oxygen vacancies are aligned with respect to the silicon band edges. The vacancies are shown to preferentially reside in the amorphous transition layer, consistent with experimental observations of Fermi-level pinning.

Tutorial: Defects in semiconductors—Combining experiment and theory

Point defects affect or even completely determine physical and chemical properties of semiconductors. Characterization of point defects based on experimental techniques alone is often inconclusive. In such cases, the combination of experiment and theory is crucial to gain understanding of the system studied. In this tutorial, we explain how and when such comparison provides new understanding of the defect physics. More specifically, we focus on processes that can be analyzed or understood in terms of configuration coordinate diagrams of defects in their different charge states. These processes include light absorption, luminescence, and nonradiative capture of charge carriers. Recent theoretical developments to describe these processes are reviewed.

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

In this work we present theoretical calculations and analysis of the vibronic structure of the spin-triplet optical transition in diamond nitrogen-vacancy (NV) 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 NV 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 (NV) 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.