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

O2 oxidation reaction at the Si(100)-SiO2 interface: A first-principles investigation

We investigated the oxidation reaction of the O2 molecule at the Si(100)-SiO2 interface by using a constrained ab initio molecular dynamics approach. To represent the Si(100)-SiO2 interface, we adopted several model interfaces whose structural properties are consistent with atomic-scale information obtained from a variety of experimental probes. We addressed the oxidation reaction by sampling different reaction pathways of the O2 molecule at the interface. The reaction proceeds sequentially through the incorporation of the O2 molecule in a Si-Si bond and the dissociation of the resulting network O2-species. The oxidation reaction occurs nearly spontaneously and is exothermic, regardless of the spin state of the O2 molecule. Our study suggests a picture of the silicon oxidation process entirely based on diffusive processe

The vibrational dynamics of vitreous silica: Classical force fields vs. first-principles

We compare the vibrational properties of model SiO_2 glasses generated by molecular-dynamics simulations using the effective force field of van Beest et al. (BKS) with those obtained when the BKS structure is relaxed using an ab initio calculation in the framework of the density functional theory. We find that this relaxation significantly improves the agreement of the density of states with the experimental result. For frequencies between 14 and 26 THz the nature of the vibrational modes as determined from the BKS model is very different from the one from the ab initio calculation, showing that the interpretation of the vibrational spectra in terms of calculations using effective potentials can be very misleading.Comment: 7 pages of Latex, 4 figure

Structure and energetics of the Si-SiO_2 interface

Silicon has long been synonymous with semiconductor technology. This unique role is due largely to the remarkable properties of the Si-SiO_2 interface, especially the (001)-oriented interface used in most devices. Although Si is crystalline and the oxide is amorphous, the interface is essentially perfect, with an extremely low density of dangling bonds or other electrically active defects. With the continual decrease of device size, the nanoscale structure of the silicon/oxide interface becomes more and more important. Yet despite its essential role, the atomic structure of this interface is still unclear. Using a novel Monte Carlo approach, we identify low-energy structures for the interface. The optimal structure found consists of Si-O-Si "bridges" ordered in a stripe pattern, with very low energy. This structure explains several puzzling experimental observations.Comment: LaTex file with 4 figures in GIF forma

Structure and oxidation kinetics of the Si(100)-SiO2 interface

We present first-principles calculations of the structural and electronic properties of Si(001)-SiO2 interfaces. We first arrive at reasonable structures for the c-Si/a-SiO2 interface via a Monte-Carlo simulated annealing applied to an empirical interatomic potential, and then relax these structures using first-principles calculations within the framework of density-functional theory. We find a transition region at the interface, having a thickness on the order of 20\AA, in which there is some oxygen deficiency and a corresponding presence of sub-oxide Si species (mostly Si^+2 and Si^+3). Distributions of bond lengths and bond angles, and the nature of the electronic states at the interface, are investigated and discussed. The behavior of atomic oxygen in a-SiO2 is also investigated. The peroxyl linkage configuration is found to be lower in energy than interstitial or threefold configurations. Based on these results, we suggest a possible mechanism for oxygen diffusion in a-SiO2 that may be relevant to the oxidation process.Comment: 7 pages, two-column style with 6 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#ng_sio

Charging Induced Emission of Neutral Atoms from NaCl Nanocube Corners

Detachment of neutral cations/anions from solid alkali halides can in principle be provoked by donating/subtracting electrons to the surface of alkali halide crystals, but generally constitutes a very endothermic process. However, the amount of energy required for emission is smaller for atoms located in less favorable positions, such as surface steps and kinks. For a corner ion in an alkali halide cube the binding is the weakest, so it should be easier to remove that atom, once it is neutralized. We carried out first principles density functional calculations and simulations of neutral and charged NaCl nanocubes, to establish the energetics of extraction of neutralized corner ions. Following hole donation (electron removal) we find that detachment of neutral Cl corner atoms will require a limited energy of about 0.8 eV. Conversely, following the donation of an excess electron to the cube, a neutral Na atom is extractable from the corner at the lower cost of about 0.6 eV. Since the cube electron affinity level (close to that a NaCl(100) surface state, which we also determine) is estimated to lie about 1.8 eV below vacuum, the overall energy balance upon donation to the nanocube of a zero energy electron from vacuum will be exothermic. The atomic and electronic structure of the NaCl(100) surface, and of the nanocube Na and Cl corner vacancies are obtained and analyzed as a byproduct.Comment: 16 pages, 2 table, 7 figure

Design of a low band gap oxide ferroelectric: Bi6_6Ti4_4O17_{17}

A strategy for obtaining low band gap oxide ferroelectrics based on charge imbalance is described and illustrated by first principles studies of the hypothetical compound Bi$_6$Ti$_4$O$_{17}$, which is an alternate stacking of the ferroelectric Bi$_4$Ti$_3$O$_{12}$. We find that this compound is ferroelectric, similar to Bi$_4$Ti$_3$O$_{12}$ although with a reduced polarization. Importantly, calculations of the electronic structure with the recently developed functional of Tran and Blaha yield a much reduced band gap of 1.83 eV for this material compared to Bi$_4$Ti$_3$O$_{12}$. Therefore, Bi$_6$Ti$_4$O$_{17}$ is predicted to be a low band gap ferroelectric material

Non-linear macroscopic polarization in III-V nitride alloys

We study the dependence of macroscopic polarization on composition and strain in wurtzite III-V nitride ternary alloys using ab initio density-functional techniques. The spontaneous polarization is characterized by a large bowing, strongly dependent on the alloy microscopic structure. The bowing is due to the different response of the bulk binaries to hydrostatic pressure, and to internal strain effects (bond alternation). Disorder effects are instead minor. Deviations from parabolicity (simple bowing) are of order 10 % in the most extreme case of AlInN alloy, much less at all other compositions. Piezoelectric polarization is also strongly non-linear. At variance with the spontaneous component, this behavior is independent of microscopic alloy structure or disorder effects, and due entirely to the non-linear strain dependence of the bulk piezoelectric response. It is thus possible to predict the piezoelectric polarization for any alloy composition using the piezoelectricity of the parent binaries.Comment: RevTex 7 pages, 7 postscript figures embedde

Acceleration Schemes for Ab-Initio Molecular Dynamics and Electronic Structure Calculations

We study the convergence and the stability of fictitious dynamical methods for electrons. First, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground-state than first-order steepest descent algorithms while retaining their numerical cost per time step. Our damped dynamics has efficiency comparable to that of conjugate gradient methods in typical electronic minimization problems. Then, we analyse the factors that limit the size of the integration time step in approaches based on plane-wave expansions. The maximum allowed time step is dictated by the highest frequency components of the fictitious electronic dynamics. These can result either from the large wavevector components of the kinetic energy or from the small wavevector components of the Coulomb potential giving rise to the so called {\it charge sloshing} problem. We show how to eliminate large wavevector instabilities by adopting a preconditioning scheme that is implemented here for the first-time in the context of Car-Parrinello ab-initio molecular dynamics simulations of the ionic motion. We also show how to solve the charge-sloshing problem when this is present. We substantiate our theoretical analysis with numerical tests on a number of different silicon and carbon systems having both insulating and metallic character.Comment: RevTex, 9 figures available upon request, to appear in Phys. Rev.

Dynamical-charge neutrality at a crystal surface

For both molecules and periodic solids, the ionic dynamical charge tensors which govern the infrared activity are known to obey a dynamical neutrality condition. This condition enforces their sum to vanish (over the whole finite system, or over the crystal cell, respectively). We extend this sum rule to the non trivial case of the surface of a semiinfinite solid and show that, in the case of a polar surface of an insulator, the surface ions cannot have the same dynamical charges as in the bulk. The sum rule is demonstrated through calculations for the Si-terminated SiC(001) surface.Comment: 4 pages, latex file, 1 postscript figure automatically include