Thermal migration processes of the As interstitial in GaAs were investigated using density-functional theory and the local-density approximation for exchange and correlation. The lowest-energy processes were found to involve the −1, 0, and +1 charge states, and to produce migration along ⟨110⟩-type directions. In the −1 and 0 charge states, migration proceeds via hops between split-interstitial stable configurations at bulk As sites through bridging saddle-point configurations in which the interstitial atom is equidistant from two adjacent bulk As sites. In the +1 charge state, the roles of these two configurations are approximately reversed and migration proceeds via hops between bridging stable configurations through higher-energy split-interstitial stable configurations bounded by a pair of distorted split-interstitial saddle-point configurations. The predicted activation energies for migration in the 0 and +1 charge states agree well with measurements in semi-insulating and p-type material, respectively. Also consistent with experiments, the approximate reversal of the stable and saddle-point configurations between the 0 and +1 charge states is predicted to enable carrier-induced migration with a residual activation energy of 0.05 eV.

While point defects in elemental (Si) and compound (GaAs, GaN, AlN) semiconductors have been extensively studied both experimentally and theoretically, only limited theoretical studies of these defects exist for technologically important binary $(\mathrm{S}{\mathrm{i}}_{x}\mathrm{G}{\mathrm{e}}_{1\text{\ensuremath{-}}x})$ and pseudobinary $(\mathrm{I}{\mathrm{n}}_{x}\mathrm{G}{\mathrm{a}}_{1\text{\ensuremath{-}}x}\mathrm{As}$, $\mathrm{I}{\mathrm{n}}_{\mathrm{x}}\mathrm{G}{\mathrm{a}}_{1\text{\ensuremath{-}}x}\mathrm{N}$, $\mathrm{A}{\mathrm{l}}_{x}\mathrm{G}{\mathrm{a}}_{1\text{\ensuremath{-}}x}\mathrm{N})$ semiconductor alloys. Here, we use density-functional theory and a recently developed bounds-analysis approach to survey the atomic structures, formation energies, and charge-state transition levels of the stable and metastable states of As interstitials in the pseudobinary alloy $\mathrm{I}{\mathrm{n}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}\mathrm{As}$. Our studies consider seven different candidate defect structures for the As interstitial, with calculations performed for selected defect charge states in the range $q=\ensuremath{-}2$ to $+3$. In each case, the mean and standard deviations of the defect-formation energy are determined using statistical sampling methods that place the defect into a wide variety of differing local-alloy environments. When examined from the point of view of the mean formation energy of the defect, the stable configurations of the As interstitial in $\mathrm{I}{\mathrm{n}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}\mathrm{As}$ are found to resemble previous findings for GaAs, with a ${\mathrm{C}}_{1\mathrm{h}}\text{\ensuremath{-}}\mathrm{p}{001}_{\mathrm{III}}$ interstitial structure in a $q=+1$ charge state favored near midgap and below, and a ${\mathrm{C}}_{2\mathrm{v}}\text{\ensuremath{-}}11{0}_{\mathrm{a}}$ split-interstitial structure in a $q=\ensuremath{-}1$ charge state favored above midgap (the named point-group symmetries refer to the underlying symmetry that the alloy defect would possess if within GaAs). The statistical sampling reveals a strong dependence of the defect-formation energy on the local-alloy environment, with the standard deviation $\ensuremath{\sigma}$ of the formation energy approaching 0.21 eV for the most stable As-interstitial structures. Because the range of ground-state energies encountered by an As-interstitial defect when moving through the alloy is found to be quite large, approaching $\ensuremath{\sim}1.2\phantom{\rule{0.16em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}(\ifmmode\pm\else\textpm\fi{}3\ensuremath{\sigma})$, defect-diffusion pathways in $\mathrm{I}{\mathrm{n}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}\mathrm{As}$ will have spatial and temporal complexities not found in GaAs.

Carrier recombination due to defects can have a major impact on device performance. The rate of defect-induced recombination is determined by both defect levels and carrier capture cross-sections. Density functional theory (DFT) has been widely and successfully used to predict defect levels, but only recently has work begun to focus on using DFT to determine carrier capture cross-sections. Lang and Henry worked out the fundamental theory of carrier-capture by multiphonon emission in the 1970s and showed that, above the Debye temperature, carrier-capture cross-sections differ between defects primarily due to differences in their carrier capture activation energies. We present an approach to using DFT to calculate carrier capture activation energies that does not depend on an assumed configuration coordinate and that fully accounts for anharmonic effects, which can substantially modify carrier activation energies. We demonstrate our approach for the -3/-2 level of the Ga vacancy in wurtzite GaN.

A recently developed bounds-analysis approach has been used to interpret density-functional-theory (DFT) results for the As and Ga antisites in GaAs. The bounds analysis and subsequent processing of DFT results for the As antisite yielded levels---defined as the Fermi levels at which the defect charge state changes---in very good agreement with measurements, including the \ensuremath{-}1/0 level which is within 0.1 eV of the conduction-band edge. Good agreement was also obtained for the activation energies to transform the $\mathrm{A}{\mathrm{s}}_{\mathrm{Ga}}$ from its metastable state to its stable state. For the Ga antisite, the bounds analysis revealed that the \ensuremath{-}1 and 0 charge states are hole states weakly bound to a localized \ensuremath{-}2 charge state. The calculated levels are in good agreement with measurements.

Defects in semiconductors and insulators are characterized by their levels, which are defined as the values of the Fermi level at which the charge state of the defect changes. Kohn-Sham density functional theory calculations for charged defects have been widely and successfully used to predict defect levels. Due to their lower computational cost and demonstrated ability to predict levels spanning the measured band gap, semilocal exchange-correlation functionals are widely used in these calculations. However, there is a potential pitfall in using semilocal functionals: although they often predict accurate energies for adding or removing electrons from states that are localized near the defect, the famous band gap error results in overly small energies for adding or removing electrons from extended band edge states. As a result, electrons (or holes) that should occupy localized states may become partially or fully delocalized. In order to help detect and analyze such cases, we introduce bounds on the defect levels that can be obtained using a given functional, supercell, and Brillouin zone sampling. Since these bounds correspond to the charge transition levels of the corresponding defect-free supercell, comparison with the bounds reveals when a calculated level is behaving in a bulk-like rather than defect-like manner. We find that the bounds depend significantly on supercell size due to band-filling effects that arise from the finite charge density created when one electron is added to or removed from a finite-sized supercell, and this size dependence helps explain the success of defect level calculations using semilocal functionals. (C) 2014 Elsevier B.V. All rights reserved.

The atomic configurations and formation energies of a silicon vacancy in the +2, +1, 0, -1, and -2 charge states have been computed using density-functional theory with norm-conserving pseudopotentials and a plane wave basis. Calculations were performed in simple cubic supercells using two different forms of exchange and correlation: the local-density approximation (LDA) and the Perdew, Burke, Ernzerhof formulation of the generalized-gradient approximation (GGA). Convergence with respect to Brillouin zone sampling was tested for all charge states, and effects due to electrostatic interactions between the periodically repeated vacancies were removed by extrapolating the formation energies obtained in 215-, 511-, and 999-atom supercells to an infinite sized supercell. In agreement with experimental results, the GGA yielded a configuration with C-2v symmetry in the -1 charge state, whereas the LDA yielded D-3d symmetry. Transition energies between the charge states were also computed. The experimentally observed negative-U behavior of the donor states was reproduced in the GGA results, but not in the LDA results. Both the LDA and GGA predict negative-U behavior for the acceptor states.

The elevated-temperature properties of the N vacancy in Mg-doped, p-type GaN containing H were modeled using atomic-configuration energies and phonon densities of states obtained with density-functional theory. This study encompassed both equilibrium thermodynamics and the rates of diffusion and reaction processes and included the influences of a number of bound complexes involving the vacancy, the Mg dopant, and H. A comparison was made with published experimental information. Our results indicate that N vacancies extensively compensate Mg acceptors at higher doping levels.

Using density-functional total energy calculations, we investigated N interstitial migration in GaN. Two migration paths were considered. The first path confines motion to a single c-plane of the lattice, while the second path involves movement both perpendicular and parallel to the c-axis. The latter path has a lower barrier for the positive charge states and will be the dominant mechanism for migration of the N interstitial in p-type GaN. The calculated barriers are 1.79, 2.12, and 1.98 eV for the +1, +2, and +3 charge states. These barriers are consistent with recent experimental results and indicate that interstitials will be mobile at typical processing temperatures.

Atomic configurations, formation energies, electronic transition energies, and binding energies of the silicon divacancy in the +1, 0, -1, and -2 charge states were obtained from density functional theory calculations. The calculations were performed using the local density approximation (LDA) and also the Perdew, Burke, Ernzerhof (PBE) formulation of the generalized-gradient approximation. Supercells of nominally 216, 512, and 1000 atoms were used to extrapolate formation energies for infinite-sized supercells corresponding to isolated defects. The predicted ground-state configuration was found to depend on charge state and the chosen formulation of exchange and correlation (LDA or PBE). Structures, binding energies, and transition energies are compared to values reported in the literature.

The reactions V-N(+1) + H+ -> (VNH)(+2) and (MgVN)(0) + H+ -> (MgVNH)(+1) in GaN were investigated using density-functional theory. Estimates of the reaction rates indicate that (VNH)(+2) and (MgVNH)(+1) will form rapidly above 400 degrees C, and modeling predicts that their populations will be substantial at elevated temperatures. These results indicate that compensation by V-N is important in p-type GaN and that H suppression of V-N, formation is less effective than previously suggested.(c) 2005 Elsevier B.V. All rights reserved.

We report the implementation of an iterative scheme for calculating the Optimized Effective Potential (OEP). Given an energy functional that depends explicitly on the Kohn-Sham wave functions, and therefore, implicitly on the local effective potential appearing in the Kohn-Sham equations, a gradient-based minimization is used to find the potential that minimizes the energy. Previous work has shown how to find the gradient of such an energy with respect to the effective potential in the zero-temperature limit. We discuss a density-matrix-based derivation of the gradient that generalizes the previous results to the finite temperature regime, and we describe important optimizations used in our implementation. We have applied our OEP approach to the Hartree-Fock energy expression to perform Exact Exchange (EXX) calculations. We report our EXX results for common semiconductors and ordered phases of hydrogen at zero and finite electronic temperatures. We also discuss issues involved in the implementation of forces within the OEP/EXX approach.

Density-functional-theory calculations were performed for the unrelaxed +2 Si vacancy and +2 self-interstitial utilizing periodic boundary conditions and two different methods-the uniform background charge method and the local moment counter charge method-for circumventing the divergence of the Coulomb potential. Formation energies in nominal 64-, 216-, 512-, 1000-, and 1728-atom supercells were converged with respect to Brillouin zone sampling and then extrapolated to an infinite sized supercell by fitting to a polynomial in odd powers of 1/L where L is the cubed root of the supercell volume. The extrapolated values from the two methods agreed very well (2 meV difference for the vacancy and 13 meV difference for the interstitial) as expected from inspection of their respective energy expressions. The extrapolated values and fitting parameters were then employed to evaluate analytic correction formulas that have been proposed to remove spurious electrostatic contributions from defect formation energies. The results indicate that existing formulas are not capable of removing these contributions and that further development is needed in this area.

The optimized effective potential (OEP) method provides an additional level of exactness in the computation of electronic structures, e.g. the exact exchange energy can be used. This extra freedom is likely to be important in moving density functional methods beyond traditional approximations such as the local density approximation. We provide a new density-matrix-based derivation of the gradient of the Kohn–Sham energy with respect to the effective potential. This gradient can be used to iteratively minimize the energy in order to find the OEP. Previous work has indicated how this can be done in the zero temperature limit. This paper generalizes the previous results to the finite temperature regime. Equating our gradient to zero gives a finite temperature version of the OEP equation.

Density-functional theory and the generalized gradient approximation were utilized to investigate the interaction of N interstitials with neutral MgH centers in p-type GaN. Formation energies and the corresponding local-energy minimum configurations of the defect complex are reported along with the energy to dissociate the complex into isolated MgH and a N interstitial. The conclusion is that N interstitials will bind with MgH centers in p-type GaN(Mg,H), with binding energies of 0.71, 0.44, and 0.29 eV in the +3, +2, and +1 charge states, respectively. Hydrogen local-mode vibrational frequencies for the bound complex were estimated and compared to previous results for isolated MgH. The binding of a N interstitial to MgH perturbs the H stretch-mode frequency by 25 cm(-1). These results are discussed in the context of recent experiments at Sandia National Laboratories, which suggest that N interstitials, created by proton irradiation, become mobile during subsequent annealing and bind with MgH centers in p-type GaN(Mg,H).