For the case of n-type doping of β-Ga2O3 by group 14 dopants (C, Si, Ge, Sn), a defect phase diagram is constructed from defect equilibria calculated over a range of temperatures (T), O partial ...pressures (pO2), and dopant concentrations. The underlying defect levels and formation energies are determined from first-principles supercell calculations with GW bandgap corrections. Only Si is found to be a truly shallow donor, C is a deep DX-like (lattice relaxed donor) center, and Ge and Sn have defect levels close to the conduction band minimum. The thermodynamic modeling includes the effect of association of dopant-defect pairs and complexes, which causes the net doping to decline when exceeding a certain optimal dopant concentration. The optimal doping levels are surprisingly low, between about 0.01% and 1% of cation substitution, depending on the (T, pO2) conditions. Considering further the stability constraints due to sublimation of molecular Ga2O, specific predictions of optimized pO2 and Si dopant concentrations are given. The incomplete passivation of dopant-defect complexes in β-Ga2O3 suggests a design rule for metastable doping above the solubility limit.
Lattice defects in semiconductors and wide‐gap materials which create deep levels in an open‐shell electronic configuration can give rise to so‐called defect bound small polarons. This type of ...defects present a challenge for electronic structure methods because the localization of the defect state and the associated energy levels depend sensitively on the ability of the total‐energy functional to satisfy the physical condition that the energy E(N) must be a piecewise linear function of the fractional electron number N. For practical applications the requirement of a linear E(N) is re‐cast as a generalized Koopmans condition. Since most functionals do not fulfill this condition accurately, we use parameterized perturbations that cancel the non‐linearity of E(N) and recover the correct Koopmans behavior. Starting from standard density functionals, we compare two types of parameterized perturbations, i.e., the addition of on‐site potentials and the mixing of non‐local Fock exchange in hybrid‐functionals. Surveying a range of acceptor‐type defects in II–VI and III–V semiconductors, we present a classification scheme that describes the relation between hole localization and the lattice relaxation of the polaronic state.
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Existing defect models for In(2)O(3) and ZnO are inconclusive about the origin of conductivity, nonstoichiometry, and coloration. We apply systematic corrections to first-principles calculated ...formation energies Delta H, and validate our theoretical defect model against measured defect and carrier densities. We find that (i) intrinsic acceptors ("electron killers") have a high Delta H explaining high n-dopability, (ii) intrinsic donors ("electron producers") have either a high Delta H or deep levels, and do not cause equilibrium-stable conductivity, (iii) the O vacancy V(O) has a low Delta H leading to O deficiency, and (iv) V(O) has a metastable shallow state, explaining the paradoxical coexistence of coloration and conductivity.
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Despite the great success that theoretical approaches based on density functional theory have in describing properties of solid compounds, accurate predictions of the enthalpies of formation ( delta ...Hsubf) of insulating and semiconducting solids still remain a challenge. In this paper we present an approach based on GGA + U calculations, including the spin-orbit coupling, which involves fitted elemental-phase reference energies (FERE) and which significantly improves the error cancellation resulting in accurate values for the compound enthalpies of formation. The FERE method, hence, represents a simple and general approach, as it is computationally equivalent to the cost of pure GGA calculations and applies to virtually all insulating and semiconducting compounds, for predicting compound ( delta Hsubf) values with chemical accuracy. We also show that by providing accurate ( delta Hsubf) the FERE approach can be applied for accurate predictions of the compound thermodynamic stability or for predictions of Li-ion battery voltages.
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The theoretical description of defects and impurities in semiconductors is largely based on density functional theory (DFT) employing supercell models. The literature discussion of uncertainties that ...limit the predictivity of this approach has focused mostly on two issues: (1) finite-size effects, in particular for charged defects; (2) the band-gap problem in local or semi-local DFT approximations. We here describe how finite-size effects (1) in the formation energy of charged defects can be accurately corrected in a simple way, i.e. by potential alignment in conjunction with a scaling of the Madelung-like screened first order correction term. The factor involved with this scaling depends only on the dielectric constant and the shape of the supercell, and quite accurately accounts for the full third order correction according to Makov and Payne. We further discuss in some detail the background and justification for this correction method, and also address the effect of the ionic screening on the magnitude of the image charge energy. In regard to (2) the band-gap problem, we discuss the merits of non-local external potentials that are added to the DFT Hamiltonian and allow for an empirical band-gap correction without significantly increasing the computational demand over that of standard DFT calculations. In combination with LDA + U, these potentials are further instrumental for the prediction of polaronic defects with localized holes in anion-p orbitals, such as the metal-site acceptors in wide-gap oxide semiconductors.
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