Implications of the band gap problem on oxidation and hydration in acceptor-doped barium zirconate

Abstract

Charge carrier concentrations in acceptor-doped proton-conducting perovskites are to a large extent determined by the hydration and oxidation of oxygen vacancies, which introduce protons and holes, respectively. First-principles modeling of these reactions involves calculation of formation energies of charged defects, which requires an accurate description of the band gap and the position of the band edges. Since density-functional theory (DFT) with local and semi-local exchangecorrelation functionals (LDA and GGA) systematically fails to predict these quantities this can have serious implications on the modeling of defect reactions. In this study we investigate how the description of band gap and band edge positions affects the hydration and oxidation in acceptordoped BaZrO3. First-principles calculations are performed in combination with thermodynamic modeling in order to obtain equilibrium charge carrier concentrations at different temperatures and partial pressures. Three different methods have been considered: DFT with both semi-local (PBE) and hybrid (PBE0) exchange-correlation functionals, and many-body perturbation theory within the G0W0-approximation. All three methods yield similar results for the hydration reaction, which are consistent with experimental findings. For the oxidation reaction, on the other hand, there is a qualitative difference. PBE predicts the reaction to be exothermic while the two others predict an endothermic behavior. Results from thermodynamic modeling are compared with available experimental data, such as enthalpies, concentrations and conductivities, and only the results obtained with PBE0 and G0W0, with an endothermic oxidation behavior, give a satisfactory agreement with experiments.

First principles calculations of the thermodynamic stability of Ba, Zr, and O vacancies in BaZrO3

“…46 It should be mentioned that the so-called over binding problem (oxygen energy see third section of this work) by the RPBE exchange-correlation functional as well as the underestimation of the band gap by this procedure might be overcome using the Heyd-Scuseria-Ernzerhof (HSE) functional [47][48][49] as well as other sophisticated approaches. 50 However, this would increase the computational costs and was therefore not considered in this work.…”

DFT+ U study of self-trapping, trapping, and mobility of oxygen-type hole polarons in barium stannate

“…Theoretically, previous studies have revealed that advanced electronic structure calculations are needed to correctly describe this oxidation phenomenon. Indeed, the generalized gradient approximation (GGA) finds it exothermic in several perovskite oxides [10][11][12], while hybrid functionals (PBE0) provide an endothermic picture [12]. This is related to the band-gap problem, more precisely to the incorrect position of the valence band maximum, formed by oxygen-2p states, obtained with GGA.…”

“…Alternatively, the hole mobility could be dominated by the few holes thermally excited in the itinerant level [12].…”

Polaronic contributions to oxidation and hole conductivity in acceptor-dopedBaZrO3

“…[6][7][8][9] When fitted to the Arrhenius-like expression T σ h = Ae −Ea/kT (8) these conductivities (σ h ) yield activation energies (E a ) within the range of 0.6 eV to 1.1 eV. In previous work 24 we calculated the activation energy for the hole conductivity based on the endothermic oxidation reaction in Eq. (1) assuming that the hole mobility could be described by band conduction, i.e., B h ∼ T −1 .…”

“…It is well-known that DFT using local and semi-local XC functionals severely underestimates band gaps and this can affect the description of holes, which is sensitive arXiv:1603.06728v2 [cond-mat.mtrl-sci] 4 Jul 2016 to the position of the valence band maximum (VBM). In a previous paper 24 we went beyond the semi-local approximation and used DFT with hybrid functionals as well as many-body perturbation theory (G 0 W 0 ) in order to study how the description of the band gap affects the formation of band state holes. Along with a more accurate band gap we found the oxidation reaction [Eq.…”