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

Abstract

The charge-transfer insulating perovskite oxides currently used as fuel cell electrolytes undergo, at high temperature, an oxidation reaction 12O2(g)+VO••→OOX+2h•, that produces oxygen-type holes. Understanding the nature and mobility of these oxygen-type holes is an important step to improve the performance of devices, but presents a theoretical challenge since, in their localized form, they cannot be captured by standard density functional theory. Here, we employ the DFT+U formalism with a Hubbard correction on the p orbitals of oxygen to investigate several properties of these holes, in the particular case of BaSnO3. We describe the small oxygen-type hole polarons, the self-trapping at their origin, and their trapping by trivalent dopants (Ga, Sc, In, Lu, Y, Gd, La). Strong similarities with protonic defects are observed concerning the evolution of the trapping energy with ionic radius of the dopant. Moreover, we show that long-range diffusion of holes is a complex phenomenon, that proceeds by a succession of several mechanisms. However, the standard implementation of DFT+U within the projector augmented-wave (PAW) formalism leads to use very large, unphysical values of U for the O-p orbital. We propose here a slightly modified DFT+U scheme, that takes into account the fact that the O-p is truncated in usual DFT+U implementation in PAW. This scheme yields more physical values of U than the ones traditionally used in the literature, and describes well the properties of the hole polaron.