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A Simulation Study of Oxygen-Vacancy Behavior in Strontium Titanate: Beyond Nearest-Neighbor Interactions Marcel Schie, Rainer Waser, and Roger A. De Souza J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 18 Jun 2014 Downloaded from http://pubs.acs.org on June 28, 2014
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The Journal of Physical Chemistry
A Simulation Study of Oxygen-Vacancy Behavior in Strontium Titanate: Beyond Nearest-Neighbor Interactions AUTHOR NAMES Marcel Schie*,†, Rainer Waser† and Roger A. De Souza*,‡ AUTHOR ADDRESS †
Institute of Materials in Electrical Engineering and Information Technology, RWTH Aachen University, 52074 Aachen, Germany
‡Institute of Physical Chemistry, RWTH Aachen University and JARA-FIT, 52056 Aachen, Germany ABSTRACT We investigate the effect of acceptor-dopant cations on oxygen-vacancy migration in the perovskite oxide SrTiO3 by static lattice simulation techniques. We focus on two themes: dopant cations modifying the activation energies for vacancy migration, and dopant cations binding oxygen vacancies in binary associates. In both cases a variety of defect configurations exceeding
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the scope of first nearest neighbor (1NN) interaction is examined, i.e. 1NN, 2NN, 3NN, 4NN and 5NN. The behavior of four divalent dopants (Ni2+, Fe2+, Co2+ and Mn2+) and one trivalent dopant (Al3+) is compared. The simulations predict that the binding energy of an oxygen vacancy to any of these dopants is negative at 1NN sites, but only converges to zero for 4NN sites. In addition the simulations show that the migration energy of a vacancy is affected by an acceptor dopant cation over a length scale of several unit cells. A simple analytical model is used, together with the calculated site and activation energies, to predict how in general the ionic conductivity is affected by the interactions between oxygen vacancies and acceptor-dopant cations. The model predicts that the magnitude of these effects depends on the specific dopant, its concentration and the temperature. KEYWORDS ionic conductivity, defect chemistry, empirical potential, interatomic potential, acceptor doping, association 1. Introduction In acceptor-doped perovskites, such as SrTiO3 (ST), BaTiO3 (BT), Pb(Ti,Zr)O3 (PZT), (Na,Bi)TiO3 (NBT) and LaGaO3 (LG), the most important point defects from both fundamental and technological standpoints are, arguably, oxygen vacancies. The behavior of these point defects — their distribution and their diffusion kinetics — plays a central role in determining the functioning principle, the performance or the reliability of devices as varied as multilayer ceramic capacitors 1, solid oxide fuel cells 2, 3 and resistive switching memories 4, 5. In such perovskite oxide systems, oxygen vacancies form preferentially to charge compensate acceptor dopant species that are either intentionally added as dopants or inadvertently included
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as impurities in nominally undoped material (and they are also generated readily under reducing conditions). Microscopic investigations of various acceptor-dopant cations in titanate perovskites 6-11
by means of Electron Paramagnetic Resonance (EPR), indicate unambiguously that, at room
temperature, these defects trap oxygen vacancies in defect associates at nearest neighbor sites. This model is also supported by simulation studies 12-18. Applying such a model to transport data, such as diffusion or conductivity data, is, however, questionable. This is because the activation barriers for vacancy migration may be modified by the dopant cation, and this is not included in the simple static model. In this study, taking SrTiO3 as a model system for acceptor-doped perovskite oxides, we examine the effect of acceptor-dopant cations on the motion of oxygen vacancies. We start by applying the standard defect chemical model to show that the results of macroscopic conductivity studies can be interpreted qualitatively and quantitatively by introducing an effective association enthalpy (as a nearest neighbor approximation) for trapping of oxygen vacancies by acceptor dopant cations. In the main part of the paper we employ atomistic simulations to probe the energy landscape of an oxygen vacancy in the vicinity of various acceptor-dopant cations, in order to go beyond the approximation of nearest-neighbor interactions. From the simulation data, we extract for the oxygen-vacancy site energies and migration energies. In the second part of the paper we present a simple analytical model that allows us to predict, from our calculated energies, the ionic conductivity of acceptor-doped systems as a function of the dopant type, temperature and dopant concentration.
2. Defect chemistry model
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The initial question concerns data reported for the ionic conductivity of Ni-doped SrTiO3 at low temperatures
19
. In contrast to high temperature data
20-22
and Density-Functional-Theory
(DFT) calculations 23-25 that yield an activation enthalpy of vacancy migration of ∆Hm = 0.62 eV, the low-temperature data is characterized by an activation enthalpy of 1.0 eV. We first reconcile the low-temperature conductivity data of Waser
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with the high temperature data by using a
standard defect chemical model. We derive the model from first principles so that all assumptions are evident; as a consequence the model has only one single fitting parameter. In the standard literature model only the nearest-neighbor association of vacancies with dopants is considered. Thus there is a dynamic equilibrium between trapped and free oxygen vacancies. The ionic conductivity can be expressed as the product of the free vacancies’ charge z, concentration V.. and mobility , = ⋅ ⋅ V.. ⋅ . (1)
The mobility of oxygen vacancies is given by = 151
from oxygen tracer diffusion data reported by De Souza et al.
/K < 1123. The conductivity data of Waser
19
⋅
20
. " !
#
, and was calculated
for high temperatures 948
