Dynamic Simulation of the Migration of Oxygen Vacancy Defects in Rutile TiO 2
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Dynamic Simulation of the Migration of Oxygen Vacancy Defects in Rutile TiO2 Jan M. Knaup1,*, Michael Wehlau1 and Thomas Frauenheim1 1 Bremen Center for Computational Materials Science, Universität Bremen, Am Fallturm 1, 28359 Bremen, Germany * [email protected] ABSTRACT We simulate the thermodynamics and kinetics of the drift/diffusion of oxygen vacancy defects in rutile TiO2, using the density-functional based tight-binding (DFTB) method. Both static and dynamic simulations have been performed. Results indicate that DFTB is well suited to examine the dynamic behavior of oxygen vacancies in TiO2. Detailed analysis shows, that strong model size dependence in relative diffusion barrier heights between different diffusion processes requires great care in defect diffusion simulations in TiO2. Thermodynamic results on the influence of an external electric field show that, due to the large dielectric constant, the coulomb driving force on oxygen vacancy diffusion is very small. Dynamic simulation of the influence of electric fields on the diffusion requires the use of advanced molecular dynamics acceleration schemes. INTRODUCTION Oxygen deficient TiO2 has garnered considerable interest as an active material for resistive switching memory (ReRAM)[1]. The resistive switching process is based on the formation of conductive nanofilaments of TinO2n-1 Magnéli phases[2] through the insulating TiO2 thin films upon soft dielectric breakdown[1,3]. To better understand the formation and dissolution of these inclusions of oxygen deficient titania inside stoichiometric films, it is vital to understand how electric fields and temperature gradients drive the migration of oxygen vacancy defects (VO). In this study we perform semi ab initio simulations of both thermodynamics and kinetics of oxygen Vacancy diffusion in rutile TiO2, with and without the influence of external electric fields. THEORY We simulate the behavior of diffusion VO defects in TiO2 using the self-consistent charge density-functional based tight-binding (SCC-DFTB)[4] method. We employ the tiorg[5] set of parameters for the Ti-Ti, Ti-O and O-O interactions. We iterate the charge self-consistency until all atomic charge differences are below 10-7 electrons or better for static simulations and 10-5 electrons or better for dynamic simulations to minimize force noise. In static simulations, the atomic positions are optimized until all atomic forces are below 10-4 H/Bohr. The time step for all MD simulations is 1 fs. Since the trajectories of molecular dynamics simulations can be severely influenced by thermostats[6], we follow an advanced procedure for our molecular non meta dynamics simulations. For every target temperature, the system is thermalized for 5-10 ps, then the thermostat is switched off and the simulation is continued in a micro canonical (NVE) ensemble.
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Only the trajectory parts from the NVE simulation are evaluated. This ensures that no thermostating artifacts influence the diffusion rates. We simulate the influence of a homogeneous extern
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