Kinetics of Frenkel Defect Formation in TiO 2 from First Principles
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Kinetics of Frenkel Defect Formation in TiO2 from First Principles Sergey V. Barabash1,2, Charlene Chen1, Dipu Pramanik1, Blanka Magyari-Köpe2, Yoshio Nishi2 1 Intermolecular Inc, San Jose, CA, U.S.A. www.intermolecular.com. 2 Electrical Engineering, Stanford University, Stanford, CA, U.S.A. ABSTRACT Motivated by the unusual behavior of TiO2 films seen in electrical stress and defect annealing experiments, we studied the energy profile for forming a Frenkel defect in rutile TiO2, using first-principles calculations with a nudged-elastic-band method. We found strongly asymmetric diffusion barriers. The Frenkel pairs with small separation are exceedingly shortlived: the Ti interstitial position nearest to the the Ti vacancy is separated by only a 0.15eV barrier, and the next-nearest interstitial position is dynamically unstable. The formation enthalpies of Frenkel pairs with larger separation gradually vary between 4.2 and 5.0 eV, separated by 0.3-0.4eV barriers along the (001) direction. Contrary to some previous studies, we do not find Frenkel configurations with tetrahedrally bonded Ti interstitials. The very low barriers for Frenkel defect evolution are consistent with the observations from the electrical stress damage annealing experiments. INTRODUCTION In strong electric fields, individual ions in a solid may migrate away from the equilibrium lattice positions, generating a Frenkel defect. In devices that utilize high dielectric constant (k) materials, including MOSFETs and various memory devices, this affect the reliability and leads to performance degradation. Electrically active defects substantially increase the leakage currents in DRAMs and other capacitance-based memory devices, affect channel mobilities in MOSFETs, and contribute to the 1/f noise via trapping and de-trapping charge on the defectlocalized states. The defects generated by the electric field also play a key role in emerging nonvolatile memory technologies. Thus, understanding the kinetics and the mechanism of generation of Frenkel defects in high-k dielectrics is key to controlling both the desired and the undesirable phenomena in a wide range of electronics applications. Our measurements (reported below in the Experimental Motivation section) indicated that TiO2 stands out from other high-k materials in terms of unusual behavior in electrical stress and annealing experiments. We therefore turn to first principles calculations to study the defects generated by the electric field in TiO2. Previous Studies of Frenkel defects in TiO2 In Table I, we compare some of the earlier experimental and theoretical data for Ti Frenkel (Tiint + VacTi ) and O anti-Frenkel (Oint +VacO ) defect pairs in rutile TiO2. Based on these data, one is lead to conclude that an electric stress would primarily promote generation of Ti Frenkel rather than O anti-Frenkel defects. Indeed, the fully ionized state of a Ti Frenkel defect is already energetically favored over the ionized O anti-Frenkel at zero field (the ionized state of the O anti-Frenkel defect is ~0.5eV hig
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