Ab Initio Study of HfO2/Ti Interface VO/Oi Frenkel Pair Formation Barrier and VO Interaction With Filament

Abstract

Frenkel pair (FP) formation at HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Ti interface and oxygen vacancy interaction with the filament in HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Ti-based resistive random access memory (ReRAM) are the important mechanisms in the ReRAM operations. In this article, the formation barriers, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{A}$ </tex-math></inline-formula> , and formation energies of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{O}/{O}_{i}$ </tex-math></inline-formula> FP across the HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Ti interface with and without preexisting vacancy are calculated using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ab initio</i> tool under zero external electric field. It is found that both the formation barrier and energy can be increased or decreased due to a preexisting oxygen vacancy. The spread of the effect increases inversely with the distance between the FP and the preexisting vacancy. A compact model is then proposed. The parallel migration barrier of an oxygen vacancy at the nearest and the second nearest neighbors (NNs) of a filament is also studied. It is found that the second NN has the lowest barrier due to its ability to retain a +2 charge state. The merging and dissolution of an oxygen vacancy with a filament (equivalent to perpendicular migration) is found to have a similar behavior that +2 states enhance the interaction. It is found that the fourfold coordinated oxygens (4C) and threefold coordinated oxygens (3C) filaments behave similarly during dissolution. However, 4C and 3C filaments prefer merging with 4C and 3C vacancy, respectively. The barrier of merging a +2 4C vacancy with a 4C filament is only 0.56 eV. The data and model obtained from this study may be used to implement device-level simulators, such as kinetic Monte Carlo (KMC) simulators, for ReRAM.