First principles calculations of oxygen vacancy-ordering effects in resistance change memory materials incorporating binary transition metal oxides
- First Online:
- Cite this article as:
- Magyari-Köpe, B., Park, S.G., Lee, H. et al. J Mater Sci (2012) 47: 7498. doi:10.1007/s10853-012-6638-1
- 850 Views
Resistance change random access memories based on transition metal oxides had been recently proposed as promising candidates for the next generation of memory devices, due to their simplicity in composition and scaling capability. The resistance change phenomena had been observed in various materials, however the fundamental understanding of the switching mechanism and of its physical origin has not been agreed upon. We have employed first principles simulations based on density functional theory to elucidate the effect of oxygen vacancies on the electronic structure of rutile TiO2 and NiO using the local density and generalized gradient approximations with correction of on-site Coulomb interactions (LDA + U for TiO2 and GGA + U for NiO). We find that an ordered oxygen vacancy filament induces several defect states within the band gap of both materials, and can lead to the defect-assisted electron transport. This state may account for the “ON”-state low resistance conduction observed experimentally in rutile TiO2 and NiO. As the filament structure is perturbed by oxygen ions moving into the ordered chain of vacancies under applied electric field, charges are trapped and the conductivity can be significantly reduced. We predict this partially disordered arrangement of vacancies may correspond to the “OFF”-state of the resistance change memories.
Resistive switching devices for data storage are currently considered a high-risk, but possibly a high-payoff solution for an embedded non-volatile memory (NVM) module. Along this line, the switching devices based on the resistance change induced in a metal–insulator–metal (MIM) stack, received increased interest lately. As for materials, the binary metal oxides, e.g., TiOx, NiOx, HfOx, AlOx, TaOx were considered, with the prospect of low cost, high scalability, and low power consumption characteristics. In terms of resistance-switching models for these memory cells, there is no general consensus about how the switching occurs. Based on experiments performed for various MIM stacks, several models had been proposed: e.g., charge trapping mechanism , conductive filament formation , Schottky barrier modulation , electrochemical migration of point defects , ionic transport and electrochemical redox reactions . The role of defects in the resistance-switching, in particular oxygen vacancy diffusion effects describing the transition between the high and low resistive state has been recently a topic of interest [6–10]. The oxygen vacancies have been shown to induce a metal–insulator transition in SrTiO3 (STO) single crystals , and the aggregation of these dopants into an extended defect network was postulated to drive the generation of conductive filaments during the resistive switching . Before the bi-stable switching can be achieved, an electroforming step is required for most of the samples. On the surface of STO single crystals, Janousch et al.  identified the existence of a channel of oxygen vacancies (VO) after electroforming.
Both the crystalline and thin film reduced TiO2−x, have been found to have substantially higher n-type conductivity than their stoichiometric structures. For the reduced TiO2 there are, however, several stable titanium–oxygen phases between Ti2O3 and TiO2, in the phase diagram of the Ti–O system. An oxygen vacancy created in stoichiometric TiO2 behaves as a positively charged double donor [13, 14], and with increasing concentration of vacancies, vacancy-ordering trends had been identified theoretically by Park et al.  using ab initio simulations of vacancies in bulk TiO2. Yang et al.  also studied the vacancy formation mechanisms in Pt/TiO2/Pt devices. A positive electroforming voltage applied to the top electrode was found to induce the formation of an oxygen gas composed of O2− ions, which drift towards the anode. Simultaneously the oxygen vacancies (VO) are drawn to the cathode and decrease the field in this region .
For nanoscale filaments inside vertical Pt/TiO2/Pt devices, in a recent study, Kwon et al.  identified the filaments to be of TinO2n−1 composition, which are known as room temperature conducting Magnéli phases. Using high-resolution transmission electron microscopy (HRTEM) and electron diffraction they observed that the filaments form a bridge between the two electrodes in the SET state. Direct probing of the filaments using conductive atomic force microscopy revealed that the filaments were both localized and conducting. The character changed abruptly from metallic to semiconducting near 130 K. Conversely, after RESET, no Magnéli phases were observed in the regions previously occupied by the conducting filaments. Thus, TiO2 is believed to spontaneously order into Ti4O7 when the concentration of oxygen vacancies reaches a critical density.
The nature of nanofilament formation [7–9, 18, 19] and that of electronic charge injection  had also been the subject of intense discussion over the past years. In addition, it was pointed out that electrode–oxide interfaces may play an important role in the forming and switching, and the properties can be material and/or deposition controlled. Jameson et al. , and Dong et al. , identified that oxygen vacancies were responsible for TiO2 bipolar switching through field-driven drift, which alters the Schottky barriers at the electrode interfaces. The atomic interactions at the interfaces between the metal oxide and reactive electrodes can influence the filament formation, as addressed by Jeong et al. .
The NiO-based RRAM has also been extensively investigated, in particular due to its unipolar switching characteristics. The filament model discussed above has been found to give qualitative explanation for unipolar switching as well . Up to date, various models had been proposed to explain the switching phenomena in this material i.e., migration of oxygen into the Pt anodic electrode after the forming process , metallic nickel defects in NiO , oxygen migration , thermal energy considerations , crystal disorder, and electrode interface effects [29–31]. An atomistic description of the filament has been recently proposed , with a detailed investigation of the role of oxygen vacancies in the switching.
In this article, we review and discuss the fundamental aspects of the switching mechanism models developed based on first principles calculations. A nanofilament formation model is constructed and its implications for “ON” and “OFF” state conduction in TiO2 and NiO are predicted.
The structures and energies of oxygen deficient rutile TiO2 and cubic NaCl-type NiO were calculated using density functional theory. In the past decade, several theoretical investigations employed the local density (LDA) and the gradient-corrected approximations (GGA), to calculate the electronic band structure of transition metal oxides [33–35]. Going beyond LDA and GGA, however, was necessary, to correct for some of the most severe shortcomings of the conventional LDA and GGA, i.e., the accurate prediction of the energy band gap and the position of the electronic defect states in the band gap. Recent theoretical developments, as the addition of the on-site Coulomb correction within LDA/GGA + U , dynamical mean field theory approaches , hybrid functional  and GW implementations , have been very successful in predicting realistic properties for these materials.
In this study, the electronic interactions are described within the LDA/GGA + U formalism for TiO2 and NiO, where on-site Coulomb corrections are applied. While for NiO the GGA + Ud approach yields an acceptable band structure, for TiO2 is necessary to go beyond LDA + Ud . The on-site Coulomb corrections are applied on the 3d orbital electrons of Ti or Ni ions (Ud) for TiO2 and NiO, respectively, and in addition on the 2p orbital electrons of the O ions (Up), in the case of TiO2.
The density functional calculations were done using the Vienna ab initio program package, (VASP) [40, 41], and the projector augmented-wave (PAW) pseudopotentials [42, 43]. An energy cutoff of 353 eV for TiO2, and 500 eV for NiO was employed for the plane wave expansion. The supercells size was chosen to minimize the spurious electrostatic interactions between defect images. All the structures were optimized at T = 0 K and vibrational and entropic effects were not included. For k-point integration, a Monkhorst–Pack grid of 8 × 8 × 12 grid for the TiO2 primitive cell, 4 × 4 × 4 for the Ti72O144 supercell, and a 2 × 2 × 2 grid for the supercell of Ni64O64 was used. The O 2s22p4, Ti 3s23p63d24s2, and Ni 3d84s2 states were considered valence electrons. All ions were allowed to relax with energy convergence tolerance of 10−6 eV/atom and by minimizing the force on each atom to be less than 0.01 eV/Å.
Oxygen vacancy-ordering effects in TiO2
Single oxygen vacancy in TiO2
As the isolated oxygen vacancy induces a defect state around 0.4 eV below the CBM, these states are too deep to elevate electrons to the conduction band at room temperature. Thus, to describe the n-type semiconductivity observed experimentally in this material, the concentration of vacancies needs to be increased and we investigated their ordering trends.
Filament of ordered vacancy configurations in TiO2
We conclude that the oxygen vacancies act as mediators of electron conduction, which is achieved through the successive metallic Ti ions in the channel. Most of the defect states originate from the Ti ions in the vacancy chains, and the electronic charge density around them is considerably enhanced compared to the stoichiometric TiO2.
Disruption of the ordered filament in TiO2
Oxygen vacancy-ordering effects in NiO
Single oxygen and nickel vacancies in NiO
Filament formation and disruption in NiO
As a general remark on elucidating the role of oxygen vacancies in the resistive switching, assuming that the transition between “ON” and “OFF” states is described by oxygen migration in and out of the filament for materials like TiO2 and NiO, we have found that a very small amount of oxygen migration may change the conductivity drastically. Also, the possible variation of the exchanged oxygen site during the memory operation may induce randomness in the switching process, and influence the retention time of the memory.
The “ON” and “OFF”-state implications of vacancy-ordering/disordering on the conduction mechanism were discussed based on first-principle calculations for rutile TiO2 and cubic NiO incorporating oxygen vacancies. The formation and disruption of a conductive channel between nearest metals (i.e. Ti or Ni ions in the filament) were investigated. It was found that the oxygen vacancy chains could mediate the conduction. When the oxygen vacancy concentration is further increased and the vacancies become nearest neighbors significant charge redistribution is observed, which ultimately enhances the metallic nature of the interaction between nearest Ti and Ni ions, respectively. We predict that the electronic transport can be described as defect-assisted tunneling through the channel of Ti and Ni ions in these binary metal oxides.
The Stanford Non-Volatile Memory Technology Research Initiative (NMTRI), and the Marco Focus Center (MSD) sponsored this study. The computational study was carried out using the National Nanotechnology Infrastructure Network’s Computational Cluster at Stanford.