Journal of Materials Science

, Volume 47, Issue 21, pp 7498–7514

First principles calculations of oxygen vacancy-ordering effects in resistance change memory materials incorporating binary transition metal oxides

Authors

    • Department of Electrical EngineeringStanford University
  • Seong Geon Park
    • Department of Materials Science and EngineeringStanford University
  • Hyung-Dong Lee
    • Department of Electrical EngineeringStanford University
  • Yoshio Nishi
    • Department of Electrical EngineeringStanford University
First Principles Computations

DOI: 10.1007/s10853-012-6638-1

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

Abstract

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.

Introduction

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 [1], conductive filament formation [2], Schottky barrier modulation [3], electrochemical migration of point defects [4], ionic transport and electrochemical redox reactions [5]. 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 [610]. The oxygen vacancies have been shown to induce a metal–insulator transition in SrTiO3 (STO) single crystals [11], and the aggregation of these dopants into an extended defect network was postulated to drive the generation of conductive filaments during the resistive switching [5]. 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. [12] 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. [15] using ab initio simulations of vacancies in bulk TiO2. Yang et al. [16] 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 [5].

For nanoscale filaments inside vertical Pt/TiO2/Pt devices, in a recent study, Kwon et al. [17] 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 [79, 18, 19] and that of electronic charge injection [20] 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. [21], and Dong et al. [22], 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. [23].

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 [24]. 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 [25], metallic nickel defects in NiO [26], oxygen migration [27], thermal energy considerations [28], crystal disorder, and electrode interface effects [2931]. An atomistic description of the filament has been recently proposed [32], 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.

Computational details

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 [3335]. 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 [36], dynamical mean field theory approaches [37], hybrid functional [38] and GW implementations [39], 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 [14]. 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

The unit cell of rutile TiO2 is shown in Fig. 1. TiO2n-type semiconducting behavior was attributed to extra electrons generated by intrinsic defects, such as oxygen vacancies [44, 45]. The oxygen vacancy is found to induce a defect state in the band gap, and the semiconducting behavior depends on the position of the defect state relative to the conduction band minimum (CBM). The determination of the exact position of the oxygen vacancy defect state in reduced transition metal binary oxides has been however a long standing challenge of theoretical methods based on density functional theory (DFT) [4650]. The level of accuracy in describing the electronic interactions is crucial to obtain reasonable results. On the other hand, the computational cost of more accurate methods such as GW [39] or HSE [38, 49] for large supercells is a limiting factor for their usage. Here we use the computationally efficient LDA + U approach and apply corrections on both the Ti 3d and O 2p electrons. The LDA + Ud method with corrections on the 3d electrons of Ti, had been employed in a couple of earlier studies with different choices of the optimal value of Ud. Calzado et al. [50] used the Ueffd = UdJ of 5.5−0.5 eV within the LDA + U implementation the VASP code to correct the description of the defect state. On the other hand, Deskins and Dupuis [51] used a Ueffd value of 10 eV with the same code and found a band gap in satisfactory agreement with experiment for rutile TiO2. In most LDA + Ud studies of transition metal oxides, Ud values are fitted in an empirical way, but schemes based on theoretical determination of the U parameter had been also performed [52]. Within the LDA + Ud approach the Ud parameter was shown to affect only the character of the conduction band and values higher than 8 eV produce an unphysical description of the electronic interactions in TiO2 [14], partly because the conduction band states are rigidly moved up with increasing Ud value (Fig. 2a). The results are dramatically improved, when corrections are introduced additionally on the O 2p orbitals by employing the LDA + Ud + Up approach, and we observe systematic shifts for both the valence and conduction bands (Fig. 2b). This combined approach produces a corrected band structure and the band gap energy is in very good agreement with experimental data for TiO2. In the oxygen deficient structure with a neutral oxygen vacancy, Ti d electrons become localized and induce defect states within the band gap. These electronic states are strongly localized on the three Ti ions surrounding the oxygen vacancy, composed of two equatorial and one apical Ti. In Fig. 3, we show the partial density of states corresponding to Ti ions for the Ud parameter of 7 and 8 eV. For Ud = 7 eV the defect states appear in the band gap, but since the band gap is still underestimated their relative position is not correct (Fig. 3a, b). Values above 8 eV for Ud induce additional defect states in the band gap, and at the same time still underestimate the band gap, as depicted in Fig. 3b, d for equatorial and apical Ti ions in the vicinity of the oxygen vacancy. Electron localization function [53] and interatomic distances between the nearest Ti ions to an oxygen vacancy shown in Fig. 4a for Ud = 7 eV and Fig. 4b for Ud = 8 eV point to the source of this error, the unphysical repulsive interaction as the Ud value is larger than 8 eV, from 3.58 Å Ti–Ti distance to 3.82 Å. When Up = 6 eV is introduced to correct for O p orbital repulsion in addition to Ud = 8 eV for the d orbitals of Ti the description is improved as shown in Fig. 5a–b for the partial density of states and Fig. 5c electron localization function. The interatomic distances between nearest Ti–Ti ions become 3.54 Å. With this combination of Ud and Up the band gap (Eg ~ 2.9 eV, Exp. Eg = 3 eV), lattice parameters and the position of the defect states are greatly improved.
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Fig. 1

Unit cell structure of rutile TiO2 (P42/mnm)

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Fig. 2

Energy band structure and density of states calculated by a LDA + Ud and b LDA + Ud + Up

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Fig. 3

Partial density of state of two equatorial and one apical Ti ions surrounding an oxygen vacancy calculated by LDA + Ud (Ud = 7 eV and 8 eV). a Equatorial Ti (Ud = 7 eV). b Equatorial Ti (Ud = 8 eV). c Apical Ti (Ud = 7 eV). d Apical Ti (Ud = 8 eV). An additional defect states is observed for Ud = 8 eV

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Fig. 4

Electron localization function and corresponding structural relaxation around neutral oxygen vacancy calculated by a LDA + Ud (Ud = 7 eV) and b LDA + Ud (Ud = 8 eV)

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Fig. 5

Partial density of states of Ti ions surrounding the oxygen vacancy for a equatorial Ti and b apical Ti. c Electron localization function for the same structure calculated with LDA + Ud + Up (Ud = 8 eV and Up = 6 eV)

The localization of electrons on the oxygen vacancy site, occupying the defect state in the band gap is illustrated by the band-decomposed charge density in Fig. 6. The defect states are found to originate only from the nearest neighboring Ti ions as stated above and also supported by the partial density of states of Ti ions in the nearest and next nearest neighbor shell around the oxygen vacancy (Fig. 7). Within this method the defect state induced by an isolated oxygen vacancy is at 0.4 eV below the CBM, in very good agreement with experimental observations [45].
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Fig. 6

Band decomposed partial charge density distribution in TiO2 (110) plane containing one isolated single oxygen vacancy

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Fig. 7

a Schematic picture of the (110) plane in rutile TiO2. The partial density of states for the nearest neighboring Ti ions. b, c, d Ti ions as next nearest neighbors from the oxygen vacancy. e, f Nearest neighboring O ions

Positively charged vacancies in rutile TiO2 are found to increase the interatomic Ti–Ti distance to 3.78 Å for VO1+ and 3.98 Å for VO2+, thus the extraction of electrons from the vacancy site enhances the ionic character of Ti ions (Fig. 8a, b). In the case of negatively charged vacancies the interatomic distances first slightly decrease for VO1− at 3.53 Å, then increase for VO2− to 3.59 Å, with increasing electronic electrostatic repulsion (Fig. 8c, d).
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Fig. 8

Electron localization function and structural relaxations around a charged oxygen vacancy using LDA + Ud + Up (Ud = 8 eV, Up = 6 eV). a VO1+, b VO2+, c VO1−, and d VO2−

The doubly positively charged oxygen vacancy is found to be stable over the neutral oxygen vacancy in a large range of Fermi energy values (Fig. 9), with a transition to singly positively charged vacancy around 0.7 eV and to the neutral state around 0.5 eV below the CBM. The vacancy formation energies show significant dependence on the deposition conditions, i.e., Ti or O-rich environments (Fig. 9b, c).
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Fig. 9

Charged oxygen vacancy formation energies in rutile TiO2. a Unrelaxed in Ti-rich condition, b relaxed in Ti-rich condition, and c relaxed in O-rich condition

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

A number of oxygen vacancy configurations had been considered, ranging from di-vacancies, tri-vacancies to four, five, six and eight vacancies in a supercell of 3 × 3 × 4 TiO2 (Fig. 10) to investigate the effect of vacancy-ordering on the conduction properties of reduced TiO2. Previously, Szot et al., [54] have examined the effect of dislocations containing oxygen vacancies on the conduction properties in SrTiO3. More recently, the switching between an insulating and conductive TiO2−x was associated with a phase transition to a Magnéli phase in a filament that showed metallic conduction behavior [17]. Therefore, our investigation is directed towards characterizing vacancy-ordering mechanisms, in which certain configurations are found to exhibit properties of increased metallic conductivity. Figure 11 shows the electron localization function corresponding to the structures in Fig. 10. By adding more oxygen vacancies, the localization of electrons on the vacancy sites can be significantly altered, based on the coordination number of vacancies. It is found that 8 vacancies in a supercell, periodically repeated along the [001] direction, stabilize the formation of a conductive chain (Fig. 11b). The formation energy of these structures (Fig. 12) decreases with the number of ordered vacancies, and the [001] direction is energetically preferred. The conductivity implications are shown in Fig. 13 for the 8 vacancies along [001] (Fig. 13a) and 6 vacancies along [110] (Fig. 13b). The electron localization function, partial density of states and band-decomposed charge density corresponding to Ti ions in the first nearest neighbor shell around the vacancy clusters along [001] are found to be responsible for the increased conductivity. The equatorial Ti ions induce discrete defect states with partial overlap between them covering the entire band gap, and yielding the metallic behavior. These Ti–Ti bonds involve strong overlap of t2gt2g type orbitals. We note that the [001] direction with 8 vacancies/supercell has two rows of oxygen vacancies, while [110] direction has 6 vacancies/supercell in a single row. The single row of vacancies along the [110] direction (Fig. 13b) induces defect states from mid gap up to the conduction band. The band-decomposed partial charge density including all the vacancy induced defect states in the band gap is shown in the lower row of Fig. 13 with an iso-surface of 0.1 e/Å.
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Fig. 10

Schematic picture of oxygen vacancy clusters in reduced rutile TiO2 (110). a Vacancy-ordering in the [110] plane, and b vacancy-ordering in the [001] plane

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Fig. 11

Electron localization function calculated for the structures shown in Fig. 10. a Vacancy-ordering in the [110] plane, and b vacancy-ordering in the [001] plane

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Fig. 12

Oxygen vacancy cluster formation energies along the [110] and [001] directions in reduced rutile TiO2

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Fig. 13

Electron localization function, partial density of states of equatorial and apical Ti ions surrounding oxygen vacancies and partial charge densities for the a vacancy-ordered structure along [001], and b vacancy-ordered structure along [110]

In order to investigate the thermodynamic stability of ordered vacancy configurations along the [001] direction with 8 vacancies/supercell, three randomly distributed vacancy configurations R1, R2, and R3 containing also 8 vacancies/supercell were considered (Fig. 14a, b, c). In R1 the vacancies are randomly distributed in the supercell, in R2 and R3 the vacancies are randomly distributed in the same plane.
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Fig. 14

Schematic picture of the a R1, b R2 and c R3 random configurations of oxygen vacancies and d the [001] ordered vacancy chain in the 3 × 3 × 4 supercell of rutile TiO2. Red spheres denote O; blue spheres are for Ti, and the black spheres represent the oxygen vacancies (Color figure online)

The vacancy formation energy was determined using the following formula:
$$ E_{\text{vf}} = E\left( {{\text{TiO}}_{ 2- x} } \right) - E\left( {{\text{TiO}}_{ 2} } \right) \, + n\mu_{O} $$
where E(TiO2−x) is the total energy of a supercell containing the oxygen vacancy, E(TiO2) is the total energy of a perfect TiO2 in the same size of supercell, μO is the oxygen chemical potential, and n is the number of oxygen vacancies.
From Fig. 15, the ordered vacancy structure has the lowest vacancy formation energy relative to all three randomly configured vacancy structures of percolative nature. The iso-surface of the band-decomposed charge density of all defect states within the band gap for the random and ordered oxygen vacancy configurations presented in Fig. 14 are shown in Fig. 16. Entropic effects not included in the present calculations may alter the relative stability of these structures, however the random configurations had been found to be less conductive than the ordered chain of vacancies and behaving very similarly to the isolated vacancy cases. The random vacancy configurations can be stabilized during the material deposition, however once an electric field is applied the vacancy-ordering process will be favored to form a conductive filament. Then, for the repetitive switching process of the memory, an order–disorder transition can involve large diffusion barriers, thus in the present study a filament cohesion–disruption model supported by experimental observations [17] is investigated.
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Fig. 15

Total energies calculated for the structures in Fig. 14

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Fig. 16

Band decomposed charge density of defect states for the a R1; b R2; c R3 and d vacancy chain structure. The iso-surface corresponds to 0.1 e/Å3

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

Considering the vacancy filament model incorporating an ordered array of two rows of oxygen vacancies as the model describing the conductive “ON” state of the memory operation, we further investigated how a transition to the “OFF” state might take place during the switching process of a memory operation. The proposed models are shown in Fig. 17. The number of oxygen vacancies placed away from the ordered filament is gradually increased from 1 VO-off (Fig. 17b) to 2 adjacent VO-off (Fig. 17c), and 4 adjacent VO-off (Fig. 17c). The implication of these geometries to the conductivity is explored. For the 1 VO-off structure the band-decomposed charge density corresponding to the occupied defect states in the band gap indicates that electronic conduction is still possible, although the total number of defects states is reduced in the band gap (Fig. 18e) compared to the ordered filament (Fig. 18d). This arrangement corresponds to a conductive “imperfect filament”, which might serve as a more realistic model for the “ON” state, depending on the degree of ordering and materials properties. For the 2 VO-off structure the band-decomposed partial charge density point to a totally disrupted filament (Fig. 18c) and in the density of states a small bandgap is observed. The electron localization function for the filament and 1 VO-off and 2 VO-off structures are shown for the most stable charge state corresponding to each configuration (Fig. 18g, h, i). The degree of electron delocalization is decreasing as a more vacancies are placed away from the filament structure.
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Fig. 17

Schematic picture of the a the filament structure in the [001] direction, b disrupted filament obtained with one vacancy away from the filament (1 VO-off), c disrupted filament with two vacancies away from the filament (2 VO-off), and d 4 vacancies away from the filament (4 VO-off)

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Fig. 18

Upper row band decomposed partial charge density for the neutral oxygen vacancy chain in: a the filament, b 1 VO-off and c 2 VO-off structures. Middle row total density of states corresponding to the most stable charge state of each structure d 1+ for filament e 1+ for 1 VO-off and f 2+ for 2 VO-off. Lower row electron localization function for the most stable charge state for each structure g 1+ for filament, h 1+ for 1 VO-off and i 2+ for 2 VO-off

The vacancy formation energies corresponding to the arrangements presented in Fig. 17 are shown in Fig. 19. As the number of vacancies placed away from the ordered filament is increased, the stability of the charge states changes from 1+ to 2+ for a wide range of the chemical potential, i.e. Fermi level of the system. The filament and the 1 VO-off arrangement are most stable in the 1+ state. Here and in the following the 1+ notation refers to the average charge per vacancy, i.e., all eight vacancies are depleted by one electron. However, when more than two vacancies are placed away from the filament the transition state between the 2+ and 1+ states falls closer to mid gap and yields a larger range of stability for the 2+ state/vacancy. We note that the isolated vacancies were also found to be stable in the 2+ state for a wide range of the chemical potential, up to 0.7 eV below the CBM (Fig. 9). Thus, the transition between an ordered and disrupted filament is found to be accompanied by a change in the charge state that can be induced by the applied electric field during the memory operation. A schematic picture of the “ON” to “OFF” transition [20] based on charge state change is depicted in Fig. 20a. The calculated cohesive energies of a filament formation relative to isolated vacancies in bulk TiO2, in the three charge states, as defined in Ref. 20, are shown in Fig. 20b, further confirm the finding that the filament formation is energetically preferred if the average charge per vacancy is neutral or 1+ [20].
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Fig. 19

Oxygen vacancy cluster formation energies for a a connected vacancy filament, b 1 VO-off, c 2 VO-off and d 4 VO-off structures, in the neutral, 1+ and 2+ charge states

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Fig. 20

a Schematic picture describing a possible “ON” to “OFF” transition by the cohesion and disruption of the conducting channel formed by charged oxygen vacancies. b Cohesive energy as a function of the charge state of the oxygen vacancy chain model relative to the isolated oxygen vacancy configurations

Oxygen vacancy-ordering effects in NiO

Single oxygen and nickel vacancies in NiO

The unit cell of NiO has cubic symmetry and is of NaCl-type (Fig. 21). NiO had been proposed to have p-type conductivity. Isolated single oxygen and nickel vacancies in a supercell Ni64O64 were considered to elucidate the nature of this property. GGA + Ud was employed in all the calculations for NiO, and the Ud was chosen in accordance with previous studies [56]. Partial densities of states are shown in Fig. 22 for neutral, 1 and 2 charge states for Ni vacancies (Fig. 22a) and neutral, 1+ and 2+ charge states for O vacancies (Fig. 22b). Defect states near the valence band maximum are observed for Ni vacancies, while the oxygen vacancies induce gap states closer to the mid gap. With the introduction of charge defects the band gap is slightly altered ranging from 3.41 eV for neutral Ni vacancies to 3.14 eV for the 2 state (Fig. 23a). For the neutral Ni vacancy there is an additional perturbation close to the conduction band. A defect state in the proximity of the valence band maximum at ~0.37 eV is depicted. For the neutral oxygen vacancies defect states are found around 1.3 eV above the valence band maximum and at 0.3 eV below the CBM. As the vacancy becomes more positively charged several defect states are created throughout the gap and the band gap is decreased from 3.66 eV (neutral) to 3.41 eV (2+) (Fig. 23b).
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Fig. 21

Unit cell for NiO (NaCl-type, Fm-3 m)

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Fig. 22

Partial density of states for a Ni vacancies and b O vacancies in NiO

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Fig. 23

Band gaps and defect states positions of a Ni vacancies and b O vacancies, in reduced NiO

The as-deposited NiO samples had been found nickel deficient. We show that the vacancy states of charged nickel vacancies are stable for EF near the valence band maximum as shown in Fig. 24a. The transition states of nickel vacancies are 0.04 eV for q = −1 and 0.16 eV for q = −2. These low energies for acceptor-like states support the possibility of p-type conductivity in Ni-deficient NiO films observed in experiments [56]. After the forming process, oxygen vacancies were shown to generate [25] and cluster due to the favorable interaction between oxygen vacancies [55]. Based on formation energy calculations (Fig. 24b), the stable charge state of oxygen vacancy is found to be 2+ closed to the valence band, then a neutral vacancy is stabilized in the mid gap region and a transition is observed to 1 around 3 eV below the CBM.
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Fig. 24

Formation energy of charged vacancies in reduced NiO a VNi, b for VO

Filament formation and disruption in NiO

To describe the “ON” state conduction in NiO a filamentary arrangement of six ordered oxygen vacancies in two rows along the 〈110〉 direction were chosen. For the “OFF” state, we investigate the possibility of the oxygen vacancy sites in the filament becoming occupied by oxygen ions diffusing from adjacent sites [41]. We have considered three different positions of diffusing oxygen ions denoted A (Fig. 25a), B (Fig. 25b) and D (Fig. 25c) in the neighboring shells around the filament arrangement. The oxygen vacancy coordination number varies for these structures. These positions are similar to the 1 VO-off arrangement type described in the section for TiO2. In this section however, we have also explored the effect of various oxygen vacancy coordination shells on the conduction and filament stability. The structures corresponding to the A and B positions from Fig. 25 for the 1 VO-off arrangement, induce a semiconducting band gap of 0.25 eV (A) and 0.6 eV (B) and exhibit reduced conductivity based on the total densities of states plotted in Fig. 26a, b. On the other hand, a weak metallic character is observed for the oxygen vacancy in position D (Fig. 26c). While in the nearest neighbor shell of the oxygen vacancy in position A there is only one vacancy, in the B position there are two oxygen vacancies and for the D position there are four nearest neighbor oxygen vacancies. The vacancy–vacancy interactions in NiO had been previously found to be stronger in nearest neighbor di-vacancies [55] and stabilize these configurations. Therefore, the position in D may correspond to an intermediate state in the switching process and could be similar to the “imperfect filament” observed in TiO2 showing reduced conductivity, but being still weakly metallic.
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Fig. 25

Schematic picture of the disrupted filament obtained by moving one oxygen atom into a vacancy site. The considered positions for the vacancy 1 VO-off away from the filament are a A position, b B position, or c D position

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Fig. 26

Total density of states for the reduced NiO supercell structures with vacancy off configurations shown in Fig. 25

Electron localization functions and total density of states for the “ON” state and the “OFF” state with the largest band gap (A) are shown in Fig. 27. The charge integrated around Ni ions in the filament case has 9.8 e/Ni around the vacancies in the middle of the supercell, which also have the largest nearest neighbor vacancy coordination. The Fermi level is positioned in a band dominated by the spin-down electron component (Fig. 27a). The 4 metallic nickel ions surrounded by oxygen vacancies dominate the density of states near EF for the proposed “ON” state configuration. In average there are 9.8 electrons localized near each Ni site, which account for the metallic conduction observed through the metallic nickel ions. On the other hand, when one oxygen atom is moved into a vacancy site in the middle of the supercell, the neighboring Ni ions reduced their charges to 9.6 e/Ni, while those placed between the filament and the new vacancy site increased their charge to 9.2 e/Ni. These Ni ions contribute to the defect states below the Fermi level in the band gap, while those with only one vacancy in the nearest neighbor shell contribute to the states below the CBM.
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Fig. 27

Band decomposed partial charge density for the (110) plane, within (EF, EF + 0.3 eV) window for the a “ON” state (filament), b “OFF” state (vacancy off structure). Total density of states corresponding the c “ON” state and d “OFF” state

The calculated band decomposed charge density for the “ON” state is shown in Fig. 28a, and for the “OFF” state in Fig. 28b. Figure 28 shows the band-decomposed partial charge density for different regions in the band gap (EF, EF + 0.3 eV), (EF − 0.25 eV, EF) and (EF − 0.45 eV, EF − 0.28 eV) describing the formation (a) and disruption (b) of the filament. In the case of ordered oxygen vacancy chain (Fig. 28a) the metallic type Ni ions have a strong contribution to the defect states at the Fermi level. As mentioned above, the Ni ions outside the filament, but within the first coordination shell around the vacancies induce the low-lying defect states close to the valence band. With an applied voltage if the Fermi level is repositioned in the band gap towards the conduction band, the Ni ions from the center of the filament may have the most significant contribution. In contrary, for a disrupted filament (Fig. 28b) the Ni ions participating in the filament do not retain a main role in their neutral charge state, however localized conductive clusters are observed around the Ni ions outside of the filament with a coordination of at least two oxygen vacancies. The filamentary Ni ions show a more localized nature and would contribute to the conduction if the system becomes negatively charged under an applied electric field. Based on an experimental investigation of NiO, Jung et al. [57] had shown evidence that weak metallic conduction and correlated barrier polaron hopping coexist in the high-resistance off state.
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Fig. 28

Band decomposed partial charge density corresponding to the various regions in the band gap around the EFa for the “ON” state, b for the “OFF” state

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.

Conclusions

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.

Acknowledgements

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.

Copyright information

© Springer Science+Business Media, LLC 2012