Mechanistic Analysis of Oxygen Vacancy-Driven Conductive Filament

Feb 28, 2018 - For bulk NiO (see Figure 1a), the integration of the Brillouin zone was done with .... Including the Lattice Constant (a0), Magnetic Mo...
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Research Article Cite This: ACS Appl. Mater. Interfaces 2018, 10, 9802−9816

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Mechanistic Analysis of Oxygen Vacancy-Driven Conductive Filament Formation in Resistive Random Access Memory Metal/NiO/Metal Structures Handan Yildirim* and Ruth Pachter* Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Dayton, Ohio 45433, United States S Supporting Information *

ABSTRACT: Electrically switchable resistive random access memories have drawn much interest as nonvolatile memory device candidates based on metal−insulator−metal (MIM) structure concepts. However, atomic level mechanisms that lead to conductive filament (CF) formation in MIM structures are often lacking, such as for the system with NiO as the oxide layer, which was found promising for resistive random access memory (RRAM) device applications. In this work, using density functional theory with a Hubbard-type on-site Coulomb correction, which we carefully benchmarked, we analyzed the intrinsic propensity toward CF formation in NiO upon introduction of oxygen vacancies, including interfacial effects of Ag or Pt electrodes. First, for stoichiometric MIM structural models, contributions from metal-induced gap states to the electronic density of states (DOS) were identified, accommodating oxygen vacancy states and showing that the interface region is reduced more easily than the bulklike region, for example, for the Ag/NiO/Ag structure. Moreover, a tendency toward oxygen vacancy clustering was demonstrated, important for CF formation. Indeed, by introducing ordered oxygen vacancies into the oxide layer for both MIM models, several extended defect states within the forbidden gap have resulted, which lead to defect-assisted transport. These were shown to be influenced by the spatial distribution and number of oxygen vacancies in the filament, where the degree of reduction of Ni atoms changes based on the immediate surroundings. Projected electronic DOS for individual Ni atoms in regions near and away from oxygen vacancies indicated that those Ni close to oxygen vacancies contribute most to the conductivity. Interestingly, based on charge analyses, these atoms are revealed to undergo significant reduction, generating a locally conductive region in the oxide layer that consists of metallic/near-metallic Ni (Ni0), formed through local reduction. KEYWORDS: NiO, metal−insulator−metal structures, metal-induced gap states, RRAM, conductive filament, DFT

1. INTRODUCTION Resistive random access memory (RRAM) devices have drawn much interest in the last decade, particularly following the work of Williams and co-workers based on the concept of a memristor,1 as proposed by Chua.2 In this case, the so-called memristance, which provides the relationship between the change in the charge (time integral of the current) and flux (time integral of the voltage), is not a constant as in linear elements, but a function of the charge, resulting in a nonlinear circuit element. Applications of such two-terminal electrical devices that provide high integration densities and low-power operation include, for instance, neuromorphic-type computing elements. This area of research led to numerous reviews3−6 © 2018 American Chemical Society

(see citing and cited references), including a study on the effects of ionizing radiation on such devices.7 Significant focus on filamentary-type resistive switching (RS) mechanisms has emerged, where formation/rupture of a conductive filament (CF) ensures successive switching in the nonvolatile metal− insulator−metal (MIM) memristors, dependent on the switching material. In such an RRAM device, binary oxide MIM structures are constructed using an insulating layer stacked between two electrodes, which can be built either symmetrically Received: November 19, 2017 Accepted: February 28, 2018 Published: February 28, 2018 9802

DOI: 10.1021/acsami.7b17645 ACS Appl. Mater. Interfaces 2018, 10, 9802−9816

Research Article

ACS Applied Materials & Interfaces

demonstrates encouraging characteristics for RRAM application, the system still poses questions on the type of filament formed and the role of oxygen vacancies in the RS, which motivated our study. To understand RS phenomenologically, an ion migration model to describe the CF growth and rupture was developed,27 showing, for example, effects of the CF geometry, whereas in more recent work on filamentary RS, a model that solves selfconsistently for vacancy migration, electrical conduction, and Joule heating enabled assessment of the relative importance of various parameters that determine RS, emphasizing the importance of electrode selection,28 and effects of the interface on the resistance were also shown for NiO devices upon varying the electrode.29 However, establishing parameters that will influence device performance by phenomenological modeling does not provide insight into the electronic properties that affect those parameters. At the same time, although first principles studies explored defect thermodynamics in bulk NiO, not only for their relevance in RRAMs but also for gaining an understanding of such defects,25,30−36 details on the formation of a CF in NiO-based MIM structures, taking into account the interface with varying electrode compositions, unlike previous work,32,37 are notably lacking. For example, although RS by formation/rupture of a CF was related to oxygen-ion migration, only bulk NiO was considered.34 Energetically favorable vacancy pair configurations in bulk NiO were explored,36 whereas Ni and O vacancies in bulk NiO were shown to be favorable over interstitials.31 Effects of local nonstoichiometry on the electronic structure and transport found that the carrier concentration is modified by oxygen vacancies near nickel vacancies.25 In this study, by applying density functional theory (DFT) calculations, we discerned atomic-level mechanisms of CF formation in an NiO-based MIM system with varying electrodes, noting that NiO, an example of a late 3d transition metal oxide, is especially challenging to treat theoretically because of strong electron correlation, requiring careful benchmarking. We addressed the intrinsic propensity of NiO toward oxygen vacancy formation, as well as interactions at the electrode interface. Moreover, structural and electronic implications of filament formation on the conductivity were elucidated with varying oxygen vacancy concentrations and spatial distributions. Analyses of stoichiometric interfaces showed contribution from metal-induced gap states (localized at the interface layer) to the electronic density of states (DOS), which assist in the reduction at the interface, and also that the contact type depends on the electrode composition. Oxygen vacancies were found to prefer clustering. Projected DOS (PDOS) and charge distributions for Ni atoms revealed that those near oxygen vacancy regions contributed the most to the overall conductivity, where remarkably, chainlike metallic nickel (Ni0) formation was shown to occur, forming a locally conductive channel throughout the oxide between the electrodes. The proposed conductance mechanism, in which a conducting Ni filament is formed, assisted by proximate oxygen vacancies, is therefore not considered as an ECM mechanism. Our results, providing a mechanistic understanding of the system’s behavior, will motivate further experimental work on NiO-based MIM structures, to ultimately achieve improved performance of RRAM devices. The paper is organized as follows. In section 2, we report methods and computational details. Section 3 is devoted to results and discussion. In section 3.1, we summarize the

or asymmetrically using the same or different top or bottom electrodes, respectively. In the filamentary RS mechanism, following the CF forming stage, where a compliance current is used for controlling its size, operation depends on the migration of ions across the metal oxide in the SET (RESET) stages upon application of a positive (negative) voltage in a bipolar RRAM or of the same polarity voltage in a unipolar system. The rupture of the CF causes a high-resistance state, and its re-formation results in a low-resistance state (LRS). However, a consensus on materials selection has still not been reached because properties such as reliability, switching speed, or the range of resistance states depend on the materials used,8 and despite much promise and progress in the development of MIM structures, further understanding of the memristive mechanism is crucial in enabling improvement of the devices. Here, we investigate p-type NiO-based MIM structures, which is one of the earliest studied. Following early work,9 the RS characteristics of NiO were determined in a number of ways,10−14 demonstrating high stability and reliable memory characteristics, high speed, low voltage, fast programming, and compatibility with the complementary metal−oxide−semiconductor (CMOS) process. Coexistence of unipolar and bipolar RS in Pt/NiO/Pt devices was shown to require lower voltages than in the unipolar mode.15 However, questions are still raised on the mechanism of operation of NiO-based MIM structures. Generally, proposed conductance mechanisms of filamentary-type switching in oxides include those by metal cations that originate from electrochemically reactive electrodes (e.g., Cu and Ag), leading to the formation of a conductive bridge between them, namely the so-called electrochemical metallization (ECM) memory or conductive-bridge random access memory (CBRAM) or those by anions (oxygen vacancies, resulting from drift and diffusion of oxygen ions under an applied bias), that is, the valence change memory (VCM) mechanism. Additionally, a thermochemical mechanism was also proposed.16 For NiO, characterization of Ni filaments by magnetoresistance17,18 demonstrated their structural evolution and also that multifilaments are involved in the LRS, rupturing separately during RESET.18 Experiments for NiO/Pt films using time-of-flight secondary ion mass spectroscopy and conductive atomic force microscopy (C-AFM) measurements showed that oxygen atoms move to the anode, changing the surface composition and therefore the resistance.19 Unipolar memristive behavior for NiO-based MIM structures was demonstrated,20,21 indicating that reliable RS depends on the oxygen partial pressure during growth. This observation demonstrates that the initial oxygen vacancy defect concentration and configuration is important and will affect RS reliability.20 We note that although Ni vacancies exist in p-type NiO films,22 upon modification of growth conditions, for example, by changing the oxygen partial pressure during deposition, appreciable concentration of intrinsic oxygen vacancies can be achieved. Investigation of diffusion of oxygen vacancies in epitaxial NiO by local multimodal scanning probe microscopy was reported, 23 consistent with earlier work.19,22,24,25 Bipolar memristive behavior was also observed in NiO-based MIM structures,19,22,24 rationalized by C-AFM characterization and theoretical work,25,26 revealing the role of oxygen vacancies and formation of a Ni-CF. Oxygen vacancy migration, such as in a VCM system , has been postulated. 19,22,24 Thus, although the NiO-based MIM 9803

DOI: 10.1021/acsami.7b17645 ACS Appl. Mater. Interfaces 2018, 10, 9802−9816

Research Article

ACS Applied Materials & Interfaces structural and electronic properties of stoichiometric and nonstoichiometric bulk NiO and of the NiO(100) surface. In section 3.2, we discuss stoichiometric and nonstoichiometric MIM interfaces, whereas details on the CF formation are presented in section 3.3, with conclusions in section 4.

2. METHODS AND COMPUTATIONAL DETAILS NiO crystalizes in the NaCl (Fm3̅ m ) structure and forms antiferromagnetic type-II ordering, where the spin direction alternates between adjacent (111) Ni planes below the Néel temperature (523 K). A narrow 3d bandwidth leads to a strong on-site Coulomb repulsion, and the localized nature of d-electrons cannot be described by the traditional generalized gradient approximation (GGA) exchange−correlation functionals. The local density approximation plus dynamical mean-field theory (LDA + DMFT) approach or a combination of LDA + DMFT with the GW [Green’s (G) function with screened Coulomb interaction (W)] approximation were previously used to take into account electron correlation and predict the electronic structure and local magnetic moment.38 GW using the range-separated hybrid Heyd−Scuseria−Ernzerhof (HSE) functional39 rather than Perdew−Burke−Ernzerhof (PBE)40 for the wave functions and energy eigenvalues was also employed,41 moving beyond previous GW calculations.42−44 We employed an effective Hubbard-type on-site Coulomb correction U modified by the exchange J to the functional, which increases the splitting between occupied and unoccupied states,45 previously applied to study the electron-energy-loss spectra and structural parameters for NiO46 or adsorption of transition metal atoms on NiO(100) and NiO/Ag(100) thin films.47 LDA + U or GGA + U were also used for modeling NiO(100) surfaces, also on Ag(100).47−49 We used the spin-polarized SGGA-PBE + U with a Ueff (U − J) value of 5.3 eV, with U and J of 6.3 and 1 eV, respectively. These values were used to accurately describe the physical properties of NiO bulk and Ni(100) surfaces.50,51 To benchmark the performance of the SGGA + U functional with the selected Ueff value, calculations using HSE06 (separation parameter 0.11 bohr−1) and comparison to experiment and previous computations, for example, using HSE0352 or applying the hybrid B3LYP53 functional,54 were undertaken. All calculations were performed using the Vienna Ab initio simulation package55 within the framework of DFT, applying the projector augmented-wave method to treat core and valence electrons. (Ni_pv) was used for the Ni potential. Antiferromagnetic ordering was included. A plane wave energy cutoff of 520 eV was used in all calculations. Charge-transfer calculations were performed using Bader charge analyses. For bulk NiO (see Figure 1a), the integration of the Brillouin zone was done with k-point meshes of 2 × 2 × 2 and 12 × 12 × 12 for the 4 × 4 × 4 and 2 × 2 × 2 supercells, respectively. The atomic positions were relaxed until the Hellmann−Feynman force on each atom converged to within 0.03 eV/Å. The lattice constant/geometry, magnetic moment, band gap, DOS, and valence and conduction band edges of bulk NiO were evaluated. The band gap was determined from the difference between the conduction band minimum (CBM) and valence band maximum (VBM). A 4 × 4 × 4 large supercell of NiO bulk was used for calculations of vacancy defects to ensure that the results do not suffer from spurious defect−defect interactions, following the calculations for bulk NiO using 2 × 2 × 2, 3 × 3 × 3, and 4 × 4 × 4 supercells, where defect states and their location within the forbidden gap were analyzed. The Ni(100) surface was modeled using a 4 × 3 × 1 supercell with five layers and a 20 Å vacuum region to ensure no interaction between the surfaces (Figure 1b,c) and then inserted between the two metal electrodes to generate initial MIM model structures with different interface configurations (on-top O and Ni), which were subsequently optimized. We found that the 4 × 3 × 1 supercell describes appropriately the NiO(100) surface when compared to results using a 6 × 4 × 1 supercell with five layers (240 atoms), based on convergence tests of surface properties. A dipole correction was employed perpendicular to the surface plane. The integration of the Brillouin zone was done with a 3 × 4 × 1

Figure 1. Initial atomic structures for (a) bulk NiO antiferromagnetic type-II, (b) metal/NiO/metal structural model with on-top oxygen interface configuration where electrode atoms (Ag or Pt) reside on-top of the oxygen atoms at the interface, and (c) metal/NiO/metal structural model with on-top nickel interface configuration where electrode atoms (Ag or Pt) reside on-top nickel atoms at the interface. The models consist of three metallic layers (Ag or Pt) epitaxially built on five NiO layers. The balls represented by gray, red, and yellow correspond to nickel, oxygen, and electrode atoms (Ag or Pt), respectively. The bond distance at the interface between the electrode and the oxide layer is shown by “d”. The “optimized cell” illustrates atoms subject to relaxation (optimization), whereas the others are kept frozen. regular k-point mesh. The total energy convergence was also tested by doubling the size of the k-point mesh. Ab initio molecular dynamics (AIMD) simulations within an NVT ensemble were performed to study the interface stability for the MIM structural models constructed by incorporating fcc-Ag(100) or Pt(100) with a NiO(100) surface. Although the simulation time (2− 4 ps) was short for obtaining any diffusion-related parameters, interface structural stability was observed. Note that even with the thin oxide layer that we used in these simulations (∼1 nm), the number of atoms in the supercell sums up to ∼200, consisting of Ni, Ag (or Pt), and O atoms, and with the choice of a Ni_pv potential, a large number of electrons (>2000) have to be considered, therefore becoming computationally intensive.

3. RESULTS AND DISCUSSION 3.1. Stoichiometric and Nonstoichiometric Bulk NiO and the NiO(100) Surface. The structure and electronic properties of bulk single crystal NiO are summarized in Table 1. The lattice constant and magnetic moment calculated for bulk NiO for an antiferromagnetic-ordered ground state using SGGA + U and HSE06 are consistent with the experimental data (see Table 1). However, using SGGA-PBE results in an underestimated magnetic moment, an overestimated lattice constant was also noted with B3LYP. The optimized NiO(100) surface structure shows only a small buckling of the surface 9804

DOI: 10.1021/acsami.7b17645 ACS Appl. Mater. Interfaces 2018, 10, 9802−9816

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Table 1. Structural and Electronic Properties of Bulk NiO and the NiO(100) Surface, Including the Lattice Constant (a0), Magnetic Moment of Ni Atoms m (μB), Band Gap (Eg), and Surface Energy (γ) Calculated Using Different Methods in Comparison to Available Computational and Experimental Data (Results without an Associated Reference Indicate Current Study)a bulk NiO SGGA + U LDA + DMFT GW HSE06 B3LYP PBE experiment NiO(100) γ (meV/Å2) SGGA + U

47 [5 layers]; 52 [6 layers]; (54,48 55,494951)

a0 (Å)

m (μB)

Eg (eV)

4.19 (4.19,684.2648) 4.1738

1.69 (1.825) 1.7038 1.72,43 1.8344 1.68 1.6854 1.30 (1.28)51 1.64−1.9069,70 m (μB)

3.12 (2.50−3.20)25,30,46,51 4.338 3.7,44 4.2,42 4.7,41 4.843 4.17 (4.252)b 4.2054 0.66 (0.4,540.5,510.631) 4.356 (photoemission) 4.357 (optical absorption) Eg (eV)

4.18 4.2354 4.20 4.17,56 4.1946,58

1.695 (1.63,481.7160); 1.690 [1st subsurface]; 1.687 [2nd subsurface]; (1.685−1.689)49

2.45 [5 layers]; 2.49 [6 layers]; (2.48,602.66,49 2.9,513.0248)

For SGGA + U, Ueff = U − J = 5.3 eV was used, unless indicated otherwise in the text. All results are based on spin-polarized calculations. bThis result was obtained using HSE03.

a

orbitals. These findings, therefore, suggest that the band gap of NiO is of a charge transfer type, in agreement with previous reports.25,56 Qualitatively, the features of the VBM and the CBM are found similar to those obtained using HSE06 (see Figure S2). Larger changes were noted for the NiO(100) band gap of 2.45 and 2.49 eV for five- and six-layer slabs, respectively, narrowed by 0.67 eV compared to the bulk NiO value of 3.12 eV. Earlier LDA + U studies with varying Ueff reported band gaps of 2.4851 and 2.90 eV,60 and a reduced band gap (0.5 eV smaller than that of bulk NiO) was also reported on the B3PW level, varying with the number of layers from 2.14 eV (1L) to 2.66 eV (4L).49 DOS and PDOS for the stoichiometric NiO(100) surface and first three-layer-resolved DOS are summarized in Figure S1b,c. A comparison with the bulk NiO DOS shows similar contributions to the valence and conduction band edges from the Ni 3d and O 2p states, but with a narrower band gap. This is due to the emergence of surface states,48 which diminish significantly for the second subsurface (Figure S1c), demonstrating that the symmetry breaking is mostly observed at the first atomic layer. According to the PDOS, the top of the valence band comprises a mixture of Ni 3d and O 2p states with a dominance of O 2p (see Figure S1b). On the other hand, the bottom of the conduction band is mostly formed by Ni 3d states (Figure S1b). The distribution of charges on Ni and O on the NiO(100) surface is similar to those in bulk NiO. Overall, we show that SGGA-PBE + U (Ueff = 5.3 eV) is suitable for description of NiO-based MIM systems and is employed in all calculations henceforth, whereas the HSE06 functional could not be used because it is too intensive computationally. Next, the formation energy of an oxygen vacancy (VO) in bulk NiO was evaluated for the SGGA-PBE + U optimized structure, using Eform(VO) = Etot(VO) − Etot(pristine) + μO, where Etot(VO) and Etot(pristine) are the total energies of the supercells with and without a neutral VO, respectively. The chemical potential of oxygen, μO, is taken to be half of the calculated total energy of a free, isolated, spin-polarized oxygen molecule [Etot(O2)] in the triplet state, calculated (SGGA-PBE level) in a 24 × 24 × 24 supercell. A correction for O2 overbinding was also performed. The calculated vacancy formation energy of 4.54 eV is in good agreement with earlier studies.31,32,34

layer, of 0.04 Å, as compared to bulk NiO. Note that the surface energy of NiO(100), defined by γ = (Eslab − N × Ebulk)/2A, where Eslab, Ebulk, and N are the total energy of the surface slab, the total energy per Ni−O pair in the bulk, and the number of Ni−O pairs in the surface slab, respectively, and A corresponds to the area of a p(4 × 3) supercell, of 47 meV/Å2 for a five-layer slab is only slightly lower (by 5 meV/Å2) than for a six-layer slab. The magnetic moment converges to the bulk value of 1.687 μB at the second subsurface layer (layer 3), thus capturing the bulklike properties of NiO. Similar values were reported in earlier work (listed in Table 1), for example, a LDA + U study for an unsupported NiO thin film49 has shown that the magnetic moment varies with the number of layers, resulting in 1.685−1.689 μB for outer and inner layers, respectively. We found the magnetic moment to increase slightly to 1.695 μB on the surface as compared to the inner layers (subsurface, Table 1) because of the low coordination and the modest structural relaxation of the surface. Regarding the NiO band gap, experimentally, X-ray photon spectroscopy (XPS) and bremsstrahlung isochromatic spectroscopy measurements demonstrated a charge-transfer insulator energy gap of 4.3 eV,56 with a similar value obtained from optical reflectance spectra.57 Clearly, PBE considerably underestimates the band gap, as was previously demonstrated (see Table 1). The SGGA + U result is improved, yet still underestimated and dependent on the Ueff value, where a larger U value will modify the band gap.58 Such an approach, however, leads to an overall poor description of the electronic spectrum and other physical properties50 and was not employed here. For further analysis of the band structures for bulk NiO and the NiO(100) surface, the total DOS and PDOS are plotted in Figure S1a−c, decomposed by electron spin, atomic orbitals, and by layer for the NiO(100) surface. The PDOS for bulk NiO are shown as the sum of nickel 3d and oxygen 2p orbitals in the supercell (Figure S1a), indicating strong orbital hybridization between the Ni 3d and O 2p orbitals at the VBM, with the oxygen 2p orbitals contribution predominant, whereas the CBM is composed of nickel 3d orbitals. The mixed character of the top of the valence band is in good agreement with the B3LYP calculations54 and with the experimental O Kα X-ray emission spectra.59 Crystal field splitting also showed that the valence band top is composed of Ni t2g and O 2p orbitals, and the conduction band bottom is mainly formed by Ni eg 9805

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Figure 2. Optimized MIM structural models for Ag/NiO/Ag with (a) O on-top and (b) Ni on-top; Pt/NiO/Pt with a tensile-strained lattice with (c) O on-top and (d) Ni on-top; Pt/NiO/Pt with the Pt lattice constant with (e) O on-top and (f) Ni on-top. The balls represented by gray, red, yellow, and blue correspond to nickel, oxygen, silver, and platinum atoms, respectively. The optimized (final) configurations of the interfaces for the O on-top initial configuration are shown in (a,c,e), whereas those in (b,d,f) correspond to the final configurations of the interfaces with the Ni on-top initial configuration.

higher voltage as the voltage drop was small.63 Two types of metal electrodes, with low (Ag, polycrystalline, W = 4.26 eV) and high (Pt, polycrystalline, W = 5.64 eV) work functions, were therefore chosen as electrodes in this study. In ECM cells, often, Ag can be used as a reactive electrode to lead to the growth of a metallic CF. Applied positive voltage to the reactive (active) electrode dissolves cations from the electrode, leading to field-assisted injection and transport of cations into the oxide layer. In these cells, however, an inert counter electrode, for example, Pt or TiN is required. In our simulations, no voltage bias was applied the electrode; therefore, any field-assisted injection and transport of Ag cations into NiO layer is out of context. Moreover, for both the Ag- and Pt-electrode based MIM systems constructed, we use symmetric cells; therefore, Ag-based filamentary formation is not of concern. Stoichiometric MIM interface models were constructed with NiO(100) interposed between metal electrodes (Ag or Pt), combining fcc-Ag(100) or Pt(100) and NiO(100) surfaces (see Figure 2a−f for the optimized structures and section 2 for Computational Details). Using the GGA-PBE calculated lattice constants for Ag (4.152 Å) and Pt (3.985 Å), we find a lattice mismatch between Ag/NiO and Pt/NiO, of 1 and 5% (NiO lattice constant is 4.19 Å), respectively, indicating that the Ag/ NiO interface is almost free of interfacial strain. Thus, to reduce the effects of lattice mismatch, one of the Pt/NiO/Pt MIM models was constructed using an Ag lattice constant in the surface plane, thereby modeling a tensile-strained interface, yet keeping the out-of-plane Pt lattice constant (see Figure 2c,d). AIMD simulations at 300 and 800 K indicated interface structural stability. Indeed, Ag(100) is considered as a suitable template for NiO epitaxial growth64 because of similar lattice parameters for Ag and NiO.49,64 Primary beam diffraction-modulated electron emission experiments showed that the epitaxially grown NiO films with an Ag(100) template have an O on-top configuration for Ag, with an oxide−metal interface distance of 2.3 ± 0.1 Å, and polarization-dependent X-ray absorption at the Ni K edge measured a distance of 2.37 ± 0.05 Å.64 A DFT study that considered growth of one to four layers of NiO deposited on Ag(100) has also reported preference for the O on-top interface configuration.49 Corrugation with a short Ag−O bond length (2.37 Å, GGA + U; 2.45 Å, B3PW) was reported for a single layer, but increasing the thickness to three layers reduced it, increasing the Ag−O bond to 2.54 Å (GGA + U) or 2.41 Å (B3PW).49 To model the interface between NiO and the electrodes in our case, configurations where the metal atoms

In addition, to mimic VO clustering in the oxide layer and understand the propensity toward CF formation in a MIM system, aligned vacancies in close proximity were studied. Thus, we introduced double oxygen vacancies in bulk NiO. The interaction energy at various distances (ca. 3−9 Å) was evaluated by Eint = E(2VO) − E(0VO) + E(1VO), where E(2VO), E(0VO), and E(1VO) are the total energies for two vacancies in the supercell, for the pristine supercell, and for a single vacancy in the supercell, respectively. Vacancy−vacancy interactions were found to be weakened after the second nn (nearest neighbor), as the separation increased from 2.966 Å (first nn) to 4.194 Å (second nn). The first and second nn configurations are energetically similar, with an energy difference of 34 meV, but the first nn configuration is slightly more favorable. Notably, on the other hand, when both Ni and O vacancies are present in bulk NiO, the first nn configuration is more favorable over the second nn by a much larger difference of 0.75 eV in the total energy. We conclude that introducing dual oxygen vacancies into bulk NiO causes clustering by reducing the interaction energy, which is also consistent with previous work.36 Furthermore, to explore the effects of nonstoichiometry on the electronic structure and vacancy defect states in bulk NiO, the electronic structure properties were calculated, demonstrating localized states in the gap, consisting primarily of d orbitals (see Figure S3). The first defect level is located at about 1 eV above the VBM, whereas the other two defect levels are found at about 0.25 eV below the CBM. 3.2. NiO-Based MIM Interfaces. Experimentally, it was suggested that Ag(Pt)−Ni immiscibility (miscibility) controls RS, where Ni clusters are assumed to remain at the interface in Pt/NiO but are embedded into Ag in Ag/NiO.61 Therefore, during oxidation, Ni clusters can diffuse out of the Ni−Pt alloy but cannot escape an Ag electrode. At the RESET stage, reoxidation of Ni clusters and filament rupture will be difficult, and no RS is to be expected for Ag/NiO.29 Effects of the interface in epitaxial NiO films were also demonstrated.62 The RS dependence on the metal electrodes was explored in Pt/ NiO/Pt MIM structures, where the RS behavior was examined when varying the top electrode.63 NiO formed an Ohmic contact with Pt and Au top electrodes, and a negligible voltage drop occurred at the interface. Therefore, the field inside the oxide was strong enough to induce RS.63 On the other hand, for example, for Ti, a Schottky barrier was formed at the Ti/ NiO interface, leading to a large voltage drop, so that the field was not strong enough to induce RS. Because of a low Schottky barrier at the Al/NiO interface, RS was established with a 9806

DOI: 10.1021/acsami.7b17645 ACS Appl. Mater. Interfaces 2018, 10, 9802−9816

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whereas for the tensile-strained Pt/NiO/Pt MIM models, the charge transfer is 0.73e and 0.57e for on-top Ni and O interface configurations, respectively. DOS and PDOS for various stoichiometric MIM interface models are summarized in Figures 3 and 4. Total DOS

reside either on-top Ni or O sites were considered (see Figure 1b,c). After structural optimization, both Ag/NiO/Ag models converged to the same final configurations (on-top O) (Table S1). The structures for these models show a uniform distribution of atoms at the interface with only a small rumpling of Ag atoms, of 0.017 Å, due to the small lattice mismatch. Optimized structures illustrate that Ag atoms reside above O, whereas Ni is below the hollow sites in between two Ag atoms at the interface (see Figure 2a,b). Therefore, Ag has shorter bonds with the O atoms at the interface (d = 2.56−2.59 Å) than with Ni (3.26−3.31 Å) for the on-top O interface model (see Table S1). Analysis of the magnetization for the Ag/NiO interfaces showed that no magnetization is induced in the Ag(100) layer, and the value is only slightly reduced to 1.67 μB per Ni, as compared to values in bulk NiO and pristine NiO(100) (Table 1). At inner NiO layers, the magnetization is of the order of 1.689 μB, suggesting that the effect of creating an interface is confined to the NiO interface layer in direct contact with the Ag electrode. For the Pt/NiO/Pt structural models, however, the final configurations using a tensile-strained Pt lattice (Figure 2c,d) illustrate distinct interface configurations for on-top Ni and O, with the on-top O configuration slightly more favorable energetically (see Table S1). In this case, for the on-top O interface (Figure 2c), the shortest Pt−O distances at the interface vary between 2.99 and 3.01 Å, whereas the shortest Pt−Ni distance is 3.60−3.70 Å. The distribution of atoms at the interfacial region is rather uniform with almost no evidence of corrugation, as expected. On the other hand, when the Pt lattice constant was used, the optimized on-top O and Ni configurations showed rumpling at the interface (Figure 2e,f) of ∼0.35 Å for the Pt layer and ∼0.2 Å for the oxide layer. Energetically, the on-top O configuration was more stable, where two O atoms are lifted toward the Pt electrode, and two Pt atoms approach toward O interface atoms, resulting in shorter bonds (see Table S1). In this case, the shortest distances between the two O and Pt atoms are 2.26−2.29 Å, and the shortest distances between two of the Pt and Ni atoms are 2.76−2.78 Å (Figure 2e and Table S1), where also the distance between Pt and O at the interface can reach 3.25 Å.32,37 A small magnetization (0.1−0.2 μB) was induced at the Pt(100) layer. For the NiO layer, the magnetization per Ni was found to vary (1.66−1.68 μB), slightly reduced for some of the Ni atoms at the interface, as compared to those in the bulk and pristine surface. The magnetization of the inner NiO layers of ca. 1.687−1.689 μB is similar to that of inner NiO layers for the Ag/NiO interface. Once again, a slight reduction of magnetization at the interface layer suggests that the effect of interface bond formation with metal atoms is confined mostly to the interface layer. Charge transfer from Ag metal layers to NiO at the Ag/NiO/ Ag MIM interface (for on-top Ni and O configurations, listed in Table S1), calculated by subtracting the sum of the total charges of both Ag electrode layers (top and bottom) from that of the total charges obtained using the valence charges of Ag layers (the same was done for NiO charges), was found on the order of 0.85e. Considerable charge rearrangement among Ag layers and within the inner regions of the NiO layers was observed. For Pt/NiO/Pt structural models, in all cases, there is charge transfer from NiO to Pt (∼0.57−0.80e, see Table S1), mostly at the Pt interface with a strong rearrangement within Pt layers. The charge transfer for the strained model is about 0.8e (Ni on-top configuration) and 0.65e (O on-top configuration),

Figure 3. Ag/NiO/Ag MIM structure: (a) total DOS for an on-top O interface configuration, (b) PDOS for Ag metal states (magenta lines), (c) PDOS for Ni and O atoms (blue and red lines, respectively); Pt/ NiO/Pt MIM structure: (d) total DOS with a Pt lattice constant for an on-top Ni interface configuration, (e) PDOS for Pt metal states (magenta lines), and (f) PDOS of Ni and O atoms in a Pt/NiO/Pt MIM structure. In (b,c,e,f), which illustrate individual contributions from each species to the electronic spectrum, the total electronic DOS associated with the interface models (electrodes + oxide layers) are kept in the background (gray area). The Fermi level is illustrated with a dashed line and is taken as the zero energy.

comprise a continuous broad spectrum, with finite DOS at the Fermi level clearly evident in all structural models. Contributions from electrode metal states to the DOS are indicated in Figures 3b,e and 4b,e,h, but also from Ni and O states (Figures 3c,f and 4c,f,i), suggesting hybridization between states of Ag or Pt and the oxide. Contributions to the Fermi level from the oxide states in both Ag/NiO and Pt/NiO structures were reported experimentally for MgO thin films supported on Ag(100).65 This was also revealed in our analysis of the first three NiO layer-resolved DOS (Figures S4a−h and S5a−l for the metal interface layer, oxide interface layer 1, subsurface layer 2, and middle layer 3). Although layer 3 demonstrated bulklike properties (Figures S4d,h and S5d,h,l), local DOS at the interface layer illustrated a continuous spectrum of states in the forbidden gap, corresponding to the metal-induced gap states in both MIM systems (Figures S4b,f and S5b,f,j). Layerresolved PDOS also indicate that the Fermi level for the stoichiometric interface is located approximately in the middle of the NiO band gap for the third layer, comprising the bulklike region of the Ag/NiO/Ag structure. Evidently, the NiO interface layer (NiO layer 1) is metallic, whereas the inner NiO layers have an insulating character, with no contribution to the DOS at the Fermi level from layer 2 or 3. The local DOS for the Ag and Pt interface layers are also summarized for all MIM structures in Figures S4a,e and S5a,e,i, indicating a continuous spectrum of states in the forbidden gap of the MIM models with hybridization between Ag or Pt d- and oxygen porbitals (not shown). 9807

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Figure 4. (a) Total electronic DOS for the Pt/NiO/Pt MIM structure with a tensile-strained lattice with O on-top interface configuration (see Figure 2c), (b) PDOS for Pt metal states (magenta lines), (c) PDOS for Ni and O atoms (blue and red lines, respectively), (d) total DOS for the Pt/ NiO/Pt MIM structural model with tensile-strained lattice with on-top Ni interface configuration (see Figure 2d), (e) PDOS for Pt metal states (magenta lines), (f) PDOS of Ni and O atoms in the MIM structural model, (g) total DOS for Pt/NiO/Pt MIM structure with Pt lattice constant with O on-top interface configuration (see Figure 2e), (h) PDOS for Pt metal states (magenta lines), and (i) PDOS for Ni and O atoms (blue and red lines, respectively) in the MIM structural model. In (b,c,e,f,h,i), which illustrate the individual contributions from each species to the electronic spectrum, the total electronic DOS associated with the interface models (electrodes + oxide layers) are kept in background (gray area). The Fermi level is illustrated with a dashed line and is taken as the zero energy.

S6h), similar to those observed in bulk NiO (Figure S3). The DOS of a VO residing at the interface, on the other hand, show no defect states (Figure S6b) but instead a broad spectrum of states similar to those observed in stoichiometric MIM models (Figures S4b,f and S5b,f,j). These results indicate that the excess electrons introduced by the removal of an oxygen from the interface are accommodated by the metal-induced gap states at the interface layer. The partially occupied states at the Fermi level assist in lowering the VO formation energy at the interface, enabling easier reduction. 3.3. CF Formation in NiO MIM Structural Models. Aligned neutral oxygen vacancies were introduced into the NiO layer for both metal/NiO/metal systems to understand the propensity of NiO toward VO formation, which will result in the formation of a CF in the MIM structure (at the LRS), in comparison to the pristine MIM model. Although the atomic structures of CFs under an applied bias in a realistic RRAM device are complicated and the microscopic filament models constructed here are considered only as basic representations, these models capture the intrinsic behavior in the metal/NiO/ metal systems, unraveling propensity toward spatial distribution of oxygen vacancies (configuration/geometry), number of oxygen vacancies (degree of reduction of the Ni atoms), and interaction with the metal electrodes, all of which affect the conductive properties. We considered several microscopic filament models with different spatial distributions and number of oxygen vacancies (models 2−7 in Figure 5), where model 1 is a pristine Ag/NiO/Ag MIM system with an on-top O interface configuration. Two different stoichiometric MIM structural models with different interface geometries for Pt/ NiO/Pt, as discussed above, were considered. On the basis of the total energy, charge distribution, and DOS analyses performed for each filament model, we selected three representative examples by introducing 3, 5, and 10 oxygen vacancies in the oxide, namely, as a single filament formed by 3

We note that in the bulklike region of Ag/NiO/Ag MIM (NiO slab layer 3), the Fermi level is far from the band edges and is located in the middle of the band gap (see Figure S4d), indicating that the stoichiometric interface is a Schottky-type contact, as anticipated for the low work function Ag metal. For Pt/NiO/Pt stoichiometric MIM models with an on-top Ni configuration, the DOS for the bulklike NiO layer illustrate that the Fermi level is near the valence band edge (Figures S4h and S5h), and the contact is expected to be Ohmic for the high work function Pt metal.63 The Fermi level shows a slight shift toward higher energy for the on-top O Pt/NiO/Pt interface configurations compared to the Ag/NiO/Ag MIM model, suggesting effects of the interface configuration and hence hybridization, although it is still near the valence band edge (Figure S5d,l). As described above, the contact type for an Ag/ NiO interface would cause a large voltage drop at the interface, leading to a weak field in the oxide layer, whereas for the Pt/ NiO interface with an Ohmic-type contact, a negligible voltage drop at the interface is to be expected. The partially occupied metal-induced gap states, observed at the Fermi level in both MIM systems, can accommodate the excess electrons when an oxygen is removed, thus helping reduction at the interface. To analyze the role of these partially occupied states, we examined the formation energies of a VO introduced at the interface, subsurface, and middle layers of the Ag/NiO/Ag MIM structure, in comparison to VO formation in bulk NiO (summarized in section 3.1). The results indicate that vacancy formation becomes easier at the interface, with a formation energy of 3.04 eV, as compared to both the subsurface (4.20 eV) and middle layers (4.49 eV), whereas the formation energy for the bulk is 4.54 eV. Layer-resolved PDOS with a VO at the interface (Figure S6a−d) and the middle layer (Figure S6e−h) illustrate that when a VO is introduced in the bulklike region, the defect states associated with the vacancy appear within the forbidden gap (shown by an arrow in Figure 9808

DOI: 10.1021/acsami.7b17645 ACS Appl. Mater. Interfaces 2018, 10, 9802−9816

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First, a CF model was constructed by removing three oxygen atoms from the first, third, and fifth layers of the oxide along the [001] direction (CF model 2 in Figure 5). Oxygen vacancies were introduced in every other layer separated by Ni atoms, where two Ni atoms (in layers 2 and 4) have the same number of VO neighbors. The optimized structure of this filament model in Ag/NiO/Ag was found to be similar to the corresponding stoichiometric system, where the Ag atom above the VO was lowered toward the vacancy site, causing localized rumpling near the vacancy at the interface. The nn Ni atoms surrounding the VO at the interface were lifted up slightly (by 0.04 Å), but the rumpling was localized at the immediate vacancy region. The interface structure for the CF model for Pt/NiO/Pt is however different, resembling the on-top Ni configuration in the stoichiometric structure. In this case, nn Ni atoms of the VO relax (in plane) outward, and rumpling of the Pt interface layer is apparent (0.2 Å). Another filament model was formed by introducing five oxygen vacancies, where one VO at each NiO layer forms a zigzag or diagonal distribution of oxygen vacancies in the oxide lattice (models 3 and 4 in Figure 5, respectively). Optimized structures of Pt/NiO/Pt with an on-top O interface configuration indicate that the Pt atoms are lowered toward

Figure 5. Schematic representation of the Ag/NiO/Ag pristine (model 1) MIM structural model (O on-top configuration) and filament models 2−7, constructed with varying number and spatial distribution of oxygen vacancies. Dashed lines denote the filament region. Gray, red, and yellow balls represent Ni, O, and Ag atoms, respectively.

and 5 oxygen vacancies consisting of an aligned VO chain or a double filament formed by 10 oxygen vacancies constructed by two aligned VO chains.

Figure 6. Layer-resolved projected electronic DOS of the MIM structures with filament models of (a) 3 oxygen vacancies in Ag/NiO/Ag with ontop O configuration, (b) 5 oxygen vacancies in Ag/NiO/Ag with on-top O configuration, (c) 10 oxygen vacancies in Ag/NiO/Ag with on-top O configuration, (d) 3 oxygen vacancies in Pt/NiO/Pt with on-top Ni configuration, (e) 5 oxygen vacancies in Pt/NiO/Pt with on-top Ni configuration, and (f) 10 oxygen vacancies in Pt/NiO/Pt with on-top Ni configuration. The Fermi level is at zero energy. 9809

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To further assess the potential for improved conductivity in the presence of oxygen vacancies, as established by the PDOS, and explain the origin of defect states contributing to the formation of the metallic character in the nonstoichiometric MIM systems, we examined different types of Ni atoms in the oxide layer (Figures 6a−f and 7a−f), particularly regarding the contribution from Ni atoms to the DOS at/above the Fermi level, existence of finite DOS at the Fermi level, and the number of VO neighbors surrounding the Ni atom. PDOS of two types of Ni atoms were calculated in each layer, namely those near oxygen vacancies and those further away, for layers 1−5 for filament model 2 and layers 1−3 for filament models 3 and 5 (shown in Figure 8a−c; other layers are omitted because of the symmetry of the system) and are summarized in Figures 9a−f, 10a−f, and 11a−d. Considering CF model 2, PDOS are given for Ni atoms that are first nn of oxygen vacancies or in the immediate proximity in layers 1, 3, and 5 (nnNi1_lay* and nnNi2_lay*, with “*” referring to the layer number) and those that are further away from the vacancies, residing in layers 2 and 4 (Ni_lay2 and Ni_lay4), having two VO neighbors (one from the layer above and one from below), as shown in Figures 9a,d and 10a,d, for Ag/NiO/Ag and Pt/NiO/Pt structures, respectively. For Ni atoms close to a VO in the first or fifth layer, several defect states emerge in the forbidden gap of the oxide (see Figure 9a), mostly from near vacancy regions and not from Ni atoms that are away from the oxygen vacancies, thus not likely to be part of the filament (Figure 9d). A dispersive character around the Fermi level because of the existence of the metallic states is noted, appearing primarily below the Fermi level for the third layer, for which transport would be similar to polaron hopping. For Ni atoms in the second and fourth layers with two VO neighbors above and below, which are different than (nnNi1_lay1, nnNi2_lay1) having a single VO neighbor, the contribution to the DOS is larger, which will result in increased conductivity within the filament. PDOS for Ni away from the oxygen vacancies (six Ni atoms in layers 1, 3, and 5 and two in layers 2 and 4), shown in Figure 9d, indicate mostly minimal contributions to the conductivity. However, for corresponding filaments in the Pt/ NiO/Pt MIM structural model, we observe a more similar contribution to the DOS at the Fermi level from Ni atoms with a higher number of VO neighbors (Ni_lay2, and Ni_lay4) and those further away (Figure 10a,d). Also, the contributions to the DOS at and above the Fermi level from Ni atoms is overall slightly smaller for Pt/NiO/Pt, where the interface structure explains, in part, this difference. PDOS for individual Ni atoms for filament model 3 are similar to those for model 2 (Figures 9b,e, 10b,e, and 11a−d), where extended defect states appear within the forbidden gap, mostly contributed by Ni atoms that are the first nn of oxygen vacancies. Among the six Ni atoms residing in the second and third layers that contribute to the DOS at the Fermi level, the contribution from Ni atoms with three VO neighbors is notable (PDOS shown by red and yellow lines in Figure 9b). Contributions to the DOS at and above the Fermi level are enhanced for this filament model as compared to model 2, apparently as a result of the increased number of oxygen vacancies and further reduction of Ni near oxygen vacancies. The interface configuration has a negligible effect, as summarized for model 3 for Pt/NiO/Pt with an on-top O interface (Figure 11a−d). PDOS associated with Ni atoms in the double filament model (model 5 in Figure 5) are depicted in Figures 9c,f and 10c,f for Ag/NiO/Ag and Pt/NiO/Pt,

the vacancy sites, whereas the nn Ni atoms of the vacancy are lifted toward the Pt electrode. For comparison of the stability of CF models formed by a different number and spatial distribution of oxygen vacancies, we considered vacancy distributions in the models without the electrodes. Total energies for CF models 3 and 4 show that model 3 (zigzag distribution of oxygen vacancies) is energetically more favorable by 0.6 eV, in comparison to the filament model in which the vacancies are diagonally aligned within the oxide layer. Subsequently, filament models that consist of two aligned VO chains (five vacancies in each) formed in a zigzag distribution in the NiO layer between the two electrodes were constructed (CF models 5 and 6 in Figure 5), by varying the distance between vacancy chains. On the basis of the total energy analysis, model 5 was found to be energetically more favorable by 1.21 eV than model 6, suggesting that these aligned oxygen vacancies tend to cluster, as we have also shown for dual VO in bulk NiO structures (section 3.1). An additional double filament model formed by two diagonally aligned VO chains (model 7 in Figure 5) was also generated, but is less favorable than model 5 by about 0.7 eV. Model 5 was therefore considered in the following. Effects of filament formation on the overall electronic structure were analyzed by layer-resolved DOS for both MIM systems with varying interface configurations [see Figure 6a−f for all filament models with 3, 5, and 10 VO and Figure 7a−f for

Figure 7. Layer-resolved total and projected electronic DOS of Pt/ NiO/Pt MIM structures with filament model 3, with interface configurations of (a−c) tensile-strained lattice with O on-top interface (see Figure 2c for stoichiometric interface), and (d−f) Pt lattice constant with O on-top interface configuration (see Figure 2e for stoichiometric interface). The Fermi level is at zero energy.

filament model 3 (with 5 VO) in the Pt/NiO MIM system with two different interface configurations]. The results indicate that in all cases, there are several defect states distributed across the forbidden gap, and each layer demonstrates a metallic character including inner layers. The primary contribution to these defect states is from Ni atoms, with some contribution from oxygen atoms. We also found that the contribution to the DOS at the Fermi level is further enhanced by increasing the number of oxygen vacancies for a given filament model. These findings are confirmed by the DOS for Pt/NiO/Pt MIM systems with ontop O interface configurations with filament model 3 of five oxygen vacancies (see Figure 7a−f). 9810

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Figure 8. CF models shown by zooming into the filament regions both in parallel and perpendicular to the surface plane for clarity consisting of (a) 3, (b) 5, and (c) 10 oxygen vacancies. The identities of the Ni atoms near oxygen vacancies are shown with the arrows at each layer of interest, with L1−L5 representing layer numbers. For each structure, because of mirror symmetry, the immediate neighboring/properties of Ni atoms in layer 4 and layer 5 are identical to those in layer 2 and layer 1, respectively. Black dashed lines are used to highlight the region of the filaments. Gray, red, and yellow balls represent Ni, O, and electrode atoms (Ag or Pt), respectively.

Figure 9. PDOS of Ni atoms near oxygen vacancies in the Ag/NiO/Ag MIM system for (a) filament model 2 with 3 oxygen vacancies, (b) filament model 3 with 5 oxygen vacancies, (c) filament model 5 with 10 oxygen vacancies. PDOS of Ni atoms in NiO layers away from oxygen vacancies for (d) filament model 2 with 3 oxygen vacancies, (e) filament model 3 with 5 oxygen vacancies, and (f) filament model 5 with 10 oxygen vacancies. The colors represent DOS for different types of Ni atoms that are near/away from the oxygen vacancies. The Fermi level is shown by the dashed line.

two to four. The PDOS show that Ni atoms with three and four VO neighbors have a broad peak around the Fermi level, suggesting higher potential conductivity. In each layer, the contribution to the DOS is often found to be the largest for Ni atoms with the larger number of VO neighbors, not only within

respectively. For inner Ni atoms in layers 2 and 3, there are four VO neighbors (nnNi1_lay2, nnNi1_lay3 in Figure 9c), whereas nnNi2_lay1 Ni atoms have two and three VO neighbors (nnNi2_lay2 and 3). Therefore, in this filament model, the number of VO neighbors surrounding each Ni atom varies from 9811

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Figure 10. PDOS of the Ni atoms near oxygen vacancies in the Pt/NiO/Pt MIM system for (a) filament model 2 with 3 oxygen vacancies, (b) filament model 3 with 5 oxygen vacancies, and (c) filament model 5 with 10 oxygen vacancies. PDOS of the Ni atoms away from oxygen vacancies for the (d) filament model 2 with 3 oxygen vacancies, (e) filament model 3 with 5 oxygen vacancies, and (f) filament model 5 with 10 oxygen vacancies. The colors represent DOS for individual Ni atoms that are near/away from oxygen vacancies. The Fermi level is at zero energy, shown by a dashed line.

bulk NiO from those in the oxide in MIM systems, namely the excess charge (Δρ) on each Ni, were examined as a function of an increasing number of oxygen vacancies (from left to right, see Figure 12a−c) and are summarized for both MIM structural models. The dependence on the varying number of VO surrounding the Ni atoms is evident, where for model 2 (three oxygen vacancies) in Ag/NiO/Ag, for instance, there are two Ni atoms with two VO neighbors, Δρ is 0.39e, but varies between 0.1e and 0.26e for other Ni atoms. For the same filament model in Pt/NiO/Pt, although there is a similar trend, a slightly lower overall Δρ on Ni was calculated, between 0.11e and 0.14e (see Figure 12a). For this system, the largest Δρ for two of the Ni atoms with two VO neighbors is 0.45e. However, by increasing the number of oxygen vacancies in model 3, the Ni atoms undergo further reduction, and Δρ is in the range of 0.5e to 0.67e (Figure 12b for Ag/NiO/Ag), approaching that of metallic Ni in the local nonstoichiometric region. For this model, Δρ for Ni atoms at the interface in Pt/NiO/Pt is slightly less than for Ag/NiO/Ag and follows the same trend with similar values. The Pt/NiO/Pt system demonstrates a minimal effect on Δρ for the two interface structures, that is, on-top O with and without a strained lattice (see red, yellow, and green bars in Figure 12b). For the double filament model in Ag/NiO/Ag, Δρ on the Ni atoms with a higher number of vacancy neighbors can reach almost one electron, demonstrat-

the same plane but also below/above that plane (see PDOS data shown by solid red lines in Figure 9c as compared to Figure 9f). PDOS of the Ni atoms in layers with no VO neighbors show no contribution to the DOS at and above the Fermi level. Similar trends were obtained with the same filament for Pt/NiO/Pt (Figure 10d,f). Overall, because of the presence of oxygen vacancies in the oxide and because of their generation upon application of an electric field in a RRAM device, often in a clustered configuration, the charge states of Ni atoms in close proximity to oxygen vacancies can change from a high valence state in bulklike NiO (Ni2+) to a lower valence state via Ni2+ + ne− ⇒ Ni(2−n)+, that is, Ni1+ or Ni0. Therefore, reduced Ni atoms near oxygen vacancies can form an ordered chainlike configuration and lead to the formation of a metallic filament by reduced Ni. Our calculations suggest that there are different types of Ni atoms within the reduced oxide layer whose conductivity is affected by their immediate surrounding, in particular, the number of nn oxygen vacancies. Our DOS analyses for the filament models, showing finite DOS particularly around the Fermi level, are consistent with electron transport calculations upon the application of a low bias (linear response) in a metal oxide-based MIM,66 which is to be considered in future work. Changes in the charge distribution in the filament models considered, calculated by subtracting charges of Ni atoms in 9812

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Upon electroforming, several states of the oxygens can be hypothesized, namely in “escaping” to the atmosphere (oxygenescape model), moving to the oxide−electrode interface or to the electrode, as assumed for a TiN/HfO2/TiN MIM system.66 We examined these suggestions66 and related models for a filament consisting of five vacancies in the Ag/NiO/Ag MIM structure (models 1 to 9, with initial and final structures shown in Figure S8; energies are summarized in Table S2; and the total electronic DOS and PDOS for individual Ni atoms for selected models 1 and 5 are shown in Figure S9). The results demonstrate that the models where the oxygens are assumed to have moved to the oxide−electrode interface are mostly stable, whereas in those where the oxygens were introduced in the electrode, migration toward the oxide−electrode interface can occur, creating a mixed configuration where some oxygens reside at the electrode while others reside at the electrode− oxide interface. The oxygen-escape model is less stable, consistent with previous work.66 The results of the total DOS and PDOS indicate that similar to the observations made for the as-prepared oxide models discussed above, these additional systems also demonstrate conduction, metallic filament formation, and significant contribution to the electronic DOS from individual Ni atoms near oxygen vacancies. Our conclusions are therefore applicable also to cases in which oxygen atoms exist in the device. Finally, the suggested formation of a locally conductive near metallic/metallic (Ni0) region upon reduction of Ni atoms in close proximity to aligned VO clusters is visualized by band decomposed charge density distribution of the extended defect state in the NiO layer in the energy range of −0.5 < E < 0.5 eV. As a representative example, the result for the Ag/NiO/Ag MIM system for filament model 3 (Figure 13a,b) indicates that the charge is delocalized in the oxide layer connecting the two electrodes (yellow region in Figure 13a), and an extended conductive channel bridging the two electrodes is formed because of aligned oxygen vacancies in the oxide (Figure 13b, a 2D charge-density contour plot). We note that this locally conducting region is the region in the oxide layer where the Ni atoms have the largest number of VO neighbors, contributing the most to the DOS at the Fermi level. The conductive region is formed through Ni reduction, having metallic or nearmetallic character (Ni0). The description of such a Ni-based metallic filament model was supported by XPS measurements showing the appearance of neutral metallic peaks in NiO films with RS behavior.67 Interestingly, also in other studies, it was postulated that through oxygen ion loss at the anode, Ni interstitials are generated and increased in concentration, forming tiny metallic Ni filaments (see ref 68 and references therein).

Figure 11. PDOS of the Ni atoms near oxygen vacancies for filament model 3 (5 oxygen vacancies) in the Pt/NiO/Pt MIM system with an O on-top interface; (a) tensile-strained lattice and (b) Pt lattice constant. PDOS of Ni atoms away from oxygen vacancies for filament model 3 in the Pt/NiO/Pt MIM system with an O on-top interface; (c) tensile-strained lattice and (d) Pt lattice constant. The colors represent the DOS for individual Ni atoms that are near/away from oxygen vacancies. The Fermi level is at zero energy, shown by a dashed line.

ing the formation of a locally conducting channel with metallic character (see Figure 12c) and in a similar way for Pt/NiO/Pt. Differences between the two MIM systems can be attributed to structural differences at the interfaces. In addition, changes in the charges of oxygen and electrode metal atoms were examined (see Figure S7a−f) for all filament models in both systems and for different interface configurations. We find small changes in Δρ for metal atoms (∼0.1−0.2e for Ag and slightly larger values for Pt, i.e., 0.2−0.5e) as well as for oxygen atoms (