A Mechanistic Analysis of Oxygen Vacancy Driven Conductive

Subscriber access provided by UNIV OF SCIENCES PHILADELPHIA

Article

A Mechanistic Analysis of Oxygen Vacancy Driven Conductive Filament Formation in Resistive Random Access Memory Metal/NiO/Metal Structures Handan Yildirim, and Ruth Pachter ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b17645 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 1, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Applied Materials & Interfaces is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Materials & Interfaces

A 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, Ohio 45433, USA

*

Corresponding authors: HandanYildirim, [email protected], Ruth Pachter, [email protected] ACS Paragon Plus Environment

1

ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 42

ABSTRACT Electrically switchable resistive random access memories have drawn much interest as nonvolatile memory device candidates, also based on metal-insulator-metal (MIM) structure concepts. However, atomic-level mechanisms that lead to conductive filament (CF) formation in MIMs are often lacking, such as for the system with NiO as the oxide layer, which was found promising for 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 towards 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 were identified, accommodating oxygen vacancy states, and showing that the interface region is reduced more easily than the bulk-like region, e.g. for the Ag/NiO/Ag structure. Moreover, a tendency towards 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 density of states for individual Ni atoms in regions near and away from oxygen vacancies indicated that oxygen vacancies close to Ni 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.

ACS Paragon Plus Environment

2

Page 3 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


I.

Introduction

Resistive Random Access Memory (RRAM) devices have drawn much interest in the last decade, particularly following the work of Williams an 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 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 (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 emerged, where formation/rupture of a conductive filament (CF) ensures successive switching in the non-volatile metalinsulator-metal (MIM) memristors, dependent on the switching material. In such a RRAM device, binary oxide MIM structures are constructed using an insulating layer stacked between two electrodes, which can be built either symmetrically 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 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 (HRS), 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 development of MIMs, further understanding of the memristive mechanism is crucial in enabling improvement of the devices. Here, we investigate p-type NiO-based MIMs, which is one of the earliest studied. Following early work,9 RS characteristics of NiO were determined in a number of examples,10-14 demonstrating high stability and reliable memory characteristics, high speed, low voltage, fast programming, and compatibility with the CMOS process. Co-existence of unipolar and bipolar resistive switching in ACS Paragon Plus Environment

3


Page 4 of 42

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 MIMs. Generally, proposed conductance mechanisms of filamentary-type switching in oxides include those by metal cations that originate from electrochemically reactive electrodes (e.g. Cu, Ag), leading to the formation of a conductive bridge between them, namely so-called electrochemical metallization (ECM) memory or conductive-bridge memory (CBRAM), or those by anions (oxygen vacancies, resulting from drift and diffusion of oxygen ions under applied bias), i.e. the valence change memory (VCM) mechanism. Additionally, A thermochemical mechanism (TCM) was also proposed.16 For NiO, characterization of Ni filaments by magnetoresistance17,18 demonstrated their structural evolution, and also that multi-filaments 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 MIMs was demonstrated,20,21 yet 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 ptype NiO films,22 upon modification of growth conditions e.g. 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 NiObased MIMs,19,22,24 rationalized by C-AFM characterization and theoretical work,25,26 revealing the role of oxygen vacancies and formation of a Ni conducting filament. Oxygen vacancy migration, such as in a VCM mechanism-type system has been postulated.19,22,24 Thus, although the NiO-based MIM 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.


4

Page 5 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


To understand RS phenomenologically, an ion migration model to describe CF growth and rapture was developed,27 showing, for example, effects of the CF geometry, while in more recent work on filamentary RS, a model that solves self-consistently 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 reported, related to oxygen-ion migration, only bulk NiO was considered.34 Energetically favorable vacancy pair configurations in bulk NiO were explored,36 while Ni- and O- vacancies in bulk NiO were shown to be favorable over interstitials.31 Effects of local non-stoichiometry 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 towards oxygen vacancy formation, as well as interactions at the electrode interface, but moreover, structural and electronic implications of filament formation on the conductivity, when introducing oxygen vacancies of different spatial distribution and number, were elucidated. 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 electrode composition. Oxygen vacancies were found to prefer clustering. Projected DOS ACS Paragon Plus Environment

5


Page 6 of 42

(PDOS) and charge distributions for Ni atoms revealed that those near oxygen vacancy regions contributed most to the overall potential conductivity, where, remarkably, chain-like 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 NiObased MIMs, to ultimately achieve improved performance of RRAM devices. The paper is organized as follows. In section II, we report methods and computational details. Section III is devoted to results and discussion. In section III.1., we summarize structural and electronic properties of stoichiometric and non-stoichiometric bulk NiO, and of the NiO(100) surface. In section III.2., we discuss stoichiometric and non-stoichiometric MIM interfaces, while details on the conductive filament formation are presented in section III.3., with conclusions in section IV. II.

Methods and Computational Details

NiO crystalizes in the NaCl (Fm-3m) structure and forms antiferromagnetic (AFM) 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 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 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-ScuseriaErnzerhof (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 NiO,46 or molecular adsorption of ACS Paragon Plus Environment

6

Page 7 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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 eV 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, e.g. using HSE0352 or applying the hybrid B3LYP53 functional,54 were undertaken. All calculations were performed using the Vienna ab initio simulation package VASP55 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. AFM ordering was included. A planewave energy cut-off of 520 eV was used in all calculations. Charge transfer calculations were performed by Bader charge analyses. For bulk NiO (see Figure 1.a), the integration of the Brillouin zone was done with k-point meshes of 2x2x2 and 12x12x12 regular meshes for 4x4x4 and 2x2x2 cells, 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 4x4x4 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 2x2x2, 3x3x3, and 4x4x4 supercells, where defect states and their location within the forbidden gap were analyzed. The Ni(100) surface was modeled using a 4x3x1 supercell with five layers and a 20 Å vacuum region to ensure no interaction between the surfaces (Figure 1.b-c), 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 4x3x1 supercell describes appropriately the NiO(100) surface when comparing to results using a 6x4x1 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 ACS Paragon Plus Environment

7


Page 8 of 42

Brillouin zone was done with a 3x4x1 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 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 diffusionrelated 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) has to be considered, therefore become computationally intensive. III.

Results and Discussion

III.1. Stoichiometric and Non-Stoichiometric 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 AFM ordered ground state using SGGA+U and HSE06 are consistent with experimental data (see Table 1). However, using SGGA-PBE results in an underestimated magnetic moment, and overestimated lattice constant, also noted with B3LYP. The optimized NiO(100) surface structure shows only small buckling of the surface layer, of 0.04Å, as compared to bulk NiO. Note that the surface energy of Ni(100) (defined by ɣ=(Eslab–NxEbulk)/2A, where Eslab, Ebulk, and N are the total energy of the surface slab, the total energy per Ni-O pair in bulk, and the number Ni-O pairs in the surface slab, respectively; A corresponds to the area of a p(4x3) supercell), of 47 meV/Å2 for a five layers slab, is only slightly lower (by 5 meV/Å2) than for a six layers slab. The magnetic moment converges to the bulk value of 1.687 µB at the 2nd subsurface layer (layer 3), thus capturing the bulk-like properties of NiO. Similar values were reported in earlier work (listed in Table 1), e.g. 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 µB to 1.689 µB for outer and inner layers, respectively. We found the magnetic moment to increase slightly to 1.695 µB at the surface as compared to the inner layers (subsurface, Table 1) due to the low coordination and the modest structural relaxation of the surface. ACS Paragon Plus Environment

8

Page 9 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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 properties,50 and was not employed here. For further analysis of the band structures for bulk NiO and the NiO(100) surface, the total and PDOS are plotted in Figure S.1.a-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 S.1.a), indicating strong orbital hybridization between the Ni 3d and O 2p orbitals at the VBM, with the oxygen 2p orbitals contribution predominant, while the CBM is composed of nickel 3d orbitals. The mixed character of the top of the valence band is in good agreement with B3LYP calculations,54 and with 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 bottom is mainly formed by Ni eg 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 valence band top and the conduction band minimum are found similar to those obtained using HSE06 (see Figure S.2). 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 2.48 eV51 and 2.90 eV,60 and a reduced band gap (0.5 eV smaller than that of bulk NiO), was also reported at the B3PW level, varying with the number of layers from 2.14 eV (1L) to 2.66 eV (4L).49 DOS/PDOS for the stoichiometric NiO(100) surface and first three layerresolved DOS are summarized in Figure S.1.b-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 ACS Paragon Plus Environment

9


Page 10 of 42

second subsurface (Figure S.1.c), 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 dominance of O 2p (see Figure S.1.b). On the other hand, the bottom of the conduction band is mostly formed by Ni 3d states (Figure S.1.b). The distribution of charges on Ni and O in the NiO(100) surface are 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 was employed in all calculations henceforth, while 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 SGGAPBE+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 24x24x24 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 In addition, to mimic VO clustering in the oxide layer and understand the propensity towards 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 2nd nn (nearest neighbor), as the separation increased from 2.966 Å (1st nn) to 4.194 Å (2nd nn). The 1st and 2nd nn configurations are energetically similar, with an energy difference of 34 meV, but the 1st nn configuration is slightly more favorable. Notably, on the other hand, when both Ni and O vacancies are present in bulk NiO, the 1st nn configuration is more favorable over the 2nd nn by a much larger difference in total energy, of 0.75 eV. 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 effects of nonACS Paragon Plus Environment

10

Page 11 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


stoichiometry 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 S.3). The first defect level is located at about 1 eV above the VBM, while the other two defect levels are found at about 0.25 eV below the CBM. III.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 Ni-Pt alloy, but cannot escape an Ag electrode. At the RESET stage, re-oxidation 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 MIMs, where 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. Due to a low Schottky barrier at the Al/NiO interface, RS was established with 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 e.g. Pt, TiN is required. In our simulations, no voltage bias was applied at the electrode, therefore, any field-assisted injection and transport of Ag cations into NiO layer is out of the context. Moreover, for both Ag- and Pt-electrode based MIM systems constructed, we use symmetric cells, therefore, Ag-based filamentary formation is not of concern.


11


Page 12 of 42

Stoichiometric MIM interface models were constructed with NiO(100) interposed between metal electrodes (Ag or Pt), combining fcc-Ag(100)/Pt(100) and NiO(100) surfaces (see Figure 2.a-f for the optimized structures and section II 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 were constructed using an Ag-lattice constant in the surface plane, therefore, modeling a tensile-strained interface, yet keeping the out-of-plane Pt lattice constant (see Figure 2.c-d). AIMD simulations at 300°K 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 1 to 4 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 reside either on-top Ni or O sites, were considered (see Figure 1.b-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 small rumpling of Ag atoms, of 0.017 Å, due to the small lattice mismatch. Optimized structures illustrate that Ag atoms reside above O, while Ni is below the hollow sites in between two Ag atoms at the interface (see Figure 2.a-b). Therefore, Ag has shorter bonds with the O atoms at the interface (d = 2.56-2.59 Å) than with Ni (3.263.31 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 ACS Paragon Plus Environment

12

Page 13 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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 Ag electrode. For the Pt/NiO/Pt structural models, however, the final configurations using a tensile-strained Pt lattice (Figure 2.c-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 2.c), the shortest Pt-O distances at the interface vary between 2.99–3.01 Å, while the shortest PtNi 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 2.e-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 towards the Pt electrode, and two Pt atoms approach towards 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 Å-2.29 Å, and the shortest distances between two of the Pt and Ni atoms are 2.76 Å-2.78 Å (Figure 2.e and Table S1), where also the distance between Pt-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 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, and the same was done for NiO charges, and found in the order of 0.85e. Considerable charge rearrangement among Ag layers and within the inner regions of the NiO layers, was observed. For ACS Paragon Plus Environment

13


Page 14 of 42

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 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), while 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 comprise of 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 3.b, 3.e, 4.b, 4.e, and 4.h, but also from Ni and O states (Figures 3.c 3.f, 4.c, 4.f, and 4.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 S.4.a-h and S.5.a-l for the metal interface layer, oxide interface layer 1, subsurface layer 2, and middle layer 3). Although layer 3 demonstrated bulk-like properties (Figures S.4.d, S.4.h, S.5.d, S.5.h, and S.5.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 S.4.b, S.4.f, S.5.b, S.5.f, and S.5.j). Layer-resolved 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 bulk-like region of the Ag/NiO/Ag structure. Evidently, the NiO interface layer (NiO layer 1) is metallic, while the inner NiO layers have insulating character, with no contribution to the DOS at the Fermi level from layers 2 or 3. The local DOS for the Ag and Pt interface layers are also summarized for all MIMs in Figures S.4.a, S.4.e, S.5.a, S.5.e, S.5.i, indicating a continuous spectrum of states in the forbidden gap of the MIM models with hybridization between Ag or Pt d- and oxygen p-orbitals (not shown). We note that in the bulk-like region of the 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 S.4.d), indicating that the stoichiometric interface is a Schottky type contact, as anticipated for the low work function Ag metal. For ACS Paragon Plus Environment

14

Page 15 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Pt/NiO/Pt stoichiometric MIM models with an on-top Ni configuration, the DOS for the bulk-like NiO layer illustrate that the Fermi level is near the valence band edge (Figures S.4.h and S.5.h), and the contact is expected to be ohmic for the high work function Pt metal.63 The Fermi level shows a slight shift towards higher energy for 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 S.5.d and S.5.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, while 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 III.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), while the formation energy for the bulk is 4.54 eV. Layer-resolved PDOS with a VO at the interface (Figure S.6.a-d) and the middle layer (Figure S.6.e-h) illustrate that when a VO is introduced in the bulk-like region, defect states associated with the vacancy appear within the forbidden gap (shown by an arrow in Figure S.6.h), similar to those observed in bulk NiO (Figure S.3). The DOS of a VO residing at the interface, on the other hand, show no defect states (Figure S.6.b), but instead a broad spectrum of states similar to those observed in stoichiometric MIM models (Figures S.4.b, S.4.f, S.5.b, S.5.f, and S.5.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. III.3.

Conductive Filament Formation in NiO MIM Structural Models


15


Page 16 of 42

Aligned neutral oxygen vacancies were introduced into the NiO layer for both metal/NiO/metal systems in order to understand the propensity of NiO towards VO formation, which will result in a CF in a MIM structure (at the LRS), in comparison to the pristine MIM model. Although the atomic structures of conductive filaments 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 towards 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 conductive properties. We considered several microscopic filament models with different spatial distribution 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. Based on 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 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. First, a CF model was constructed by removing 3 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 towards the vacancy site, causing localized rumpling near the vacancy at the interface. The nn Ni atoms surrounding the VO at the interface were noted to get 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) outwards, and rumpling of the Pt interface layer is apparent (0.2 Å). ACS Paragon Plus Environment

16

Page 17 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Another filament model was formed by introducing 5 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 towards vacancy sites, while the nn Ni atoms of the vacancy are lifted towards 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 (5 vacancies in each) were formed in a zigzag distribution in the NiO layer between the two electrodes were constructed (CF models 5 and 6 in Figure 5), varying the distance between vacancy chains. Based on a total energy analysis, model 5 was found to be energetically more favorable by 1.21 eV than the model 6, suggesting that these aligned oxygen vacancies tend to cluster, as we have also shown for dual VO in bulk NiO structures (section III.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, and with varying interface configurations (see Figure 6.a-f for all filament models with 3, 5, and 10 VO, and Figure 7.a for 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 levels 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 on-top O interface configurations with the filament model 3 of 5 oxygen vacancies (see Figure 7.a-f). ACS Paragon Plus Environment

17


Page 18 of 42

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 levels contributing to the formation of the metallic character in the non-stoichiometric MIM systems, we examined different types of Ni atoms in the oxide layer (Figure 6.a-f and Figure 7.a-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 the filament models 3 and 5 (shown in Figure 8.a-c; other layers are omitted because of the symmetry of the system), and summarized in Figures 9.a-f, Figures 10.a-f, and Figures 11.a-d. Considering CF model 2, PDOS are given for Ni atoms that are 1st 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 9.a, 9.d, 10.a and 10.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 9.a), 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 9.d.) A dispersive character around the Fermi level due to 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 9.d, 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 ACS Paragon Plus Environment

18

Page 19 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(Figures 10.a and 10.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 9.b, 9.e, 10.b, 10.e, 11.a-d), where extended defect states appear within the forbidden gap, mostly contributed by Ni atoms that are the 1st 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 9.b). Contributions to the DOS at and above the Fermi level is 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 ontop O interface (Figure 11.a-d). PDOS associated with Ni atoms in the double filament model (model 5 in Figure 5) are depicted in Figures 9.c, 9.f, 10.c and 10.f, for Ag/NiO/Ag and Pt/NiO/Pt, respectively. For inner Ni atoms in layers 2 and 3, there are four VO neighbors (nnNi1_lay2, nnNi1_lay3 in Figure 9.c), while 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 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 the same plane but also below/above that plane (see PDOS data shown by solid red lines in Figure 9.c as compared to Figure 9.f). 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 (Figures 10.c and 10.f). Overall, because of the presence of oxygen vacancies in the oxide, and due to 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 bulk-like NiO (Ni2+) to a lower valence state via Ni2+ + ne- => Ni(2-n)+, i.e. Ni1+ or Ni0. Therefore, reduced Ni atoms near oxygen vacancies can form an ordered chain-like configuration, and lead to formation of a metallic ACS Paragon Plus Environment

19


Page 20 of 42

filament formed 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 to be considered in future work. Changes in the charge distribution in the filament models considered, calculated by subtracting charges of Ni atoms in 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 12.a-c), 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, for which 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 12.a). 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 12.b for Ag/NiO/Ag), approaching 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, however follows the same trend with similar values. The Pt/NiO/Pt system demonstrates a minimal effect on Δρ for the two interface structures, i.e. on-top O with and without a strained lattice (see red, yellow, and green bars in Figure 12.b). 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, demonstrating the formation of a locally conducting channel with metallic character (see Figure 12.c), and similarly for Pt/NiO/Pt. Differences between the two MIM systems can be attributed to structural differences at the interfaces. In addition, changes in charges of oxygen and electrode metal atoms were examined (see Figure S.7.a-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. 0.2-0.5 e), as ACS Paragon Plus Environment

20

Page 21 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


well as for oxygen atoms (

A Mechanistic Analysis of Oxygen Vacancy Driven Conductive

Recommend Documents