Quantitative Observation of Threshold Defect Behavior in Memristive

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Quantitative Observation of Threshold Defect Behavior in Memristive Devices with Operando X-Ray Microscopy Huajun Liu, Yongqi Dong, Mathew J Cherukara, Kiran Sasikumar, Badri Narayanan, Zhonghou Cai, Barry Lai, Liliana Stan, Seungbum Hong, Maria K. Y. Chan, Subramanian KRS Sankaranarayanan, Hua Zhou, and Dillon D. Fong ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b02028 • Publication Date (Web): 01 May 2018 Downloaded from http://pubs.acs.org on May 1, 2018

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Quantitative Observation of Threshold Defect Behavior in Memristive Devices with Operando X-Ray Microscopy Huajun Liu,1,2 Yongqi Dong,1,3 Mathew J. Cherukara,4 Kiran Sasikumar,5 Badri Narayanan,5 Zhonghou Cai,4 Barry Lai,4 Liliana Stan,5 Seungbum Hong,1,6 Maria K. Y. Chan,5 Subramanian KRS Sankaranarayanan,5 Hua Zhou,4* & Dillon D. Fong1* 1

Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA

2

Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology

and Research), Singapore 138634, Singapore 3

National Synchrotron Radiation Laboratory, University of Science and Technology of China,

Hefei, Anhui 230026, China 4

X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne, IL

60439, USA 5

Center for Nanoscale Materials, Nanoscience and Technology Division, Argonne National

Laboratory, Argonne, IL 60439, USA 6

Department of Materials Science and Engineering, KAIST, Daejeon 34141, Korea

* [email protected] * [email protected]

ACS Paragon Plus Environment

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ABSTRACT Memristive devices are an emerging technology that enables both rich interdisciplinary science and novel device functionalities, such as non-volatile memories and nanoionics-based synaptic electronics. Recent work has shown that the reproducibility and variability of the devices depend sensitively on the defect structures created during electroforming as well as their continued evolution under dynamic electric fields. However, a fundamental principle guiding the material design of defect structures is still lacking, due to the difficulty in understanding dynamic defect behavior under different resistance states. Here we unravel the existence of threshold behavior by studying model, single-crystal devices: resistive switching requires that the pristine oxygen vacancy concentration reside near a critical value. Theoretical calculations show that the threshold oxygen vacancy concentration lies at the boundary for both electronic and atomic phase transitions. Through operando, multimodal X-ray imaging, we show that field tuning of the local oxygen vacancy concentration below or above the threshold value is responsible for switching between different electrical states. These results provide a general strategy for designing functional defect structures around threshold concentrations to create dynamic, fieldcontrolled phases for memristive devices.

KEYWORDS: Memristive devices, operando X-ray imaging, quantitative oxygen vacancy profile, threshold defect behavior, WO3.


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Memristive or resistive switching devices have two-terminal, capacitor-like metal-insulatormetal structures, with resistance states that can be reversibly changed by an applied electric field1,2. Early studies of these devices focused on their application in non-volatile memories, exploiting their low operational energy, good compatibility with semiconductor processing steps, and highly scalable behavior.3–7 More recently, the dependence of resistance state on the history of the applied electric field has generated tremendous interest due to the many possibilities in synaptic electronics, where the implementation of brain-like neural networks in next-generation computers remains the long-term goal.2,8–11 However, there are many materials-related issues with these devices, of which the reproducibility and the variability of switching behavior are the most pressing.2 These are largely determined by the electroforming process, which is responsible for creating the conduction pathway in the normally insulating material prior to switching.12–15 Although the creation and migration of oxygen vacancies are known to play key roles in electroforming,16,17 the results thus far have been largely qualitative due to the complexity of the defect structures and processes in polycrystalline or amorphous samples.18 In transition metal oxide-based systems, in-situ studies have been essential in proving that memristive switching behavior originates from the field-induced migration of oxygen vacancies.19–27 For instance, X-ray absorption microscopy showed that the conduction channel in Cr-doped SrTiO3 consists of a high density of oxygen vacancies.19 In-situ transmission electron microscopy revealed that a vacancy-ordered Magnéli phase provides the conducting pathway in TiO2 memristive devices.20,21 Furthermore, high performance TaOx-based devices are known to exhibit an amorphous Ta-O solid solution, as well as an oxygen-deficient TaO1-x and a rutiletype TaO2 phase in the conduction channels.24–27 These exciting results have inspired more investigations into the defect structures necessary for high-endurance memristive devices and the


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complex interactions between electric field and ionic defects. Unfortunately, quantitative imaging of dynamic oxygen vacancy profiles at different resistance states has remained elusive, due to the difficulty in quantifying defect concentrations during device operation. This has hindered detailed understanding of the microscopic mechanism of oxygen vacancy behavior. The microscopic picture is made complex by the many possible chemical reactions and defect generation/ redistribution, triggered by the electric field, thermal gradient and chemical concentration gradient. Therefore, multimodal imaging with structural and chemical information collected simultaneously at the same location is necessary for clarifying the detailed microscopic mechanism. Here, we perform operando X-ray multimodal imaging of a single-crystal resistive switching system in which we intentionally prepare the metal oxide (WO3-δ) with different oxygen vacancy concentrations in the initial “pristine” state. We discover the existence of a threshold vacancy concentration in the pristine state that is essential for enabling memristive behavior. Density functional theory and reactive molecular dynamics show that an insulator-to-metal transition and a crystalline-to-amorphous phase transition both take place at the threshold concentration. Furthermore, we directly observe local tuning of the oxygen stoichiometry above or below the threshold value when switching between different electrical states. Our work identifies the mechanistic origin of threshold behavior and illustrates the importance of engineering the ionic defect concentration for materials design in memristive devices.

RESULTS AND DISCUSSION Effects of pristine ionic defects on electrical behavior


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To study the effect of oxygen vacancies on resistive switching, a model system with a welldefined homogeneous vacancy concentration is necessary. We chose WO3-δ for the following reasons. First, WO3-δ has been identified as a highly promising material for memristive devices in neuromorphic applications, exhibiting a variety of functionalities that emulate biological information processes.10,28–30 Second, WO3-δ is a binary oxide that maintains a perovskite-like structure, comprised of W6+ ions surrounded by corner-sharing oxygen octahedra.31 This and its pseudocubic lattice parameter (~0.376 nm) lend itself to epitaxial growth on perovskite substrates,32,33 making WO3-δ a physically and chemically simple system with a variable defect concentration in the as-grown state. Single crystalline WO3-δ films were grown on SrTiO3 (001) substrates by sputter deposition (Methods, Fig. S1). The electrical behavior of WO3-δ depends strongly on the oxygen vacancy concentration,34,35 and the conductivities of the films were tuned by processing in different oxygen environments. Defining the oxygen vacancy concentration as δ/3,36 the vacancy concentration of the samples varied from 3 to 13%. Lateral Pt electrodes were patterned on top of the WO3-δ films to form two-terminal, planar resistive switching devices; the horizontal geometry permits high-resolution investigation of the sample with X-ray microscopy. Figure 1 shows the effect of pristine defects on the electrical behavior of metal oxides with different levels of defect concentration, as quantified by X-ray absorption spectra (Fig. S2). For the sample with the lowest oxygen vacancy concentration of ~3% (WO2.9) in Fig. 1a, a large applied voltage leads to conventional dielectric breakdown (Fig. 1d). Figure 1g shows that subsequent voltage sweeps from negative to positive exhibit overlapping I-V curves without hysteresis. For the sample with an intermediate oxygen vacancy concentration of ~ 8% (WO2.75) in Fig. 1b, a large applied voltage leads to electroforming (Fig. 1e). The film is switchable afterwards,


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demonstrating the pinched hysteresis loop in the I-V curve characteristic of resistive switching (Fig. 1h). Results for the sample with the highest oxygen vacancy concentration of ~13% (WO2.6) are depicted Fig. 1c. Here, electroforming also takes place (Fig. 1f), but subsequent voltage sweeps do not exhibit hysteresis, as shown in Fig. 1i. Previous reports37–39 regarding the effect of oxygen vacancy concentration on the resistive switching behavior have shown that devices with higher oxygen vacancy concentrations can exhibit lower electroforming voltages or improved switching characteristics. Instead of this monotonic dependence on oxygen vacancies, we reveal the existence of a threshold concentration that enables pronounced resistive switching. The threshold behavior observed here is consistent with a recent report showing that maximum memristance is obtained in samples with moderate oxygen vacancy concentrations,40 which was controlled by substitutional doping. In the following sections, we describe investigations into the microscopic mechanism behind threshold behavior through both computational theory and operando X-ray imaging


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Figure 1. Threshold oxygen vacancy concentration for memristive devices. (a) - (c) Schematic drawing of WO3-δ with low (~3%), moderate (~8%) and high (~13%) oxygen vacancy concentration in pristine state. When applying a high electroforming voltage, sample (a) with a low vacancy concentration shows dielectric breakdown, sample (b) with a moderate vacancy concentration and sample (c) with a high vacancy concentration show electroforming behavior. Their corresponding I-V curves in positive voltage range are shown in (d) - (f). After applying the high voltage, the I-V curves sweeping in both negative and positive voltage range for samples (a) - (c) are shown in (g) - (i). Sample (b) shows the characteristic pinched hysteresis loop of resistive switching memory, while samples (a) and (c) are not switchable.


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Theoretical calculations of defect concentration dependent phase transition The nature of the switching mechanism was first investigated by different computational studies, including unit-cell-level density functional theory (DFT) calculations of electronic structure and large-scale reactive molecular dynamics (MD) simulations of atomic structure, using an ab initio-based bond-order potential (AI-BOP) (Supplementary Information). Figure 2a shows the electronic density of states (DOS) near the Fermi level of WO3-δ as a function of oxygen stoichiometry. While a bandgap is observed for the fully oxidized material, it disappears for large defect concentrations (inset of Fig. 2a). The transition from an insulating to a metallic state occurs at 3-δ ~ 2.7, where the density of states reaches saturation (blue circles in Fig. 2a). These results are in general agreement with the measured oxygen stoichiometry of 3-δ ~ 2.75 (~8% defect concentration) for the switchable sample shown in Fig. 1. From a structural standpoint, such large defect concentrations may cause the loss of long-range order, particularly in ABO3- δ perovskites without the usual A-site cation. We show the difference in energy between the crystalline and amorphous phases in Figure 2b, as a function of oxygen off-stoichiometry. As shown, the amorphous phase becomes energetically favorable when the oxygen stoichiometry drops below 3-δ ~ 2.7. Furthermore, MD simulations show that the diffusivities of both the cations and anions are much higher in the amorphous phase compared with crystalline WO3-δ and that field-induced migration is dominated by the more mobile oxygen ions (Fig. S3). Ionic transport under an electric field is therefore likely to favor oxygen migration through an amorphous phase rather than through extended defects41 or an oxygen vacancyordered structure (e.g., Magnéli phase20). However, the value of the vacancy concentration is important: an amorphous WO3-δ film with a defect concentration of ~3% (grown by room temperature deposition) could not be electroformed to enable resistive switching (Fig. S4). This


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is supported by calculations of the density of states at the Fermi level for amorphous structures (red circles in Fig. 2a) that indicate the insulator-to-metal transition depends on the total vacancy concentration and not on the atomic structure. As the defect concentration in most samples are not spatially homogeneous, regions near the threshold concentration are difficult to predict a priori. This is particularly true for amorphous or polycrystalline materials, where the locations of the conducting channels appear to be stochastic. 2

Figure 2. Oxygen stoichiometry dependent electronic and atomic phase transition of WO3-δ. (a) The integrated density of states (DOS) around the Fermi level as a function of oxygen stoichiometry. The insets show the total DOS versus energy relative to the valence band maximum (VBM) for WO3 (right) and WO2.266 (left). The blue (red) circles were calculated for crystalline (amorphous) WO3-δ. (b) Difference in total energies determined by the ab initio based bond order potential for crystalline (Ec) and amorphous (Ea) WO3-δ, showing that Ea < Ec for (3-


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δ) < 2.7. The crystalline and amorphous structures are shown in the right and left insets, respectively. Operando X-ray microscopy We now focus on the WO2.75/SrTiO3 (001) heterostructure that exhibits the current-voltage (IV) behavior characteristic of resistive switching (Figs. 1e and 1h). As changes to the local concentration of lattice oxygen can lead to electronic states within the band gap as well as an altered bonding environment, multiple probes are essential for unraveling the complex relationships governing defect behavior. To capture both structural and chemical evolution during the operation of resistive switching devices, we utilized operando, multimodal X-ray microscopy. Electrical measurements were performed on the sample while it was mounted on an X-ray goniometer at the Advanced Photon Source using the configuration shown in Fig. 3a. The incident X-rays were focused by a Fresnel zone plate and scanned along the 400 µm length of the electrodes and across the 5 µm gap. The scattered X-rays were collected by a 2D pixel array detector, providing structural information as a function of the momentum transfer, Q, while spectroscopic data near the W L3 absorption edge were measured simultaneously with an energy resolving detector, permitting detailed investigations into the chemical state of the oxide. Real space maps of the 003 Bragg intensity at Q = 5.12 Å-1 and fluorescence at E = 10.21 keV for the initial, pristine film are displayed in Figs. 3b and 3c, respectively. As shown by these figures and the atomic force microscopy (AFM) image in the inset of Fig. 3a, the sample initially exhibits a smooth surface with uniform crystallinity and composition across the electrode gap.


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Figure 3. Operando multimodal X-ray imaging of WO3-δ memristive devices. (a) Schematic setup of the operando multimodal X-ray microscopy. The incident X-rays are focused by a zone plate to a ~200 nm spot, while the exiting X-rays are collected simultaneously by a 2D pixel array detector and energy resolving detector. Inset shows an AFM image of the WO3-δ surface, with vertical height range of 2.6 nm. (b) Real space images of the 003 Bragg intensity and (c) WLα fluorescence intensity at 10.21 keV for pristine state of device.

Electroforming and the switching process The direct visualization of ionic defects and how they reversibly flow in electrochemical systems has long been a scientific challenge due to the size of the defects, their poor image contrast, and their migratory nature (being sensitive to many forces, often including the probe itself). Here we use the operando X-ray microscopy, employing both scattering and spectroscopy to image and quantitatively profile the oxygen vacancy concentration in a working device. By


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imaging at X-ray energies near and away from the W L3-edge, the oxidation states of W for each pixel were quantified, allowing determination of the O3-δ distribution with sub-micron spatial resolution, as shown in Supplementary Information and Fig. S5. The oxygen vacancies do not need to exhibit long-range order for imaging, 42,43and sample environments that can alter vacancy behavior during the measurement (e.g., high vacuum)20,44 were avoided. The operando X-ray imaging technique employed here is operated at ambient conditions (at room temperature in air). Other than the pristine condition, we identify the three electrical states shown in Figs. 1e and 1h: electroformed, low resistance state (LRS), and high resistance state (HRS). Below +32 V, the pristine state remained unaltered, i.e., X-ray scans across the electrode gap revealed no changes, and the I-V curve (the black segment in Fig. 1e) was fully reversible. Exceeding +32 V, however, triggered an irreversible transformation to the electroformed state, which persisted throughout the magenta portion of the I-V curve in Fig. 1e. While most of the WO3-δ within the gap was unchanged (Fig. S6a), the exception is shown along the left column of Fig. 4, which depicts the tungsten distribution from WLα fluorescence (4a), the oxygen distribution from X-ray absorption spectroscopy (4b), and the film thickness (t)-normalized WO3-δ Bragg intensity (4c), where the anode and cathode are labeled in Fig. 4a. Electroforming therefore leads to significant redistribution of the tungsten ions due to localized Joule heating, which is estimated to be several hundred degrees (Supplementary Information and Fig. S7). Aided by the elevated temperatures, oxygen can evolve from the film into the ambient environment by the reaction ଵ

ܱை× → ܱଶ ሺ݃ሻ + ܸை•• + 2݁′, while the applied field drives positively charged oxygen vacancies ଶ toward the cathode. This is confirmed by the O3-δ map for the electroformed state in Fig. 4b, which shows an enhancement in the oxygen concentration at the anode interface and significant reduction near the cathode. The combination of oxygen evolution and thermal diffusion of W


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ions away from the heated center is observed to lead to the build-up of WO3-δ along the edges of the Pt electrodes and some delamination of the Pt on the anode side. Interestingly, in the active region showing oxygen redistribution, a loss of intensity from the WO3-δ Bragg reflection is observed (Fig. 4c and Fig. S8), indicating a local phase transition from the single crystal to an amorphous phase. This is most likely due to large oxygen vacancy concentration in the active region, leading to reduced long range atomic order, as shown by MD simulation in Fig. 2b. Therefore, the actual switching phase is not the single crystalline phase in the pristine state but the local amorphous phase created during the electroforming process. Local X-ray absorption measurements (Fig. S9) show that the short-range order is preserved,45 however, such that the point defect model can still be utilized.46 The electroformed state is maintained until reaching the negative compliance current of -4.5 mA, when it transforms into the LRS (the black portion of the I-V curve in Fig. 1h). Minor differences are seen in the W distribution with respect to the electroformed state (Fig. 4d), but significant changes can be observed in the O3-δ map (Fig. 4e), where vacancies are driven from the cathode toward the anode. This results in a single channel of highly reduced oxide extending from the anode to the cathode (as indicated by the dashed black lines in Fig. 4e) and thus a state of low resistance; the corresponding conductive AFM image confirms this conducting channel in Fig. S10. The movement of oxygen ions is concomitant with a small change in the normalized (003) Bragg peak intensity (Fig. 4f), where more oxidized regions show greater intensity (i.e., crystallinity) and reduced regions show less. As we increase the applied voltage and reach the positive compliance current of 4.5 mA, the system switches to the HRS represented by the red portion of the curve in Fig. 1h. Figure 4g shows the occurrence of negligible W ion migration, but the oxygen vacancies return to the


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cathode region (Fig. 4h). This results in a more oxygenated region at the anode interface with an overall oxygen ion distribution similar to that of the electroformed state, thereby dissolving a portion of the conducting channel and causing high resistance behavior. According to the I003/t map in Fig. 4i, the more oxygenated regions regain a small amount of long-range order.

Figure 4. Multimodal operando X-ray microscopy images of the active switching region. The W distribution, O3-δ distribution, and variation in the normalized WO3-δ Bragg intensity are shown in (a-c) for the electroformed state, (d-f) for the low resistance state, and (g-i) for the high resistance state, respectively. These distributions are determined from the WLα fluorescence intensity, the W L3 near-edge absorption spectra, and the integrated intensity of the 003 Bragg peak I003 normalized to the thickness t determined from the WLα data. For all images, the redder hues indicate larger values (log scale).

Mapping the oxygen concentration in different resistance states We now present quantitative close-ups of the O3-δ maps in Fig. 5 for the electroformed state (5a), LRS (5b), and HRS (5c), with the conducting channel in the LRS indicated by the dashed


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violet curves. At the anode interface, due to the partial delamination of the Pt anode (top), a local concavity is created, leading to a localized enhancement of the electric field (Supplementary Information and Fig. S7). Region of interest-1 (ROI-1) represents the area with the largest field line density and is the active switching region, where enhanced oxygenation after electroforming (Fig. 5a), increased reduction after transitioning to the LRS (Fig. 5b), and reoxygenation in the HRS (Fig. 5c) are observed. At the cathode interface, there are two regions of interest, ROI-2 and ROI-3. In the electroformed state, Fig. 5a shows the accumulation of oxygen vacancies at ROI-3, extending the cathode towards anode. When switched to the LRS, however, it is ROI-2 that becomes reduced and connected with ROI-1 to form the conduction channel. Because there is no localization of the electric field as for the anode interface, the cathode interface exhibits stochastic behavior, and it is possible to switch between ROI-2 and ROI-3 during device operation. This may result in the variation of resistance values after multiple switching cycles. Profiles of the oxygen content along the conducting channel for each of the three electrical states are presented in Fig. 5d-f. In the pristine state, Schottky barriers are formed at both Pt/WO3-δ interfaces, resulting in the highest resistance. After electroforming, the cathode interface is accumulated with oxygen vacancies, as shown in Fig. 5d, changing the cathode interface into an ohmic contact. In the LRS, both electrode interfaces are in ohmic contact (Fig. 5e). When switched to the HRS, the anode interface is re-oxidized, reforming the Schottky barrier (Fig. 5f). The results clearly illustrate that the active switching region is the anode electrode interface, while the cathode interface maintains ohmic contact after electroforming. As the local oxygen stoichiometry in the channel, especially at anode interface, is modulated above or below the threshold value of 3-δ ~ 2.75 (indicated by the dashed blue line), the conduction pathway from anode to cathode closes or opens, respectively.


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Diffraction scans along Q across the WO3-δ 003 Bragg peak are displayed in Fig. 5g-i as a function of position along the vertical, dashed blue lines shown in Fig. 5a-c. While the region within the electrode gap is primarily amorphous after electroforming, the 003 intensity is recovered under the Pt electrodes with little observed strain (Fig. 5g). However, in the LRS shown in Fig. 5h, the crystalline regions underneath the Pt electrodes and adjacent to the gap exhibit large out-of-plane expansion (up to ~1%) and reduced long-range order. The WO3-δ lattice has been reported to expand with increasing oxygen vacancy concentration.34,35 After switching to the HRS, the lattice expansion is reduced as the crystalline lattice is reoxygenated through both redox reactions and oxygen ion migration. A more detailed description of the strain behavior will require further studies as a function of voltage and time, but the present results suggest that substantial defect migration can take place under the electrodes, even several microns away from the gap.


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Figure 5. Quantitative chemical and structural maps of the active switching region. (a-c) O3-δ maps illustrating the distribution of oxygen ions in the electroformed, LRS and HRS (top, middle, and bottom row, respectively). The black scale bar indicates 1 µm. The dashed white lines show the Pt electrodes after the initial delamination, and the dashed violet curve follows the conducting channel formed in the LRS. (d-f) The O3-δ distribution along the curved conducting channel. The blue dashed line at (3−δ) = 2.75 refers to the value of the pristine state. The red (cyan) areas within the gap represent regions with oxygen stoichiometries > 2.75 (< 2.75). (g-i) Scattered X-ray intensity along the specular rod near the 003 peak for the blue vertical line shown in (a-c). The distances between the horizontal white dashed lines are 5 µm.

CONCLUSION


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It has been well recognized in many condensed matter systems that materials driven near phase transitions can exhibit multiple order parameters, enabling giant and correlated responses to external stimuli.47–49 The current work shows that in memristive devices, there exists similar behavior that depends on and can be configured by the defect concentration of the pristine state. The engineering of next-generation memristive devices requires the prediction and quantification of such threshold defect concentrations. As the operation of these devices relies on the control of ions or ionic defects by an electric field, multimodal techniques that enable observation of the multiple and simultaneous electrochemical processes are key to their development. In summary, we find that a threshold defect concentration in the pristine state is necessary for resistive switching in WO3-δ. Breaking or connecting the conduction pathway and simultaneously changing the interfacial Schottky barrier relies on modulating the local oxygen stoichiometry above or below a threshold defect concentration. In the ongoing search for materials systems in which ionic defects are coupled with electronic properties, our results demonstrate that control of the pristine defect concentration around a threshold value is key to the design of switchable devices.

Methods Device preparation. The WO3-δ epitaxial thin films were grown on TiO2-terminated SrTiO3 (STO) (001) single crystal substrates by 90° off-axis RF sputtering from a 3-inch WO3 ceramic target. The growth temperature was optimized at 923 K and gas pressure was kept at 50 mTorr with Ar/O2 ratio of 4:1. The growth rate, calculated from X-ray reflectivity measurement, was ~0.33 nm/min using an RF power of 240 W (Fig. S1). Due to the large lattice mismatch between STO and WO3, ~5.2% in tension, the films are partially relaxed, as shown in the X-ray scans of


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Figs. S1d-f. As-grown film has a stoichiometry of WO2.9 (Fig. S2). To introduce more oxygen vacancies, the films were annealed at 923 K in vacuum within the growth chamber for three hours. The annealed film has a stoichiometry of WO2.75. To further increase oxygen vacancy concentration, the films were grown using pure Ar gas at 50 mTorr without introducing O2 gas, which has a stoichiometry of WO2.6. Lateral Pt electrodes were patterned by standard lithographic processes with a length of 400 µm and gap of 5 µm. Characterization was performed in air and at room temperature with a Keithley 2400 source meter. DFT calculations. DFT calculations were performed on the structures described in supplementary information, using the plane wave code Vienna Ab-initio Simulation Package (VASP) .

50,51

To treat the exchange-correlation, the generalized gradient approximation (GGA)

of Perdew-Burke-Ernzerhof (PBE) potentials were used,

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was employed. Projector augmented wave (PAW) atom

specifically the one with six valence electrons for tungsten and the soft

version for oxygen. The kinetic energy cutoff was 370 eV. Ionic relaxations were performed, twice, using Gamma-only Brillouin zone sampling until the energy difference was 0.1 meV/supercell. The electronic densities of states (DOS) were evaluated using a Gamma-centered 2×2×2 k-point grid. The DOS near the Fermi level, as shown in Fig. 2a, was evaluated by integrating the DOS from EFermi-0.3 eV to EFermi+0.3 eV. Molecular dynamics simulation. To study the relative stabilities of the crystalline and amorphous phases as a function of stoichiometry, we start from the crystalline samples. These samples are minimized to the lowest energy configuration (at 0 K) as predicted by the AI-BOP potential. To generate the amorphous structures, the same crystalline samples were heated at 3000 K for 5 ps to melt the structures, before being quenched to 100 K and subsequently minimized at 0 K. The amorphous energies were averaged over 3 independent runs, with the


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same initial atomic configurations, but different initial atomic velocities, which were assigned randomly on a Gaussian centred at 3000 K. The difference between the ground state energies of the crystalline and amorphous phases was used to calculate the relative stabilities of the two phases (Fig. 2b). Operando X-ray imaging. Multimodal X-ray imaging was conducted at sector 2-ID-D at Advanced Photon Source (APS), Argonne National Laboratory. The setup is shown in Fig. 3a, with the X-ray beam focused by a Fresnel zone plate to a spot size of ~200 nm. High-resolution images were raster-scanned with a count time of 1 s, simultaneously collecting fluorescence Xrays with an energy resolving detector (Vortex) and diffracted X-rays with a pixel array detector (Pilatus). X-ray absorption near-edge spectra (XANES) of standard WO3 and WO2 powder samples were measured before and after imaging of device. After imaging the pristine state of device, the sample underwent electroforming. To find the electroformed area, a scan was measured along the length of the electrode. As shown in Fig. S6a, only one region displayed a change in fluorescence. We then focused on this active area for detailed mapping, as shown in Fig. 4. Data were typically measured at two different incident X-ray energies, 10.210 keV and 10.400 keV, in order to quantify the W oxidation state for each pixel, using the two-energy quantification method described in the Supplementary Information. The electroformed state was imaged without an applied voltage. The HRS and LRS were imaged in similar way to the electroformed state but with a small applied voltage (0.2 V) to monitor the resistance during imaging. It was confirmed that the electrical state was not changed during imaging, as shown in Fig. S6b. To further demonstrate that the X-ray probe is not perturbing the electrical states, we compared the switching I-V curves for devices switched with and without X-ray imaging, as shown in Fig. S6c. These two curves are very similar, suggesting no X-ray beam effect during


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operando X-ray imaging. Although the current manuscript focuses on a particular heterostructure, similar images and defect behavior were observed for multiple WO3-δ/STO samples with initial stoichiometries near 3-δ = 2.75.

AUTHOR INFORMATION Corresponding Authors * [email protected] * [email protected] ACKNOWLEDGMENT We thank J. W. Freeland and J. A. Eastman for helpful discussions. Research was supported by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. Use of the Advanced Photon Source and the Center for Nanoscale Materials, an Office of Science user facility, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC0206CH11357. H. Liu acknowledges support from an A*STAR International Fellowship.

ASSOCIATED CONTENT Supporting Information. The method of quantification of oxygen stoichiometry is presented. Evidence for long range atomic disordering and preservation of local octahedral coordination is


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shown for the amorphous active switching region. Structural models and parameterization for Ab-initio and molecular dynamic simulation are shown. The method of Finite Element Modeling is presented. Conductive atomic force microscopy images are shown. This material is available free of charge via the Internet at http://pubs.acs.org.

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Figure 1. Threshold oxygen vacancy concentration for memristive devices. (a) - (c) Schematic drawing of WO3-δ with low (~3%), moderate (~8%) and high (~13%) oxygen vacancy concentration in pristine state. When applying a high electroforming voltage, sample (a) with a low vacancy concentration shows dielectric breakdown, sample (b) with a moderate vacancy concentration and sample (c) with a high vacancy concentration show electroforming behavior. Their corresponding I-V curves in positive voltage range are shown in (d) - (f). After applying the high voltage, the I-V curves sweeping in both negative and positive voltage range for samples (a) - (c) are shown in (g) - (i). Sample (b) shows the characteristic pinched hysteresis loop of resistive switching memory, while samples (a) and (c) are not switchable. 226x127mm (220 x 220 DPI)


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Figure 2. Oxygen stoichiometry dependent electronic and atomic phase transition of WO3-δ. (a) The integrated density of states (DOS) around the Fermi level as a function of oxygen stoichiometry. The insets show the total DOS versus energy relative to the valence band maximum (VBM) for WO3 (right) and WO2.266 (left). The blue (red) circles were calculated for crystalline (amorphous) WO3-δ. (b) Difference in total energies determined by the ab initio based bond order potential for crystalline (Ec) and amorphous (Ea) WO3-δ, showing that Ea < Ec for (3-δ) < 2.7. The crystalline and amorphous structures are shown in the right and left insets, respectively. 228x128mm (220 x 220 DPI)


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Figure 3. Operando multimodal X-ray imaging of WO3-δ memristive devices. (a) Schematic setup of the operando multimodal X-ray microscopy. The incident X-rays are focused by a zone plate to a ~200 nm spot, while the exiting X-rays are collected simultaneously by a 2D pixel array detector and energy resolving detector. Inset shows an AFM image of the WO3-δ surface, with vertical height range of 2.6 nm. (b) Real space images of the 003 Bragg intensity and (c) WLα fluorescence intensity at 10.21 keV for pristine state of device. 338x190mm (300 x 300 DPI)


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Figure 4. Multimodal operando X-ray microscopy images of the active switching region. The W distribution, O3-δ distribution, and variation in the normalized WO3-δ Bragg intensity are shown in (a-c) for the electroformed state, (d-f) for the low resistance state, and (g-i) for the high resistance state, respectively. These distributions are determined from the WLα fluorescence intensity, the W L3 near-edge absorption spectra, and the integrated intensity of the 003 Bragg peak I003 normalized to the thickness t determined from the WLα data. For all images, the redder hues indicate larger values (log scale). 152x114mm (220 x 220 DPI)


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Figure 5. Quantitative chemical and structural maps of the active switching region. (a-c) O3-δ maps illustrating the distribution of oxygen ions in the electroformed, LRS and HRS (top, middle, and bottom row, respectively). The black scale bar indicates 1 µm. The dashed white lines show the Pt electrodes after the initial delamination, and the dashed violet curve follows the conducting channel formed in the LRS. (d-f) The O3-δ distribution along the curved conducting channel. The blue dashed line at (3−δ) = 2.75 refers to the value of the pristine state. The red (cyan) areas within the gap represent regions with oxygen stoichiometries > 2.75 (< 2.75). (g-i) Scattered X-ray intensity along the specular rod near the 003 peak for the blue vertical line shown in (a-c). The distances between the horizontal white dashed lines are 5 µm. 254x190mm (300 x 300 DPI)


Quantitative Observation of Threshold Defect Behavior in Memristive

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