Subfilamentary Networks Cause Cycle-to-Cycle Variability in

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Subfilamentary Networks Cause Cycleto-Cycle Variability in Memristive Devices Christoph Bäumer, Richard Valenta, Christoph Schmitz, Andrea Locatelli, Tevfik Onur Mente#, Steven P Rogers, Alessandro Sala, Nicolas Raab, Slavomir Nemsak, Moonsub Shim, Claus M. Schneider, Stephan Menzel, Rainer Waser, and Regina Dittmann ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b02113 • Publication Date (Web): 29 Jun 2017 Downloaded from http://pubs.acs.org on June 30, 2017

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Subfilamentary Networks Cause Cycle-to-Cycle Variability in Memristive Devices Christoph Baeumer1*, Richard Valenta1, Christoph Schmitz1, Andrea Locatelli2, Tevfik Onur Menteş2, Steven P. Rogers3, Alessandro Sala2, Nicolas Raab1, Slavomir Nemsak1, Moonsub Shim3, Claus M. Schneider1, Stephan Menzel1, Rainer Waser1,4, Regina Dittmann1 1 2 3 4 *

Peter Gruenberg Institute, Forschungszentrum Juelich GmbH and JARA-FIT, 52425 Juelich, Germany Elettra-Sincrotrone, S.C.p.A, S.S 14 - km 163.5 in AREA Science Park, 34149 Basovizza, Trieste, Italy Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA Institute for Electronic Materials, IWE2, RWTH Aachen University, 52074 Aachen, Germany; Corresponding author: [email protected]

KEYWORDS: Resistive switching; memristive devices; variability; PEEM; graphene

ABSTRACT A major obstacle for the implementation of redox-based memristive memory or logic technology is the large cycle-to-cycle and device-to-device variability. Here, we use spectromicroscopic photoemission threshold analysis and operando XAS analysis to experimentally investigate the microscopic origin of the variability. We find that some devices exhibit variations in the shape of the conductive filament or in the oxygen vacancy distribution at and around the filament. In other cases, even the location of the active filament changes from one cycle to the next. We propose that both effects originate from the coexistence of multiple (sub-)filaments and that the active, current-carrying filament may change from cycle to cycle. These findings account for the observed variability in device performance and represent the scientific basis, rather than prior purely empirical engineering approaches, for developing stable memristive devices. 1 ACS Paragon Plus Environment

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Redox-based memristive devices are one of the most attractive emerging memory technologies in terms of scaling, power consumption and speed, even allowing multibit operation, logic-in-memory applications and neuromorphic computing architectures.1-6 In these devices, external electrical stimuli cause changes of the resistance of an oxide layer sandwiched between two metal electrodes. In the simplest application, the device can be set into a low resistance state (LRS) and reset into a high resistance state (HRS), which may encode a logical one and zero, respectively. The major obstacle delaying large-scale implementation of memristive devices into state-of-the art memory or logic applications, however, is their large cycle-to-cycle (C2C) and device-to-device (D2D) variability of both LRS and HRS resistance values.7,

8

These variabilities, which typically follow a log-normal distribution,8 describe the

stochastic nature of the switching process within one cell, resulting in different resistances obtained for each switching cycle and different resistances obtained for different cells on the same chip. The switching process in transition metal oxides is believed to be driven by the nanoscale motion of donor-type defects such as oxygen vacancies, which may tune the resistance of the oxide layer or the resistance of the electrode/oxide interface.1, 9-10 The stochastic nature of the resulting conductive filament has been suspected phenomenologically to result from an interplay of the thermodynamic stability of the filament,11 generation/recombination effects of oxygen vacancies12 and especially the shape and oxygen vacancy distribution of the conductive filament.13-15 It has therefore been attempted to achieve higher switching uniformity employing filament precursors16 or preferred sites for oxygen vacancy enrichment.17,

18

Importantly, and

despite the promising results obtained empirically, changes of the microscopic structure of a single conductive filament, which might cause the C2C variability in redox-based memristive 2 ACS Paragon Plus Environment

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devices, have not yet been directly observed in experiment. In addition, it has to be considered if the location of the conductive filament may change during operation of redox-based memristive devices,19,

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as has been previously shown for so-called electrochemical metallization (ECM)

cells,21, 22 where also highly non-symmetrical filament shapes have been observed.23, 24 In this letter, we employ spectromicroscopic photoemission threshold analysis and operando XAS analysis on the recently introduced model system of graphene/SrTiO3/Nb:SrTiO3 memristive devices10 to identify the microscopic origin of variability. We find that a change of the shape of the conductive filament or variations in the oxygen vacancy distribution within the filament are indeed responsible for the observed variability. Interestingly, we even observe that the location of the active filament may change from one cycle to the next, suggesting that each switching event can be understood as a competition between multiple filaments.

RESULTS AND DISCUSSION The device schematic of our model system and a representative I-V curve are shown in Figure 1a and b. As we demonstrated recently, the graphene top electrodes employed here allow the characterization of buried layers using surface sensitive electron spectromicroscopy, as graphene scarcely dampens the intensity of low-energy photoelectrons.10 The switching mechanism in such devices has been demonstrated to be based on oxygen removal from the SrTiO3 lattice during the current-compliance-limited Set operation (positive bias at the top electrode) and oxygen reincorporation during the gradual Reset operation (negative bias at the top electrode).10,

25

The C2C variability of these memristive devices can be seen in the

resistances obtained during 150 switching cycles (Figure 1c-d), which show a rather typical 3 ACS Paragon Plus Environment

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distribution of obtained LRS and HRS values with median resistance values of 5.7×104 and 1.2×108 Ω, respectively. These values are typical of SrTiO3 cells operated at high current compliances.10, 25, 26 The standard deviations normalized to the mean resistance values 0.042 and 0.056, respectively, which are typical values for redox-based memristive devices.7 In pulsed operation, we obtain similar distributions (Supporting Information, Figure S1). For operation at different current compliances, we obtain an inverse relationship between the LRS resistance value and the current compliance, i.e. higher currents lead to lower resistance states (Supporting Information, Figure S1). As is typically observed,13 the normalized standard deviation increases steeply with the LRS resistance value, reaching 0.4 for 0.5 mA current compliance, indicating that lower programming currents lead to increased C2C variability. Interestingly, the HRS resistance distributions remain similar for all current compliances tested. Presumably, these observations can be explained by smaller LRS filaments created with lower currents,13 while the HRS appears to be dominated by area-dependent leakage, which is independent of the filament size. Even for a filament-dominated HRS resistance, one would expect the variability to be independent of the current compliance, because more conductive filaments are easier to reoxidize due to the increase in temperature during Reset.27 In the following, we will focus on results obtained with comparably high current compliances to facilitate the observation of the filament. The variability mechanisms derived from these measurements also have to be considered for low-power and highly scaled devices. We investigated these devices using photoelectron emission microscopy (PEEM) aiming at verifying the microscopic origin of the observed variability. To this purpose, we carried out combined XPEEM measurements (Nanospectroscopy beamline at Elettra synchrotron laboratory, Trieste, Italy28) and threshold photoemission PEEM measurements using illumination by a 4 ACS Paragon Plus Environment

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mercury lamp (NanoESCA, Scienta Omicron GmbH, Taunusstein, Germany). For the threshold photoemission analysis, several devices were switched into the LRS or HRS using the quasistatic I-V sweeps shown in Figure 1 in air and mounted into the PEEM for each separate switching step as no biasing is possible within this instrument, while the XPEEM measurements were performed operando employing the same Set and Reset operations within the instrument. A

threshold

photoemission

PEEM

image

of

a

representative

graphene/Al2O3/SrTiO3/Nb:SrTiO3 device in the LRS is shown in Figure 2a. Here, the Al2O3 layer was incorporated to guarantee sufficient retention of the device (compare methods for details).29 Within the rather homogeneous graphene area, a region with enhanced contrast is clearly visible. The intensity of this feature varies reversibly with the resistance state after additional Reset and Set operations (Figure 2a-d), substantiating the hypothesis that this feature is the conductive filament and demonstrating that this contrast did not arise from inhomogeneities in the graphene layer or residues from the transfer and photo lithography processes. Extracting threshold photoemission spectra from the filament and the surrounding allows the determination of the energy difference between the secondary electron cut-off (the rising edge of the spectra) and the Fermi level. The spectra were fitted with a convolution of Gauss and Heaviside functions to extract the relative energy of the photoemission threshold.30-32 As surface adsorbates may have a large impact on the absolute value of the photoemission threshold,33 only relative changes between the filament and the unaltered surrounding will be considered in the following. Figure 2e shows that for both LRS and HRS, the photoemission threshold of the filament ߔ ୊ is significantly lower than the reference photoemission threshold of the unaltered surrounding ߔ ୖ . It is evident that in the LRS, the energy difference ߂ߔ = ߔ ୊ − ߔ ୖ is significantly more negative than in the HRS. Figure 2f indicates that the resistances obtained 5 ACS Paragon Plus Environment

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during these cycles before each PEEM measurement fall into the same range as the resistance distribution shown in Figure 1c-d. Comparing the average value of the resistances (R) measured before and after the PEEM experiment with ߂ߔ, it can be concluded that the change in the photoemission threshold tracks the actual device resistance. Essentially, an almost exponential dependence between ߂ߔ and R is observed (Figure 3a). The photoemission threshold of the LRS is approximately 0.10 to 0.15 eV lower than for the HRS, indicating a direct correlation between photoemission threshold and device resistance. This correlation can be understood based on the band alignment in the device and the relative position of the Fermi energy in the SrTiO3 band gap. In the LRS, the presence of oxygen vacancies are known to lower the Schottky barrier at the electrode/oxide interface1 as they are shallow donors in SrTiO3 and their presence at the oxide/electrode interface shifts the Fermi energy closer to the SrTiO3 conduction band edge . This shift of the Fermi energy towards the vacuum level results in more mobile carriers in the conduction band and a reduction of the photoemission threshold (Figure 3b). As most typically considered conduction mechanisms across a Schottky barrier, such as thermionic emission or field emission, depend on the barrier height in an exponential manner, the exponential dependence between observed ߂ߔ and measured R is in line with this interpretation. Even though this trend is based only on a limited number of data points and the simplified assumption of exponential dependence, the observed shift of the threshold photoemission spectra corresponds well to our earlier work, where we estimated a difference in the barrier height of 0.07 eV in addition to a significant barrier narrowing for the LRS based on the concentration of oxygen vacancies in the filament10. Together, barrier lowering and narrowing are in good agreement with the photoemission threshold differences observed in this work. 6 ACS Paragon Plus Environment

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As the photoemission threshold determined by PEEM experiments typically corresponds to the topmost layer, one may question whether or not the graphene layer, rather than the SrTiO3, may be responsible for the observed changes. But our experimental observation contradicts the expected shift of the graphene work function (Supporting Information, Figure S2).34 It therefore appears that the measured photoemission threshold represents the band alignment in the SrTiO3 layer. This interpretation also corresponds to the observation that the X-ray absorption analysis of the SrTiO3 layer is possible through the graphene electrode, indicating that the secondary electrons used to acquire the PEEM image pass through the graphene (Ref. 10 and Supporting Information, Figure S3). For the device under investigation, our X-ray absorption analysis shows that the identified filament indeed exhibits the characteristic signature of reduced SrTiO3, validating the interpretation that this is the conductive filament (Supporting Information, Figure S3). Additional, small filaments below the lateral resolution may exist in the cell. But strongly reduced features, which might contribute to the current flow of the device, should still be visible in the PEEM image in Figure 2a (broadened because of the limited resolution) due to the strong contrast. No such features are present in this device, further supporting the assignment of the conductive filament. Coming back to the question of C2C variability, it is very obvious from this experiment that the microscopic details of the filament change from cycle to cycle, and may in turn be responsible for differences in the resistance. Figure 3a shows that LRS II exhibits a lower filament photoemission threshold and a lower resistance than LRS I. The same is true for HRS I and HRS II. This trend therefore confirms that changes in the oxygen vacancy concentration at the interface may be responsible for the C2C variability. In addition, the shape of the filament 7 ACS Paragon Plus Environment

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and the distribution of regions of different photoemission threshold therein are significantly different in each state (Insets of Figure 2a-d), confirming that the shape of the filament can vary as well. Operando XPEEM analysis of a similar device shows a non-circular, irregular filament shape (Figure 4a-d) of approximately 200 nm in diameter, similar to recent findings for filaments in Ta2O5 and HfO2.35 Here, we chose a sample without an additional Al2O3 layer to allow unambiguous interpretation of the O K-edge; sufficient retention was guaranteed through the use of Sr-rich SrTiO3 (see methods for details).26 The filament observed here exhibits a rather complex shape and varying oxygen vacancy concentration across and around its core, as is evident from the map of the O K-edge A/B2 peak ratio plotted in Figure 4c-d. Within the filament, there are regions of very different (high or medium) vacancy concentration. On average, the oxygen vacancy concentration is higher in the LRS than in the HRS, as is evident from the reduced peak A in the O K-edge spectrum and the reduction of the first peak of the Ti L-edge spectrum (Ti L3, t2g peak) (Figure 4e-h). From a comparison of the A/B2 peak ratio with reference measurements, the Ti3+ concentration can be deduced.10 In the LRS, the average Ti3+ concentration is about 9 %, in good agreement with our previous findings.10 For the red area visible in Figure 4c, however, we find even a higher concentration, approximately 24 % Ti3+ (Supporting Information, Figure S4). This observation confirms that conductive filaments do not necessarily exhibit a symmetric shape with a homogeneous gradient from a high oxygen vacancy concentration in the center to a low concentration at the edge, but rather possess a fine structure with regions with higher and lower vacancy concentration. We expect that the filament fine structure could be more complex than shown in Figure 4, demanding even higher lateral resolution to be fully resolved. 8 ACS Paragon Plus Environment

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When repeating the threshold photoemission investigation for a second device (Figure 5), we found further evidence supporting the aforementioned C2C variability in memristive devices. During the first switching cycle (Set to LRS I and Reset to HRS I), we found a conductive filament in the center of the device, which exhibited the expected increase of the filament photoemission threshold during Reset (Figure 5a,b,e). Surprisingly, at the following Set operation the filament photoemission threshold did not change; it remained indicative of the HRS state. Instead, we found that a new filament with a low photoemission threshold had formed at the edge of the device (Figure 5c). During Reset, the photoemission threshold of this filament increased (Figure 5c,d,f), corresponding to a decrease in the oxygen vacancy concentration. Based on the observation of a change in the position of the conductive filament during repeated cycling it is clear that the LRS and HRS may vary from filament to filament, which may account for the observation of multimodal resistance distributions.19, 37 Summarizing, the filamentary structure observed in our devices is clearly more complex than so far assumed. Each filament possesses a non-symmetric shape and a fine structure of higher and lower oxygen vacancy concentrations in the lateral direction. Additionally, we found that more than one location within the device area may exhibit an increased amount of oxygen vacancies. It is noteworthy that for both devices shown in Figures 2 and 5, many small regions of enhanced contrast appear upon repeated cycling, indicating that a multitude of such reduced regions can develop, which can be thought of as pre-filaments. The PEEM investigation shows that in the LRS, these pre-filaments possess an intermediate photoemission threshold lower than their surroundings, but still much higher than the conductive filament, indicating that the current flow will still be dominated by the main filament (Figure 6a-c). During Reset, these prefilaments are reoxidized (Figure 6d). 9 ACS Paragon Plus Environment

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It is very likely that both – the appearance of multiple filaments and their complex shape – are related to the presence of nanoscale subfilamentary structures,38,

39

similar to the scenario

recently described for ECM cells40 and as schematically depicted in Figure 7. For this drawing, the recently published atomically resolved images and spectroscopic information on subfilaments in SrTiO3 memristive devices was used as a guideline.41 The switching process in SrTiO3 is governed by the oxygen exchange between oxide layer and electrode,25 drift and diffusion of oxygen vacancies within the SrTiO39 and localized Joule heating,27 and can therefore be described as a thermally assisted oxygen migration driven by the electric field. During the forming process, a multitude of pre-filaments appear in regions where oxygen evolution reactions at the electrode/oxide interface are favorable, such as defects in the oxide or at the interface, as has been observed experimentally.41-43 These filaments grow and become more and more conductive, resulting in a self-accelerating process, as their growth is facilitated at higher temperature. Here, the temperature increase due to Joule heating of neighboring pre-filaments may also come into play. Once one filament is sufficiently conductive, the desired current compliance is reached, lowering the voltage drop over the device and thus lowering the driving force, and the growth of the other filaments stops.42-44 Upon repeated cycling, all filaments – the conducting filament and the pre-filaments – are reoxidized during the gradual Reset operation as evidenced in Figure 6d. For the conductive filament, the temperature-acceleration due to Joule heating27 will be most pronounced. Therefore, the previously most conductive filament may under some circumstances be oxidized more strongly than individual pre-filaments. In the next cycle, the Set operation causes all pre-filaments to grow anew in a self-accelerated manner, which results in an amplification of stochastic differences between the (partially) reoxidized filaments, such that the location of the conductive filament may randomly change to a 10 ACS Paragon Plus Environment

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neighboring filament (Figure 2 and Figure 7c) or a filament farther away (Figure 5 and Figure 7d), especially if the previous conductive filament was fully oxidized during Reset. Although we cannot exclude that the location of the filament changes because the quality of the graphene-SrTiO3 contact may suffer during switching, we believe that this is a realistic scenario for metal electrodes as well, given that similar scenarios have been observed for ECM cells.21-22, 40 In addition to the filament shape variations, the possibility of random changes of the active filament position demand for a careful filament control to reduce C2C variability in redoxbased memristive devices such as demonstrated by Hayakawa et al.17 and Niu et al.45 As the shape and oxygen vacancy concentration of the filaments in the devices presented here is very different for each device, addressing these factors may also be necessary to reduce D2D variability. In addition, the occurrence of multiple filaments suggests that for aggressively scaled devices, variability caused by multifilamentary networks may be decreased as the number of possible filaments scales with the area.40 But even for small devices with only one main active filament, we expect that the shape and especially the oxygen vacancy concentration within the filament will change from cycle to cycle due to the subfilamentary structure. This indicates that the nature of variability in redox-based memristive devices is more complicated than realized in previous descriptions through fluctuations in the radius of a single filament.13 Further, current drift-diffusion device simulations – while successfully describing important aspects like the gradual Reset – have not yet considered such non-symmetric and variable filament shapes for the sake of simplicity,46, 47 suggesting that more-dimensional models may be necessary to accurately describe all nanoscale processes in memristive devices.48

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CONCLUSIONS In conclusion, our direct observation of the conductive filament after repeated switching allowed us to confirm that the non-regular shape of the filament and the variable concentration of oxygen vacancies therein are the microscopic origin of the C2C variability in memristive devices. In addition, the location of the active filament may also vary during operation, contributing further to the variability. These processes can be explained through the competitive growth of multiple pre-filaments during forming and repetitive switching, as each pre-filament may act as the preferred site for the evolution of the new conductive filament in the next cycle. Our experimental findings provide the scientific basis for empirical pathways already pursued in the engineering of memristive devices and may therefore accelerate their educated design based on a physical understanding of the microscopic processes giving rise to variability.

METHODS Device Fabrication 20 nm single-crystalline undoped SrTiO3 thin-films with 2-3% Sr excess and 2 nm singlecrystalline undoped, stoichiometric SrTiO3 thin-films covered with 1 nm of Al2O3 were fabricated via pulsed laser deposition on 0.5-wt% Nb:SrTiO3 substrates (CrysTec GmbH, Germany). The single-crystalline SrTiO3 target was ablated by a KrF excimer laser (λ=248 nm) with a repetition rate of 5 Hz and a spot size of 2 mm2 at a target-to-substrate distance of 44 mm. The laser fluence was 0.67 J cm−2 or 1.05 J cm−2 for Sr-rich and stoichiometric films, respectively SrTiO3 films were grown in an oxygen atmosphere of 0.1 mbar at a substrate temperature of 800 °C. The film growth was monitored using reflection high-energy electron 12 ACS Paragon Plus Environment

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diffraction. The Al2O3 was deposited ex situ by pulsed laser deposition with a laser fluence of 2.1 J cm−2, a repetition rate of 5 Hz and a spot-size of 1.5 mm2 at a target-to-substrate distance of 60 mm in an oxygen atmosphere of 10-4 mbar. Stoichiometric SrTiO3/Nb:SrTiO3 devices typically exhibit extremely poor retention of the LRS,26, 29 which makes time consuming measurements like our PEEM investigation impossible. Therefore, we circumvented this limitation by using heterostructures of Al2O3/SrTiO3/Nb:SrTiO3 or Sr-rich SrTiO3 layers, both of which we demonstrated to possess strongly improved retention26, 29. The switching mechanism, on the other hand, remained the same in all device types described above. The reason we chose a sample without Al2O3 for Figure 4 is that interpretation of the O K-edge is more direct without an additional oxide on top of the SrTiO3. We also found that the ionic nature and extremely thin layer thickness of the Al2O3 layer did not result in measurable changes between STO layers with and without Al2O3 capping, but we decided to ensure maximum clarity of the O K-edge interpretation. In a next step, graphene grown by chemical vapor deposition was deposited on the SrTiO3 surface as described elsewhere.49 For the structuring of top electrodes, the graphene layer was patterned through optical lithography and oxygen plasma etching. Before photoresist lift-off, a 30 nm Y:ZrO2 insulating layer was deposited via pulsed laser deposition at room temperature. The repetition rate was 5 Hz and the spot size was 1.5 mm2 at a target-to-substrate distance of 60 mm in an oxygen atmosphere of 10−4 mbar. The laser fluence was 2.1 J cm−2. Afterwards, the graphene electrode was partially covered by an additional 80 nm Y:ZrO2 insulating layer (optical lithography and pulsed laser deposition). This insulating layer allows for contacting the graphene with Pt/Au leads, which are separated from the continuous bottom electrode. The leads connect to the graphene in one specific position, leaving most of the graphene uncovered, allowing for 13 ACS Paragon Plus Environment

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spectromicroscopic investigation of the SrTiO3 layer. The leads are prepared via optical lithography and electron beam evaporation of 10 nm Pt followed by 130 nm Au.

Electrical characterization For electrical characterization, the Pt/Au leads were contacted with W whisker probes or through Al wire bonding. The Nb:SrTiO3 substrate served as an electrically grounded bottom electrode and was contacted through silver paste. Both ex situ and operando I–V sweeps were performed with a Keithley 2611A SourceMeter. The different sweeps were performed using the following voltage cycles: 0 V to positive voltages (maximum +5 V) for forming and set, 0 V to negative voltages (maximum −5 V) for reset and +0.2 V to −0.2 V for read-out. Unless stated otherwise, the device resistance was obtained from the slope of a linear fit of the read-out sweeps between −0.1 and +0.1 V. The step size was 20 mV and the holding time before measurement was 5 ms; the current compliance for the forming step and the set process was 35 mA unless indicated differently. During the reset sweeps no current compliance was necessary.

Spectromicroscopy The threshold photoemission characterization was performed using a NanoESCA with illumination by a mercury lamp. The XPEEM experiments have been performed at the Nanospectroscopy beamline at Elettra synchrotron laboratory, Trieste, Italy and the beamline UE56/1-SGM at BESSY II (Berlin, Germany) using secondary electrons as detection method. 14 ACS Paragon Plus Environment

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Various series of images were taken at increasing photon energies with a step size of 0.1 eV for the Ti L-edge and 0.2 eV for the O K-edge. The image stacks were analyzed and spectra were extracted using the IGOR Pro software. The spatial resolution as described in Ref. 50 (full-width half-maximum of a Gaussian profile convoluted with a step function, which was fitted to a sharp edge within the PEEM image), was determined to be 110 nm for the NanoESCA measurements and 30 nm for the measurements at the Nanospectroscopy beamline. All spectra in the main text and in the Supplementary Information were background corrected by a linear fit of the pre-edge and subsequent normalization by fitting a third-order polynomial to the post-edge using the Athena software.36 To avoid artifacts from normalization, we always refer to the peak A intensity normalized to the intensity of peak B2 at 538 eV. The relative peak ratio trends described here are the same before and after normalization.

FIGURES Figure 1. (a) Schematic of the device geometry. A SrTiO3 layer (blue) is sandwiched between a Nb:SrTiO3 bottom electrode (dark grey) and graphene top electrode (grey honeycomb lattice). The graphene electrode is contacted through a metal lead, which is electrically separated from the continuous bottom electrode, allowing for biasing inside PEEM instruments. (b) Quasistatic I-V curve of a representative graphene/SrTiO3/Nb:SrTiO3 device operated with a current limit of 30 mA controlled by Keithley 2611A source meter. The bottom electrode serves as virtual ground, while the bias is applied to the graphene top electrode. (c) LRS and HRS resistance extracted from 150 switching cycles of the same device (resistance value at 80 mV). (d) Weibull plot of the resistance distribution for the measurement shown in (c). Figure 2: (a) PEEM image of a graphene/Al2O3/SrTiO3 device in the LRS at an electron energy ࡱ − ࡱࡲ of 3.4 eV. Scale bar, 5 µm. (b) PEEM image of the same device after Reset. (c) and (d) PEEM images after one additional Set


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and Reset operation, respectively. Insets: magnified photoemission threshold map of the area around the conductive filament. The maps were obtained by fitting the threshold spectrum for each pixel31. (e) Threshold photoelectron spectra extracted from the filament and a reference region close to the filament. (f) Evolution of device resistance during the switching cycle for the PEEM investigation. Figure 3: (a) Average value of the device resistance before and after each PEEM measurement as a function of the photoemission threshold difference ࢤࢶ between filament and reference area. The error bars indicate the measured resistances before and after the PEEM measurement. The dotted line is a guide to the eye only. The average value is used because the device resistance changed during investigation. (b) Schematic band diagram for the LRS and HRS demonstrating how the SrTiO3 photoemission threshold, valence band (VB) and conduction band (CB) shift for different oxygen vacancy concentrations. Occupied states are indicated in black, unoccupied states are white. Panel (b) was modified with permission from Ref. 30. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Figure 4: (a) PEEM image of a graphene/SrTiO3/Nb:SrTiO3 device under consideration with a photon energy of 538.2 eV. The diagonal brighter stripe is the footprint of the synchrotron beam. (b) PEEM image of the same device imaged at a higher magnification (photon energy of 538.2 eV). The red arrow indicates the conductive filament. (c) Image representing the ratio of LRS PEEM images acquired at photon energies of 530.2 (A) and 537.1 eV (B2), as indicated by the labels in the O K-edge spectrum shown in (e). (d) Image representing the ratio of HRS PEEM images acquired at photon energies of 530.2 (A) and 537.1 eV (B2). (e) O K-edge for the filament (averaged over the entire filament) in the LRS (red line) and the surrounding device area (black line). (f) O K-edge for the filament in the HRS (blue line) and the surrounding device area (black line) extracted from the same ROI as in (e). (g) Ti Ledge for the filament in the LRS (red line) and the surrounding device area (black line). (h) Ti L-edge for the filament in the HRS (blue line) and the surrounding device area (black line). All were background corrected by a linear fit of the pre-edge and subsequent normalization by fitting a third-order polynomial to the post-edge using the Athena software.36 Figure 5: (a) PEEM image of another graphene/Al2O3/SrTiO3 device in the LRS at an electron energy ࡱ − ࡱࡲ of 3.45 eV. Scale bar, 5 µm. (b) PEEM image after a Reset operation. (c) and (d) PEEM images after additional Set and Reset operations, respectively. Insets: magnified photoemission threshold map of the area around the suspected


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conductive filaments. (e) Threshold photoelectron spectra extracted from the filament active during the first switching cycle. (f) Threshold photoelectron spectra extracted from the filament active during the second switching cycle. Figure 6: (a) PEEM image of the LRS II of the device in Figure 2. Colored rectangles indicate regions of interest (ROIs) for extracted spectra. (b) Photoemission spectra extracted from the ROIs indicated in (a). For the filament indicated in red, a much more pronounced threshold shift is evident than for the other features. (c) Photoemission threshold map for the entire device area confirming the observations in panel (b). (d) Photoemission threshold differences between LRS II and HRS II for each feature indicated in (a). Figure 7: Schematic representation of the filamentary changes causing the C2C variability. (a) A representative device in the HRS. Rather many pre-filaments can be seen. (b) A representative device in the LRS. A rather large region with many pre-filaments and one conductive filament connecting top and bottom electrode can be seen. In another location, single pre-filaments may exist. (c) Situation I (“Changes of in the shape of the filament”): After Reset and Set, the original conductive filament does not connect bottom and top electrode, but another conductive filament in the immediate surrounding was created. (d) Situation II (“Changes of the filament location”): Alternatively, Reset and Set may create a conductive filament in a new location farther away from the original filament.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions C.B. and R.D. conceived and designed the experiments. C.B., R.V., S.P.R. and N.R. fabricated the samples. C.B., and R.V. performed the threshold photoelectron analysis. C.B., C.S., A.L., T.O.M., A.S. and N.R. performed the XPEEM experiments. C.B. and R.V. analyzed the 17 ACS Paragon Plus Environment

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experimental data. C.B. wrote the manuscript. S.N., M.S., C.M.S., S.M., R.W. and R.D. supervised the research. All authors discussed the results and commented on the manuscript. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT Funding from the DFG (German Science Foundation) within the collaborative research center SFB 917 ‘Nanoswitches’ is gratefully acknowledged. C.B. and R.D. also acknowledge funding from the W2/W3 program of the Helmholtz association. M.S. acknowledges support from the National Science Foundation under grant DMR-1507170. We thank Dr. D. Wouters for critical reading of the manuscript and J. Hackl and M. I. Khan for support during the synchrotron experiments at Bessy II.

SUPPORTING INFORMATION Supporting Information Available: C2C variability measurements in pulsed operation. Discussion of graphene contribution to the photoemission threshold. XPEEM analysis of the filament from figure 2. Spatial distribution of the Ti3+ contribution. This material is available free of charge via the Internet at http://pubs.acs.org

REFERENCES 18 ACS Paragon Plus Environment

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Figure 1. (a) Schematic of the device geometry. A SrTiO3 layer (blue) is sandwiched between a Nb:SrTiO3 bottom electrode (dark grey) and graphene top electrode (grey honeycomb lattice). The graphene electrode is contacted through a metal lead, which is electrically separated from the continuous bottom electrode, allowing for biasing inside PEEM instruments. (b) Quasistatic I-V curve of a representative graphene/SrTiO3/Nb:SrTiO3 device operated with a current limit of 30 mA controlled by Keithley 2611A source meter. The bottom electrode serves as virtual ground, while the bias is applied to the graphene top electrode. (c) LRS and HRS resistance extracted from 150 switching cycles of the same device (resistance value at 80 mV). (d) Weibull plot of the resistance distribution for the measurement shown in (c). 86x88mm (600 x 600 DPI)

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Figure 2: (a) PEEM image of a graphene/Al2O3/SrTiO3 device in the LRS at an electron energy E-E_F of 3.4 eV. Scale bar, 5 µm. (b) PEEM image of the same device after Reset. (c) and (d) PEEM images after additional Set and Reset operations, respectively. Insets: magnified photoemission threshold map of the area around the conductive filament. The maps were obtained by fitting the threshold spectrum for each pixel26. (e) Threshold photoelectron spectra extracted from the filament and a reference region close to the filament. (f) Evolution of device resistance during the switching cycle for the PEEM investigation. 125x185mm (600 x 600 DPI)


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Figure 3: (a) Average value of the device resistance before and after each PEEM measurement as a function of work function difference ∆Φ between filament and reference area. The error bars indicate the measured resistances before and after the PEEM measurement. The dotted line is a guide to the eye only. The average value is used because the device resistance changed during investigation. (b) Schematic band diagram for the LRS and HRS demonstrating how the SrTiO3 photoemission threshold, valence band (VB) and conduction band (CB) shift for different oxygen vacancy concentrations. Occupied states are indicated in black, unoccupied states are white. Panel (b) was modified with permission from Ref. 25. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 119x169mm (300 x 300 DPI)


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Figure 4: (a) PEEM image of a graphene/SrTiO3/Nb:SrTiO3 device under consideration with a photon energy of 538.2 eV. The diagonal brighter stripe is the footprint of the synchrotron beam. (b) PEEM image of the same device imaged at a higher magnification (photon energy of 538.2 eV). The red arrow indicates the conductive filament. (c) Image representing the ratio of LRS PEEM images acquired at photon energies of 530.2 (A) and 537.1 eV (B2), as indicated by the labels in the O K-edge spectrum shown in (e). (d) Image representing the ratio of HRS PEEM images acquired at photon energies of 530.2 (A) and 537.1 eV (B2). (e) O K-edge for the filament (averaged over the entire filament) in the LRS (red line) and the surrounding device area (black line). (f) O K-edge for the filament in the HRS (blue line) and the surrounding device area (black line) extracted from the same ROI as in (e). (g) Ti L-edge for the filament in the LRS (red line) and the surrounding device area (black line). (h) Ti L-edge for the filament in the HRS (blue line) and the surrounding device area (black line). All were background corrected by a linear fit of the pre-edge and subsequent normalization by fitting a third-order polynomial to the post-edge using the Athena software.30


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ACS Nano

Figure 5: (a) PEEM image of another graphene/Al2O3/SrTiO3 device in the LRS at an electron energy E-E_F of 3.45 eV. Scale bar, 5 µm. (b) PEEM image after a Reset operation. (c) and (d) PEEM images after additional Set and Reset operations, respectively. Insets: magnified photoemission threshold map of the area around the suspected conductive filaments. (e) Threshold photoelectron spectra extracted from the filament active during the first switching cycle. (f) Threshold photoelectron spectra extracted from the filament active during the second switching cycle. 125x185mm (600 x 600 DPI)


ACS Nano

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Figure 6: (a) PEEM image of the LRS II of the device in Figure 2. Colored rectangles indicate regions of interest (ROIs) for extracted spectra. (b) Photoemission spectra extracted from the ROIs indicated in (a). For the filament indicated in red, a much more pronounced threshold shift is evident than for the other features. (c) Photoemission threshold map for the entire device area confirming the observations in panel (b). (d) Photoemission threshold differences between LRS II and HRS II for each feature indicated in (a). 86x89mm (600 x 600 DPI)


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ACS Nano

Figure 7: Schematic representation of the filamentary changes causing the C2C variability. (a) A representative device in the HRS. Rather many pre-filaments can be seen. (b) A representative device in the LRS. A rather large region with many pre-filaments and one conductive filament connecting top and bottom electrode can be seen. In another location, single pre-filaments may exist. (c) Situation I (“Changes of in the shape of the filament”): After Reset and Set, the original conductive filament does not connect bottom and top electrode, but another conductive filament in the immediate surrounding was created. (d) Situation II (“Changes of the filament location”): Alternatively, Reset and Set may create a conductive filament in a new location farther away from the original filament. 119x167mm (300 x 300 DPI)


ACS Nano

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TOC graphic 82x44mm (300 x 300 DPI)


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Subfilamentary Networks Cause Cycle-to-Cycle Variability in

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