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In-Gap States and Band-Like Transport in Memristive Devices Christoph Bäumer, Carsten Funck, Andrea Locatelli, Tevfik Onur Mente#, Francesca Genuzio, Thomas Heisig, Felix Hensling, Nicolas Raab, Claus M. Schneider, Stephan Menzel, Rainer Waser, and Regina Dittmann Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03023 • Publication Date (Web): 21 Sep 2018 Downloaded from http://pubs.acs.org on September 23, 2018

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In-Gap States and Band-Like Transport in Memristive Devices Christoph Baeumer1*, Carsten Funck2, Andrea Locatelli3, Tevfik Onur Menteş3, Francesca Genuzio3, Thomas Heisig1, Felix Hensling1, Nicolas Raab1, Claus M. Schneider1, Stephan Menzel1, Rainer Waser1,2, Regina Dittmann1 1 2 3 *

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

KEYWORDS: In-gap states; resistive switching; electronic structure; electronic transport; SrTiO3

ABSTRACT Point defects such as oxygen vacancies cause emergent phenomena like resistive switching in transition metal oxides, but their influence on the electronic transport properties is far from being understood. Here, we employ direct mapping of the electronic structure of a memristive device by spectromicroscopy. We find that oxygen vacancies result in in-gap states which we use as input for single band transport simulations. Since the in-gap states are situated below the Fermi level, they do not contribute to the current directly, but impact the shape of the conduction band. Accordingly, we can describe our devices with band-like transport and tunneling across the Schottky-barrier at the interface.

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The creation of point defects in matter can profoundly affect the physical and chemical properties of materials 1. If appropriately controlled, these modifications can be exploited in applications promising advanced and novel functionalities. Redox-based memristive devices – one of the most attractive emerging memory technologies – provide one of the most striking examples for the potential exploitation of defects

2-5

. Applying an external electric field to an

initially insulating oxide layer is known to induce a non-volatile switching between a low resistance state (LRS) and a high resistance state (HRS). This switching occurs through the creation and annihilation of the so-called conductive filaments, which are generated at the nanoscale by assembly of donor-type point defects, namely oxygen vacancies or cation interstitials 6-13. The electron transport mechanism giving rise to these resistance states critically depends on the material characteristics at both atomic and mesoscopic length-scales, as well as on the abundance and spatial arrangement of the defects 4, 14-15. To optimize the performance of oxidebased electronic devices in general and memristive devices in particular, it is of paramount importance to acquire a basic understanding of the electronic structure and the transport properties of the material, which in turn govern the electrical resistance, i.e., the key state variable of these cells. To date, the exact relationship between concentration and nanoscale distribution of the defects and the electronic properties is still under debate owing to the existence of different competing transport mechanisms: Schottky emission, Fowler–Nordheim tunneling, direct tunneling and trap-assisted tunneling, to name just a few 4. Further, the reduced spatial dimensions of these devices make it rather challenging to distinguish bulk and interface effects 14. Due to limitations in sensitivity or spatial resolution of most characterization methods, the electronic structure of the conductive filament has not yet been characterized. As an 2


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alternative to this approach, analytical conduction models are typically used to fit experimental current-voltage data and assess plausible conduction mechanisms 16-23. In particular, trap-assisted tunnelling mechanisms have been widely postulated

14-15, 24-29

. As we recently showed, such

fitting based on analytical models contains an inherent risk for misinterpretation

30

. Therefore,

other means for determining the conduction mechanism must be found. Aiming at solving the above issue, we focus here on the well-known memristive model material SrTiO3-x, for which different descriptions of electronic transport have been proposed. Whereas it is agreed upon that oxygen vacancies are responsible for the resistance change, it is strongly debated how they affect the electronic structure to give rise to a conducting state. In agreement with other reports, we previously described the switching behaviour and the electronic conduction in SrTiO3-x through band transport and tunnelling through a Schottky barrier 6, 16-17, 3033

. In contrast, other groups found indications for trap-assisted tunnelling or (small polaron)

hopping mechanisms

34, 35

, for example at very low

36

or very high carrier concentrations 37. To

further complicate the scenario, the coexistence of both mechanisms was suggested theoretically 38, 39

and experimentally

40-42

. Given the multitude of contradicting models used to describe this

material, a direct experimental characterization of the electronic structure of the conductive filament is mandatory. With this in mind, we characterized the electronic structure of epitaxial SrTiO3-x -based memristive devices and compare it to that of single crystalline SrTiO3-x. To gain access to the defect states in the band gap, we employed soft X-ray resonant photoelectron spectroscopy (RESPES), which allows element-specific measurement of valence and defect levels of SrTiO3-x through resonant emission when the excitation energy corresponds to an absorption edge

40

.

Importantly, these measurements were carried out in a photoelectron emission microscope 3


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(PEEM) setup at the Nanospectroscopy beamline of Elettra synchrotron laboratory

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43

, enabling

us to spatially resolve the filament in the memristive device and presenting the first report of spatially resolved RESPES, a powerful tool to map the electronic structure of small features.

Figure 1: (a) Ti 2p3/2 level of a SrTiO3-x single crystal. (b) Ti 2p3/2 level as a function of time and pressure (c) RESPES map measured under reducing conditions. (d) RESPES map measured under oxidizing conditions and Ti L edge for reference. In both cases, second order light was subtracted from the RESPES map, see Supplementary Figures S1-S4. (e) Valence Band spectra. (f) Zoom-in for the valence band spectrum in reducing conditions.

In a first step, we investigated the spectroscopic fingerprint of oxygen vacancies in SrTiO3x

single crystals. The vacancies can be formed upon irradiation with an intense soft X-ray beam 4


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in ultra-high vacuum

32, 44

. Following this approach, we irradiated a micron-sized region of the

SrTiO3-x single crystal with the micro-focused soft X-ray beam serving the PEEM microscope and probed the stoichiometry and electronic structure using X-ray photoelectron spectroscopy (XPS) and RESPES. During irradiation, we monitored the Ti 2p3/2 core level emission (see Supplementary Methods for details) and characterized the Ti valence state (Figure 1a). Under UHV conditions (base pressure of 2 × 10 mbar) we found a mixture of Ti4+ and Ti3+, indicating formation of oxygen vacancies, consistent with the available literature

32, 42, 44

. Upon

exposure to oxygen at 5 × 10 mbar, we found that the SrTiO3-x re-oxidizes readily, exhibiting only Ti4+ states. This indicates that the vacancy formation process is fully reversible, in agreement with an earlier report 42. Notably, for both reducing and oxidizing conditions, a steady redox state establishes quickly (Figure 1b). Thus, we have access to a model system of SrTiO3-x with a high and low abundance of oxygen vacancies, for reducing and oxidizing conditions, respectively. In the next step, we probed the occupied part of the electronic states near the Fermi energy using laterally-averaged RESPES. To this end, the valence band and the possibly occupied states within the band gap were mapped as a function of photon energy (Figure 1c-e) near the Ti L absorption edge (see Supplementary Methods for details). The relative position of the Fermi energy changes from the oxidized to the reduced case, as can be seen from the binding energy position of the valence band maximum (VBM), which can be extracted from the zerophotoemission intensity intercept of a linear regression fit of the low-binding-energy edge of the valence band spectra 45. For the oxidized and reduced case, respectively, the VBM is at ~2.71 eV and ~2.98 eV below the Fermi-level = 0 eV, indicating that the Fermi-level is ~270 meV

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closer to the conduction band for the reduced case, similar to previous observations

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42

and in

accordance with the ~280 meV shift observed for the Ti 2p3/2 photoemission peak (Figure 1a).

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Figure 2: (a) I-V curve of a memristive SrTiO3-x device. (b) Schematic of electrode removal and PEEM

investigation. (c) Secondary electron image of the device.

Interestingly, we find occupied states of Ti 3d character between the Fermi energy and the valence band for the reduced case (light blue/green spots at photon energies ~458.9 eV and ~464.1 eV in Figure 1c), which are absent in the oxidized case (Figure 1d and e), suggesting that

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they are caused by the existence of oxygen vacancies. These in-gap states have relative maxima at ~0.31 eV and ~1.11 eV below the conduction band (calculated using the VBM and the electronic band gap of SrTiO3-x of 3.2 eV

46

, Figure 1f), and the photon energies at which they

are observed indicate that these states are of Ti3+ eg character, as observed before for similar ingap states

40

. These energy levels can be interpreted as the defect states for singly and doubly

charged oxygen vacancies

37, 47

. Combined with the relative position of the Fermi level, these

states are the key features of the electronic structure induced by a high density of oxygen vacancies in SrTiO3-x.

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We now turn to the investigation of a memristive SrTiO3-x device. A 20 nm epitaxial SrTiO3-x layer was sandwiched between a Pt top electrode and a Nb:SrTiO3 bottom electrode, allowing for reproducible switching with high on/off ratio (Figure 2a). The first application of

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positive voltages to the top electrode led to a forming step, resulting in the LRS. Afterwards, the device was switched to the HRS using negative voltage and back to the LRS before spectromicroscopic investigation. Sufficient retention was guaranteed through the choice of slightly Sr-rich SrTiO3

48

. After mechanical removal of the top electrode

49

(Figure 2b, see

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Supplementary Methods for details), the device was imaged using secondary electrons, revealing an irregularly shaped region of darker contrast (Figure 2c), which, for the moment, we tentatively attribute to be the conductive filament. The conductive filament is comparably large (several µm2) due to the intentional use of a very high current limit during the forming process to

Figure 3: (a) Ti3+ map based on the Ti 3p3/2 spectrum. (b) Ti 2p3/2 spectra for the filament and the surrounding. (c) Spatial map of the in-gap state distribution. (d) Valence band spectrum extracted from the filament with a fit of the valence band maximum and the in-gap states (red lines).

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facilitate spectromicroscopic investigation 50, 51.

Using an intermediate oxygen pressure of 2 × 10 mbar, which does not generate or annihilate substantial amounts of oxygen vacancies within the measurement time, we recorded the Ti 3p core level for this device in real space. The conductive filament corresponds to an inhomogeneously reduced SrTiO3-x with up to 30 % Ti3+ (Figure 3a and b), while the

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surrounding device area is composed almost entirely of Ti4+. This confirms that – as expected – the filamentary valence change mechanism is responsible for the observed resistance change. At the same time, the coexistence of reduced and oxidized regions confirms that at this pressure, the oxygen vacancy concentration can be mapped without beam-induced artifacts. In the next step, we mapped the valence band region in real space at a photon energy of 463.3 eV, an energy at which we could detect the in-gap states induced by the oxygen vacancies in the single crystalline reference. Again, we observe a clear contrast in the region of the conductive filament for the energies corresponding to the in-gap states (Figure 3c). Extracting spectra from the filament and

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the surrounding region reveals that only the former exhibits significant weight of the in-gap states in the spectra (Figure 3d), whereas no in-gap states can be detected for the surrounding area. This first application of spatially resolved RESPES thus allowed us to experimentally probe the defect electronic structure of the conductive filament. The filament formation goes along with the existence of in-gap states, which lie at the same energy positions compared to the valence band maximum as found for the reduced single crystalline reference (Figure 3d), indicating they are caused by the presence of oxygen vacancies. These states could represent the small polaron states found in DFT simulation 37, giving rise to trap-assisted, small polaron-like transport as often invoked for memristive devices. Importantly, we also found that the VBM for 9


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the filament area is 2.89 eV. Note that because of the electrode removal prior to measurement, we thus probed the SrTiO3-x surface without the Schottky junction. Given that the Fermi level is very close to the conduction band, band transport must be considered. Band transport is indeed a very likely scenario, as Janotti et al. showed that despite the existence of defect levels within the band gap, a large fraction of electrons will be located within the conduction band

38

. So upon

intuitive consideration of the experimental fingerprint of the electronic structure, one might argue for either defect-mediated transport or band-like transport. To assess this situation more deliberately, we will now determine if band-like transport including the tunneling at the Schottky interface is consistent with our measurements of the filamentary electronic structure. For this purpose, we used the experimental insights to simulate the band diagram and electronic current transport for the device applying single-band transport theory. The implemented model is close to the electron drift-diffusion model published by Marchewka et al. 52, a detailed description is shown in the Supplementary Information. In short, we self-consistently solved a coupled equation system of Poisson equation, charge conservation law and current transport equation based on the gradient of the quasi-Fermi-level

∇ε fn .

The

tunneling probability through the Schottky barrier was calculated by the WKB approximation and integrated into the charge conversation law by an energy dependent generation rate. The simulation model is implemented within in one dimension and therefore only describes the current transport within the filament, a justified simplification given that the largest part of current transport necessarily occurs via the filament in the LRS. One of the main outcomes of the PEEM characterization is the position of the defect states within the band gap. The two peaks are consistent with the interpretation of oxygen vacancies as 10


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twofold donors with ionization energies ED1 and ED2, as indicated in Figure 1, which can be

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described using the Fermi-Dirac statistic for twofold donors as applied in 52, 53. The concentration of singly positively charged oxygen vacancies is calculated by  Ec − ε f ED1  1 N VO exp  −  2 kBT   kBT  V  =  Ec − ε f ED1   Ec − ε f ED1 + ED2  1 1 + N VO exp  − −  + exp  2  2 kBT  kBT kBT   kBT  • O

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(1)

and twofold positively charged oxygen vacancies by

 VO••  =

 E − ε fn ED1 + ED2  N VO exp  2 c −  k BT kBT   . E − E − ε ε    E E + ED2  1 fn fn 1 + N VO exp  c − D1  + exp  2 c − D1  kBT  kBT kBT  2  k BT 

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(2)

To test if the interpretation as donor levels is consistent with the experimentally observed electronic transport properties we used the previously unavailable experimental values of ED1 and ED2 as an input for the simulation model. The band diagram obtained by the self-consistent solution is shown in Figure 4a. It shows a parabolic conduction band increase within the depletion zone at the Pt Schottky interface. At the Nb:SrTiO3 contact, we find a small depletion region at the Nb:SrTiO3 site leading to flat bands. In between, the conduction band increases linearly, because a depletion zone is generated by the different work functions at the contact between Nb:SrTiO3 and SrTiO3-x. As the Fermi-level is located below the conduction band within the SrTiO3-x layer, three processes may limit the current transport: Within the bulk, only thermally excited band-like transport is plausible, as the distance is too large for tunneling; in the vicinity of the Pt interface, the transport across the Schottky barrier may be dominated by either thermionic emission or tunneling processes.

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As the conduction band is located above the Fermi-level only thermally excited charge carriers can be injected into the SrTiO3-x resistive switching layer. Therefore, the calculation results in a temperature dependent j-V characteristic, with a monotonic increase in the current for higher temperatures T (Figure 4 b). Further, we find that all j-V curves are parallel. Therefore, the current appears to be limited by a voltage-independent thermal activation process. To clarify at which energy level the current transport occurs, i.e., to which energy the electrons must be thermally activated for significant current contribution, we define the spectral current density

Figure 4: (a) Band diagram of the device calculated based on the position of the in-gap states. The blue line show the conduction band and the dashed green lines shows position of the defect states obtained by PEEM in respect to the conduction band (b) Current density-voltage dependence within the conductive filament obtained from the simulation for different temperatures in 10 K steps between 203 K and 303 K. (c) Charging probability for singly charged oxygen vacancies and doubly charged oxygen vacancies according to equation (1) and (2) (d) Calculations of the modulation of the Schottky barrier under selected external voltages (V=0.1-0.5). Spectral

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current density for five different voltages of (V=0.1-0.5).

$j ( E ) = d j ( E ) . dE

(3)

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The spectral current describes the current density which is injected into the Pt metal electrode at each energy E. The zero level of the energy (E=0) is set to the Fermi-level. A peaklike distribution occurs, i.e., most current flows at a specific energy level (Figure 4d). As the

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peak is located above the Fermi-level at 0 eV, the temperature dependence of the device is a direct outcome. The most important information gained by the spectral current density is the position of the peak, which is the same for all applied voltages, i.e. 0.31 eV. This confirms that the current transport occurs at one voltage-independent energy level, resulting in parallel J-V curves for different temperatures. This energy level corresponds to the energy level . = − shown in the calculated band diagram, which marks the onset of the Schottky depletion region. In the PEEM characterization we found not only the position of the ionization energies used for the simulation, but also the valence band offset and, hence, the value − at the SrTiO3-x surface (after removal of the Pt electrode, without applied bias). As one may expect, this experimental result of − = 0.31 eV at the SrTiO3-x surface is almost identical to the simulated result. Hence, we can describe the electronic transport in forward direction as band like-transport of thermally excited electrons in the conduction band within the SrTiO3-x bulk, which are injected into the SrTiO3-x from the Nb:SrTiO3 electrode, and direct tunneling through the Schottky depletion region close to the Pt interface. Throughout this process, the in-gap states within the SrTiO3-x bulk remain almost completely filled, as their energetical position is located well below the Fermi-energy (Figure 4c), so that a significant contribution from hopping 13


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conduction or trap assisted tunneling can be disregarded. Summarizing, the observation of the ingap states are not in opposition to the proposed band transport. Rather than contributing to the conduction directly, the defect levels affect the overall band structure, enabling the injection of mobile carriers from the Nb:SrTiO3 into the conduction band of SrTiO3-x, which then dominates the transport in SrTiO3-x. Coming back to the original question of how to describe the electronic transport in a memristive device correctly, we have shown that dedicated combination of experiment and simulation, including direct experimental probes of the electronic structure of the filament using spatially resolved RESPES rather than only transport measurements, allowed us to deduce the prevailing mechanisms. For the model material investigated here and, presumably, any oxide material with a similar band gap and defect levels, band transport is the correct descriptor, despite the existence of in-gap states. Our simulation, which used the experimentally determined defect levels as an input, revealed that most of the current transport occurs at energies above the Fermi level, i.e., the conduction band offset − , which is in remarkable agreement with the experimentally determined value. For memristive devices with oxides of larger band gap such as HfO2, the impact of in-gap states on the electronic transport properties might be different from the case described here, yet our experimental approach presents a novel pathway to determine these properties for each type of device.

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FIGURES

Figure 1: (a) Ti 2p3/2 level of a SrTiO3-x single crystal. (b) Ti 2p3/2 level as a function of time and pressure (c) RESPES map measured under reducing conditions. (d) RESPES map measured under oxidizing conditions and Ti L edge for reference. In both cases, second order light was subtracted from the RESPES map, see Supplementary Figures S1-S4. (e) Valence Band spectra. (f) Zoom-in for the valence band spectrum in reducing conditions.

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Figure 2: (a) I-V curve of a memristive SrTiO3-x device. (b) Schematic of electrode removal and PEEM

investigation. (c) Secondary electron image of the device.

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Figure 3: (a) Ti3+ map based on the Ti 3p3/2 spectrum. (b) Ti 2p3/2 spectra for the filament and the surrounding. (c) Spatial map of the in-gap state distribution. (d) Valence band spectrum extracted from the filament with a fit of the valence band maximum and the in-gap states (red lines).

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Figure 4: (a) Band diagram of the device calculated based on the position of the in-gap states. The blue line show the conduction band and the dashed green lines shows position of the defect states obtained by PEEM in respect to the conduction band (b) Current density-voltage dependence within the conductive filament obtained from the simulation for different temperatures in 10 K steps between 203 K and 303 K. (c) Charging probability for singly charged oxygen vacancies and doubly charged oxygen vacancies according to equation (1) and (2) (d) Calculations of the modulation of the Schottky barrier under selected external voltages (V=0.1-0.5). Spectral current density for five different voltages of (V=0.1-0.5).

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Formatted: English (U.S.)

SUPPORTING INFORMATION Methods: Device fabrication, electrical characterization, top electrode removal, and Spectromicroscopy. Energy calibration of the dispersive plane. Subtracting second order light. Dependence of the oxidation state on the oxygen pressure. Simulation model. Thermionic emission approximation. Thermionic emission fit. Discussion of electronic conduction in reverse direction. This material is available free of charge via the Internet at http://pubs.acs.org. ACKNOWLEDGMENT Funding from the DFG (German Science Foundation) within the collaborative research center SFB 917 ‘Nanoswitches’ is gratefully acknowledged. C.B., T.H. and R.D. also acknowledge funding from the W2/W3 program of the Helmholtz association. C. F. and S. M. gratefully acknowledge the computing time granted by the JARA-HPC Vergabegremium and VSR commission on the supercomputer JURECA at Forschungszentrum Jülich. We thank Dr. S. Karthäuser and Dr. M. Moors for critical discussions and Dr. C. Schmitz for synchrotron beamtime assistance.

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REFERENCES 1.

Tuller, H.; Bishop, S. Point Defects in Oxides: Tailoring Materials Through Defect Engineering. Annu. Rev. Mater. Res. 2011, 41, 369-398.

2.

Waser, R.; Aono, M. Nanoionics-based resistive switching memories. Nat. Mater. 2007, 6, 833-840.

3.

Lee, M.-J.; Lee, C. B.; Lee, D.; Lee, S. R.; Chang, M.; Hur, J. H.; Kim, Y.-B.; Kim, C. -J.; Seo, D. H.; Seo, S.; Chung, U.-I.; Yoo, I.-K.; Kim, K. A fast, high-endurance and scalable non-volatile memory device made from asymmetric Ta2O5-x/TaO2-x bilayer structures. Nat. Mater. 2011, 10, 625-630.

4.

Yang, J. J.; Strukov, D. B.; Stewart, D. R. Memristive Devices for Computing. Nat. Nanotechnol. 2013, 8, 13-24.

5.

Baeumer, C.; Dittmann, R. Redox-based memristive metal-oxide devices. Elsevier, Amsterdam 2018, 489-522.

6.

Baeumer, C.; Schmitz, C.; Marchewka, A.; Mueller, D. N.; Valenta, R.; Hackl, J.; Raab, N.; Rogers, S. P.; Khan, M. I.; Nemsak, S.; Shim, M.; Menzel, S.; Schneider, C. M.; Waser, R.; Dittmann, R. Quantifying redox-induced Schottky barrier variations in memristive devices via in operando spectromicroscopy with graphene electrodes. Nat. Commun. 2016, 7, 12398.

7.

Dirkmann, S.; Kaiser, J.; Wenger, C.; Mussenbrock, T. Filament Growth and Resistive Switching in Hafnium Oxide Memristive Devices. ACS Appl. Mater. Interfaces 2018, 10, 14857-14868. 20


Page 20 of 34

Page 21 of 34 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

8.

Nano Letters

Yang, Y.; Zhang, X.; Qin, L.; Zeng, Q.; Qiu, X.; Huang, R. Probing nanoscale oxygen ion motion in memristive systems. Nature Communications 2017, 8, 15173.

9.

Xue, K.; Traore, B.; Blaise, P.; Fonseca, L.; Vianello, E.; Molas, G.; De Salvo, B.; Ghibaudo, G.; Magyari-Kope, B.; Nishi, Y. A Combined Ab Initio and Experimental Study on the Nature of Conductive Filaments in rmPt/HfO2/Pt Resistive Random Access Memory. Electron Devices, IEEE Transactions on 2014, 61, 1394-1402.

10.

Celano, U.; Goux, L.; Degraeve, R.; Fantini, A.; Richard, O.; Bender, H.; Jurczak, M.; Vandervorst, W. Imaging the Three-Dimensional Conductive Channel in FilamentaryBased Oxide Resistive Switching Memory. Nano Letters 2015, 15, 7970-7975.

11.

Du, H.; Jia, C.; Koehl, A.; Barthel, J.; Dittmann, R.; Waser, R.; Mayer, J. Nanosized conducting filaments formed by atomic-scale defects in redox-based resistive switching memories. Chem. Mater. 2017, 29, 3164-3173.

12.

Cooper, D.; Baeumer, C.; Bernier, N.; Marchewka, A.; La Torre, C.; Dunin-Borkowski, R. E.; Menzel, S.; Waser, R.; Dittmann, R. Anomalous Resistance Hysteresis in Oxide ReRAM: Oxygen Evolution and Reincorporation Revealed by in situ TEM. Adv. Mater. 2017, 29, 1700212.

13.

Wedig, A.; Luebben, M.; Cho, D.-Y.; Moors, M.; Skaja, K.; Rana, V.; Hasegawa, T.; Adepalli, K.; Yildiz, B.; Waser, R.; Valov, I. Nanoscale cation motion in TaOx, HfOx and TiOx memristive systems. Nat. Nanotechnol. 2016, 11, 67-74.

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Nano Letters 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

14.

Nakamura, H.; Asai, Y. Competitive effects of oxygen vacancy formation and interfacial oxidation on an ultra-thin HfO2-based resistive switching memory: beyond filament and charge hopping models. Physical Chemistry Chemical Physics 2016, 18, 8820-8826.

15.

Wang, M.; Bi, C.; Li, L.; Long, S.; Liu, Q.; Lv, H.; Lu, N.; Sun, P.; Liu, M. Thermoelectric Seebeck effect in oxide-based resistive switching memory. Nature Communications 2014, 5, 4598/1-.

16.

Lee, E.; Gwon, M.; Kim, D. W.; Kim, H. Resistance state-dependent barrier inhomogeneity and transport mechanisms in resistive-switching Pt/SrTiO3 junctions. Appl. Phys. Lett. 2011, 98, 132905/1-3.

17.

Kim, H.; Park, C.; Lee, S.; Kim, D. W. Inhomogeneous barrier and hysteretic transport properties of Pt/SrTiO3 junctions. J. Phys. D Appl. Phys. 2009, 42, 55306/1-3.

18.

Mikheev, E.; Hwang, J.; Kajdos, A. P.; Hauser, A. J.; Stemmer, S. Tailoring resistive switching in {Pt}/{SrTiO}3 junctions by stoichiometry control. Scientific Reports 2015, 5, 11079.

19.

Kim, K.; Choi, B.; Lee, M.; Kim, G.; Song, S.; Seok, J.; Yoon, J.; Han, S.; Hwang, C. A detailed understanding of the electronic bipolar resistance switching behavior in Pt/TiO2/Pt structure. Nanotechnology 2011, 22

20.

Walczyk, C.; Walczyk, D.; Schroeder, T.; Bertaud, T.; Sowinska, M.; Lukosius, M.; Fraschke, M.; Wolansky, D.; Tillack, B.; Miranda, E.; Wenger, C. Impact of Temperature on the Resistive Switching Behavior of Embedded HfO2-Based RRAM Devices. IEEE Trans. Electron Devices 2011, 58, 3124-3131. 22


Page 22 of 34

Page 23 of 34 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

21.

Nano Letters

Yu, S.; Guan, X.; Wong, H. P. Conduction mechanism of TiN/HfOx/Pt resistive switching memory: A trap-assisted-tunneling model. Appl. Phys. Lett. 2011, 99, 063507-063507.

22.

Miao, F.; Strachan, J. P.; Yang, J. J.; Zhang, M.-X.; Goldfarb, I.; Torrezan, A. C.; Eschbach, P.; Kelly, R. D.; Medeiros-Ribeiro, G.; Williams, R. S. Anatomy of a Nanoscale Conduction Channel Reveals the Mechanism of a High-Performance Memristor. Advanced Materials 2011, 23, 5633.

23.

Syu, Y.-E.; Chang, T.-C.; Lou, J.-H.; Tsai, T.-M.; Chang, K.-C.; Tsai, M.-J.; Wang, Y.-L.; Liu, M.; Sze, S. M. Atomic-level quantized reaction of HfOx memristor. Appl. Phys. Lett. 2013, 102, 172903.

24.

Abbaspour, E.; Menzel, S.; Jungemann, C. KMC Simulation of the Electroforming, Set and Reset Processes in Redox-based Resistive Switching Devices. In 2016 International Conference On Simulation of Semiconductor Processes and Devices (SISPAD), Nuremberg, Germany, September 6-8, 2016; 2016 International Conference On Simulation of Semiconductor Processes and Devices (SISPAD), Nuremberg, Germany, September 68, 2016, 2016; pp 141 - 144.

25.

Chiu, F. C. Conduction Mechanisms in Resistance Switching Memory Devices Using Transparent Boron Doped Zinc Oxide Films. Materials 2014, 7, 7339-7348.

26.

Vandelli, L.; Padovani, A.; Larcher, L.; Bersuker, G. Microscopic Modeling of Electrical Stress-Induced Breakdown in Poly-Crystalline Hafnium Oxide Dielectrics. IEEE Trans. Electron Devices 2013, 60, 1754-1762.

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Nano Letters 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

27.

Page 24 of 34

Butcher, B.; Bersuker, G.; Gilmer, D.; Larcher, L.; Padovani, A.; Vandelli, L.; Geer, R.; Kirsch, P. Connecting the physical and electrical properties of Hafnia-based RRAM. In Electron Devices Meeting (IEDM), 2013 IEEE International; Electron Devices Meeting (IEDM), 2013 IEEE International, 2013; pp 22.2.1-22.2.4.

28.

Wei, Z.; Eriguchi, K. Analytic Modeling for Nanoscale Resistive Filament Variation in ReRAM with Stochastic Differential Equation. IEEE Trans. Electron Devices 2017, 64, 2201-2206.

29.

Gritsenko, V. A.; Perevalov, T. V.; Voronkovskii, V. A.; Gismatulin, A. A.; Kruchinin, V. N.; Aliev, V. Sh.; Pustovarov, V. A.; Prosvirin, I. P.; Roizin, Y. Charge Transport and the Nature of Traps in Oxygen Deficient Tantalum Oxide. ACS Appl. Mater. Interfaces 2018, 10, 3769-3775.

30.

Funck, C.; Marchewka, A.; Baeumer, C.; Schmidt, P. C.; Mueller, P.; Dittmann, R.; Martin, M.; Waser, R.; Menzel, S. A Theoretical and Experimental View on the Temperature Dependence of the Electronic Conduction through a Schottky Barrier in a Resistively Switching SrTiO3-based Memory Cell. Adv. Electron. Mater. 2018, 4, 1800062

31.

Marchewka, A.; Waser, R.; Menzel, S. Physical Simulation of Dynamic Resistive Switching in Metal Oxides Using a Schottky Contact Barrier Model. In 2015 International Conference On Simulation of Semiconductor Processes and Devices (SISPAD), 9-11 September, Washington D.C, USA; 2015 International Conference On Simulation of Semiconductor Processes and Devices (SISPAD), 9-11 September, Washington D.C, USA, 2015; pp 297-300.

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32.

Nano Letters

Wang, Z.; McKeown Walker, S.; Tamai, A.; Wang, Y.; Ristic, Z.; Bruno, F. Y.; de la Torre, A.; Riccò, S.; Plumb, N. C.; Shi, M.; Hlawenka, P.; Sánchez-Barriga, J.; Varykhalov, A.; Kim, T. K.; Hoesch, M.; King, P. D. C.; Meevasana, W.; Diebold, U.; Mesot, J.; Moritz, B.; Devereaux, T. P.; Radovic, M.; Baumberger, F. Tailoring the nature and strength of electron–phonon interactions in the SrTiO 3 (001) 2D electron liquid. Nat. Mater. 2016, 15, 835-839.

33.

Cancellieri, C.; Mishchenko, A. S.; Aschauer, U.; Filippetti, A.; Faber, C.; Barišic, O. S.; Rogalev, V. A.; Schmitt, T.; Nagaosa, N.; Strocov, V. N. Polaronic metal state at the LaAlO3/SrTiO3 interface. Nat. Commun. 2016, 7

34.

Manger, D.; Kaczer, B.; Menou, N.; Clima, S.; Wouters, D. J.; Afanas'ev, V. V.; Kittl, J. A. Comprehensive investigation of trap-assisted conduction in ultra-thin SrTiO3 layers. Microelectr. Eng. 2009, 86, 1815-1817.

35.

Mojarad, S. A.; Goss, J. P.; Kwa, K. S. K.; Petrov, P. K.; Zou, B.; Alford, N.; O'Neill, A. Anomalous resistive switching phenomenon. J. Appl. Phys. 2012, 112, 124516/1-7.

36.

Spinelli, A.; Torija, M. A.; Liu, C.; Jan, C.; Leighton, C. Electronic transport in doped SrTiO3: Conduction mechanisms and potential applications. Phys. Rev. B 2010, 81, 155110/1-14.

37.

Hao, X.; Wang, Z.; Schmid, M.; Diebold, U.; Franchini, C. Coexistence of trapped and free excess electrons in SrTiO3. Physical Review B 2015, 91, 085204.

38.

Janotti, A.; Varley, J. B.; Choi, M.; van de Walle, C. G. Vacancies and small polarons in SrTiO3. Phys. Rev. B: Condens. Matter 2014, 90, 85202/1-6. 25


Nano Letters 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

39.

Saraf, S.; Riess, I.; Rothschild, A. Parallel Band and Hopping Electron Transport in SrTiO3. Advanced Electronic Materials 2016, 2, 1500368/1-9.

40.

Berner, G.; Sing, M.; Fujiwara, H.; Yasui, A.; Saitoh, Y.; Yamasaki, A.; Nishitani, Y.; Sekiyama, A.; Pavlenko, N.; Kopp, T.; Richter, C.; Mannhart, J.; Suga, S.; Claessen, R. Direct k-Space Mapping of the Electronic Structure in an Oxide-Oxide Interface. Phys. Rev. Lett. 2013, 110, UNSP 247601/1-.

41.

Berner, G.; Glawion, S.; Walde, J.; Pfaff, F.; Hollmark, H.; Duda, L.; Paetel, S.; Richter, C.; Mannhart, J.; Sing, M.; Claessen, R. LaAlO3/SrTiO3 oxide heterostructures studied by resonant inelastic x-ray scattering. Phys. Rev. B: Condens. Matter 2010, 82, 241405/1-4.

42.

Dudy, L.; Sing, M.; Scheiderer, P.; Denlinger, J. D.; Schütz, P.; Gabel, J.; Buchwald, M.; Schlueter, C.; Lee, T.-L.; Claessen, R. In Situ Control of Separate Electronic Phases on SrTiO3 Surfaces by Oxygen Dosing. Adv. Mater. 2016, 28, 7443-7449.

43.

Mentes, T. O.; Zamborlini, G.; Sala, A.; Locatelli, A. Cathode lens spectromicroscopy: methodology and applications. Beilstein Journal of Nanotechnology 2014, 5, 1873-1886.

44.

Santander-Syro, A. F.; Copie, O.; Kondo, T.; Fortuna, F.; Pailhes, S.; Weht, R.; Qiu, X. G.; Bertran, F.; Nicolaou, A.; Taleb-Ibrahimi, A.; Le Fevre, P.; Herranz, G.; Bibes, M.; Reyren, N.; Apertet, Y.; Lecoeur, P.; Barthelemy, A.; Rozenberg, M. J. Two-dimensional electron gas with universal subbands at the surface of SrTiO(3). Nature 2011, 469, 189193.

26


Page 26 of 34

Page 27 of 34 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

45.

Nano Letters

Chambers, S. A.; Droubay, T.; Kaspar, T. C.; Gutowski, M. Experimental determination of valence band maxima for SrTiO3, TiO2, and SrO and the associated valence band offsets with Si(001). J. Vac. Sci. Technol. B 2004, 22, 2205-2215.

46.

Waser, R.; Baiatu, T.; Hardtl, K. H. DC electrical degradation of perovskite-type titanates. II. Single crystals. J. Am. Ceram. Soc. 1990, 73, 1654-62.

47.

Moos, R.; Menesklou, W.; Hardtl, K. H. Hall-mobility of undoped n-type conducting strontium-titanate single-crystals between 19K and 1373K. Appl. Phys. A-Mater. Sci. Process. 1995, 61, 389-395.

48.

Raab, N.; Bäumer, C.; Dittmann, R. Impact of the cation-stoichiometry on the resistive switching and data retention of SrTiO3 thin films. AIP Advances 2015, 5, 047150.

49.

Baeumer, C.; Schmitz, C.; Ramadan, A. H. H.; Du, H.; Skaja, K.; Feyer, V.; Muller, P.; Arndt, B.; Jia, C.; Mayer, J.; De Souza, R. A.; Schneider, C. M.; Waser, R.; Dittmann, R. Spectromicroscopic insights for rational design of redox-based memristive devices. Nat. Commun. 2015, 6, 9610.

50.

Wei, Z.; Takagi, T.; Kanzawa, Y.; Katoh, Y.; Ninomiya, T.; Kawai, K.; Muraoka, S.; Mitani, S.; Katayama, K.; Fujii, S.; Miyanaga, R.; Kawashima, Y.; Mikawa, T.; Shimakawa, K.; Aono, K. Retention model for high-density ReRAM. In 4th IEEE International Memory Workshop (IMW); 4th IEEE International Memory Workshop (IMW), 2012; pp.

51.

Butcher, B.; Koveshnikov, S.; Gilmer, D.; Bersuker, G.; Sung, M.; Kalantarian, A.; Park, C.; Geer, R.; Nishi, Y.; Kirsch, P.; Jammy, R. High endurance performance of 1T1R HfOx 27


Nano Letters 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

based RRAM at low (20uA) operative current and elevated (150C) temperature. In IEEE International Integrated Reliability Workshop Final Report; IEEE International Integrated Reliability Workshop Final Report, 2011; pp 146-150. 52.

Marchewka, A.; Roesgen, B.; Skaja, K.; Du, H.; Jia, C. L.; Mayer, J.; Rana, V.; Waser, R.; Menzel, S. Nanoionic Resistive Switching Memories: On the Physical Nature of the Dynamic Reset Process. Adv. Electron. Mater. 2016, 2, 1500233/1-13.

53.

Ma, J.; Wei, S. H.; Gessert, T. A.; Chin, K. K. Carrier density and compensation in semiconductors with multiple dopants and multiple transition energy levels: Case of Cu impurities in CdTe. Phys. Rev. B: Condens. Matter 2011, 83, 245207/1-7.

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Nano Letters

TOC GRAPHIC

29


b Letters 1200

Time (s)

Intensity (arb. units.)

oxidizing reducingNano

Page 30 of 34 Intensity

a

Intensity (Arb. Units)

Photon energy (eV)

800 1 2 400 3 4 0 0 2 4 462 460 458 456 454 462 460 458 456 454 5 Binding energy EB (eV) EB (eV) p (10-7 6 mbar) 7 c d Intensity Intensity 8 475 9 470 10 465 11 460 12 455 13 14 8 6 4 2 0 -2 8 6 4 2 0 -2 15 Binding energy EB (eV) Binding energy EB (eV) reducing e16 f 17 ED1 18 ED2 19 oxidizing 20 21 ACS Paragon Plus Environment 22 23 8 6 4 2 0 22 0 Binding energy EB (eV) 24 Binding energy EB (eV)

Current I (A)

aPage 10-2 31 of 34

Nano Letters

c

10-4 LRS

10-6

1 -8 210 310-10 4 5 6 7 8 9 10 11 12

2 µm

HRS

-4 -3 -2 -1 0 1 2 3

Voltage V (V)

hν

b ACS Paragon Plus Environment SrTiO 3 Nb:SrTiO 3

b

Page 32 of 34 Filament

Intensity (arb. units) Intensity (arb. units)

Rel. Ti3+ intensity

Reference

42

40

38

36

34

Binding energy (eV)

d

Intensity (arb. units)

1 2 3 4 5 6 7 8c 9 10 11 12 13 14 15 16

Nano Letters

Rel. IG intensity

a

ED1 ED2

Filament

2

0

2

0

ACS Paragon Plus Environment 8

6

4

-2

Binding energy (eV)

Energy (eV)

0.7 0.5 0.3 10.1 -0.1 2-0.3 3-0.5 4-0.7 -0.9 5-1.1

Energy (eV)

6 d7 8 1.0 9 0.8 10 110.6 12 130.4 14 0.2 15 16 17

ΦB

ED1

ED2

-3

-1

1

3

5

b

100

7

Position x (nm)

c

9

T⁭

T = 303 K

-1

10 Nano Letters 10-2 -3

tunneling path

EC

εƒ

Pt

SrTiO3

J (A cm-2)

0.9 Nb:SrTiO3 Page 33 of 34

Probability

a

10 10-4 10-5 10-6

T = 203 K 0.1

0.2

0.3

0.4

0.5

8

10

Voltage V (V)

1.0

Single charged Double charged T = 303 K

0.0

0

0.1 V 0.2 V 0.3 V 0.4 V 0.5 V

2

4

6

Position x (nm)

Peak position EA=EC -εƒ

ACS Paragon Plus Environment 6

7

8

Position x (nm)

9

2

4

6

8

Spec. Cur. Dens. (A eV-1cm-2)

Nano Letters 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

TOC graphic 34x13mm (300 x 300 DPI)


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