Understanding the Coexistence of Two Bipolar Resistive Switching

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Functional Inorganic Materials and Devices

Understanding the Coexistence of Two Bipolar Resistive Switching Modes with Opposite Polarity in Pt / TiO / Ti / Pt Nano-sized ReRAM Devices 2

Hehe Zhang, Sijung Yoo, Stephan Menzel, Carsten Funck, Felix Cüppers, Dirk J. Wouters, Cheol Seong Hwang, Rainer Waser, and Susanne Hoffmann-Eifert ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b09068 • Publication Date (Web): 08 Aug 2018 Downloaded from http://pubs.acs.org on August 9, 2018

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ACS Applied Materials & Interfaces

Understanding the Coexistence of Two Bipolar Resistive Switching Modes with Opposite Polarity in Pt / TiO2 / Ti / Pt Nano-sized ReRAM Devices Hehe Zhang 1, Sijung Yoo 3, Stephan Menzel 1, Carsten Funck 2, Felix Cüppers 1, Dirk J. Wouters 2, Cheol Seong Hwang 3, Rainer Waser 1,2, and Susanne Hoffmann-Eifert 1* 1

Peter Grünberg Institute (PGI 7 & 10) and JARA - Fundamentals in Future Information Technology, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

2

Institute of Materials in Electrical Engineering and Information Technology II, RWTH Aachen University, 52062 Aachen, Germany 3

Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Seoul 151-744, Republic of Korea

KEYWORDS TiO2, ReRAM, bipolar-type resistive switching, switching polarity, interfacial oxygen exchange, tunneling, Schottky barrier lowering

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ABSTRACT

Redox-type resistive random access memories (ReRAM) based on transition metal oxides are studied as adjustable two-terminal devices for integrated network applications beyond von Neumann computing. The prevailing, so-called, counter-eight-wise (c8w) polarity of the switching hysteresis in filamentary-type valence change mechanism (VCM) devices originates from a temperature and field controlled drift-diffusion process of mobile ions, predominantly oxygen vacancies in the switching oxide. Recently, a bipolar resistive switching (BRS) process with opposite polarity, so-called, eight-wise (8w) switching has been reported that, especially for TiO2 cells, is still not completely understood. Here, we report on nano-sized (< 0.01 µm2) asymmetric memristive cells from 3- and 6-nm-thick TiO2 films by atomic layer deposition, which reveal a coexistence of c8w- and 8w-switching in the same cell. As important characteristics for the studied Pt / TiO2 / Ti / Pt devices the resistance states of both modes are non-volatile and share one common state, i.e. the high resistance state of the c8w-mode equals the low resistance state of the 8w-mode. A transition between the opposite hysteresis loops is possible by voltage control. Specifically, 8w BRS in the TiO2 cells is a self-limited low-energy non-volatile switching process. Additionally, the 8w reset process enables the programming of multi-level high resistance states. Combining the experimental results with data from simulation studies allows to propose a model, which explains 8w BRS by an oxygen transfer process across the Pt / TiO2 Schottky interface at the position of the c8w filament. Therefore, the co-existence of c8w and 8w BRS in the nanoscale asymmetric Pt / TiO2 / Ti / Pt cells is understood from a competition between drift/diffusion of oxygen vacancies in the oxide layer and an oxygen exchange reaction across the Pt / TiO2 interface. 2 ACS Paragon Plus Environment

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INTRODUCTION Non-volatile redox-based resistive switching random access memories (ReRAM) are intensively studied for next-generation data storage and processing. New applications embrace storage class memory (SCM) 1, logic-in-memory

2, 3

and neuromorphic computing

4-7

. The advantages of

ReRAM devices comprise high-speed data access 8, high reliability with the high packaging density 9, 10, low power consumption 11, and the compatibility with CMOS technology regarding processing and device operation 12. Bipolar-type switching valence change memory (VCM) cells are often built from (transition) metal oxide layers sandwiched between metal electrodes, e.g., Pt / TiO2 / Ti 8, Pt / TaOx / Ta 13-15 or Pt / HfOx / Hf 16. Typically, the switching regime is located close to the metal electrode with high work function and low oxidation enthalpy. Therefore, the Schottky interface is also named the active interface in VCM cells. The low work function metal with high oxidation enthalpy forms an almost ohmic contact and also acts as oxygen exchange layer (OEL) 17. In VCM-type ReRAM, the switching mode for bipolar resistive switching (BRS) can vary between the counter-eight-wise (c8w) and eight-wise (8w) polarity according to Waser et al.

18

. Applying the voltage signal to the Schottky electrode regular c8w-BRS indicates the

SET event, which switches the cell state from high resistance (HRS) to low resistance (LRS), to occur at negative bias. Complementarily, the RESET process appears at opposite bias. In this reference system, the I(V)-characteristic will show an opposite drawing direction of the handwritten "8"

18

. Therefore, “c8w” established as the abbreviation for regular filamentary

VCM-type BRS. The switching scenario of opposite polarity is named eight-wise (8w)

19

.

Multiple complex processes might take place during the resistive switching phenomena in VCM cells such as the redox processes at the anode and cathode, Joule heating, drift- and diffusion processes of electrons and ions

20-23

. A widely accepted model for the filamentary c8w-BRS in 3

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VCM-type transition metal oxide systems includes mainly two processes: (1) the oxygen exchange at the interface between the ohmic electrode and the switching layer

15

and (2) the

movement of oxygen vacancies driven by the electrical field and influenced by Joule heating, which gives a consequent modification of the Schottky barrier at the Pt/oxide interface 18. On the contrary, 8w-BRS switching in epitaxial grown SrTiO3 thin film devices, the Nb:SrTiO3 / SrTiO3 / Pt system, has been analyzed by nano-analytical and nano-spectroscopic methods

24, 25

. The

proposed model for this 8w-BRS behavior in epitaxial SrTiO3 devices identifies an exchange of oxygen between the switching oxide and the atmosphere as the dominant mechanism 26, 27. Lee et al.

28, 29

applied the ‘semiconductor with mobile dopants’ (SMD) model to the system

Nb:SrTiO3/SrTiO3/Pt. In this system, the two opposite switching modes are correlated to the distance over which the oxygen vacancies move with respect to the Schottky interface and to the formation of the resulting Schottky barrier. Opposite switching polarities in Ta2O5 and ZrO2 based devices with stable states for the c8w-hysteresis and volatile states for the 8w-loop were addressed to a combination of ionic motion and electronic charge trapping effects, respectively 30

. A combination of different switching polarities was proposed to cause the limitation in the

high resistance state of TiN / Ta2O5 / Pt cells 31. Even for extremely down-scaled nano-devices of 28 nm diameter with Ta2O5 layers of 0.5 to 2 nm thickness different switching modes were reported. The regular c8w switching of the extremely thin Ta2O5 layers is related to a conical shaped filament. In contrast, the abnormal switching of the thin Ta2O5 films was attributed to hourglass-shaped filaments

32, 33

. The conical shaped filament for regular c8w switching is

observed by scaple SPM tomography in HfOx based ReRAM devices recently 34, which indicates the universality of conical shaped filament for regular c8w switching in various materials. Eightwise BRS is also described in different memristive devices from polycrystalline TiO2 films, but, 4 ACS Paragon Plus Environment

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so far, no consensus was found on its physical origin. Two switching polarities in a symmetric Pt / TiO2 / Pt structure were attributed to switching events, which occur at either one or the other Schottky interface

35, 36

. However, this assumption is in contradiction to other studies, which

show that the switching behavior of a transition metal oxide cell with two Schottky interfaces tends to show the complementary resistive switching behavior

37, 38

. In a different work on

devices made from anodic oxidized TiO2, the appearance of two switching polarities was attributed to a competition of ionic and electronic processes 39. For small devices with a feature size of (40 nm)2 built from polycrystalline TiO2 and TiN metal the 8w BRS correlates with a modulation of the oxygen vacancy concentration at the TiO2/TiN interface 40. In this study, we report on two opposite polarities in the bipolar resistive switching behavior of Pt / TiO2 / Ti / Pt nano-crossbar devices of (60 nm)2 to (100 nm)2 size with an integrated TiO2 layer of 3 nm and 6 nm thickness. The two modes refer to filamentary VCM-type c8w switching and the opposite 8w BRS. We discuss the phenomena of coexistence and transition between the modes for hysteresis curves obtained from sweep and pulse voltage operation. Furthermore, we evaluate the charge transport mechanisms of the different non-volatile states using its temperature and voltage dependence. Analysis using the Simmons’ formalism

41

provides first

results on the electrical characteristics of the switching regime. The data obtained for different modes are verified by a recently established continuum model simulation 42. Additional evidence is gained from intentionally modified device stacks by means of an interfacial Al2O3 layer. Combining the results, a mixed electronic-ionic conduction and switching mechanism is proposed, which consistently describes the coexistence of c8w- and 8w-BRS sharing a common state. The model considers competition between oxygen vacancy movement in the TiO2-x



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filament and oxygen ion exchange across the Pt / TiO2-x interface at the local position of the filament.

EXPERIMENTAL SECTION The nano-crossbar metal/oxide/metal structures utilized in this study are shown in Figure 1. For the bottom electrode (BE), 30 nm Pt was sputtered onto the Si/SiO2 substrate with a 5 nm Ti adhesion layer between the Pt and the SiO2. The 60 nm, 80 nm, and 100 nm wide BE lines were prepared by nanoimprint lithography (Nanonex NX-2000) and reactive ion beam etching (Oxford IonFab). Ultra-thin metal oxide films with the thickness of a few nanometers were grown by thermal atomic layer deposition in an Aixtron FE-200 reactor. The metal precursors were supplied by means of a pulsed liquid injection method coupled with a flow-type vaporizer. Details on the system and the operation principle are described in 43. The metal sources utilized for the TiO2 and Al2O3 growth were tetrakis-dimethylamido titanium (TDMAT, 99%, Strem Chemicals Inc.) and dimethylaluminum isopropoxide (DMAI, 99.99%, Strem Chemicals Inc.), respectively, dissolved in toluene with a concentration of 0.1 mol/L and kept at room temperature. Water vapor obtained from deionized ultra-pure H2O kept at 5 °C and fed into the reactor chamber by its vapor pressure was used as the oxygen source. The growth rate in the unit of growth per cycle (GPC) for the TiO2 and Al2O3 films deposited at 250 °C were around 0.04 nm/cycle and 0.12 nm/cycle, respectively. Details of the deposition conditions and of the films’ quality are described in ref. 44. The thickness of the individual layers grown in this study was controlled by X-ray reflectivity measurements on a Pro X’panalytical® MRD system. The metal layers forming the top electrode (TE) composed of 10 nm Ti and 20 nm Pt as a capping layer, which were obtained from electron beam evaporation. The TE lines with underlying 6 ACS Paragon Plus Environment

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switching oxide were patterned by electron beam lithography (Vistec EBPG 5000plus) and structured by reactive ion beam etching. Details of the process flow for the nano-crossbar device fabrication are given in

45

. The precision of the resulting nano-crossbar devices with active

switching areas of 60 x 60 nm2, 80 x 80 nm2 and 100 x 100 nm2 were controlled by scanning electron microscopy (SEM) using a Hitachi SU8000 system (see Fig. 1a). The film homogeneity and conformity on the structured Pt BE is seen in the TEM cross-section of a cut along the TE line (cf. Fig. 1b). The various TiO2 single layer and Al2O3/TiO2 bilayer devices were electrically characterized as a function of applied voltage and temperature in a semi-automatic probe station SUESS MicroTec PA-200. For the current transport measurements and current-voltage (I-V) cycling an Agilent B1500A semiconductor analyzer was utilized with the voltage ramp set to about 2.0 V/sec. Additional pulse voltage measurements were performed with a Keithley 4200 SCS system. All nano-crossbar structures were fabricated in the stack sequence that reads from the BE to the TE, Pt / metal oxide / Ti / Pt (see Fig. 1c). In order to point on the asymmetry of the VCM devices the topmost Pt capping layer is not mentioned in the discussion part. For consistency with the switching model (cf.

18

), the voltage signal is always referred to the high

work function Pt BE with the Ti TE set to ground.

RESULTS AND DISCUSSION Coexistence of c8w and 8w BRS in TiO2 based nano-crossbar cells Characteristic I(V)-hysteresis loops for a Pt / 6 nm TiO2 / Ti / Pt nano-crossbar device of (100 nm)2 size are shown in Figure 2. Two different modes of VCM-type resistive switching with opposite polarity are obtained. Following the definition provided in ref. 18, this is the c8w 7 ACS Paragon Plus Environment


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BRS and 8w BRS behavior identified as the black and red hysteresis loop, respectively. Most striking for this type of TiO2 based nano-crossbar devices is that the black c8w loop and the red 8w hysteresis share a common state which is discussed in the following. Typically, the as-prepared TiO2 based devices are electrically conductive in their initial states (cf. line ‘A’ in Fig. 2), and a positive voltage signal to the Pt BE is required to enable a c8w RESET process (cf. point ‘B’ in Fig. 2). This RESET is limited with respect to the achievable insulating properties of the high resistance state ‘C’ = HRS. Following the black curve in Figure 2 to the negative voltage regime, an abrupt SET event into the LRS = ‘A’ state is observed if the voltage exceeds the threshold value for a filamentary-type c8w SET process (cf. point ‘D’ in Fig. 2). The current in the c8w SET has to be limited by setting a current compliance Icc (here, ~10-4 A) to avoid irreversible destruction of the device. Summing up, the black cycle ‘A – B – C – D – A’ in Fig. 2 defines the filamentary-type c8w BRS mode, characterized by an abrupt c8w SET from HRS to LRS at negative polarity, and a gradual c8w RESET at positive polarity. Starting from the c8w HRS = ‘C’ state and applying a negative voltage, which is insufficient to initiate a c8w SET process, this is |V| < |Vc8w,SET|, changes the state of the device to an even higher insulating state (cf. line ‘E’ in Fig. 2) named HRS*. If a positive voltage with increasing amplitude is subsequently applied, a moderately abrupt change to a higher current level is observed by the voltage amplitude exceeding a certain value (cf. point ‘F’ in Fig. 2). The current increase is intrinsically limited by the c8w RESET occurring in the same voltage range. Therefore, the LRS* = ‘C’ obtained from the 8w SET process is identical to the HRS. Following the red loop for a full cycle, it becomes obvious that the sequence ‘C – D – E – F – C’ defines an


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eight-wise (8w) BRS mode, with opposite polarity compared to the black loop. For clarity, the inset gives the red loop in linear scale together with the orientation as to how the ‘8’ is drawn. The continuous hysteresis curves in Figure 2 show that the transition between the two hysteresis polarities appears in a very sharp voltage range. However, the c8w-SET voltage depends on the thickness of the TiO2, and for a given thickness, it depends on the actual HRS resistance value that also reveals a statistical cycle-to-cycle variation. The mean values of the c8w-SET voltage are about (-2.2 ± 0.4 V) and (< -3.5 V) for cells with a 3 nm and a 6 nm thick TiO2 layer, respectively. For the technical utilization of the two resistive switching modes, a sufficient margin should be considered in the programming between the highest 8w-RESET voltage and the mean c8w-SET voltage to avoid an unintended transition from the 8w to the c8w mode. Therefore, for stable 8w-BRS of Pt/3 nm TiO2/Ti/Pt devices the 8w RESET voltage was limited to (- 1.7 V). The coexistence of 8w and c8w BRS in one cell is observed for different

thickness values of the ALD grown TiO2 film, which is demonstrated by the 3 nm and 6 nm thick layers used in this study. In contrast to the volatile effects found in the Ta2O5 based systems, the 8w BRS states of the TiO2 based nano-crossbar cells are non-volatile, which is exemplarily

demonstrated

by

Figure 3a.

The

LRS*

(Vread = - 0.2 V)

in

a

Pt/ 3 nm TiO2 / 10 nm Ti / Pt nano-crossbar device reveals a stable retention for 3.5 hours at 125 °C. This is a characteristic value also reported for regular switched states in standard Ta2O5 devices

46

. Furthermore, the stability of the HRS* and LRS* in the TiO2-based devices is

supported by the repeated application of consecutive voltage sweeps with the same voltage polarity to the devices being in a certain state. This reproducibility of the HRS* and LRS* tested by several sweeps is shown in Figure 3b.

8w BRS in Pt / TiO2 / Ti / Pt nano-crossbar devices



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The 8w BRS behavior obtained in the Pt / TiO2 / Ti / Pt nano-crossbar devices shows a characteristic self-limiting behavior with respect to the maximum current flowing during the 8w SET and the 8w RESET events. This feature makes the 8w BRS mode in the TiO2 based nanodevices interesting over the more standard c8w BRS behavior, which often suffers from current overshoot phenomena (see 1, 18, 47). Therefore, the 8w BRS in the TiO2 nano-crossbar devices are investigated in more detail. Figure 4a shows representative 8w BRS loops in the TiO2 devices taken for different values of the 8w RESET voltage. Increasing the negative voltage amplitude (for |V8w,RESET| < |Vc8w,SET|) results in a reduction of the current flowing in the HRS*. This gradual behavior of the 8w RESET characteristics enables a tailoring of the read resistance in HRS*, R8w,OFF, by means of the voltage amplitude |V8w,RESET|. The current conduction behavior of the HRS* states shows a significant asymmetry with respect to the voltage polarity, especially for higher voltage amplitudes. This might partly explain the weak dependence of the 8w SET voltage on the HRS* level, which becomes obvious in the positive voltage region shown in Figure 4a. The LRS* is defined by the c8w HRS state obtained for the highest applied c8w RESET voltage. Figure 4b summarizes the resistance values readout at -0.3 V obtained for a series of 8w RESET voltages for Pt/ 3 nm TiO2 / 10 nm Ti / Pt nano-crossbar devices of different size, (60 x 60) nm2 and (100 x 100) nm2. It turns out that the read out resistance values for LRS*, R8w,ON (open sybols), are almost constant, and, especially, that they are independent of the device size. This size-independency is consistent with the LRS* being identical to the c8w filamentarytype HRS. This implies that the 8w BRS behavior obtained in the TiO2 based nano-crossbar devices represents a filamentary-type switching phenomenon, which coexists with the filamentary-type c8w switching sharing a common state, HRS = LRS*. This finding is important for the switching model proposed later. Furthermore, the semi-logarithmic graph in Figure 4b 10 ACS Paragon Plus Environment

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shows an increase in the R8w,OFF values (solid symbols) with increasing |V8w,RESET| amplitude. Interestingly, this effect becomes more significant for smaller device size. In particular, a resistance increase by a factor of ten is achieved by an increase in the voltage ∆|V8w,RESET| of about 0.83 V and 1.58 V for devices of (60 nm)2 and (100 nm)2 size, respectively. This pad size dependence might originate from residual leakage current of the non-switching device area, which is parallel to the filamentary current path 14.

Multilevel HRS* in sweep and pulse mode The gradual RESET behavior of the 8w BRS mode enables the programming of multilevel HRS* as it is shown in Figure 4. The states are obtained by I(V) cycling for increased values of |V8w,RESET| applied to the cell. In addition, Figure S1 in the supplementary information shows an 8w RESET series, which is obtained from a consecutive increase of |V8w,RESET|, but in contrast to Figure 4, always starting from the previous (n-1)th HRS* level. Multiple HRS* level can be programmed by running 8w I(V)-loops either as full or half cycles. In addition, the Pt/ 3 nm TiO2 / Ti / Pt devices of (100 nm)2 size are switched by means of consecutive voltage pulses of 100 ns. The pulse sequence drawn in Figure 5a, and Fig. 5b shows the corresponding read resistance values over the RESET pulse signal. All readouts are performed with a 1 ms pulse of -0.4 V amplitude. The reference state is defined by the condition LRS* = HRS. The corresponding resistance value after a sweep 8w SET reads R8w,ON ≈ 700 kΩ shown as the green square in Fig. 5b. For easier visibility, this resistance value is also indicated by the dashed line. In a sequence of four switching cycles (see Fig. 5a) the negative voltage amplitude of the write pulse is step-wise increased from -1.1 V to -2.2 V, while an intermediate SET pulse of 2.2 V is applied to switch the device back into the ‘reference’ state. Fig. 5b shows 11 ACS Paragon Plus Environment


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that the first pulse of -1.1 V resets the device into an HRS* with R8w,OFF ≈ 2 MΩ. Subsequent pulses of negative polarity and increased voltage amplitudes enable 8w RESET processes into even higher insulating HRS* conditions reaching values of up to R8w,OFF ≈ 40 MΩ for V8w,RESET = -1.7 V. The successful pulsed SET operations are demonstrated by the restored reference resistance states of ~700 kΩ given as the red circles in Fig. 5b. If the write signal exceeds the threshold voltage for c8w SET, that is -2.2 V, the device switches into the c8w LRS with a readout resistance of only Rc8w,ON ≈ 2.5 kΩ. And again, a positive voltage pulse of 2.2 V applied for 1.0 µs recovers the stable ‘reference’ state HRS = LRS*. These experiments demonstrate that the coexistence of c8w and 8w BRS modes in the TiO2 nano-devices shows up for various operation modes ranging from continuous voltage sweeps (~ 2 V/s) to short voltage pulses of 100 ns.

Temperature dependence of the current-voltage behavior in various c8w and 8w BRS states The current response in the nano-sized transition metal oxide based devices is strongly dominated by the electronic contribution. The accompanying Joule heating increases the ion mobility in the filamentary switching regime and thus enables switching times as short as 10 ns 48-51

. Therefore, the knowledge of the electronic charge transport behavior in various switching

states is of utmost importance. In this section, the charge transport behavior of the Pt/ 3 nm TiO2 / 10 nm Ti / Pt nano-crossbar devices is discussed. For this purpose, continuous I(V)-hysteresis loops were performed at room temperature to program the cells into LRS, HRS = LRS*, and various HRS* states. Subsequently, the switching states were analyzed with respect to the voltage and temperature dependence of the current response, i.e., I(V,T).


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The c8w LRS reveals a linear I(V) behavior with minor temperature dependence. The read out resistance values of c8w LRS, Rc8w,ON, are typically about 2 to 3 kΩ indicating a conductive filament connecting the Pt and Ti electrode 52, 53. This behavior is characterized by means of the temperature coefficient of the resistance (TCR) determined at Vread = 0.3 V. Figure 6 shows the normalized resistance change, (R(T) – R0) / R0, as a function of the change in temperature, (T – T0). The reference value R0= R(T0) is the read out resistance in LRS at 25 °C. The linear fitting of the data points provides a TCR value of (1.18 ± 0.01) ∙ 10-3 K-1. Regarding the electronic charge transport, the TCR value of the LRS indicates that the properties of the conductive filament can be described as semiconducting or (almost) metallic. This behavior is consistent with the findings of Magnéli-type phases forming conductive filaments in VCM-type switching TiO2 devices 54-56. In contrast, the I(V,T) characteristics of the HRS = LRS* and HRS* states reveal an exponentialtype voltage dependence combined with a weak temperature dependence of the current (see Fig. 7c). Therefore, a tunneling transport mechanism is proposed to describe the electronic conduction mechanism of the 8w states. For example, the behavior of the 8w LRS* of a Pt/ 3 nm TiO2 / 10 nm Ti / Pt nano-crossbar cell of (80 nm)2 size is discussed here. Subsidiarily, the I(V,T) characteristics of an 8w HRS* programmed at V8w,RESET = -2.0 V are given in Figure S2 in the supplementary information. Figure 7a shows the ln (I / V2) versus (|1 / V|) plot of the weakly temperature dependent LRS* data measured at temperatures between 293 K and 343 K. The characteristic dependency observed in Figure 7a notifies the transition from direct tunneling to Fowler-Nordheim (F-N) tunneling with a voltage inflection point at VT, which indicates that the tunneling barrier height of the TiO2 /Ti interface are rather small (see for example 57). 13 ACS Paragon Plus Environment


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Electronic conduction behavior in the 8w BRS states The nano-crossbar devices of Pt/ 3 nm (or 6 nm) TiO2 / 10 nm Ti / Pt stacks reveal a reproducible 8w switching behavior. The 8w BRS shows several advantages over the c8w switching event: (1) no current limitation by means of an external compliance is required, (2) a reduced overall current level, and (3) the 8w RESET process with a potential for multilevel switching into well-defined states. Therefore, the 8w states, which are LRS* and multilevel HRS*s, are further analyzed regarding the involved electronic conduction mechanism. From Figure 7a it becomes clear that the total current in the LRS* can be described by a superposition of temperature-assisted tunneling dominating at low voltages up to about VT ≈ (0.15 ± 0.05) V and field-assisted tunneling showing up for higher applied voltages. Comparable behavior is found in the I(V)-characteristics in the HRS*, which is described in the Figure S2 of the supplementary information. This characteristic behavior is properly described by the process of electron charge carrier tunneling through an asymmetric (trapezoidal) barrier. A one-dimensional schematic of the energy diagram is drawn in Fig. 7b. The z-axis is perpendicular to the electrodes and along the center of the switching filament. The figure shows the situation of a negative voltage applied to the Pt BE with an amplitude that enables field assisted (F-N) tunneling in addition to the direct tunneling. Φ1 denotes the barrier height between the conductive and insulating regimes of the titanium oxide, and Φ2 denotes the barrier height at the Pt BE. Moreover, L is the length of the filament’s disc region 13. This equals the width of the tunneling barrier for the case of zero electric field. The quantum mechanical tunneling through a trapezoidal barrier is calculated by means of the generalized formula of Simmons

58

. With this

the total current I is calculated as follows: 14 ACS Paragon Plus Environment

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= ∙ ∙ ∙ exp − ∙ − + ∙ exp − ∙ +

with

=

1 ∙ 2ℎ

=

and

4 ∙ 2 ℎ

∗

(1)

.

Here, A is the tunneling area, m* the effective tunneling mass of electrons

59

, h the Planck

constant, q the elementary charge, and V is the applied voltage. The effective tunnel barrier thickness l and the mean barrier height are voltage dependent. Therefore, different expressions are derived for the various voltage regimes representing situations of a negligible, a small and a significant field effect. With this, the effective tunnel barrier properties derive to:

% % = #% ∙ " − ( + $

and

+ ( $ 2 * + ( − = 2 # * " 2

for ≈ 0 for ( > > 0 for > (

(2)

for ≈ 0

for ( > > 0

(3)

for > (

For a negative voltage applied to the Ti electrode with the low barrier height, an equivalent set of equations can be derived (see 41). The Simmons’ equations (1) - (3) are used for the calculation of

the

I(V)-characteristics

for

the

various

8w

resistive

switching

states

in

the

Pt / 3 nm TiO2 / Ti / Pt devices. Exemplary, experimental I(V)-curves for two 8w-BRS device 15 ACS Paragon Plus Environment


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states, HRS* and LRS*, measured at temperatures ranging from 293 K to 343 K are shown as colored lines in Figure 7c. In addition, the calculated I(V) tunneling characteristics obtained from the Simmons’ equations are given as symbols. The starting parameters applied for the calculations are according with the physical properties of the materials used in the device stack, Ti, TiO2, and Pt, and with the device geometry defined by the size and the layer thicknesses involved. The length and diameter of the conductive filament or vice versa, the interfaces of the insulating disc region and the disc dimensions have to be considered

60

in more detail. Several

studies deal with the form of the switching filament in c8w VCM-type devices, differentiating conical and hourglass-like shapes

33, 52, 61-63

. However, nanoscale analytical studies on the

filament’s shape of 8w BRS devices are rare. Recently, Du et al. 64 reported a very careful study on the nature of the filaments in 8w switching Nb:SrTiO3 / Fe:SrTiO3 / Pt epitaxial devices. The authors identified a multi-filamentary switching process with a filament diameter of about 500 nm at the SrTiO3 / Pt interface consistent with simulated I(V) curves 42. Based on the mentioned reports, we developed a model for the 8w BRS in the nanoscale Pt / TiO2 / Ti devices that involves conically shaped filament(s) and a disc-like tunneling barrier at the Pt / TiO2 interface

13

. With this model, the variable parameters in the Simmons’ formula

can now be correlated to physical properties of the 8w BRS cell on the nanoscale. The effective tunneling area A in equation (1) corresponds to the ‘disc’ area, which itself is defined by the spot size of the conductive filament ‘plug’. Typical values reported for the filament’s spot size in VCM-type switching devices range from 10 to 500 nm2 technique Celano and co-workers

66

54, 61, 65

. By means of a ‘scalpel SPM’

measured size of about 102 to 104 nm2 for the conductive

filament close to the OEL. For the nano-crossbar devices investigated in this work, a direct analysis of the ‘disc’ diameter was not accessible due to topography issues. Therefore, a 16 ACS Paragon Plus Environment

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reasonable value is determined from the optimization of the fitting results and in the parameter range given by the literature. We then determined a disc diameter to about 8 nm, which provides a tunneling area of A ≈ 50 nm2. Equation (1) shows that the current is directly proportional to the area, I ~ A. This simple relationship enables minor corrections at any time, and thus, the reasonable value of A was kept constant for the calculations performed in this study. Here we assume no lateral confinement effects and therefore, laterally mesoscopic transport isn’t considered

67

. The effective tunneling mass of the electrons in TiO2 equals the free electron

mass, m* ≈ m0 68, 69. For the asymmetric Pt / TiO2 / Ti cells the low energy barrier Φ1 of the Simmons’ equation is assigned to the disc/plug interface. The analysis of the experimental data shown in Fig. 7a, provides a value of the transition voltage VT, which is about (0.15 ± 0.05) V, derived for the various temperatures and for HRS* and LRS*. According to the energy diagram in Fig. 7b (qVT) determines the energy where the shape of the tunnel barrier changes from trapezoidal to triangular. This correlates with a small barrier of about Φ1 ≈ 0.1 V at the low barrier interface. The barrier arises at the interface between the strongly oxygen deficient TiO2-y plug and the minor reduced TiO2-x disc region that is built by the electroforming process

70

. In contrast, the

ideal TiO2 / Ti interface should provide an ohmic contact considering the work function of Ti metal (~ 4.33 eV

71

) and the electron affinity of stoichiometric TiO2 (≥ 4.80 eV

72, 73

). Having

defined the values for the variables, m* = m0, A ≈ 50 nm2, and Φ1* = 0.1 eV, in agreement with the experimental findings, only two parameters remain for the fitting of the measured I(V) characteristics of the cell in LRS* and HRS*. These are the barrier height Φ2 at the Pt / TiO2 interface and the effective tunnel width L (at zero voltage), which equals the width of the ‘disc’ region between the filament ‘plug’ and the Pt BE electrode. The calculated I(V) characteristics 17 ACS Paragon Plus Environment


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shown in Fig. 7c were obtained from setting the free variables Φ2 and L to about 1.0 eV and 1.25 nm for the LRS*, and to about 1.3 eV and 1.6 nm for the HRS*. In total, the semiquantitative analysis of the current conduction behavior in the LRS* and HRS* of Pt/ 3 nm TiO2 / 10 nm Ti / Pt nano-crossbar devices makes it possible to draw several conclusions regarding the device changes, which are associated with the 8w switching process: •

The 8w BRS is reproducible and reliable with stable resistance states, which are defined by electron tunneling through an asymmetric barrier. This includes direct tunneling obtained in the low voltage regime and Fowler-Nordheim tunneling at higher voltages.

•

The change from LRS* to HRS* involves an increase in the width L and the height Φ2 of the energy barrier associated with the Pt / TiO2 interface.

•

Thus, the 8w BRS phenomenon in Pt/ TiO2 / Ti / Pt nano-crossbar devices is assigned to the same interface that controls the c8w BRS behavior, which is the Pt / TiO2-x Schottky interface.

•

Therefore, the c8w BRS and the 8w BRS events in the TiO2-based nano-crossbar devices refer to competing electrochemical reactions at the Schottky interface. The dominating process is selected by the amplitude of the negative voltage applied to the Pt electrode.

8w BRS described by a continuum model The interpretation of the current conduction behavior of the Pt / TiO2 / Ti / Pt nanocrossbar devices in the 8w BRS states by means of electron tunneling through an asymmetric 18 ACS Paragon Plus Environment

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barrier provides rather reasonable values for the derived physical parameters. However, the I(V)characteristics measured for the cells in LRS* (see Fig. 7a) and HRS* (see Fig. S2) exhibit an additional peculiar phenomenon. This is a weak, but, non-negligible temperature dependence of the current-voltage curves (see the insets in Fig. S2), which cannot be explained by the simple triangular-shaped band structure assumed in the Simmons’ equation. A more realistic approximation should consider the formation of a space charge layer at the Pt / TiO2-x Schottky interface and accompanying band bending effects. For this approach, we utilized a continuum model, which is based on the semi-classical single-band transport theory. The model combines the Fermi-Dirac statistics of electrons and two-fold donor-type oxygen vacancies with the Poisson equation for the electrostatic potential in a one-dimensional model geometry 13, 24, 24. The calculations are performed in an analogy to the procedure described in detail in ref.

42

. The

complete list of the material parameters can be found in Table S1 in the supplementary information. The switching between LRS* and HRS* is attributed to a change in the total concentration of oxygen vacancies, N VO =  VOx  +  VOg  +  VOgg  . In the Kröger-Vink notation the       gg x g symbols VO, VO, and VO stand for neutral, single and double positively charged oxygen vacancies 74

3

Two different values of the oxygen vacancy concentration in the disc region, NVO = 6∙1020 cm-

and NVO = 3∙1020 cm-3, are used for the description of the 8w switching scenarios, the LRS* and

the HRS*, respectively. The results of the simulation for the case of zero applied voltage are shown in Figure 8. Here, the energy of the conduction band EC (broken lines) and the depletion charge density ρ (solid lines) are plotted as a function of the z-coordinate between the Ti (z = 3 nm) and Pt electrode (z = 0 nm). According to 42, the maximum spectral tunneling current density is obtained at the energy (qVT). In combination with the band bending in the space charge 19 ACS Paragon Plus Environment


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layer, the direct tunneling width L is obtained. The red and blue lines represent the LRS* and HRS*, respectively. From Figure 8 several results can be derived: (1) The barrier for direct tunneling is higher for the HRS* than that for the LRS*. The stronger band bending in the LRS* results in a stronger Schottky barrier lowering leading to a higher internal electric field. (2) The direct tunneling width L is smaller for the LRS* than for the HRS*, consistent with the results of the Simmons’ equation. As a consequence of the lower vacancy concentration in HRS*, the thickness (~1.7 nm) of the depletion region exceeds that of the LRS* (~1.2 nm). This leads to an extended tunneling path L in the HRS*. The comparison of the results from the continuum model with the data obtained from the Simmons’ fits reveals a good qualitative agreement for the tunneling length and the tunneling barrier height. This allows a direct correlation of the change in the tunneling barrier parameters induced by a switching process to a change in the oxygen vacancy concentration NVö in the switching regime. The continuum model simulation also provides an explanation for the weak temperature effect on the tunneling characteristics originating from the Fermi-Dirac statistics of the electron and donor concentrations. For a small negative voltage applied to the Pt electrode, the electrons that are thermally activated above the Pt Fermi level make a significant contribution to the total tunneling current due to the strong band bending for both LRS* and HRS*. By this effect, the physical origin of the measured temperature dependence shown in Fig. 7a can be understood. Further, the model connects the changes obtained for the 8w BRS states, LRS* and HRS*, directly with a change of the concentration of oxygen vacancies NVO in the filament disc region. Finally, the continuum model provides a more real description of a parabolic band bending, and therefore of the effective tunneling barrier height and width. 20 ACS Paragon Plus Environment

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Interface modification by introduction of an additional Al2O3 layer The combination of the experimental and simulation results leads to the proposal that both the c8w and the 8w switching events originate from modifications of the space charge layer at the Pt / TiO2-x Schottky interface. In order to verify this assumption, the interface has been systematically modified. This is performed by the insertion of a thin layer of high-band gap, low ionic conducting material, Al2O3, between the Pt BE and the TiO2 switching layer. A series of nano-crossbar samples of the stacking sequence Pt / Al2O3 / 3 nm TiO2 / Ti / Pt with a thickness of the Al2O3 layer of 0, 1, 2 and 3 nm were fabricated and the switching behavior was studied. Exemplary I(V)-switching loops related to the different layer stacks are shown in Figure S3 a) to c) of the supplement. In addition Figure S3 d) summarizes the c8w SET voltage as a function of the Al2O3 thickness. A clear trend in the switching characteristics with the varied thickness of the Al2O3 interfacial layer is obtained. With increasing Al2O3 thickness the chance that the device shows 8w BRS behavior decreases continuously. The 8w BRS phenomenon completely vanishes for the 2 - 3 nm-thick Al2O3 layer. This observation is summarized in Figure S3 d), which shows the ‘threshold’ voltage for the c8w SET process, Vc8w,SET, as a function of the thickness of the interfacial Al2O3 layer. Although the devices with less than 1 nm of Al2O3 show electroformingfree behavior, the required |Vc8w,SET|-value was between ~2.0 V and 1.5 V. In contrast, devices with an interfacial layer of 2 nm Al2O3 require a preliminary electroforming step and exhibit only c8w BRS behavior (see Fig. S3 c)). For these devices the threshold voltage of the c8w SET event is reduced to ~1.0 V as shown in Fig. S3 c). This behavior is counter-intuitive – in usual conjecture, the thicker Al2O3 must induce higher SET voltage, which is obviously not the case. However, when the Al2O3 layer thickness is further increased to 3 nm, the Vc8w,SET slightly 21 ACS Paragon Plus Environment


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increases to ~1.2 V. Fig. S3 c) shows a clear trend of the threshold voltages for the c8w SET events of the Pt / Al2O3 / 3 nm TiO2 / Ti / Pt samples with variation of the Al2O3 thickness. The complete disappearance of the 8w BRS mode for samples with a slightly thick Al2O3 layer at the interface emphasizes the distinctiveness of the Pt / TiO2-x interface. To evaluate the possibility of intermixing of Al2O3 and TiO2, the 3 nm Al2O3 / 3 nm TiO2 layer structure was analyzed for the cross-section of a nano-crossbar device in HRS, after electroforming and several switching cycles had been performed. Figure 9 shows an HRTEM picture together with an energy dispersive X-ray spectroscopy (EDX) line scan perpendicular to the layer stack performed in STEM mode. The sequence of the Al2O3 and the TiO2 layer are clearly resolved. This nanoanalytical result supports the notion that the interface of the bilayer device should be properly described by the Pt / Al2O3 interface. Therefore, we conclude that the switching behavior, in particular, the coexistence of two BRS modes with opposite polarity, obtained in the single layer TiO2 based nano-crossbar cells is controlled by the changes of the space charge layer at the Pt / TiO2-x interface. This conclusion also applies for the TiO2 based nano-crossbar cells with an ultrathin (~ 1 nm) Al2O3 interfacial layer for different considerations. One reason might be, that the 1 nm Al2O3 layer is grown from only eight ALD cycles. Therefore, it is reasonable to assume that the area density of pinholes might become significant compared to the device size of about 104 nm2. Another possibility is that the 1 nm thin ALD grown Al2O3 layer might not efficiently suppress the oxygen exchange between the TiO2-x disc region and the Pt electrode. This assumption is supported by oxygen diffusion experiments in amorphous Al2O3 thin films

75, 76

.

The results indicate that the oxygen diffusion coefficient in amorphous Al2O3 thin films significantly exceeds the value for crystalline α-Al2O3 by orders of magnitude. This trend is in agreement with theoretical calculations predicting that pronounced perturbations of the crystal 22 ACS Paragon Plus Environment

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structure can enhance the ion diffusivity for those structures in which ion migration is generally slow 77.

Switching model of Pt / TiO2 / Ti nanocrossbar devices with two bipolar switching polarities The comprehension of the results presented on the extraordinary switching behavior discovered in the Pt / TiO2 / Ti / Pt nano-crossbar devices finally merges in the proposal for a switching model as follows. The model appropriately explains the coexistence of the BRS modes using a competition between the VCM-type oxygen vacancy drift and diffusion processes and an oxygen exchange reaction at the high work function Pt electrode. For the sake of completeness it should be mentioned that the oxygen exchange reaction at the Ti OEL 15 has not been discussed here for the reason of complexity. However, for an accurate description of the switching behavior in these nano-sized devices, oxygen exchange reactions at both interfaces might have to be considered in addition to the drift/diffusion processes. In addition, the effect of cation diffusion

78

on the switching behavior of nano-crossbar devices needs to be clarified. However,

all these effects are beyond the scope of this study. Instead, the proposed model should be understood as a summary of the experimental and simulation results discussed in this work. For a better understanding of the switching scenario the dimensions of the investigated nano-crossbar devices should be reminded. A sketch of a cell is shown in the abstract figure. In fact, the size of the nano-crossbar cells is in the range of about 3600 to 10000 nm2 while the switching TiO2 layer sandwiched between the electrodes is only 3 or 6 nm thick. In its pristine states the devices are conductive. This can be understood by taking into account that the switching oxide, TiO2, exhibits a moderate band gap of about 3.2 eV at room temperature and a bulk heat of formation per O atom around 4.8 eV. This value strongly decreases for oxygen-poor 23 ACS Paragon Plus Environment


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material 17. In addition, the existence of a significant number of sub-stoichiometric phases, such as Magnéli-type phases TinO2n-1

79

enables an easy phase separation in nano-crystalline material

deposited at low temperature. The same aspect makes the theoretical description of TiO2 very complex because the additional phases will interfere with conservation of vacancy numbers

17

.

However, it is reasonable to assume that the TiO2 layer in its as-deposited state consists of multiple (moderately) conductive regions of slightly reduced TiO2-x inside the otherwise insulating TiO2 matrix. This description follows the experimental findings reported by Du et al. 64

, who visualized multiple nanosized conducting filaments in Fe-doped SrTiO3 thin-film

memories by scanning transmission electron microscopy and core-loss spectroscopy. Despite the similar 8w switching observed in the Pt / TiO2 / Ti / Pt nano-crossbar devices and that in the Nb:SrTiO3/ SrTiO3 / Pt cells studied by Bäumer et al.

24

, there are two main differences which

are important for the future device integration. For the Nb:SrTiO3/ Fe:SrTiO3 / Pt cells with the high work function Pt contact forming the TE the 8w switching involves a considerable amount of oxygen exchange with the surrounding atmosphere 25. In addition, the diameter of the conical shaped filaments increases towards the Fe:SrTiO3 / Pt Schottky interface giving rise to a switching are of about 500 nm2 42. In contrast, for the nano-crossbar cells studied in this work the switching Schottky interface, i.e., Pt / TiO2, is located at the bottom of the device stack. Due to this geometrical arrangement oxygen exchange with the atmosphere in a significant amount should be negligible. Therefore, the proposed switching model assumes that the oxygen atoms which are extracted from the TiO2-x layer reside either at the interface or in the Pt layer in close proximity to the interface. Oxygen atoms can, for example, be segregated to the Pt grain boundaries 80.


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Figure 10 presents a graphical illustration of the proposed model for the two bipolar resistive switching modes sharing a common state obtained in Pt / TiO2 / Ti / Pt nano-crossbar devices. The changes on the atomic scale level are indicated by the colored spheres. The illustrations in Fig. 11 show a two-dimensional cut through the device at the position of the switching filament. The Pt BE and the Ti TE are given in grey and dark violet color, the TiO2 matrix is shown in yellow, and the constituting ions are drawn in bright violet for Ti3+ and in green for doubly gg ionized oxygen vacancies, VO . Oxygen atoms residing at the interface and at the Pt grain

boundaries are drawn as blue spheres. The conical-shaped filament is seen as the regime with an increased density of oxygen vacancies. Particulary, the highly conductive filament plug is described by a high electron charge carrier concentration in the TiO2 conduction band formed by the Ti 3d states 79. In contrast, the average vacancy concentration in the ‘disc’ region depends on the switching state. Therefore, the depletion space charge layer adjacent to the Pt BE is identified by a variable concentration of oxygen vacancies. The standard VCM-type c8w switching behavior is described by the characteristic states and transitions ‘A – B – C – D’. The 8w-loop is characterized by the sequence ‘C – D – E – F’. The full switching scenario comprises the coexistence of the c8w and the 8w switching event, the shared intermediate state and the transition between the two states that is controlled by the amplitude of the negative voltage applied to the Pt BE. This complete scenario can be explained in a self-consistent manner. For this, in addition to the oxygen vacancy drift and diffusion 48 (and the oxygen exchange reactions with the chemically active Ti electrode

15

- not included in this model -), an oxygen transfer

reaction at the interface with the inert Pt electrode is considered, which is to some extent analog to the switching mechanism reported for epitaxial SrTiO3 films

25

. With these assumptions, the

switching steps and resistance states appear as follows: The c8w LRS ‘A’ represents the situation 25 ACS Paragon Plus Environment


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with the smallest extension of the depletion zone. The c8w RESET ‘B’ involves the drift of oxygen vacancies towards the cathode (Ti TE) and a possible oxygen transfer at the high barrier interface towards the Pt electrode. For successful c8w RESET from the LRS ‘A’ to the c8w HRS ‘C’ the oxygen vacancy drift should dominate over the oxygen extraction in order to decrease the average oxygen vacancy concentration in the disc region. Consistent with the continuum model, the reduced oxygen vacancy concentration NVO results in a higher barrier and tunneling width for electron injection from the Pt into the oxide. The high symmetry of the I(V)-characteristic of ‘C’ is in agreement with a conduction process controlled by electron tunneling. When a negative voltage is applied to the Pt BE, the process is reversed. In other words, oxygen ions and oxygen vacancies are pushed into the disc region from the Pt side and from the Ti side, respectively. At position ‘D’ a c8w SET process is initiated, if the filament comes very close towards the Pt electrode and the conduction behavior in the achieved LRS is described by a bad metal type filament. In contrast, prior to the filament’s contacting of the Pt electrode, the transfer of oxygen from the ‘reservoir’ at the Pt interface into the disc region results in a decrease of the oxygen vacancy concentration NVO, and, consequently, in a higher barrier and tunneling width characterizing the HRS* represented by ‘E’. The switching from the HRS* to LRS* at positive polarity applied to the Pt BE proceeds via step ‘F’ that characterizes the 8w SET followed by step ‘B’.

CONCLUSIONS The coexistence of two stable bipolar switching modes with opposite polarity in Pt / TiO2 / Ti / Pt nano-crossbar devices is described. Important results from experiments and 26 ACS Paragon Plus Environment

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simulations are: (1) the appearance of a shared intermediate state at which the c8w HRS and the 8w LRS* are identical, (2) the conduction behavior in LRS* and HRS*, which reveals a clear tunneling mechanism, (3) the multilevel capability of the HRS* in sweep and pulse operation, (4) the strong dependence of the 8w-type switching phenomenon on the nature of the Pt / TiO2 interface, and (5) the correlation of the change in the barrier height and tunneling width to the oxygen vacancy concentration in the disc regime of the switching filament near the Pt electrode. These findings can be consistently described by means of the proposed switching model, which considers the oxygen transfer at the interface with the Pt electrode, in addition to the accepted processes of oxygen vacancy drift and diffusion (and oxygen ion exchange at the Ti electrode). The proposed switching model for the TiO2 based nano-crossbar cells is adopted from the model established for 8w-type switching SrTiO3 cells with two significant differences. They are the degree of oxygen exchange with the atmosphere and the area of the filament. This study shows that exchange reactions at all interfaces of the oxide-based VCM-type switching devices have to be considered as a proper explanation of the switching events in nanosized devices. In addition, these switching processes controlled on the atomic scale are considered to dominate the behavior for future high density integrated ReRAM devices where scaling is one of the most important requirements. At the same time, the 8w switching event with opposite polarity compared to the VCM-type standard filamentary c8w switching enables a programming of non-volatile memory states at significantly reduced power. The coexistence of two bipolar switching events with opposite polarity and a common reference state realized in the Pt / TiO2 / Ti / Pt nano-crossbar devices offers the unique opportunity of a resistance change into two directions triggered by a voltage signal of variable amplitude but with the same (positive) polarity. A ‘reference-type’ resistance state can be recovered by means of an opposite (negative) 27 ACS Paragon Plus Environment


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voltage signal at constant amplitude. This extraordinary property of the nano-crossbar TiO2 based devices could be useful for algorithms currently studied in the research for ‘beyond von Neumann’ computing.


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ASSOCIATED CONTENT Supporting Information is available from the ACS web site The calculation of tunneling current based on the Simmons’ model for multiple HRS*; The temperature dependence of the 8w BRS states; The I(V) characteristics of Pt / Al2O3 / 3 nm TiO2 / Ti / Pt with a varied Al2O3 thickness; The simulation model

AUTHOR INFORMATION Corresponding Author *Email: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Funding Sources This work was supported in part by the Deutsche Forschungsgemeinschaft (SFB917), and by the Global Research Laboratory Program (No. NRF-2012K1A1A2040157) of the National Research Foundation of the Republic of Korea.



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Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors thank René Borowski, Stephan Masberg, Alfred Steffen, and Stefan Trellenkamp for their technical assistance in device fabrication, and Alexander Schönhals, Camilla La Torre, Andreas Kindsmüller, Alexander Hardtdegen, Stephan Aussen, and Christoph Bäumer for fruitful discussions on the topic of this paper.


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and Resistive Switching in SrTiO3 Thin Film Devices. Adv. Funct. Mater. 2015, 25, 63606368. (20) Cho, D.; Lübben, M.; Wiefels, S.; Lee, K.; Valov, I. Interfacial Metal – Oxide Interactions in Resistive Switching Memories. ACS Appl. Mater. Interfaces 2017, 9, 19287–19295. (21) Valov, I. Interfacial Interactions and their Impact on Redox Based Resistive Switching Memories (ReRAMs). Semicond. Sci. Tech. 2017, 32, 093006/1-20. (22) Menzel, S.; Salinga, M.; Böttger, U.; Wimmer, M. Physics of the Switching Kinetics in Resistive Memories. Adv. Funct. Mater. 2015, 25, 6306-6325. (23) Pan, F.; Gao, S.; Chen, C.; Song, C.; Zeng, F. Recent Progress in Resistive Random Access Memories: Materials, Switching Mechanisms, and Performance. Mater. Sci. Eng. R-Rep. 2014, 83, 1-59. (24) 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, 12398/1-6. (25) 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, 1700212/1-8.


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(40) Celano, U.; Gastaldi, C.; Govoreanu, B.; Richard, O.; Bender, H.; Goux, L.; Kar, G. S.; Vandervorst, W. Evidences of Areal Switching in Vacancy-Modulated Conductive Oxide (VMCO) Memory. Microelectron. Eng. 2017, 178, 122-124. (41) Simmons, J. G. Electric Tunnel Effect between Dissimilar Electrodes Separated by a Thin Insulating Film. J. Appl. Phys. 1963, 34, 2581-2590. (42) 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, 1800062/1-12. (43) Reiners, M.; Xu, K.; Aslam, N.; Devi, A.; Waser, R.; Hoffmann-Eifert, S. Growth and Crystallization of TiO2 Thin Films by Atomic Layer Deposition Using a Novel Amido Guanidinate Titanium Source and Tetrakis-dimethylamido-titanium. Chem. Mater. 2013, 25, 2934-2943. (44) Zhang, H.; Aslam, N.; Reiners, M.; Waser, R.; Hoffmann-Eifert, S. Atomic Layer Deposition of TiOx/Al2O3 Bilayer Structures for Resistive Switching Memory Applications. Chemical Vapor Deposition 2014, 20, 282-290. (45) Kügeler, C.; Zhang, J.; Hoffmann-Eifert, S.; Kim, S. K.; Waser, R. Nanostructured Resistive Memory Cells based on 8-nm-thin TiO2 Films Deposited by Atomic Layer Deposition. J. Vac. Sci. Technol. B 2011, 29, 1AD01/1-5.



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(46) Wu, H.; Li, X.; Wu, M.; Huang, F.; Yu, Z.; Qian, H. Resistive Switching Performance Improvement of Ta2O5-x/TaOy Bilayer ReRAM Devices by Inserting AlOδ Barrier Layer. IEEE Electron Device Lett. 2014, 35, 39-41. (47) Ambrogio, S.; Milo, V.; Wang, Z. Q.; Balatti, S.; Ielmini, D. Analytical Modeling of Current Overshoot in Oxide-based Resistive Switching Memory (RRAM). IEEE Electron Device Lett. 2016, 37, 1268 - 1271. (48) Menzel, S.; Waters, M.; Marchewka, A.; Böttger, U.; Dittmann, R.; Waser, R. Origin of the Ultra-nonlinear Switching Kinetics in Oxide-Based Resistive Switches. Adv. Funct. Mater. 2011, 21, 4487-4492. (49) Fleck, K.; La Torre, C.; Aslam, N.; Hoffmann-Eifert, S.; Böttger, U.; Menzel, S. Uniting Gradual and Abrupt SET Processes in Resistive Switching Oxides. Phys. Rev. Applied 2016, 6, 064015/1-11. (50) Torrezan, A. C.; Strachan, J. P.; Medeiros-Ribeiro, G.; Williams, R. S. Sub-nanosecond Switching of a Tantalum Oxide Memristor. Nanotechnology 2011, 22, 485203/1-7. (51) Havel, V.; Fleck, K.; Rösgen, B.; Rana, V.; Menzel, S.; Böttger, U.; Waser, R. Ultrafast Switching in Ta2O5-based Resistive Memories. Silicon Nanoelectronics Workshop SNW 2016, Hawaii 2016, 82-83. (52) Degraeve, R.; Fantini, A.; Raghavan, N.; Goux, L.; Clima, S.; Chen, Y.; Belmonte, A.; Cosemans, S.; Govoreanu, B.; Wouters, D.; Roussel, P.; Kar, G.; Groeseneken, G.; Jurczak, M. Hourglass Concept for RRAM: A Dynamic and Statistical Device Model. 2014 IEEE


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(60) Siemon, A.; Menzel, S.; Marchewka, A.; Nishi, Y.; Waser, R.; Linn, E. Simulation of TaOxbased Complementary Resistive Switches by a Physics-based Memristive Model. 2014 IEEE Int. Symp. on Circuits and Systems (ISCAS) 2014, 1420-1423. (61) Kim, K. M.; Hwang, C. S. The Conical Shape Filament Growth Model in Unipolar Resistance Switching of TiO2 Thin Film. Appl. Phys. Lett. 2009, 94, 122109/1-3. (62) Celano, U.; Goux, L.; Belmonte, A.; Opsomer, K.; Franquet, A.; Schulze, A.; Detavernier, C.; Richard, O.; Bender, H.; Jurczak, M.; Vandervorst, W. Three-Dimensional Observation of the Conductive Filament in Nanoscaled Resistive Memory Devices. Nano Letters 2014, 14, 2401-2406. (63) Kim, G.; Ho Lee, J.; Yeong Seok, J.; Ji Song, S.; Ho Yoon, J.; Jean Yoon, K.; Hwan Lee, M.; Min Kim, K.; Dong Lee, H.; Wook Ryu, S.; Joo Park, T.; Seong Hwang, C. Improved Endurance of Resistive Switching TiO2 Thin Film by Hourglass Shaped Magnéli Filaments. Appl. Phys. Lett. 2011, 98, 262901/1-3. (64) 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 Sswitching Memories. Chem. Mater. 2017, 29, 3164-3173. (65) Syu, Y.; Chang, T.; Lou, J.; Tsai, T.; Chang, K.; Tsai, M.; Wang, Y.; Liu, M.; Sze, S. Atomic-Level Quantized Reaction of HfOx Memristor. Appl. Phys. Lett. 2013, 102, 172903/1-3. (66) Celano, U.; Op de Beeck, J.; Clima, S.; Luebben, M.; Koenraad, P. M.; Goux, L.; Valov, I.; Vandervorst, W. Direct Probing of the Dielectric Scavenging-Layer Interface in Oxide 40 ACS Paragon Plus Environment

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(74) Kroeger, F. A.; Vink, H. J. Relations between the Concentrations of Imperfections in Crystalline Solids. Solid State Physics 1956, 3, 307 - 435. (75) Nabatame, T.; Yasuda, T.; Nishizawa, M.; Ikeda, M.; Horikawa, T.; Toriumi, A. Comparative Studies on Oxygen Diffusion Coefficients for Amorphous and γ-Al2O3 Films using 18O Isotope. Jpn. J. Appl. Phys. Part 1 - Regul. Pap. Brief Com 2003, 42, 7205-7208. (76) Nakamura, R.; Toda, T.; Tsukui, S.; Tane, M.; Ishimaru, M.; Suzuki, T.; Nakajima, H. Diffusion of Oxygen in Amorphous Al2O3, Ta2O5, and Nb2O5. J. Appl. Phys. 2014, 116, 033504. (77) De Souza, R. Limits to the Rate of Oxygen Transport in Mixed-Conducting Oxides. J. Mater. Chem. A 2017, 5, 20334-20350. (78) 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. (79) Szot, K.; Rogala, M.; Speier, W.; Klusek, Z.; Besmehn, A.; Waser, R. TiO2 - a Prototypical Memristive Material. Nanotechnology 2011, 22, 254001/1-21. (80) Stumpf, R.; Liu, C.; Tracy, C. Retardation of O Diffusion through Polycrystalline Pt by Be Doping. Phys. Rev. B: Condens. Matter 1999, 59, 16047-16052.


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FIGURE CAPTIONS: Figure 1. The Pt / TiO2 / Ti / Pt nano-crossbar cells: (a) top view of a (60 nm)2 cross-point in SEM; (b) TEM cross section of a (100 nm)2 device cut along the top electrode (TE); (c) schematic description of the layer stack with electrical contacts. The right part in (c) is the sketch of the plug and disc region in the TiO2 layer. Figure 2. The coexistence of two bipolar switching modes with opposite polarities in a Pt (BE) / 6 nm TiO2 / Ti / Pt (TE) nano-crossbar cell of (100 nm)2 size. The voltage is applied to the Pt electrode. The switching orientation is marked by arrows and the capital letters define states or switching events. The inset shows the zoomed 8w BRS loop (red curve) in linear scale. Figure 3. The stability of 8w switching resistance states in different Pt / 3 nm TiO2 / Ti / Pt cells; (a) retention test at 125 °C performed for a (100 nm)2 cell in the 8w LRS* (cf. state ‘C’ in Fig. 2); (b) the reproducibility of the states tested for non-switching sub-loops for a HRS* in a (60 nm)2 cell (black line) and for an LRS* in a (100 nm)2 cell (red line). Figure 4. Multilevel switching in the 8w BRS mode. (a) The I(V) characteristics of a (60 nm)2 Pt (BE) / 3 nm TiO2 / Ti / Pt (TE) cell obtained with sequential 8w BRS cycles for increased negative stop biasing. (b) The read resistance at -0.3 V for HRS* (solid) and LRS* (open) as a function of |V8w,RESET| for two different cell sizes of (60 nm)2 (triangle) and (100 nm)2 (square). Figure 5. Pulsed switching behavior in the 8w BRS mode. (a) A schematic diagram of pulse procedure carried out with a (100 nm)2 Pt / 3 nm TiO2 / Ti / Pt cell. (b) The read resistance at 0.4 V measured after each write pulse. The red circles represent the LRS* programmed with a signal of 2.2 V. The green square is the initial read out value taken after I(V) loops. The triangles 43 ACS Paragon Plus Environment


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mark the read-out values after applying a negative pulse of increasing amplitude starting at 1.1 V and ending at a pulse of -2.2 V, which exceeds the threshold voltage for c8w SET. Figure 6. The temperature dependence of the resistance of a Pt / 3 nm TiO2 / Ti / Pt cell of (100 nm)2 size in the c8w LRS normalized to the resistance value R0 at the temperature T0 = 298 K. A TCR value of (1.18 ± 0.01) · 10-3 K-1 is obtained from the linear fitting of (RR0)/R0 versus (T-T0). Figure 7. Temperature and voltage dependence of the current response of an (80 nm)2 Pt / 3 nm TiO2 / Ti / Pt cell in LRS*. (a) The ln(I/V2) versus (1/V) plot of the I(V, T) behavior for the negative voltage applied to the Pt BE. (b) A schematic energy band diagram for negative bias applied to the Pt BE. The barrier region, TiO2-x, denotes the insulating gap (‘disc’) between the Pt BE and the conductive filament, TiO2-y. (c) I(V) characteristics (colored lines) measured at various temperatures for the cell in LRS* and HRS* combined with calculated (best fit) I(V) curves obtained from the Simmons’ equation (indicated by the symbols). Figure 8. Depletion charge density ρ (solid line) and conduction band Ec (dashed line) as a function of the position z from the Pt electrode (z = 0 nm) to the Ti electrode (z = 3 nm). The red and blue color stand for the LRS* and HRS*, respectively. Figure 9. Nano-chemical analysis for the cross-section in the Pt / 3 nm Al2O3 / 3 nm TiO2 / Ti device for c8w HRS. (a) High-resolution transmission electron microscopic (HRTEM) picture. (b) The element distribution profiles for O (cyan), Ti (green), Al(red) and Pt(blue) revealed by EDX measurement for this cell. The vertical axis is the distance from the Pt / Al2O3 interface in the unit of nm, while the horizontal axis is the normalized atomic fraction of each species in the unit of at%. 44 ACS Paragon Plus Environment

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Figure 10. Switching model for the two coexisting bipolar resistive switching modes with opposite polarity observed in nano-crossbar Pt / TiO2 / Ti / Pt devices. The occurrence can be understood from a competition of oxygen vacancy drift and diffusion processes with an oxygen transfer reaction at the interface to the high barrier Pt electrode. The corresponding ionic states and dominant processes marked in the I(V) plot are depicted as subfigures on the left and on the right. The color code of the subfigures is: Ti (TE) – violet square, Pt (BE) – grey square, TiO2 – gg

yellow square, Ti3+– violet spheres, double charged oxygen vacancies VO – green spheres, and oxygen atoms – blue spheres.



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Figures

Table of Contents Graphic


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Figure 1

Figure 1. The Pt / TiO2 / Ti / Pt nano-crossbar cells: (a) top view of a (60 nm)2 cross-point in SEM; (b) TEM cross section of a (100 nm)2 device cut along the top electrode (TE); (c) schematic description of the layer stack with electrical contacts. The right part in (c) is the sketch of the plug and disc region in the TiO2 layer.



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Figure 2

Figure 2. The coexistence of two bipolar switching modes with opposite polarities in a Pt (BE) / 6 nm TiO2 / Ti / Pt (TE) nano-crossbar cell of (100 nm)2 size. The voltage is applied to the Pt electrode. The switching orientation is marked by arrows and the capital letters define states or switching events. The inset shows the zoomed 8w BRS loop (red curve) in linear scale.


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Figure 3

Figure 3. The stability of 8w switching resistance states in different Pt / 3 nm TiO2 / Ti / Pt cells; (a) retention test at 125 °C performed for a (100 nm)2 cell in the 8w LRS* (cf. state ‘C’ in Fig. 2); (b) the reproducibility of the states tested for non-switching sub-loops for a HRS* in a (60 nm)2 cell (black line) and for an LRS* in a (100 nm)2 cell (red line).



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Figure 4

Figure 4. Multilevel switching in the 8w BRS mode. (a) The I(V) characteristics of a (60 nm)2 Pt (BE) / 3 nm TiO2 / Ti / Pt (TE) cell obtained with sequential 8w BRS cycles for increased negative stop biasing. (b) The read resistance at -0.3 V for HRS* (solid) and LRS* (open) as a function of |V8w,RESET| for two different cell sizes of (60 nm)2 (triangle) and (100 nm)2 (square).


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Figure 5

Figure 5. Pulsed switching behavior in the 8w BRS mode. (a) A schematic diagram of pulse procedure carried out with a (100 nm)2 Pt / 3 nm TiO2 / Ti / Pt cell. (b) The read resistance at 0.4 V measured after each write pulse. The red circles represent the LRS* programmed with a signal of 2.2 V. The green square is the initial read out value taken after I(V) loops. The triangles mark the read-out values after applying a negative pulse of increasing amplitude starting at 1.1 V and ending at a pulse of -2.2 V, which exceeds the threshold voltage for c8w SET.



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Figure 6

Figure 6. The temperature dependence of the resistance of a Pt / 3 nm TiO2 / Ti / Pt cell of (100 nm)2 size in the c8w LRS normalized to the resistance value R0 at the temperature T0 = 298 K. A TCR value of (1.18 ± 0.01) · 10-3 K-1 is obtained from the linear fitting of (RR0)/R0 versus (T-T0).


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Figure 7

Figure 7. Temperature and voltage dependence of the current response of an (80 nm)2 Pt / 3 nm TiO2 / Ti / Pt cell in LRS*. (a) The ln(I/V2) versus (1/V) plot of the I(V, T) behavior for the negative voltage applied to the Pt BE. (b) A schematic energy band diagram for negative bias applied to the Pt BE. The barrier region, TiO2-x, denotes the insulating gap (‘disc’) between the Pt BE and the conductive filament, TiO2-y. (c) I(V) characteristics (colored lines) measured at various temperatures for the cell in LRS* and HRS* combined with calculated (best fit) I(V) curves obtained from the Simmons’ equation (indicated by the symbols).



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Figure 8

Figure 8. Depletion charge density ρ (solid line) and conduction band Ec (dashed line) as a function of the position z from the Pt electrode (z = 0 nm) to the Ti electrode (z = 3 nm). The red and blue color stand for the LRS* and HRS*, respectively.


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Figure 9.

Figure 9. Nano-chemical analysis for the cross-section in the Pt / 3 nm Al2O3 / 3 nm TiO2 / Ti device for c8w HRS. (a) High-resolution transmission electron microscopic (HRTEM) picture. (b) The element distribution profiles for O (cyan), Ti (green), Al(red) and Pt(blue) revealed by EDX measurement for this cell. The vertical axis is the distance from the Pt / Al2O3 interface in the unit of nm, while the horizontal axis is the normalized atomic fraction of each species in the unit of at%.



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Figure 10.

Figure 10. Switching model for the two coexisting bipolar resistive switching modes with opposite polarity observed in nano-crossbar Pt / TiO2 / Ti / Pt devices. The occurrence can be understood from a competition of oxygen vacancy drift and diffusion processes with an oxygen transfer reaction at the interface to the high barrier Pt electrode. The corresponding ionic states and dominant processes marked in the I(V) plot are depicted as subfigures on the left and on the right. The color code of the subfigures is: Ti (TE) – violet square, Pt (BE) – grey square, TiO2 – gg

yellow square, Ti3+– violet spheres, double charged oxygen vacancies VO – green spheres, and oxygen atoms – blue spheres. 56 ACS Paragon Plus Environment

Understanding the Coexistence of Two Bipolar Resistive Switching

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