resistive memory switching in layered oxides: anbno3n+2 perovskite derivatives and bi2sr2cacu2o8+δ...

Phys. Status Solidi A 208, No. 2, 284–299 (2011) / DOI 10.1002/pssa.201026757 p s sa

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pplications and materials science

eature Article
Resistive memory switching inlayered oxides: AnBnO3nR2
perovskite derivatives andBi2Sr2CaCu2O8Rd high-Tc superconductor

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Y. Koval*,1, F. Chowdhury1, X. Jin1, Y. Simsek1, F. Lichtenberg2, R. Pentcheva3, and P. Muller1

1 Department of Physics and Interdisciplinary Center for Molecular Materials (ICMM), Universitat Erlangen-Nurnberg,

91058 Erlangen, Germany2 Experimentalphysik VI, University of Augsburg, 86135 Augsburg, Germany3 Department of Earth and Environmental Sciences, University of Munich, 80333 Munich, Germany

Received 9 August 2010, revised 17 December 2010, accepted 17 December 2010

Published online 12 January 2011

Keywords carrier injection, cuprate superconductors, current–voltage characteristics, perovskites, resistive memory switching,tunneling

* Corresponding author: e-mail [email protected], Phone: þ49 9131 8527408, Fax: þ49 9131 15249

Resistive memory switching was investigated in titanates and

niobates of the type AnBnO3nþ2 and in the high-Tc super-

conductor Bi2Sr2CaCu2O8þd. We studied the switching by

current injection perpendicular to the layers. Both dc and pulsed

measurements were performed. Out-of-plane transport proper-

ties were investigated by measurements of the resistance and

current–voltage characteristics (IVs) vs. temperature for differ-

ent resistive states. The critical temperature of superconducting

transition and the critical current of intrinsic Josephson

junctions were also analyzed for different resistive states in

Bi2Sr2CaCu2O8þd. The resistive memory switching was

explained in terms of doping of the conducting layers, which

is induced by trapped charges in the insulating layers. The

charged insulating layers act as a floating gate and reduce or

increase the carrier concentration in the conducting layers,

respectively. We found that all studied materials demonstrate a

different type of non-persistent resistive switching at low

temperatures. This type of switching shows up in a specific form

of current–voltage characteristics with a pronounced back-

bending often called s-shaped IV. Both types of resistive

switching with and without memory effect were analyzed in

terms of electron overheating. We examine the role of hot

electrons and discuss additional factors, which might lead to

persistent resistive states.

� 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction The concept of nonvolatile memory,based on change of resistance rather than on storage ofcharge, is rather attractive for microelectronics industry.There are many systems which demonstrate an electricallystimulated, programmable change of resistance. Variousphenomena like change of phase in chalcogenide-basedmaterials [1], growth and dissolution of metal filaments insolid electrolytes [2], or a number of effects like ferroelec-tricity in oxides of transition metals [3–6] were investigated.These effects are considered as potential candidates forresistive nonvolatile memory [7].

In transition metal oxides, resistive memory switchinghas been observed ranging from perovskites [4, 6, 8] tobinary oxides [9–11]. For instance, bistable resistance states

were observed in metal-oxide-metal devices with perovs-kite-type intermediate layers [6, 12]. In SrTiO3, resistiveswitching was associated with redistribution of oxygenvacancies between the electrodes [4]. Change of resistance inmanganites was attributed to doping control in the electrodeinterface due to oxygen defect redistribution [13]. The metal-insulator transition of SrTiO3 doped with Cr was explainedby a change of Cr valence under electronic charge injection[7]. Recently, we reported on resistive memory switching inhigh temperature superconductor Bi2Sr2CaCu2O8þd [14]. Inthis material, the switching was explained by change ofcarrier concentration in the conducting layers.

Several additional requirements, important for non-volatile memories like programming speed, resistance ratio,


Phys. Status Solidi A 208, No. 2 (2011) 285

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endurance, retention, etc., were discussed intensively (seee.g., Ref. [15]). Although all these characteristics areessential for applications, the core effect is a reliable changeof the resistance between low and high resistive states, whichcan be achieved by current/voltage pulses. The switching hasto be reproducible and should not require any feedback toensure that the writing signal produces the expected effect.To achieve the repeatability and guarantee the switchingevents, the mechanism of the resistance change has to be wellunderstood. In spite of the recent progress in investigation ofswitching processes on a microscopic scale (see Ref. [15]and references therein), more efforts are necessary to explainthe observed phenomena.

In this work we report on our results of experimentalinvestigation of resistive switching in different layeredoxides: (1) perovskite-related layered materials of theseries AnBnO3nþ2 [16] and (2) the high-Tc superconductorBi2Sr2CaCu2O8þd [17, 18]. All of these materials consist ofconducting planes, which are separated by insulating layers.We investigated out-of-plane transport properties andresistive memory switching induced by current injection.All studied materials demonstrate resistive switching, whichis persistent in time. While the perovskite-related materialsAnBnO3nþ2 are attractive for non-volatile memory appli-cations because of their resistance stability at roomtemperature, Bi2Sr2CaCu2O8þd is interesting for the inves-tigation of the resistive switching mechanism. InBi2Sr2CaCu2O8þd different resistive states can be investi-gated in more detail below the critical temperature. Theswitching phenomenon can be traced layer-by-layer usingthe intrinsic Josephson effect [17, 18] (see Section 2).

In addition to persistent resistive memory switching, allstudied materials also demonstrate another type of non-persistent resistive switching, when the resistance totallyrestores at low bias. Such behavior is also called a resistiveswitching [19, 20] as a sharp change of resistance takes placeat a threshold voltage. In other words, current–voltagecharacteristics (IV) is of a specific type, which is often calledan s-shaped IV [21, 22]. We analyze both types of resistiveswitching. The results are discussed in terms of out-of-planeinjection of hot electrons. We show that in layered materialsthe overheated electrons play a significant role for bothspecific s-shaped IV and resistive memory switching.Additional factors, which can lead to persistence of theresistive states are discussed.

The paper is organized as following. In Section 2 we givea brief description of the materials used in our experiments.We analyze mostly a layered nature of these materials and astrong anisotropy of conductivity along and perpendicular to(ab) plane. Different possibilities of doping are discussed.After a brief description of our experimental methods (seeSection 3) we report our experimental results on resistivememory switching in AnBnO3nþ2 perovskite derivatives (seeSection 4). DC and pulsed measurements are presented. Inthe next Section 5 we discuss out-of-plane IVs of AnBnO3nþ2

measured at high and low temperatures. The results areanalyzed in terms of tunneling and overheated electrons.

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Section 6 is devoted to resistive switching and IVs in high-Tc

superconductor Bi-2212. We emphasize a similar behaviorof AnBnO3nþ2 and Bi-2212. In view of our results, theconcept of hot electrons is discussed in more details. InSection 7 the mechanism of resistive memory switchingbased on conducting layers doping via trapping electrons inthe insulating layers is discussed in detail. Finally, wepresent our conclusions in Section 8.

2 Materials2.1 AnBnO3nR2 perovskite derivatives We stu-

died single crystals of perovskite-related materialsLaTiO3.41, SrNbO3.41, CaNbO3.41, Sr0.95NbO3.37, andSrNbO3.45, which are members of the series AnBnO3nþ2

slightly overdoped with oxygen. According to the phasediagram of AnBnO3nþ2 titanates and niobates [16], singlephase crystals can be obtained for n¼1 and for n between 5and 4.

When n is equal to 1, the stoichiometry of the materialsis reduced to ABO3, e.g. LaTiO3, SrNbO3. These materialshave a 3D perovskite crystal structure. The oxidation statesof B-cations Ti and Nb are þ3 and þ4, respectively. This isnot the highest oxidation state of Ti and Nb ions and it resultsin d1 unpaired electrons per B-cation. Generally, thematerials with n¼1 are semiconductors. The transportproperties are very sensitive to any kind of doping, which canbe achieved by either reducing the oxygen content or/andsubstitution of the cations A and B by metals with a differentvalence. E.g., Laþ3 can be substituted by Srþ2 in LaTiO3.

On the opposite side of the phase diagram there are fullyoxidized materials with B-cations Tiþ4 and Nbþ5. In this casen is equal to 4, and the corresponding nominal stoichiometryis ABO3.5, e.g. LaTiO3.5 or SrNbO3.5. There are no unpairedelectrons (d0), and the materials are ferroelectric insulatorswith a layered crystal structure. Each layer consists of 4 BO6

octahedra slabs. The layers are shifted with respect to eachother (see Fig. 1) along the (ab) plane. The distance betweenthe layers is larger than the inter-slab distances inside thelayers as the oxygen in the corners of the side BO6 octahedraare not shared. This results in a strong in-plane and out-of-plane anisotropy of the transport properties [16].

In the materials under study the oxygen content isreduced with respect to the fully oxidized materials. Thisleads to stable single-phase crystals with n¼ 5, where thelayers consist of five BO6 octahedra slabs as it is shown inFig. 1. The ideal stoichiometry is ABO3.4 and results in amixed valence of Ti and Nb ions, which is equal to 3.8 and4.8, respectively. The number of unpaired electrons per B-cation is d0.2, i.e., the cations B exist in different oxidationstates: 80% of Ti or Nb atoms are fully oxidized, and 20% ofthem are in þ3 and þ4 states, respectively. For instance,every fifth ion of Nb is in valence þ4 in CaNbO3.4 orSrNbO3.4. Apparently, the properties of these materialsdepend not only on the amount of the B-cations in differentvalences but also on the distribution of the low valencecations inside the layers. E.g., Tiþ3 cations can completelyoccupy only the middle slab of the layer or, alternatively,


286 Y. Koval et al.: Resistive memory switching in layered oxidesp

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Figure 1 (online color at: www.pss-a.com) Crystal structure of theA5B5O17 perovskite derivative. Green: A-cations, magenta: BO6

octahedra.

Figure 2 (online color at: www.pss-a.com) Crystal structure of Bi-2212.Green:Biatoms,blue:Oatoms, red:CuO2 planesdefiningasetof a half-ochahedra with the apical O atoms.

they can be distributed inside the layer. The distribution ofthe cations will be discussed later in more detail.

Our crystals are slightly overdoped with oxygen, whichresults in a reduced concentration of unpaired electrons.LaTiO3.41, CaNbO3.41, and SrNbO3.41 has d0.18. Sr0.95NbO3.37

is characterized by an even smaller value of unpairedelectrons d0.16. SrNbO3.45 consists of alternating layers withfour and five slabs of BO6. Every tenth Nb cation is in thevalence þ4, and the concentration of the unpaired electronsis d0.1 per Nb.

All materials under investigation show a strong aniso-tropy in a, b, and c crystallographic directions (see Ref. [16]and references therein). The materials demonstrate a metallictype of conductance along <a>-direction in a certaintemperature range, which depends on the number of unpairedelectrons. This type of behavior was attributed to the chain-like arrays of the corner-shared BO6 octahedra. In <b>- and<c>-directions the materials show a semiconductingbehavior, i.e. the resistance increases with cooling.Specifically for the most conducting material SrNbO3.41,the temperature dependence of resistance along <b>-direction is rather weak with a metallic-type behaviorbetween �100 and �40 K. In all materials, the highestresistance was observed along <c>-direction. According toour experimental results, out-of-plane conductance can bedescribed in terms of tunneling between conducting planes.

The conductance depends on the metal used for cationsas well as on the number of unpaired electrons per B-cation,


e.g., SrNbO3.41 with d0.18 demonstrates a higher conductivitythan Sr0.95NbO3.37 with d0.16. The room temperatureresistivities in <c>-direction are �1.5 and �2 V cm,respectively. At 4 K the difference is more significant: theresistivities are 4� 102 and 4� 103 V cm, respectively.CaNbO3.41 and LaTiO3.41 show a significantly higherresistivity in comparison to SrNbO3.41. Out-of-plane resis-tivities at RT are 20 and 50V cm. At low temperature (�4K),both materials have a similar resistivity �107 V cm.

2.2 Bi2Sr2CaCu2O8Rd Bi2Sr2CaCu2O8þd (Bi-2212) isa high-Tc superconductor. It has a layered structure withconducting (superconducting below Tc) CuO2 double layersseparated by insulating BiO layers. Schematically the crystalstructure of Bi-2212 is shown in Fig. 2. The electricalproperties of this material strongly depend on the carrierconcentration in the conducting planes. Usually, doping isachieved by changing the stoichiometry of the insulatinglayers, e.g. by oxygen excess in the BiO layers, whichprovides charge carriers for the CuO2 planes [23–25]. That iswhy the insulating layers are also called charge reservoirs ordoping layers. Upon doping, antiferromagnetic order in this

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Figure 3 (online color at: www.pss-a.com) Schematic diagram ofthe mesa-type structure preparation (a–e). Device connections forout-of-plane (f) and in-plane (g) transport measurements.

material is destroyed and metallic conductivity isestablished.

The material demonstrates a strong anisotropy oftransport properties in (ab) plane and perpendicular to thelayers. Out-of-plane transport is provided by tunnelingbetween the conducting layers and characterized by highresistance [17]. The ratio of resistivity in <c>-direction andin the (ab)-plane depends on the level and method of doping,but typically it is �104–105 [26], which is of the same orderor higher than this ratio in the AnBnO3nþ2 perovskitederivatives. Below Tc the stack of superconducting andinsulating layers can be considered as intrinsic supercon-ductor–insulator–superconductor Josephson junctions[17, 18]. At low enough temperature, the intrinsicJosephson junctions are in the underdamped state and showa strongly hysteretic multi-branch current–voltage charac-teristic [17, 18]. Each Josephson junction provides oneresistive branch on the IV. They can be easily traced up fromthe return curve of the resistive state. The number of layers inthe sample can be easily obtained by counting the number ofresistive branches on the current–voltage characteristic. It isa serious advantage in comparison to other materials,because the height of the stack is difficult to define preciselyusing only parameters of preparation like etching time, etc.

There are more advantages of a superconductingmaterial for investigation of the resistive memory switchingphenomenon. Indeed, besides the normal state properties likeresistance, the superconducting properties like the criticalcurrent density Jc and critical temperature Tc can bemeasured. Both Jc and Tc are determined by the carrierconcentration in the conducting planes [23]. Comparing thechanges in the normal resistance and in the superconductingproperties we will try to identify the mechanism of theresistive memory switching in layered materials.

3 Sample preparation for in-plane and out-of-plane measurements High quality single crystals ofLaTiO3.41, SrNbO3.41, CaNbO3.41, Sr0.95NbO3.37, andSrNbO3.45 were used. Crystal growth was described in detailin Ref. [16]. For switching experiments and measurements oftransport properties in <c>-direction we used mesa-typestructures [27]. Schematically, the preparation steps areshown in Fig. 3. Small pieces of single crystals were gluedonto a glass substrate and cleaved. A freshly cleaved surfaceof the crystal (ab) plane was covered by a thermallyevaporated double layer of Cr/Au [Fig. 3(a)]. We found thatCr guarantees a good adhesion of Au layers and provides alow contact resistance.

The first mesa structures were fabricated by electron-beam lithography and ion-beam etching as it is shown inFig. 3(b). Two side mesas labeled as A and B [see Fig. 3(c)]provide contacts to the crystal. In the next step two smallmesas D and E were fabricated on the top of the central mesaC by electron-beam lithography and ion-beam etching (seeFig. 3(c) and an enlarged view in (f)). These small mesasprovide two independent contacts to the mesa C. Afterwards,all mesas were insulated by polymethylmethacrylate

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(PMMA). The layer of PMMA was spin-coated on thesample. Electron-beam lithography was used to open thewindows above the mesas [see Fig. 3(d)]. By additional high-dose electron exposure the PMMA was cross-linked [28, 29]around the mesas. The rest of the PMMA layer was dissolvedin aceton. Then, the sample was covered by a 100 nm layer ofthermally evaporated silver. The wiring electrodes werepatterned in the next step by lithography and ion-beametching. The final structure is shown in Fig. 3(e). Typicallythe size of the central mesa C was 5� 10mm2. The resistanceof the central mesa C was measured by connecting a currentsource to the side mesa A and the small mesa D and avoltmeter to mesas B and E. In this way we were able tomeasure the resistance of the central mesa by a 4-point (4p)method [Fig. 3 (g)]. Simultaneously, we checked the voltagedrop in the current contacts A and D in order to measure theresistance by the 2-points (2p).

For in-plane measurements, the glued crystal wascleaved several times until it became semi-transparent. Thethickness of the crystal was less than 1mm. Then, byelectron-beam lithography and ion-beam etching a5� 30mm2 stripe was patterned from the crystal. In thenext steps, the sample was covered by a thermally evaporatedCr/Au layer and four in-row mesas were fabricated on thestripe. After the insulation process and fabrication of wiringelectrodes the structure looks as it is shown schematically inFig. 3(h). Using the side mesas for current injection and the



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Figure 4 (online color at: www.pss-a.com) Schematic diagram ofz-shapedstructurepreparationbythestandarddouble-sidetechnique(a–d). Device connections for out-of-plane measurements (e).

Figure 5 (online color at: www.pss-a.com) Resistive memoryswitching in SrNbO3.41. Current–voltage characteristics (a) anddifferential conductance vs. voltage (b) of the central mesa.

Figure 6 (online color at: www.pss-a.com) Resistive memoryswitching in LaTiO3.41. Current–voltage characteristics (a) anddifferential conductance vs. voltage (b) of the central mesa.

central mesas for detection of the voltage, we provided fourpoint in-plane measurements.

Out-of-plane measurements of Bi-2212 were performedon the structures with z-shaped geometry fabricated by thestandard double-side technique [30–33] shown schemati-cally in Fig. 4. A single crystal of Bi-2212 was glued onto thesapphire substrate. A freshly cleaved surface of the crystalwas covered with �50 nm of gold. Then, using electron-beam lithography and ion-beam etching, a structure withtwo stairs was fabricated [see. Fig. 4(a)]. In the next stepthe part of the crystal with stairs was covered by epoxy, andthe second sapphire substrate was glued onto the top of thesample (b). After curing of the epoxy, two substrates wereseparated (c). The top substrate labeled as sapphire 2 hasthe structure, which can be used in the next patterning stepshown in Fig. 4(d). The final structure consists of two stacksS and L in series. However, the area of the stack L is at leasttwo orders of magnitude larger than the area of the stack S,and therefore, during measurements of the stack S theresistance of L can be neglected.

4 Resistive memory switching in AnBnO3nR2

4.1 DC-measurements Qualitatively the resultsobtained for all investigated materials are similar [34]. Atlow bias, the current–voltage characteristics are slightly non-linear as it is shown in Figs. 5(a) and 6(a) for SrNbO3.41 andLaTiO3.41, respectively. Positive bias is defined as currentinjection from the base crystal. The IVs do not show anyhysteresis if the bias is smaller than a threshold value. Anincrease of the bias current–voltage over some thresholdvalue results in a fast increase of the resistance (see (1-2)parts of IVs). The new resistance is persistent even after thebias decreases to zero (3). The observed change of resistanceis usually called resistive memory switching. The original


state with low resistance and the state after the switching arecalled low-resistive (LR) and high-resistive (HR) states orON and OFF states.

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Switching back from HR to LR state is achieved on theopposite side of IV at negative bias (4-5). The absolutevalues of the threshold current and voltage for HR!LRswitching are always higher than the one for the LR!HRswitching. The restored LR state has almost the sameresistance and current–voltage characteristic. The resist-ances are stable in time, and a nondestructive readout of thestates is possible at low bias current. Typically, in I–Vmeasurements, we observed a ratio of resistances in HR andLR states of the order of 3–6 for all investigated materials.However, substantially higher (>10) and lower (see thefollowing sections) ROFF/RON ratios were also detected. Thesequence (1-2-3-4-5-6) can be repeatedly reproduced severaltimes with rather reproducible resistances of LR and HRstates.

Although, the switching from the original LR to HR stateare shown on the positive side of IV, the polarity of the biasfor the first switching event does not make any difference. Aspecial electroforming process prior the repetitive resistiveswitchings is not required, which is different from the metal-insulator-metal junctions reported previously (see e.g., [15]and references therein).

A closer look to the differential conductance shows thatin the sub-threshold region before LR!HR switching, theconductance of the samples already changes slightly [seeFigs. 5(b) and 6(b)]. This change points to the beginning ofthe transition, which is slow in the sub-threshold region. Aquick transition occurs only at higher currents. In theopposite direction, the switching from HR to LR state takesplace abruptly. However, well below the threshold current,small but evident instabilities at the voltage are visible on theIVs (not shown in dI/dV plots).

We found that the resistive memory switching inAnBnO3nþ2 depends on the temperature of the samples. InFig. 7 we present a series of switching IVs in LaTiO3.41

Figure 7 Resistive memory switching in LaTiO3.41 measured atdifferent temperatures.

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obtained between 295 and 120 K. Apparently, the thresholdcurrent increases with cooling. The switching effect in termsof ROFF/RON ratio strongly decreases at low temperatures. Infact, the strong dependence on temperature points to athermally activated nature of the resistive memoryswitching.

An influence of the resistive memory switching on themechanism of conductance was investigated by successivemeasurements of the temperature dependence of resistanceR(T) in both LR and HR states. At first, a R(T) dependence ofthe sample in the original LR state was measured. Then thesample was switched to the HR state, andR(T) was measuredagain. The switching between LR and HR states and thesubsequent R(T) measurements were performed severaltimes. In Fig. 8(a), the plot of R(T) for SrNbO3.41 is shown inlog(R)–T coordinates. Both states are stable and not affectedby the temperature change, i.e. the cooling–warming cyclesin the range of temperatures 300–4.2 K show no hysteresis inR(T).

The R(T) dependence of SrNbO3.41 is rather complex,mostly because of the unusual temperature dependence of(ab) plane resistance. According to the data of Lichtenberget al. [16], in the temperature range �120–50 K theresistance in the (ab) plane shows a metallic behavior. Athigher and lower temperatures, the (ab) plane demonstratesan increase of the resistance with cooling. We determined theactivation energies D of out-of-plane resistance in differenttemperature ranges. The results are shown in Fig. 8(a). The

Figure 8 (online color at: www.pss-a.com) Temperature depend-ence of resistivity of the central mesa of SrNbO3.41 measured in low-resistance and high-resistance states (a). Resistance ratio of HR andLR states vs. temperature (b).



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Figure 9 (online color at: www.pss-a.com) Resistance ratio ofCaNbO3.41 in HR and LR states vs. temperature.

Figure 10 (online color at: www.pss-a.com) Pulse measurementsof CaNbO3.41 in<c>-direction. Unipolar with gradually increasingamplitude (a);bipolar with pulse amplitude higher than the thresholdcurrents (b).

values of D for the LR state are in good agreement with thedata in Ref. [16]. In the HR state, the activation energy at hightemperature coincides with the activation energy in LR state.However, at lower temperatures a significant difference inDof LR and HR states was found. Thus, in the temperaturerange 130–80 K, DHR¼ 22 meV is significantly lower thanDLR ¼ 36 meV. Between 35 and 20 K the DHR¼ 2.5 meV ishigher than DLR¼ 1.5 meV.

This non-monotonous change of difference in theactivation energies with temperature can be clearly seen inthe plot of ROFF/RON vs. T presented in Fig. 8(b). In the hightemperature region the ratioROFF/RON is nearly constant, butat low temperatures it changes non-monotonously withcooling. Similar results are shown in Fig. 9 for CaNbO3.41. Inthe low temperature region, the ratio ROFF/RON has amaximum in opposite to SrNbO3.41, which demonstrates aminimum. However, both materials show a similar behaviorat high temperature: the ROFF/RON ratio is nearly constant. Arational conclusion, which can be drawn from thesemeasurements, is that the resistive memory switching cannotbe explained only by changes in the tunneling barrier.Apparently, the transport properties of the conducting layersalso change significantly. The changes in conducting layerswill be discussed later in more detail.

4.2 Pulsed measurements To investigate reprodu-cibility of the resistive memory switching and to reduce theinfluence of heating we performed pulsed measurements.Here we present our data for the pulsed measurements ofCaNbO3.41. A current pulse of required amplitude wasapplied for a short time (typically 10–50 ms). Then, thecurrent was decreased to a low level, and the resistances ofthe mesas were measured. Two values were monitoredsimultaneously. The first one R2p, is the resistance of thesmall mesa connected to the current source and the resistanceof the central mesa [see Fig. 3(f)]. The second value, R4p,characterizes only the central mesa. It is measured by usingthe second small mesa for voltage monitoring as it is shownin Fig. 3(f). In the two point configuration (R2p), the contactresistance between the small mesa and the Cr layer is alsoincluded. Because of the high anisotropy of the resistance in


(ab) plane and <c>-direction (>103), the four pointconfiguration (R4p) gives a nearly true resistance value ofthe central big mesa.

In Fig. 10(a) we show that pulses of an amplitude smallerthat the threshold current �1.3 mA produce no effect on theresistance of the sample. At higher pulse amplitude theresistance of the small mesa starts to change in a non-reproducible manner. Although, the polarity of the pulses isalways the same, the resistance changes in both directions.The big mesa (R4p) also changes slightly. Here, the resistiveswitchings are not reproducible. A reproducible switchingbetween LR and HR states was achieved by bipolar pulses ofcurrent with an amplitude well above the threshold values ofLR!HR and HR!LR transitions [Fig. 10(b)].

Both mesas (R2p and R4p) switch in phase. In the pulsemeasurements, the resistance ratio between HR and LRstates is lower than the ratio we observed in dc I–Vmeasurements. We can ascribe this effect to a smallercontribution of heating during the pulses. After a largenumber of pulsed switchings the resistance of LR and HRstates can slightly drift to higher or lower values. Although,the resistive states are well separated, a slow drift of LR andHR levels potentially creates difficulties for practicalapplications.

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Figure 11 (online color at: www.pss-a.com) Pulse measurementsof CaNbO3.41 in <c>-direction. Bipolar with a current amplitudebetween the threshold currents for LR!HR and HR!LR tran-sitions (a). In-phase and out-of-phase switching in small and centralmesas (b).

Figure 12 (online color at: www.pss-a.com) In-plane pulse meas-urements of CaNbO3.41.

Figure 13 (online color at: www.pss-a.com) Current–voltagecharacteristics of CaNbO3.41, measured at different temperaturesbetween 300 and 200 K.

As we discussed above, the threshold current forswitching from LR to HR state IOFF is smaller than thethreshold current of the switching from HR to LR states ION.Using bipolar pulses with an amplitude higher than IOFF butlower than ION we observed small subsequent switchings tohigher resistance. The effect of the pulses is accumulatedleading to a significant resistance change [see Fig. 11(a)].After the resistance increases by one order of magnitude thesample transforms irreversibly. The HR state spontaneouslyresets to LR state with reduced threshold currents. Thesubsequent switchings are characterized by a small ROFF/RON ratio and an enhanced drift of LR and HR levels.

In the next Fig. 11(b) we show that the switchings in thesmall and big mesas take place independently. The resistiveswitchings can happen in phase or out of phase. It canbe easily observed during measurements, when the ampli-tude of the pulses is below ION. At higher pulse amplitudethe switching typically takes place in phase as we showed inFig. 10(b).

We want to emphasize that for the resistive memoryswitching in AnBnO3nþ2 materials the polarity of the bias isnot important. However, after the first switching from LR to

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HR state, the switching back to the LR state is easierobserved at a bias of opposite polarity.

In the previous section we mentioned that resistivememory switching can be the result of changes in theconducting layers. This should show up as a conductancechange for transport in (ab) plane. To measure the switchingin the (ab) plane, four mesas in line were fabricated, as it wasdescribed earlier in the text. Applying current pulsesaccording to the scheme in Fig. 3(g), we have found thatinjection of current does change the (ab) plane resistance(see Fig. 12). In our experiments, the change of the resistancebetween HR and LR states was rather small because the topplanes of the crystal, where the injection occurs, are shuntedby the bulk of the crystal. Nevertheless, the influence of theinjected current on the (ab) resistance is clearly visible.

5 AnBnO3nR2 current–voltage characteristicsCurrent–voltage characteristics of the materials in LR andHR states were investigated at small bias well below theswitching thresholds. We measured a series of IVs in thetemperature range between 200 and 300 K. The current–voltage characteristics are non-linear. The non-linearitybecomes more pronounced with cooling. In Fig. 13 we



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present the data for the HR state of CaNbO3.41. In coordinatesof ln(s) vs. U2, the IVs show a linear behavior with a slopealmost independent on temperature. The current–voltagecharacteristics can be described by the formula

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� �exp bU2

� �; (1)

where D is the activation energy of conductance, s0 the pre-exponential factor, and b is a parameter. The same type ofbehavior was observed for the LR state. The activationenergy in this temperature range is the same for both states.This means that the difference in conductance at zero bias isprovided by the pre-exponential factor, which is mostlydetermined by the conducting layer properties. Theparameters b for this sample are 0.55 and �0.85 for HRand LR states, respectively. Taking into account thatbU2<<1 the formula (1) can be reduced to

I/U þ bU3; (2)

which is similar to the well known expression for thetunneling current–voltage characteristics of a metal-insulator-metal contact [35] in the limit of small voltages.Thus, we can conclude that out-of-plane transport in theinvestigated materials is provided by tunneling between theconducting layers. Then, the smaller value of b in the HRstate can be interpreted as a consequence of an increased

re 14 (online color at: www.pss-a.com) Low-temperatureent–voltage characteristics (a) and conductance vs. voltagef CaNbO3.41.

11 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

tunneling barrier thickness or height [35] after LR!HRswitching.

At lower temperatures the current–voltage character-istics demonstrate a stronger non-linearity. At �60 K inCaNbO3.41 and at �20 K in Sr0.95NbO3.37, a branch with anegative differential conductance appears [see Figs. 14(a),15(a)]. Later in the text we will call it a back-bending ors-shaped behavior. IVs are symmetrical; i.e. the back-bending does not depend on the bias polarity [see Fig. 14(b)].A further decrease of the temperature leads to a morepronounced back-bending. It is clearly visible in Fig. 15,where the measurements were performed down to 4.2 K.Sr0.95NbO3.37 is a high conducting material, which allows toobserve the s-shaped IV at lower voltages and consequentlyat lower heating power.

The first observations of s-shaped IV’s were reportedmore than 40 years ago by Ovshinsky [36]. He found a fastreversible switching of resistance in the amorphous semi-conductor Te–As–Si–Ge. Their method of measurementsalmost excludes the negative differential resistance branchbecause of a rather steep load-line. In this case, sharp changesin resistance are observed. Using a current source with anearly horizontal load-line, the IV demonstrates a smoothback-bending as it is shown in Figs 14(a) and 15(a).

Later a similar switching behavior was observed in manydifferent systems (see review of Adler et al. [37]). Morerecent examples are disordered VOx films [19], semicon-ductor heterostructures [20, 22], p–n junctions in series [38],

Figure 15 (online color at: www.pss-a.com) Low-temperaturecurrent–voltage characteristics (a) and conductance vs. voltage(b) of Sr0.95NbO3.37.

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Figure 16 Temperature dependence of the<c>-axis resistance ofSr0.95NbO3.37.

Figure 17 (online color at: www.pss-a.com) Dependence of con-ductance vs. dissipated power of Sr0.95NbO3.37 calculated from IVsmeasured at 4.2 and 15 K.

just to name a few. The back-bending was often explained byJoule overheating and interplay between the temperaturedependence of resistance, heat capacitance, conductance,and others [39]. The crystal overheating interpretation isfrequently used to explain the back-bending in super-conducting materials [40], because an additional tempera-ture dependent parameter can be used for the decrease of theresistance at higher temperatures: the superconductingenergy gap.

Although, the lattice heating cannot be excludedcompletely, the explanation of the back-bending exclusivelyby heating is rather ambiguous. Very simple arguments canbe used. E.g., it is clearly seen that above the back-bendingthe current–voltage characteristics obtained at the lower bathtemperature of 4.2 K is characterized by a higher conduc-tance in comparison to the 17 K IV [see Fig. 15(a)]. At thesame time, the power P¼ I�V dissipated in the crystal, andconsequently the overheating at 4.2 K, is smaller than theoverheating at 17 K. Thus, the lower temperature of thecrystal at 4.2 K corresponds to a higher conductance incomparison to the 17 K measurements. Definitely this is incontradiction with the temperature dependence of resistance,which shows a monotonous decrease with temperature (seeFig. 16).

The power arguments can be developed by plotting thedependence of conductance vs. the dissipated power P fortwo different bath temperatures 4.2 and 17 K (see Fig. 17). Itis clearly seen that on the right side of the plot theconductance at 4.2 K is higher than the one at 17 K for thesame dissipated power. However, the higher 4.2 K con-ductance cannot be explained by crystal overheating.

Several explanations of the back-bending were proposedincluding formation of current filaments [21, 37] or a Mottmetal–insulator transition [19]. Recently, the s-shaped IVswere observed in InOx amorphous films [41]. The authorsproposed an explanation based on the concept of electronoverheating. If the transport is provided by a subsequenttunneling between either grains or localized states and theelectron–phonon coupling is weak, the energy of electronscan rise in the successive tunneling events.

To explain our results we will use the model proposed inRef. [41]. The authors wrote the heat-balance equation in the

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form

U2

RðTelÞ¼ GV Tg

el�Tgph

� �; (3)

where U is the voltage applied between electrodes, R(T) thedependence of resistance vs. temperature measured at smallbias, Tel is the temperature of electrons, which can bedifferent from the phonon bath temperature Tph due tooverheating. Also, G is the electron–phonon couplingstrength and V is the volume of the sample. The parameter gused in [41] was equal to 6. It was calculated for a metal inthe dirty limit [42] and, actually, can be different in our case.To obtain Eq. (3), the authors made a strong assumption thatthe IV would be linear if the temperatures of the electronsand the bath were equal. The non-linear behavior of IVs thencan be explained exclusively by electron overheating.

Although, a non-linear IV can be due to many differentreasons, we assume that their contribution to non-linearity issmaller than the role of the overheated electrons. At least inthe case of Sr0.95NbO3.37 we can exclude the influence of theenergy gap in the conducting layers, because the temperaturedependence of conductance in (ab) plane is rather weak [16].

Then, following the model in Ref. [41], each point of theIV can be characterized by the value of the resistanceR ¼ U=I. The temperature of electrons at these points canbe found using the experimental resistance vs. temperaturedependenceR(T) measured at small bias. The plot ofR(T) forSr0.95NbO3.37 is shown in Fig. 16. Thus, each point on IV ischaracterized by the resistance, and corresponds to a well-defined temperature on the R(T) plot. This temperature isinterpreted as the temperature of electrons Tel. The plot of Tel

vs. U for IVs measured at different phonon bath temperaturesTph is shown in Fig. 18(a). As one can see, the temperature ofelectrons exceeds the temperature of the bath and reachesnearly 40 K at high currents.

According to Eq. (3) the dependence U2/R vs. Tel shouldbe a straight line. We found that it can be obtained for theparameter g equal to �2.2 as it is shown in Fig. 18(b). Thepower g is different from the value obtained in Refs. [41, 42].



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Figure 18 (online color at: www.pss-a.com) Sr0.95NbO3.37. Elec-tron temperature Tel vs. voltage U calculated for different bathtemperatures (a). Plot of U2/R vs. Tel (b). Linear dependences wereobtained for the parameter g equal to 2.2.

Figure 19 (online color at: www.pss-a.com) Current–voltagecharacteristics of the same Bi-2212 sample measured at 4.2 K atdifferent doping levels (a). The doping was gradually increased bycurrent injection from the original HR state (1) to LR states (2–5).Only the last resistive branch is shown. Critical current and criticaltemperature (b) corresponding to the IVs in (a).

It can be explained by the difference in the investigatedsystems. In our case the tunneling takes place between thinconducting layers of large area�5� 10mm2. In Ref. [41] thetransport is provided by tunneling between islands of asignificantly smaller size.

The next important peculiarity of our experiments is amore than two orders of magnitude higher temperature ofmeasurements than the temperatures used in Ref. [41].Consequently, in our case, the electron–phonon couplingG isstronger and also can be temperature dependent. Accordingto the Eq. (3) the slope of the lines inU2/R�Tel coordinates isproportional to G. Indeed the slope of the lines in Fig. 18(b)slightly increases with the temperature, consistent withincreasing of the electron–phonon coupling with tempera-ture. The intersection of the lines with the U2/R-axis alsoscales with Tph.

6 Bi-22126.1 Resistive memory switching Recently, resis-

tive memory switching was found in another layeredmaterial, Bi-2212 [14]. It was shown that the switching canbe performed both at room temperature and at low bathtemperatures down to 4.2 K. The change of the resistancetakes place rather slowly comparing to the switching in thematerials discussed before. The slow dynamics allows tocontrol the resistance of the samples precisely. In ourexperiments we control the bias current. Keeping the currentat a constant level we monitor the change of the voltage


across the stack of tunnel junctions. In Bi-2212 the originalstate always has a high resistance. I–V of the original state at4.2 K is shown in Fig. 19(a), curve (1). For the sake of clarity,in Fig. 19(a) we present only the last resistive branch for eachresistive memory state. The superconducting part of IVs isnot shown in the plot, but it will be discussed later. The curve(1) was obtained by increase in the bias current to �1 mA(see the arrow along (1)). After the bias current was fixed at�1 mA, we observed a slow decrease of the voltage from1.7 V to a saturation value �1.37 V, which is shown by ahorizontal arrow. The new resistive state (2) is persistent intime: by decreasing the current to zero and increasing it backto�1 mA the curve (2) does not change. In order to achieve afurther decrease of the resistance the current has to beincreased further. For instance, the current in the state (2) wasincreased up to 1.2 mA (follow the arrow along the curve(2)). At this bias current the voltage slowly decreased from1.7 to 1.4 V as it is shown by a horizontal arrow between thecurves (2) and (3). Using the same procedure of a gradualincrease of the bias current we were able to achieve LR states(4) and (5).

The LR states are stable in time up to temperatures below�270 K. Several cycles of heating and cooling did notchange the I–V, the critical temperature and the criticalcurrent of the corresponding LR state. At higher tempera-tures, the resistance slowly drifts toward higher resistance,but does not restore to the original HR state. As it was shown

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Figure 20 (online color at: www.pss-a.com) Central part of cur-rent–voltage characteristics of a Bi-2212 sample. The superconduct-ing branch and resistive branches corresponding to a differentnumber of Josephson junctions in the resistive state are shown.

in Ref. [14], a change from LR to HR state also can beperformed. The transition LR!HR was achieved by afurther increase of the bias current above the LR!HRthreshold value. The polarity of the bias makes no difference.A repeatable HR-LR-HR change can be performed at leastseveral times [14].

Bi-2212 is a well-known high-Tc superconductordemonstrating the intrinsic Josephson effect [17, 18]. Out-of-plane transport can be considered as tunneling through astack of Josephson junctions connected in series. The centralpart of the IV of a stack consisting of 38 layers is shown inFig. 20. The first zero-voltage branch corresponds to thesuperconducting state of all Josephson junctions in the stack.Above the critical current Ic all junctions switch to theresistive state, which corresponds to the most right (the last)resistive branch. The last resistive branches of differentresistive states were shown in Fig. 19(a) and discussedearlier. The intermediate resistive branches can be obtainedby decreasing the current along the last branch until some ofthe junctions switch to the superconducting state. Then thecurrent is increased again. In this way all resistive branchescan be traced. Each resistive branch corresponds to oneJosephson junction, i.e., we can easily determine the numberof layers in the stack.

For all resistive states presented in Fig. 19(a), thecurrent–voltage characteristics and R(T) dependencies weremeasured, and the critical currents Ic and critical tempera-turesTc were determined. The results are shown in Fig. 19(b).The original HR state (1) of a strongly underdoped sample ischaracterized by a small Ic (�2mA) and a low Tc (�50 K).After the first transition to LR state (2), both the criticalcurrent and critical temperature increased to 40mA and 82 K,respectively. In the next resistive switching cycles 3–5, Iccontinued to grow, but the critical temperature Tc saturatedand even slightly decreased in the last step.

Such behavior of Ic and Tc is typical for doping of hightemperature superconductors. According to the phasediagram of Bi-2212 23,, the increase of the hole

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concentration in CuO2 layers from the underdoped stateleads to an increase of the critical temperature until it reachesthe maximum at �87 K. Further doping leads to asuppression of Tc. Opposite to the critical temperature, thecritical current monotonously increases with doping 43].

Traditionally the doping can be achieved by controllingthe oxygen stoichiometry or by substitution of cations, e.g.,Sr with La [44]. In our case the stoichiometry stays intact.The results of our measurements, however, show that theresistive switching does lead to a change in the doping level.In Ref. [14] the doping by current injection was explained bycharging localized electron traps in the insulating layer. Thecharged insulator affects the carrier concentration in theconducting layers in the same way as the floating gate does ina flash memory cell.

6.2 Current–voltage characteristics Similar toAnBnO3nþ1 materials, out-of-plane low-temperature IVs ofBi-2212 demonstrate the back-bending. We have found thatstrongly underdoped samples [see Fig. 19(a) curve 1] do nothave a negative differential resistance section. However,after the first doping the back-bending of IVs becomespronounced and enhances with doping. In the previoussections we interpreted the back-bending by overheating ofelectrons in subsequent tunneling events through the stack oftunnel junctions. Here we will present more argumentssupporting the importance of electron overheating in out-of-plane transport in layered materials.

In Bi-2212, s-shaped IVs were observed regularly. Atraditional explanation of the back-bending relies mostly onthe lattice heating during measurements. Indeed, the over-heating of crystal leads to a suppression of the super-conducting gap, decrease of the critical current and normalresistance RN. Consequently, the product IcRN drops withtemperature reducing the voltage on the IV’s. The increase ofthe crystal temperature was measured by several methods[32, 45].

Although, a noticeable heating of the samples cannot beneglected, there are several arguments supporting a differentorigin of the s-shaped IVs. From the series of IVs inFig. 19(a) one can see that the voltage at the back-bendingpoint (HL transition) strongly decreases with doping. Thecurrent at the HL transition stays nearly constant and evenslightly decreases, i.e., the power dissipated in the crystal atHL transition drops with doping. At the same time the criticaltemperature grows with doping except for the last curve (5).If the lattice heating would be the main reason for the back-bending, then for a higher Tc state, it should be observed athigher dissipated power. However, the experimental datashow the opposite trend.

Similar power arguments can be also applied to thecurrent–voltage characteristics in Fig. 20. The stack of 38tunnel junctions was strongly doped by current injection andhad a critical current density of �7 kA/cm2. The criticalcurrent Ic significantly exceeds the HL transition current.The back-bending shows up not only in the last resistivebranch, but also in several intermediate resistive branches.



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Figure 21 (online color at: www.pss-a.com) Current IHL, voltageUHL, and dissipated powerPHL at the back-bending point vs.numberof resistive branches in Fig. 20.

Figure 22 (online color at: www.pss-a.com) Voltages of resistivebranches at different current levels vs. the index of the resistivebranch #N (a). Voltage spacing between the resistive brachesvs. #N (b).

Each resistive branch corresponds to a well-definednumber of the Josephson junctions in the resistive state,which can be determined by counting the number of resistivebranches from the left to the right. The rest of the junctions inthe stack are in the superconducting state and do notcontribute to the resistance. The dependence of the HLtransition voltage UHL and current IHL vs. the number of theresistive branches N is shown in Fig. 21. The voltage UHL isincreasing with N nearly linearly as more junctionscontribute to the resistance. At the same time the currentIHL is decreasing rapidly with N. The dissipated power at theback-bending point PHL¼ IHL�UHL differs by almost afactor of two for N¼ 10 and N¼ 38 (see Fig. 21). Thus, asmaller amount of junctions in the stack in the resistive staterequires a higher power at the transition point. In terms oflattice overheating this cannot be explained consistently. Incontrast to the explanation of the s-shaped IV’s by latticeoverheating, the Josephson junctions are in a stronglyunderdamped state even well above the back-bendingcurrent IHL, i.e. the IV’s are strongly hysteretic with a lowretrapping current.

A rational explanation of the back-bending would beelectron but not lattice overheating. We cannot apply directlythe model used to analyze Sr0.95NbO3.37 IV’s earlier in thispaper. The strong non-linearity of underdamped Josephsonjunction IV’s originates mostly from the superconductingenergy gap. However, the advantage of superconductivity ina stack of tunnel junctions lies in the possibility to change thenumber of junctions contributing to the resistance in situ. Inthis way we can adjust the height of the stack and investigatethe dependence of the voltage drop on the height of the stack.

We analyzed the voltages U on the resistive branches atfour different currents in Fig. 20. The lowest current of40mA is below the back-bending of IV. 75mA correspondsto the IHL of the last branch. The current values of 150 and220mA correspond to the back-bending of the �21th and�17th resistive branches, respectively. In Fig. 22(a) thedependence of the voltages U vs. the number of branches #Nis shown. The voltage drop grows non-linearly with #N. For


the highest current the tendency to saturation with #N is themost pronounced. The non-linearity is better visible inFig. 22(b) where DU vs. #N is shown. DUwas determined byderivative of theU(#N) dependence. It is clearly seen that thedistance DU between the resistive branches is slowlydecreasing with #N for the smallest current. For 75mA, thedecay rate is faster and significantly accelerates for N> 30.For the highest current (220mA), the decrease ofDU behavesin the opposite way. At first DU decreases fast and thensaturates for N>�17, when the current of the back-bendingbecomes much smaller than 220mA.DU reaches a saturationvalue of �2.4 mV, which is almost one order of magnitudesmaller than the largest distance between branches(�19 mV).

The decrease of the distance between neighboringresistive branches from the left to the right side of the IVcan be explained by overheating of electrons. If the electron-phonon coupling is weak, the electrons can gain more energyin the successive tunneling events. The probability to tunnelsubsequently into the next conducting layer increases as theenergy of electrons rises. As a consequence, the effectiveresistance of the tunnel junction is reduced. This shows up ina decreased voltage spacing DU. If the number of thejunctions in resistive state is small, a strong electronoverheating can be reached only at high bias voltage perjunction. When the number of junctions in resistive stateincreases, the electron overheating can be achieved at asmaller bias voltage per junction. Indeed, DU decreases with

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Figure 23 Dependence of the threshold voltage of doping in Bi-2212 samples vs. the height of the stacks. The height of the stacks isshown in the number of layers in the stacks, m.

#N, and this decrease is much more pronounced for highcurrents. The saturation in DU(#N) shown in Fig. 22(b) for220mA reflects the fact that the higher energy electrons arescattered so strongly that their energy grows only slowly.

A weak dependence on the number of layers in the stackwas also observed for the threshold voltage of doping in Bi-2212 [14]. Several samples with a different number of layerswere prepared. The threshold voltage of doping wasdetermined as the voltage when the resistance of the samplestarts to decrease. The measurements of the threshold voltagewere performed at 4.2 K. In Fig. 23 we show the dependenceof the threshold voltage Uth vs. the number of layers m in thestack. The data show a significant spread, because Uth

depends also on the doping level of the original crystal.However, it is clearly seen that the threshold voltage does notscale with the number of junctions. These results allow us toconclude unambiguously that the key parameter for theresistive memory switching in the layered materials is theenergy of electrons. Threshold voltage and current depend onthe geometry of the sample, its resistivity, number of layers,temperature of the sample etc., but the key parameter is thethreshold energy of electrons.

7 Discussion As we showed in the experimental partof this paper, the resistive memory switching both in theperovskite derivatives AnBnO3nþ1 and in Bi-2212 is causedby changes in their conducting layers. From the measure-ments of the critical temperature, a clear doping effect ofCuO2 layers was demonstrated for Bi-2212. The original HRstate of the stack of tunnel junctions can be changed to a LRstate with a rather precise control of the LR state properties.

In titanates and niobates, current injection leads to theopposite direction of switching from the original LR to a HRstate. The difference between Bi-2212 and the perovskitederivatives AnBnO3nþ1 is their type of charge carriers. InBi-2212 the charge carriers are holes. The investigatedAnBnO3nþ1 are n-type materials.

The main concept of our interpretation of resistivememory switching is based on the charging of the insulatinglayers by injected electrons. Indeed, under particularconditions electrons can be trapped in the insulating layers.

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Similar to the flash memory principle, the trapped chargesrealize the effect of a floating gate, i.e., in order tocompensate the negative charge of the insulating layers,positive charge is induced in the conducting layers. InBi-2212, the neutralization can be provided by holes. Themobility of the induced holes was also demonstrated inexperiments with a field effect transistor structure, where athin film of Bi-2212 was used for the channel [46–48]. Forthe n-type titanates and niobates, the same concept of trappedelectrons in the insulating layers leads to a decrease ofelectron concentration in the conducting layers.

Microscopically, the mechanism of the electron trappingin the insulating layers is not clear yet. Here we discuss apossible scenario how the electrons can be trapped andstrongly localized leading to a persistent change of thedoping level. We start with AnBnO3nþ2. All investigatedmaterials LaTiO3.41, SrNbO3.41, CaNbO3.41, Sr0.95NbO3.37,and SrNbO3.45 are characterized by 5 BO6 octahedra slabs inlayers (n¼ 5). The only exception is SrNbO3.45, whichconsists of alternating four and five slabs in the layers(n¼ 4.5). Inside layers, the ions of Ti and Nb are in a mixedvalence, as we discussed earlier. The distribution ofB-cations in the layers was investigated intensively bydifferent experimental and theoretical methods (see, e.g.[49–53]). It was found that ions in the lower oxidation stateare mostly concentrated in the middle slabs of the layers.

In the following we continue to discuss CaNbO3.41 as anexample. The same speculations can be made for the othermaterials. The results of X-ray diffraction revealed a strongdistortion of BO6 octahedra, which decreases from the outerslabs to the middle slab. For instance, the distortioncharacterized in terms of Nb-O bond length can reach valueshigher than 20% [49]. The least distorted octahedracorrespond to the reduced oxidation state of Nb. A smalldistortion of NbO6 octahedra in CaNbO3 crystals with Nbþ4

was earlier reported in Ref. [54]. Thus, the unpaired electronsare located in the center of the layers.

If the injected electrons have high enough energy, theycan temporary occupy the empty energy levels, whichcorrespond to the Nb ions in the highest oxidation stateþ5 inthe side slabs. The trapped electrons reduce Nbþ5 to Nbþ4

which lead to a stress in the deformed octahedra. This stresscan be released either by losing the extra electrons, oralternatively, by rearrangements in the neighboring atompositions in order to decrease the deformation. In the lastcase, the new resistive state is preserved. In other words,the rearrangements shift the energy level occupied by thetrapped electron e.g., below the Fermi energy of theconducting layers preventing escape of the electron fromthe insulating layer. Now the insulating layer contains thetrapped electron, which influences the conductance in themiddle slab. This picture is consistent with the model ofdoping described above.

The rearrangements of atoms can be realized if thetemperature of the lattice is high enough. Thus, there are twoessential conditions for resistive memory switching: the highenergy of electrons and high temperature of the lattice. We



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confirmed the importance of the lattice temperature in theexperiments of the temperature dependence of switching(see Fig. 7).

The new high resistive state is most probably metastable.By applying a current of opposite polarity and high enoughamplitude we induce the opposite process, when the electroncan be released from the metastable Nbþ4 in the side slabs.The deformed octahedron returns to the ground state and thesystem switches into its original resistive state. This demandseither a strong tilt of the bands or ionization by higher energyelectrons. It is consistent with our observations of theincreased threshold current/voltage for HR!LR in com-parison with LR!HR switching.

A similar scenario can be also applied for Bi-2212.According to Fig. 2, this material consists of perovskite-related slabs SrO–CuO2–Ca–CuO2–SrO separated by abismuth oxide double layer. The last has a rocksalt-typecrystal structure. Real crystals of Bi-2212 are noticeablydistorted [55, 56], and the structure in Fig. 2 can beconsidered as only a basic one. An incommensuratemodulation of the interplane distances and in-plane lengthsof bonds was explained mostly by a slight mismatch of theperovskite-related and BiO planes. More stiff CuO2 planesbend together, while the BiO planes are stacked in a nearlyantiphase configuration [55, 57]. The distortion in BiO layerscan be influenced by different factors, e.g. presence ofinterstitial oxygen or trapped electrons.

The incommensurate modulation can be considered as adisorder, which causes high energy electron states to belocalized. Filling the localized states by injection of electronswith high enough energy, the distortion of the BiO layerscan be altered giving rise to an additional stress in the crystal.As we discussed above for AnBnO3nþ2 materials, the stresscan be released by rearrangement of the neighboringatoms. In contrast to the niobates and titanates, theneighborhood of the Bi-cation is not so stiff and a longerrange adjustment of atom positions is required. Theprobability of such long-range changes is low. That is whywe observed a slow gradual change of the resistance undercurrent injection. The trapped electrons induce additionalholes in the conducting CuO2 layers leading to a decreasednormal resistance, increased critical current and changes ofthe critical temperature.

The ‘‘softness’’ of the Bi–O bonds allows to producedoping by current injection at low temperatures. Nominally,the temperature of the bath was 4.2 K. The temperature of thecrystal at the dissipated power in the order of 1 mW isdefinitely much higher. We can only speculate that thetemperature was lower than �260 K. Indeed, a partial decayof the doping starts at around 260–270 K, which wasmentioned earlier. We would like to emphasize that even ifthe decay starts below RT, the doping effect does not vanishat RT completely. Apparently, there is a significant spread ofthe energies of the trapped electrons. A gradual doping canbe also a consequence of a broad distribution of the electrontrap energies as the deformations in BiO layer are not rigidand can be affected by the trapped charges as well.


The opposite direction of resistive switching from LR toHR state is possible at higher bias voltage. It is consistentwith our assumption that the trapped electrons can bereleased in e.g., ionization processes and relaxation of thecrystal. However, in comparison to AnBnO3nþ2 materials,Bi-2212 demonstrates a significantly less reliability of theLR!HR transition. We explain this by the difference in therelaxation of the crystal structure of BO6 octahedra and BiOlayers. In the last structure some deformations can beirreversible, while in the perovskite slabs the changes arebetter defined and reversible.

The model of resistive memory switching describedabove is based on the concept of insulating layers charge byinjected high energy electrons. The charge persists if thestress, induced in the insulating layers by the trappedelectrons can be released by slight changes in the distortion,inherent to the crystals of the investigated materials. As thepossibility to produce a switching effect was undoubtedlyproved, the important question is whether multiple reversibleswitchings can be realized using this kind of processes. Wehave shown that for AnBnO3nþ2 materials a reproducibilityof switching can be achieved. However, a gradual drift of theresistance in LR and HR states in successive switchings wasalso observed. For practical applications, this drift is aserious obstacle. It can appear as a consequence of too manypossibilities, which can be realized in adjusting the atompositions for releasing the stress. There are two feasible waysto improve the performance of the switching devices. Thefirst possibility is to improve the ROFF/RON ratio, which willmake slight drifts in ROFF and RON levels not critical. Thesecond possibility is to decrease the degrees of freedom ofthe deformation in the devices, by e.g., reducing the area ofthe tunnel junction substantially by 2–3 orders of magnitude.In our opinion the second way is more promising.

8 Summary We investigated resistive memoryswitching in different layered materials: perovskite-relatedtitanates and niobates of the series AnBnO3nþ2 and the high-Tc superconductor Bi-2212. Switching was performed byout-of-plane current injection. We showed that the transportin <c>-axis direction takes place by tunneling between theconducting planes. The change of the resistance, stable intime, is explained by a change of the doping level in theconducting layers. We propose a model of the doping, wherethe high energy electrons occupy empty trap levels inthe insulating layers. The trapped charges in the insulatorsact as a floating gate inducing the change of doping in theconducting layers. High energy electrons are essential forthe resistive memory switching. Indeed, we showed that inour layered materials the out-of-plane transport is charac-terized by a significant contribution of the overheatedelectrons, whose temperature can substantially exceed thetemperature of the lattice.

The bistable resistive memory switching of theAnBnO3nþ2 series renders these materials promising forapplications as resistive memory cells. However, consider-ing the demand of up to 107 writing cycles without

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degradation of the cell parameters, the main obstacle inthe use of the titanates and niobates is a slow drift of theresistance levels in successive switchings. We believe thatthe performance of the devices can be substantially improvedby a decrease of the tunnel junction area.

Acknowledgements Financial support by the DFG program1157 is gratefully acknowledged.

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resistive memory switching in layered oxides: anbno3n+2 perovskite derivatives and bi2sr2cacu2o8+δ...

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