Mechanism for bipolar resistive switching in transition metal oxides

M. J. Rozenberg,1, 2 M. J. Sanchez,3 R. Weht,4, 5 C. Acha,2 F. Gomez-Marlasca,4 and P. Levy4

1Laboratoire de Physique des Solides, UMR8502 Universite Paris-Sud, Orsay 91405, France2Departamento de Fısica J. J. Giambiagi, FCEN, Universidad de Buenos Aires,

Ciudad Universitaria Pab. I, 1428 Buenos Aires, Argentina3Centro Atomico Bariloche and Instituto Balseiro,

CNEA, 8400 - San Carlos de Bariloche, Argentina4Gerencia de Investigacion y Aplicaciones, CNEA, 1650 - San Martın, Argentina

5Instituto Sabato, Universidad Nacional de San Martın-CNEA, Argentina

We introduce a model that accounts for the bipolar resistive switching phenomenom observed intransition metal oxides. It qualitatively describes the electric field-enhanced migration of oxygenvacancies at the nano-scale. The numerical study of the model predicts that strong electric fieldsdevelop in the highly resistive dielectric-electrode interfaces, leading to a spatially inhomogeneousoxygen vacancies distribution and a concomitant resistive switching effect. The theoretical resultsqualitatively reproduce non-trivial resistance hysteresis experiments that we also report, providingkey validation to our model.

PACS numbers: 73.40.-c, 73.50. -h

I. INTRODUCTION

There is a great deal of experimental activity currentlydevoted to explore new technologies for the next gen-eration of electronic memory devices1. Among variouspromising options, the resistive random access memory(RRAM), which is based on the resistive switching (RS)phenomenon, has emerged as a preeminent candidate2,3.The RS effect is a large, reversible and nonvolatile changein the resistance after the application of voltage or cur-rent pulses. The typical RRAM system has a capacitor-like structure composed of insulating or semiconductingmaterials sandwiched between two metal electrodes. RShas been observed in a wide variety of systems, such assimple and complex oxides, organic compounds, etc3,4.However, there are specific characteristics of the switch-ing behavior observed in each type of material. In thecase of binary oxides, which are highly insulating it isbelieved that the RS effect may be due to the formationand rupture of conductive filaments within the insulatingmedia5–7. In contrast, in the more conducting or semi-conducting complex oxides with perovskite structures,such as doped cuprates and manganites, the relevanceof oxygen vacancies is often invoked. Despite a burst-ing body of experimental data that is rapidly becomingavailable8–12 the precise mechanism behind the physicaleffect of RS remains elusive. A few qualitative modelshave been proposed emphasizing different aspects: elec-tric field-induced defect migration5,13,14, phase separa-tion15, tunneling across interfacial domains16, control ofShottky barrier’s height3,17, etc. A general consensus hasemerged on the empirical relevance of three key features:(i) a highly spatially inhomogeneous conduction in thelow resistive state, (ii) the existence of a significant num-ber of oxygen vacancy defects and (iii) a preeminent roleplayed by the interfaces, namely, the regions of the oxidethat are near each of the metallic electrodes which of-ten form Schottky barriers. Here, we shall introduce and

study the behavior of a simple model that incorporates,at a qualitative level, those three features. By meansof a numerical simulation we shall show that the modelcorrectly reproduces key non trivial hysteresis cycles ob-served in experiments on perovskite-type transition metaloxides (TMO).

II. MODEL

Several experiments revealed that the conduction inthe low resistive state is highly inhomogeneous and dom-inated by one dimensional paths that are associated withenhanced conduction channels5,7. These paths wouldbe created upon an initial application of strong electricfields, that bring the dielectric close to its breakdownpoint. Thus, we shall assume that the electric trans-port is dominated by a single conductive path embeddedwithin a more insulating host.

The second important feature incorporated into ourmodel is the relevance of defects within the dielectric.Several experiments point to a preeminent role played byoxygen vacancies5,14,18,19. Moreover, it is a universal andsalient feature of TMO that their resistivity is dramati-cally affected by the precise oxygen stoichiometry. Onemay thus expect that oxygen vacancy concentration maybe the most significant parameter controlling the local re-sistivity, ρ, of a given material. This feature is includedin our model by assuming that each nano-domain of thepath is characterized by a certain concentration of oxy-gen vacancy defects, δ. We adopt the most simple linearrelation ρ ∝ δ, which follows from the fact that in TMOperovskites the presence of oxygen vacancies severely dis-rupts the electronic conduction properties. Nevertheless,we emphasize that the specific form of ρ(δ) is not crucialfor the results that we shall describe later on.

The third important feature that our model incorpo-rates is the key role played by the interfaces16, namely,

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FIG. 1: a) Schematic model with a single conductive channelwithin the dielectric. The three regions L, R and B corre-spond to the two high resistance interfaces and the more con-ductive central bulk, respectively. The small boxes indicatethe domains. b) Detailed scheme of the conductive path. Thegrayscale qualitatively depicts the variation in the oxygen va-cancy concentration through the channel (darker correspondsto higher concentration). The top figure shows the initialstate with uniformly distributed oxygen vacancies, and thebottom one shows the inhomogeneous distribution after thefirst few “forming” voltage cycles (see text).

the regions of the dielectric that are in physical proximityto the metallic electrodes. There is growing evidence thatthese are the regions where the RS takes place13,17,20–23.

Our model is schematically shown in Fig. 1 and consistsof a single conductive channel within a more insulatingdielectric, which is represented by a one dimensional re-sistive network on N links. The first and last NI linkscorrespond to high resistance interfacial regions next tothe external electrode, and the central N − 2NI links de-scribe the bulk section. Each link is characterized by acertain concentration of oxygen vacancies, which deter-mines the resistivity of the link. They may be physicallyassociated to small domains of nanoscopic dimensionswhich may actually correspond to grains of the polycrys-talline oxide. We take ρi = Aαδi, with α = B if i is inthe bulk (NI < i ≤ N − NI), α = L if i is in the leftinterface (i ≤ NI) and α = R if i is in the right inter-face (N − NI < i ≤ N). In our study we set N = 100and NI = 10. The following equation specifies how thevacancies diffuse through the network domains under anexternal voltage,

pab = δa(1− δb) exp(−V0 + ∆Va) . (1)

It gives the probability for transfer of vacancies from do-main a to a nearest neighbor domain b. The probability

is proportional to the concentration of vacancies presentin domain a and to the concentration of “available va-cancy sites” at the target domain. The Arrhenius factorexp(−V0), is controlled by a dimensionless constant, V0,related to the activation energy for vacancies diffusion.The important factor exp(∆Va) models the enhancement(or suppression) of the diffusive process due to the localelectric field at domain a.

From Eq.(1), a constant V0 leads to an initially con-stant distribution δi = δo for all i. The value of theinitial constant concentration, δo must be much smallerthan one, since it physically represents the concentrationof defects (oxygen vacancies) within a domain. We adoptδo = 10−4.

Similarly to actual resistive switching experiments,we simulate the applied voltage protocol V (t) by lin-ear ramps that follow the sequence 0 → +Vmax → 0 →−Vmax → 0 (our convention is that the right electrodeis grounded). The duration is of s time steps. The se-quence may be repeated a number of cycles n, for a to-tal duration τmax = ns. In our simulations we chooseV0/Vmax = 0.016, that provides a non-negligible but slowdiffusive contribution to the evolution of δi with respectto the total time duration of the simulations (ie, the to-tal number of time steps). We set Vmax = 1000 thatprovides for a sufficiently large electric stress. Our quali-tative results are rather robust with respect to the choiceof model parameters, a detailed systematic study of theirdependence is left for future work.

The coefficients AB , AR and AL still remain to be spec-ified. With no loss of generality, we fix the value of thebulk coefficient to unity AB = 1 and leave the interfacialAR and AL free. In this initial study we shall concen-trate in the symmetric case, AR = AL, that correspondsto most common experimental devices.

The numerical simulations are performed through thefollowing steps: (i) at each simulation time step t (1 ≤t ≤ τmax) a given external voltage V (t) is applied to theresistive network (the electrodes are assumed perfect con-ductors). The current through the system is computedas I(t) = V (t)/RT , with RT the total (ie, two terminal)resistance

RT = c

N∑i=1

ρi =∑α

∑i∈α

Aαδi, (2)

where α = R, B, L denotes the three network regions,and c denotes an unessential geometrical constant relatedto the dimensions of the domains (which we set to unity).(ii) we compute the local voltage profile Vi(t) = I(t)ρiand the voltages drops ∆V i(t) = Vi+1(t)−Vi(t). (iii) weuse Eq. (1) to compute all the oxygen vacancy transfersbetween nearest neighboring domains, and update thevalues δi(t) to a new set of concentrations δi(t+ 1). (iv)we use these new values to recompute the current at τt+1

under the applied voltage V (t + 1) as indicated in thefirst step.

3

FIG. 2: Top panel: Resistive hysteresis loop (RT vs V) forthe subsequent voltage cycles number 5 , 6 and 7. (a). Inset:the RT vs I hysteresis (loop number 5) shows qualitativelysimilar results (the vertical axis scale is the same as in themain figure). Bottom panel: experimental hysteresis loopsmeasured in manganite (b) and cuprate (c) devices. The firstone was pulsed in current control mode while the second involtage mode. The details of the experimental procedures aredescribed in Refs. 21 and 25, respectively.

III. NUMERICAL RESULTS ANDCOMPARISON TO EXPERIMENTS

We now turn to the discussion of our results. We setAR = AL = 1000 >> AB = 1, which is consistent withour experimental data and with previous reports in bulkand thin films of conducting perovskites14,21,25. In Fig. 2we show the results for the hysteresis loop of the totalresistance RT . The different data curves in Fig. 2a dis-play the results in subsequent voltage cycles 5, 6, and7. The inset of Fig. 2a, show that the hysteresis as afunction of current remains qualitatively similar. Wenote that during the first few initial cycles the resistanceshows non-repetitive memory effects that converge to ahysteresis loop with a stable shape. Interestingly, thisis reminiscent of the initial “forming” that experimen-tal samples seem to require in order to start displayingreproducible switching effects. The peculiar type of hys-teresis loop that we obtain has been already reportedby the Houston group24 in experiments on (Pr,Ca)MnO3

manganite systems, where it has been termed “table withlegs”. It is evidently a non-trivial effect and we have ex-perimentally reproduced it in both, a related manganite(Pr,La,Ca)MnO3 and a cuprate (YBa2Cu3O7−x) sample,as shown in the bottom panels of Fig. 2.

There are several features worth pointing out: Duringeach voltage protocol loop, there is a clear variation ofthe resistance RT between a rather broad maximum for

FIG. 3: Density concentration profiles normalized to the ini-tial uniform density value δi/δo, at the beginning of voltagecycles number 5, 6 and 7 in the symmetric system.

a large range of V (ie, the “table”), and two relativelynarrow minima (ie, the “legs”). These maximum andminima correspond to the high and low resistance states,RHIT and RLOT . The RT (V ) loops are approximately sym-metric in V which reflects the left-right symmetry of thesystem. Throughout the voltage loop, the system beginsin the initial RHIT state and undergoes the sequence of re-

sistance changes → RLO+T → RHI+T under positive bias,

and then → RLO−T → RHI−T under negative bias. Thefinal state, at zero bias is RHIT , very close but not iden-tical to the previous initial state. Interestingly, a similarsmall drift is also observed in the experimental data.

The qualitative agreement between our prediction ofthe “table with legs” and the experimentally observedhysteresis loops provides a significant validation for ourmodel. Therefore, to gain physical insight into the mech-anism of the RS effect we shall discuss in detail the evolu-tion of the vacancies distribution under the applied volt-age protocol. In Fig. 3 we show successive snapshots ofthe oxygen vacancy concentration profile δi at the be-ginning of loops 5, 6 and 7. Recalling that the initialequilibrium distribution of oxygen vacancy concentrationis uniform δi = δo, these curves reveal that, under theaction of the repetitive voltage cycling, the δi evolve to-wards a new stable distribution. The salient features ofthe profile δi are a significant depletion in the interfacialregions and a strong accumulation peaks at both internalboundaries between the bulk and the interfacial regions.The reason can be understood as follows. The largestelectric fields occur at the two interfacial regions sinceinitially their resistance is much larger than the bulk one(AL, AR >> AB). Therefore, oxygen vacancy migrationis enhanced in the interfacial regions, with the ions mov-ing either towards the electrodes or the bulk, dependingon the direction of the applied voltage. When the ionsreach the metallic electrodes they start to pile-up14. Onthe other hand, the vacancies that migrate towards thebulk eventually leave the interfacial region and enter thebulk. There, their diffusion virtually stops, since the elec-tric fields in the more conducting bulk are much smaller.Successive initial cycles yield a cumulative effect, with adepletion of the interfacial regions (and some pile-up atthe edges) and a concomitant accumulation at the bulk

4

FIG. 4: Top (semi-log scale): Snapshots of the density concen-tration profiles for the symmetric configuration, normalized tothe initial uniform density value δi/δo, during the hysteresiscycle (first half). Bottom: The corresponding profiles of localresistance ρi for the same snapshots. Inset: Position of thesnapshots in the (first half) hysteresis loop.

side of the interfacial/bulk boundary. Significantly thisaccumulation, as seen in Fig. 3, is quite large and narrowleading to a substantial increase in the local resistance.This feature will be a key to understand the origin of thelegs of the hysteresis loop, which we shall consider next.

In Fig. 4 we show snapshots, during the first half ofthe voltage cycle, of the vacancy concentration and lo-cal resistance profiles in the interfacial regions and theirboundaries with the bulk. These are the active regionsof the system where the electric-field-enhanced migrationtakes place. Notice that since the current I(t) is uniformalong the conductive path, the local electric fields are di-rectly proportional to the local resistance. Let’s start atV=0, from the state at the beginning of a cycle. Interest-ingly, the ρi profile indicates significant electric fields inboth interfacial regions which extends into the neighbor-ing bulk. Thus the depletion of vacancies in the inter-faces and the accumulation at the boundaries are suchthat compensate for the difference between the respec-tive A coefficients, to yield similar electric fields acrossthe boundaries of the regions. Yet, at the very left end ofthe system there is a small pile-up of vacancies which, assoon as the voltage is ramped up, will translate into thelargest local fields and initiate the ionic migration. AtV/Vmax=0.25, we observe a snapshot of the migrationof the vacancies across the left interfacial region towardsthe bulk. From the resistance expression Eq. (2), so longthe vacancies remain within the interfacial region, thesystem remains in RHIT state. At V/Vmax=0.62, the va-cancies have moved out the left interfacial region andentered the bulk, where their migration suddenly stops.

Once in the bulk, the contribution to the total resistanceof these migrating vacancies is reduced (AB << AL),thus the system reaches the RLOT state (leg of the table).Notice that in this state, the largest fields occur at theboundaries of the bulk and the interfacial regions. Thus,as V is further increased, the left interfacial region de-pletes further and therefore the voltage drop gets lowerthere. In contrast, on the right side the electric fields arefurther enhanced and there is now a migration of vacan-cies from the accumulation peak of the bulk towards theright interfacial region. This leads to an increase of thetotal resistance and, at the maximal voltage V/Vmax=1,we find that the vacancies have entered the interfacialregion and already piled-up at the right end. Thus, thesystem is back to RHIT . The voltage protocol continueswith the decrease of V back to zero but keeping the same(positive) polarity. Therefore no significant change in theδi and ρi profiles occurs, and half of the table with legs isalready formed. When the negative polarity part of thecycle begins a similar analysis follows, since the distribu-tion of vacancy concentrations is a mirror image of theinitial one. This forms the other half of the table.

To complete our study we consider the effect of intro-ducing an asymmetry in the model parameters AR andAL. In Fig. 5 we display the results for the hystere-sis loops upon increasing the asymmetry. The results ofthe simulations show the gradual evolution of the “tablewith legs” towards a conventional rectangular hysteresiscycle24. Asymmetry in experimental samples can eitherbe due to the fabrication process, as for instance, in theobvious case of using different type of metal for the elec-trodes. Though our samples were fabricated in a sym-metric configuration, we induced a significant asymme-try by vigorous pulsing with a given polarity (ie, poling)before measuring the resistance hysteresis characteristic.Significantly, as shown in Fig. 5, we find that the ex-perimental data obtained in an asymmetric manganitesample and the cuprate, induced by intensive same po-larity pulsing, are in good qualitative agreement with oursimulations. These results provides additional validationto our model.

IV. CONCLUSIONS

To conclude, our results put on solid theoreticalgrounds the key role played by oxygen vacancies in themechanism of resistive switching in TMO. They also pro-vide valuable insights, predicting a non-trivial spatialprofile of the oxygen vacancy distribution which may beof help for device design. An exciting idea for futurework is to explore the possibility of using atomistic, firstprinciples, calculations to study properties of electrode -transition metal oxide interfaces to estimate the param-eters of the model and provide guidance in the materialchoice for actual memory devices.

5

FIG. 5: Resistive hysteresis loops obtained for an increasing degree of asymmetry. AL = 1000 and AR = 1000, 100, 50 and 25in panels a, b, c and d respectively. The right panels show experimental data for a manganite (e) and a cuprate sample (f)that were rendered asymetric by means of intense and fixed polarity pulsing. The former was pulsed in current control modeand the latter in voltage control, similarly as in Refs. 21 and 25, respectively. Notice the qualitative similarity of data of panelse and f with panel d; and of data in Fig. 2b with panel a. The data of Fig. 2c seem to be in between the results of panel aand b.

ACKNOWLEDGMENTS

Support from CONICET (grants PIP 5254/05 and PIP112-200801-00047) and ANCTyP (grants PICT 483/06

and PICT 837/07) is gratefully acknowledged.

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