# Resistive switching

Post-publication activity

Curator: Marcelo Rozenberg

Dr. Marcelo Rozenberg accepted the invitation on 2 October 2010

Resistive switching refers to the physical phenomena where a dielectric suddenly changes its (two terminal) resistance under the action of a strong electric field or current. The change of resistance is non-volatile and reversible. Typical resistive switching systems are capacitor like devices, where the electrode is an ordinary metal and the dielectric a transition metal oxide. An interesting application of resistive switching is the fabrication of novel non-volatile resistive random-access memories (RRAM). This effect is also at the base of the behavior of the so called memristor devices and neuromorphic memories.

## Contents

#### Origins of a new electronic memory concept

Figure 1: Schematic diagram of a typical resistive switching device. The electrode may be Au, Pt, Al, Ag, SrRuO$$_3\ ,$$ etc. the dielectric TMO may be TiO$$_2\ ,$$ HfO$$_2\ ,$$ NiO, SrTiO$$_3\ ,$$ PCMO, LSMO, YBCO, etc. There is a huge number of combinations, however, not all combinations work.

Resistive switching is the physical phenomenon that consists on the sudden and non-volatile change of the resistance due to the application of electric stress, typically voltage or current pulsing. This effect may allow the fabrication of future novel electronic memory concepts, such as non-volatile random access memories (RAM), hence, it is also termed resistive RAM, RRAM, or ReRAM. While non-volatile memory effects have been reported in a huge variety of systems, here we shall be concerned with those based on Transition Metal Oxides (TMO). Typical systems have a capacitor-like two-terminal configuration, metal-electrode/TMO/metal-electrode, where the TMO is the dielectric (Fig.1). In fact, TMOs usually exhibit high dielectric constants, which is considered a desirable feature towards dense electronic integration.

Resistive switching (RS) is not new. It has been originally reported in binary oxides back in the 60’s [1], and revisited periodically [2,3,4,5]. However, research for eventual technological applications of this effect have been dwarfed by the enormous success of silicon-based electronics. Following Moore’s law [6] for more than 40 years, the current feature size of industrial electronic components has shrunk down to just a couple of tens of nanometers, that is, only a few hundred atoms long. This remarkable downsizing is, however, predicted to reach its physical limits within a decade. Hence, there is a pressing need for alternative materials and new concepts for future electronic components.

#### Recent key developments

Figure 2: Reversible and non-volatile resistive switching in PCMO (figure from [9]).
Figure 3: Reversible and non-volatile resistive switching in SrZrO$$_3$$ (figure from [8]).
Figure 4: I-V characteristics with hysteresis in CuO. Note the initial forming step (black) and the compliance current (figure from [21]).
Figure 5: "R-V" hysteresis switching loop in PLCMO (figure from [32]).

During the 90s, a very strong interest developed around the physics of TMOs, following the discoveries of high temperature superconductivity in cuprates and colossal magnetoresistance in manganites. TMOs display a large variety of exotic transport behavior, among those we should mention the report of Asamitsu et al. on the observation of current-driven resistance-switching in PCMO [7]. On the other hand, and partially due the interest in TMOs, there were also key improvements in thin film fabrication methods, such as RF-sputtering and Pulsed Laser Deposition (PLD), which contributed to renew the interest in RS phenomena in TMOs. The key breakthroughs were reported in 2000 by the groups of Ignatiev [8] and Bednorz [9]. They observed reversible and reproducible non-volatile change of the resistance state of two-terminal devices. The dielectric materials were complex TMO thin films of a few hundred nanometers fabricated by PLD, a colossal magnetoresistance manganite in Ignatiev’s study (Fig.2), and strontium zirconate and strontium titanate in Bednorz’s (Fig.3).

Following these initial reports an intensive research activity begun to develop in this area. Quite remarkably a huge variety of systems exhibiting RS were reported in fast succession. They range from simple binary oxides, such as NiO, CuO, TiO$$_2\ ,$$ and HfO, to ternary perovskites such as SrTiO$$_3$$ and SrZrO$$_3\ ,$$ to even more complex multi-component compounds including the celebrated colossal magnetoresistive manganites LaCaMnO$$_3$$ and Pr$$_{\rm 1-x}$$La$$_{\rm x}$$CaMnO$$_3$$ and cuprate superconductors YBCO and BSCCO, among many other materials [10,11].

Typical experiments of RS effects are reported as either pulsed-induced resistive changes (Fig.2 and Fig.3), I-V characteristics with hysteresis (Fig.4), or R-V 'hysteresis switching loops' where the non-volatile resistance (after the pulse) is plotted as a function of voltage-pulse intensity along a full cycle (Fig.5).

#### Types of resistive switching

During the past few years of intense research a consensus has emerged on the notion that the phenomenology of RS phenomena in TMO can be roughly classified in two types, unipolar or bipolar memory effect. In the unipolar case, the memory state of the system can be switched by successive application of electric stress of either the same or opposite polarities. In contrast, the bipolar memories can be toggled between the memory states by application of successive electric stress of alternate polarity. Moreover, the switching protocols used in unipolar and bipolar systems are also different, with the need of a compliance current in the former case. However, the classification becomes less clear in systems such as TiO$$_2\ ,$$ where both types of RS have been reported.

The physical origin of the mechanism behind the resistive switching effect has also been discussed at length in the recent literature; however, the work on mathematical modeling remains relatively modest. Different groups have emphasized a variety of physical ingredients. These include, Schottky barriers, interfaces and electric 'faucets', spatial inhomogeneity, trapping of charge carriers, oxygen vacancy migration, filamentary path formation, correlation effects and Mott metal-insulator transitions, etc. In regard of all these features the great challenge in modeling the RS effect is to accommodate for the large variety of physical systems where it is experimentally observed. Therefore, a model should include many of the key features indicated by experiments, but at the same time, must remain sufficiently general to apply to the large variety of systems.

##### Unipolar switching

Unipolar systems usually have a dielectric that is a simple binary TMO. Examples are NiO [12], CuO, CoO, Fe$$_2$$O$$_3\ ,$$ HfO, TiO$$_2$$Ta$$_2$$O$$_5\ ,$$ Nb$$_2$$O$$_5$$ [10,11]. These systems are good insulators with a large resistivity. They would normally not show any RS effect. To get the systems into the switching regime it is usually required to perform and initial ‘electroforming’ step. In this process, a strong electric field is applied, which brings the system close to the dielectric break down. A full break down is prevented by a current limitation or compliance. After this ‘SET’ procedure, the resistance of the device shows a significant decrease, reaching a ‘low resistance’ state, $$R_{\rm LO}\ ,$$ which is stable, i.e., non-volatile. This state has an ohmic I-V characteristic at low bias. To switch the system to the ‘high resistance’ state, $$R_{\rm HI}\ ,$$ a voltage has to be applied to the device, with either the same or opposite polarity than the previously applied ‘forming’ voltage. In this ‘RESET’ step, the resistance of the system suddenly increases, back to a ‘high resistance’ value close to the original one. No current compliance should be used in the RESET step. In fact, the resistance change occurs when the current through the device becomes larger than the value of the compliance. To SET the system again in the low resistance state, a voltage with current compliance has to be once again applied, similarly to the forming step. The system’s resistance suddenly decreases down to a value close to $$R_{\rm LO}$$ at a threshold voltage $$V_{th}\ ,$$ which is smaller that the forming one. The SET and RESET switching process can be repeated may times. The magnitude of resistance change typically remains within well-defined values, however some dispersion is often observed. An example of a typical electroforming and successive RESET and SET steps are shown in Fig.4.

Experiments have shown that the forming voltage scales with the distance between the electrodes, consistent with a soft dielectric breakdown. They also indicate that the value of $$R_{\rm LO}$$ can be controlled with the magnitude of the current compliance. The higher the current, the lower $$R_{\rm LO}\ .$$ The reason for this effect remains unclear. On the other hand, $$R_{\rm HI}$$ is essentially the original value of the resistance of the device before the forming. These observations along with the need of a current compliance only for the SET, indicates that resistive switching on unipolar systems is driven by current for the SET process and by voltage for the RESET one.

##### Bipolar switching

Bipolar resistive switching has been observed in a variety of ternary oxides with perovskite structure such as SrTiO$$_3$$ (STO), SrZrO$$_3\ ,$$ and also in more complex systems such as the ‘colossal’ magnetoresistive manganites LSMO, LCMO, PCMO, PLCMO, and even in cuprate superconductors YBCO and BSCCO. Some reports indicate that better performance may be obtained by small chemical substitution, such as Bi:SrTiO$$_3$$ and Cr:SrTiO$$_3\ .$$ These bipolar systems may be either insulators or poor metals. Strong hysteresis in the two-terminal resistance is often observed without the need of an initial forming step. Nevertheless, electro-forming usually done, as it may improve the reproducibility of resistive switching, but this initial forming step remains not well understood [13].

The choice of a proper electrode material for each dielectric is an important issue for bipolar devices. Sawa and collaborators have performed a systematic study, concluding that a key feature for RS is the formation of Shottky barriers [10]. In fact, the observed scaling of $$R_{\rm HI}$$ and $$R_{\rm LO}$$ with the geometry of the devices indicate that the phenomenon should take place at the electrode/oxide interfaces.

Another important physical aspect that is relevant for RS is the electro-migration of oxygen vacancies along extended defects in the dielectric regions in close proximity to the electrodes. This feature has been established in STO [14,15], and in PCMO [16]. In particular, in the former case, an extended network of columnar oxygen defects has been identified as providing channels for fast oxygen ion migration [15].

One final feature that we should mention is the observation of a complementary behavior of the resistance change of the two interfaces in symmetrical devices. This effect consists in a compensation of the resistive change that takes place in the two interfaces, leading to the almost perfect cancellation of the total (two-terminal) resistive change [16,17]. The detailed study of this feature has uncovered a peculiar behavior of the R-V characteristics seen in hysteresis switching loops that was termed "table with legs" [16]. This unusual behavior provided key insights for theoretical modeling of the RS behavior in bipolar systems [18].

#### Visualizing the resistive change

Figure 6: (a) Bridge structure that appeared in the CuO channel after the forming step. (b) Bridge physically cut by FIB. (c) Re-forming of the bridge. (figure from [21]).

A central question of RS phenomena is, evidently, what is the origin of the effect. In the unipolar devices, the lack of scaling of the resistance with the electrode area suggested the existence of "filaments" that would form with a soft electric breakdown and then break as electrical fuses [19]. Direct observation of such a filament has proven elusive [20]. An attempt to directly visualize the conductive filament was done in an interesting experimental study by Fujiwara et al. [21]. A planar geometry was adopted for the fabrication of a CuO device with electrodes separated only a few microns, allowing for the direct observation of structural changes. After the initial electro-forming step (black curve in Fig.4), the observation of the surface revealed the formation of a "bridge" structure of apparently melted material connecting the two electrodes (Fig.6a). After this forming, the device went to the R$$_{\rm LO}$$ resistance state. The temperature dependence of R$$_{\rm LO}$$ revealed metallic conduction in this state [21]. To induce the RESET commutation to the R$$_{\rm HI}$$ state, a current was applied to the device, and the bridge structure was observed to detect any systematic change. However, even after several transitions between the R$$_{\rm HI}$$ and R$$_{\rm LO}\ ,$$ no noticeable change was observed . With the device in the R$$_{\rm LO}$$ state, the bridge structure was physically cut with a focused ion beam (FIB) (Fig.6b). The resistance switched to the R$$_{\rm HI}$$ state, but the RS property was lost. Applying a new strong forming voltage, regenerated the bridge and the RS behavior (Fig.6c). This experiment demonstrated that, in fact, the switching takes place within a micrometer sized bridge. However, the lack of any observable changes within the bridge upon switching also indicated that the size of the conductive filaments must be well below the sub-micron scale. The chemical characterization by Photoemission Electron Microscopy (PEEM) of the bridge structure revealed a significant reduction within the bridge region [22]. Unfortunately, the detection of any systematic change linked to switching remained beyond the experimental sensitivity. Thus, the experiment suggest the formation of conductive filaments of metal Cu within the reduced bridge structure, with a thickness at the nanometer scale [21].

Figure 7: Main panel: inhomogeneous conductance at the surface of a lightly reduced single crystal of STO observed with C-AFM. Right panels: detail of conduction change and surface topography of a single spot, before (a) and after (b) positive voltage poling with the AFM tip. (figure adapted from [15]).

Direct observation of bipolar systems has also proved challenging. In this case, studies were done using conductive atomic force microscope (C-AFM) for the observation of changes in the dielectric surface. A study on LSMO with planar device structure showed that the resistance change occurs within a spatial regions of nanometer size [23]. More extensive studies were performed on STO by the group of Waser [15]. They observed that the resistive changes were linked to conduction spots of only a few nanometers wide (Fig.7). It was argued that the spots correspond to the termination of extended defects that enable the ionic migration of oxygen, providing support for a "nanoionic" mechanism for resistive switching [15,24].

#### Modeling of resistive switching

An early attempt to model the RS effect in bipolar TMOs was made by Rozenberg et al. in 2004 [25]. Though phenomenological and solely based on the scarce data available at that time, the model remarkably captured some key experimental observations and predicted several features that were eventually confirmed. For instance, the active role of interfaces containing inhomogeneous regions of nanometer scale, where field induced migration of electronic species control the resistive switching. Eventually, the model evolved to incorporate several key physical features that have been revealed in the extensive experimental research reported in recent years [18]. The model remains phenomenological, as it aims to apply to a large variety of systems that range from band-insulator STO, to doped Mott-insulators that are strongly correlated metals, such as manganites and cuprates. The key features that the model incorporates are the presence of inhomogeneous conductive paths, active regions near the electrode/dielectric interface with large resistivity due to the presence of Shottky barriers, oxygen vacancy (V$$_O$$) migration along a network of nanometer sized domains, which may be extended defects (cf STO) or grains and grain boundaries, etc. The local resistivities along the conduction path is assumed to be determined by the V$$_O$$ concentration. In fact, a universal feature of TMOs is that their resistivity is most strongly influenced by oxygen stochiometry. This is because oxygen vacancies play a double role by providing electron dopants, but also introducing disorder in the conduction bands by disrupting the TM-O-TM bonds.

Thus, the model basically consists on a resistor network, where the links have a resistivity that is determined by their local V$$_O$$ concentration. The high resistivity of the Shottky barriers is simply modeled by and enhanced resistivity of the few outermost links at either end.

A last feature of the model is the assumption that migration of the V$$_O$$ ions from domain to domain is enhanced by electric field. Thus the model behavior is simulated through the following steps: initially, a uniform profile of V$$_O$$ concentration is assumed along the conductive domain path. This determines the resistive profile of the links of the network. An external voltage is applied, the current and the local potential drops are computed. The V$$_O$$ migration from domain to domain is simulated using the following expression for the probability to transfer ions among neighboring domains$p_{ab} \propto \delta_a (1 − \delta_b) e^{(− E_A + \Delta V_a)/V_B}$

where $$\delta_{a}$$ is the concentration of vacancies at domain "a", $$\Delta V_a$$ is the potential drop at domain "a", $$V_B$$ is potential associated to the migration barrier height, and $$E_A$$ is an energy associated to the intrinsic vacancy drift constant at the given temperature when no external potential is applied.

After the migration transfers are computed and updated in a simulation step, the new values of the resistors of the network are recalculated. At the following time step the external voltage is updated, then the new voltage drops along the networks are obtained, and so on.

As shown in Fig.8, the predictions of this simple model reproduce the "table with legs" R-V characteristics that were experimentally measured in two different symmetric devices, one with a PLCMO dielectric and another with YBCO. Moreover, introducing asymmetry in the model through a single parameter, it can also account for the RS behavior in asymmetric devices, remarkably well [18]. This study provided strong support to the mechanism of electric-ﬁeld-enhanced migration of oxygen vacancies at the nanoscale for bipolar type resistive switching. However, it also clarified the necessity of having "poorly" conductive interfaces (Shottky barriers).

Figure 8: Top panel: model prediction for the "table-with-legs" R-V characteristics of a bipolar symmetric device. Lower panels: Experimental R-V data for a PCMO (left) and a YBCO (right) samples (figure from [18]).

Another feature that was elucidated by the study is that in perfectly symmetric bipolar devices a cancellation of the resistance occurs for the extreme values of the applied voltage (positive and negative). In contrast, this cancellation does not take place in asymmetric devices. Therefore, the magnitude of RS should be larger in asymmetric devices. This is an example of how simple theoretical modeling may assist in providing useful experimental guidance.

Other theoretical modeling attempts focused on unipolar binary oxide systems [26,27,28,29]. A generic model for unipolar switching has been proposed by Chae et al. [26], based on a random circuit breaker network. The model consisted on a resistor network where the resistance of each link may undergo a resistive switching, depending on the its values of current and voltage. The model is simple and appealing as the simulations reproduce well the qualitative features of experimental data. However, one of its main limitations is the ad-hoc assumption made on the I-V characteristics of each network unit. A different model has been proposed by Ielmini et al. [27] that focused on the NiO compound. They argue that the SET transition is driven by threshold switching into a high conductive state, which leads to a structural change where stable conductive filaments are created. The RESET is, more simply, due to the dissolution of the filaments due to Joule heating.

A binary system that received particular attention is TiO$$_2\ .$$ Devices made with this compound may exhibit either, unipolar or bipolar RS, depending on fabrication details. In fact, bipolar switching has been observed only in relatively small systems, where electrode separation is less than 50 nm. Unipolar switching of this compound is not surprising, as it also observed in many other binary oxides. However, bipolar switching in this insulator is rather surprising, as it is structurally very different from the other bipolar systems, which are complex oxides.

A simple phenomenological model for the bipolar RS effect in TiO$$_2$$ has been proposed by the group of Williams [28]. They assumed a spatially inhomogeneous system, where the initial forming step induces a high concentration of oxygen vacancies on a portion of the dielectric closest to the negative electrode. The vacancies are donors of electron carriers, thus decrease the resistivity of that region. The ensuing model is that of two series resistors where one corresponds to high resistivity stoichiometric TiO$$_2\ ,$$ while the other corresponds to low resistivity TiO$$_{\rm 2-x}\ ,$$ where $${\rm x}$$ is the oxygen vacancy concentration. As external voltage is applied to the electrodes, the boundary of the oxygen vacancy reach region moves due to ionic migration, thus changing the total resistance of the system.

Another model for bipolar switching in TiO$$_2$$ has been introduced by Jeong et al. [29]. Their model is based on electrochemical redox reactions involving oxygen vacancies near the electrodes. They argue that the reactions modulate the height of the Schottky barriers formed at the interfaces. Their model seems to account for experimental RS data, however, it relies on a relatively large number of parameters.

#### Memristors, neuromorphic memories and resistive switching

In 2008, the Hewlett-Packard group announced the discovery of a fourth fundamental passive circuit element, termed "memristor" [28], that had been predicted by Chua in 1971 [30]. The memristor consists on a variable resistor, whose actual value of resistance depends on the amount of current that has circulated through it, i.e. , on its previous history. This immediately leads to hysteresis and non-linear effects.

The memristor announced by the HP group consisted of a resistive switching device with Pt electrodes and a thin 5 nm layer of binary-oxide TiO$$_{\rm 2-x}$$ as dielectric.

The existence of this fourth element was deduced by Chua from the form of the standard equations electric circuit theory. While the physical pertinence of the argument remains a matter of debate, the notion of a history dependent resistor has revived the research of neuromorphic memories for artificial intelligence. It is argued that these memory devices, of only a few nanometers size that can be implemented in dense 3D cross-bar latches, are perfectly suited for eventual neural network applications.

#### Strong correlation effects in resistive switching

An important open question in resistive switching phenomena in oxides is whether strong correlation effects may play a role. In fact, strong correlation effects, such as high temperature superconductivity, colossal magnetoresistance and metal-insulator transitions have remained a central theme of research in condensed matter physics of TMO, since the discovery of superconductivity in the cuprates in 1987. The possibility of a solely electronically-driven resistive switching transition, such as the Mott metal-insulator transition, may allow for fast devices with long endurances and low dissipation. However, the experimental evidence gathered so far in RS of TMOs is indicating that the physical origin of the switching is electric-stress driven structural changes, due to ionic migration and electrochemical reactions, rather than strong correlation effects.

Nevertheless, a strongly correlated driven resistive switching system, a "Mott transistor", may have already been realized, but not in a TMO, but in the chalcogenide compound GaTa$$_4$$Se$$_8$$ [31].

#### Final remarks

Resistive switching in transition metal oxides is a rapidly developing field. Some obstacles remain to be overcome for technological applications, such as to gain control on the reproducibility of the switching effect, and the related issues of endurance and retention time. Yet, and despite a still incomplete physical understanding of the mechanism responsible of the RS effect, the research in this field is quickly moving to the stage of applied device implementation. This is driven by the continuous succession of reports that demonstrate the competitiveness of RS based RAM devices (RRAM) versus current Flash MOSFET technology devices.

Although the mechanism of RS in current devices may not be due to strong correlation effects, the possibility to incorporate them into the realm of future oxide electronics remain an exciting open challenge.

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