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Surface diffusion-limited lifetime of silver and copper nanofilaments in resistive switching devices

Surface diffusion-limited lifetime of silver and copper nanofilaments in resistive switching devices ARTICLE https://doi.org/10.1038/s41467-018-07979-0 OPEN Surface diffusion-limited lifetime of silver and copper nanofilaments in resistive switching devices 1 2 1 1 1 1 Wei Wang , Ming Wang , Elia Ambrosi , Alessandro Bricalli , Mario Laudato , Zhong Sun , 2 1 Xiaodong Chen & Daniele Ielmini Silver/copper-filament-based resistive switching memory relies on the formation and dis- ruption of a metallic conductive filament (CF) with relatively large surface-to-volume ratio. The nanoscale CF can spontaneously break after formation, with a lifetime ranging from few microseconds to several months, or even years. Controlling and predicting the CF lifetime enables device engineering for a wide range of applications, such as non-volatile memory for data storage, tunable short/long term memory for synaptic neuromorphic computing, and fast selection devices for crosspoint arrays. However, conflictive explanations for the CF retention process are being proposed. Here we show that the CF lifetime can be described by a universal surface-limited self-diffusion mechanism of disruption of the metallic CF. The surface diffusion process provides a new perspective of ion transport mechanism at the nanoscale, explaining the broad range of reported lifetimes, and paving the way for material engineering of resistive switching device for memory and computing applications. 1 2 Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano and IUNET, Piazza L. da Vinci, 32-20133 Milano, Italy. Innovative Centre for Flexible Devices (iFLEX), School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore. Correspondence and requests for materials should be addressed to X.C. (email: [email protected]) or to D.I. (email: [email protected]) NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications 1 1234567890():,; ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 esistive switching (RS) memory, technically referred as positive voltage, followed by a reset transition, or CF dis- resistive random-access memory (RRAM), is a two- connection, at negative voltage. The formed CF usually shows a Rterminal device that can change its resistance in response non-volatile behavior, namely it remains stable after set tran- to the electrical stimulus by a voltage pulse, as a result of the sition if no further voltage excitation is applied, which forms formation and disruption of a nanoscale conductive filament (CF) the basis for the memory operation. Set operation at negative with relatively high conductance due to the high concentration of voltage and reset operation at positive voltage can also take defects. Defects can originate from the host material, such as place, thanks to the symmetric structure of the nanocontact oxygen vacancies in a metal oxide based memory , or from the device where Ag is present in both electrodes (Supplementary electrodes via ionic migration across the insulating material, e.g., Fig. 1and SupplementaryNote1). Thelifetimeof the CF copper (Cu) or silver (Ag) in the so-called conductive bridge should be longer than ten years for a practical memory appli- random-access memory (CBRAM) . Depending on the specific cation where data must be stored reliably. However, volatile application, the formed CF has a lifetime, or retention time, switching can also occur, where the CF spontaneously ruptures ranging from few microseconds to several months, or even years. after formation with a lifetime as short as few microseconds. For example, RS device finds application in non-volatile mem- Volatile and non-volatile switching can coexist within the same ories, where the formed CF must have a lifetime in the range of 10 device structure, with the transition between the two switching 1,3 years . RS device also finds application as a volatile switch which modes being controlled by the compliance current I ,namely is characterized by a short lifetime in the range of microseconds the maximum current allowed to flow across the device during 21–23 to milliseconds, providing a feasible technology for fast selection the set transition .Figure 1eshows typical I-V curves 4,5 devices in crosspoint arrays of memory or sensor devices . The for the same device in Fig. 1doperated atlower I :the RS tunable lifetime of the CF in the volatile RS device also mimics device shows non-volatile switching for I = 10 mA, while a 6,7 the short term plasticity of biological synapses , enabling a burst lower I leads to volatile switching where the CF disconnects of novel applications for brain-inspired neuromorphic comput- spontaneously as the voltage is reduced to zero after the set 8–11 ing . Recently, the coexistence of volatile and non-volatile RS transition. Bidirectional volatile switching, where the set tran- within the same device depending on the compliance current sition can take place at either positive or negative voltage, is 12–14 23 during the CF formation has been extensively reported . usually demonstrated . The value of the compliance current I However, conflicting explanations are being proposed for the CF controls the device behavior, where switching become lifetimes in non-volatile and volatile RS phenomena. In non- increasingly volatile as I is decreased (Fig. 1f). Since volatile volatile switching, the rupture of metallic filament is usually and nonvolatile switching solely differ by the lifetime of their attributed to the out-diffusion of the metallic atoms from the CF CFs, it is reasonable to attribute the two switching modes to the 15,16 to its host dielectric material . On the other hand, lifetime in same mechanism. Since a higher I generally corresponds to a 1,24 volatile switching is interpreted as the consequence of the atomic thicker CF , it is also plausible to explain the volatile and 17–19 clustering to minimize the CF-dielectric interfacial energy .A non-volatile behaviors to a strong size dependence of CF life- comprehensive physical understanding of CF lifetime in volatile time. In fact, the nanocontact effect between Ag NWs and non-volatile RS device may enable a stronger ability to (Fig. 1c) in our demonstrated device enable a fine control of the engineer the device materials and operation toward application- filament size by I since the limited Ag atoms source and based optimization of RS device. confined electric field eliminate a common overshoot issue Here, we show that metallic CF lifetime is strongly affected by during the operation of RS devices . surface atomic self-diffusion. The gradient of surface atomic Given the random nature of the Ag NW network in the host vacancy concentration induces the migration of atoms on the CF material, the distance between the two electrodes in the switching surface toward the minimization of the surface area, leading to region might be affected by variability. Each device might in fact clustering of metal atoms and eventually to CF disruption. The- have a different distance between the active NWs, thus resulting oretical analysis predicts that the surface diffusion effect is only in a variation of threshold voltage from device to device. Even dominant in the sub-10 nm scale at room temperature, due to the within the same device, the weakest point where the filament is high surface-to-volume ratio. The lifetime for disruption of a formed might change location or distance at each cycle, thus typical CF can span from microseconds to years for the CF size resulting in a cycle-to-cycle variation of threshold voltage. The (diameter) changing from <1 nm size to 14 nm size. The size- threshold voltage distribution of our devices were shown to have dependent lifetime is experimentally validated with a broad range a relatively good uniformity both from cycle to cycle, and from of data for various types of both non-volatile and volatile RS device to device , thus indicating a relatively small variation of devices. This work provides a new perspective of ion transport the distance between Ag NWs. mechanism in nanoscale, paving the way for structural and material engineering of nanoionic devices. Surface-diffusion effects. Recent in situ transmission electron 17,26 microscope (TEM) observations of metallic CFs revealed that Results Ag and Cu atoms from the CF tend to form clusters rather than Volatile and non-volatile switching.Figure 1ashows aRS out-diffuse toward the host dielectric material. The clustering of device based on a metal-insulator-metal (MIM) structure with the metal atoms leads to the formation of nanoclusters and nano- Au electrodes and a dielectric layer of silk-Ag nanowires (Ag spheres . To highlight the clustering-induced CF rupture, we run NWs) composite. Ag NWs are buried in the silk layer ,as a molecular dynamics (MD) simulation by using the LAMMPS shown by the scanning electron microscope (SEM) sectional program adopting an embedded-atom-method (EAM) poten- and planar views in Fig. 1b. Ag NWs serve as reservoirs for tial to describe the interactions between Ag atoms. We set the metallic atoms for the formation of a nanoscale CF which system temperature to 800 K to accelerate the CF morphological electrically connects the two electrodes under the application of change to a reasonable simulation time. Figure 2a–c shows the an external voltage (Fig. 1c). To erase the memory state, the CF time evolution of the simulated Ag CF between the two electro- can be ruptured by a second external stimulus. These processes des, which might represent two Ag NWs in the structure of are shown by the electrical current-voltage (I–V) characteristics Fig. 1c, or two planar Ag electrodes in a vertical MIM 4,23 in Fig. 1d, indicating a set transition, or CF formation, at structure . 2 NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ARTICLE ab c Au 5 μm AgNW Au Silk Silk-AgNWs Ag filament V AgNWs Au Au AgNW AgNWs AgNW Au 200 nm de f l = 10 mA l = 1 mA c c –2 –2 10 10 –4 –4 10 10 –6 –6 10 10 10 μA –8 –8 10 10 –10 –10 20 –12 –12 10 10 –1.5 –1 –0.5 0 0.5 1 1.5 –1.5 –1 –0.5 0 0.5 1 1.5 –7 –6 –5 –4 –3 –2 –1 10 10 10 10 10 10 10 Voltage (V) Voltage (V) l (A) Fig. 1 Volatile and non-volatile switching of RS devices. a Schematic structure of a RS device based on Ag NWs. Bottom and top Au layers act as contact pads, Ag NWs act as effective bottom and top electrodes for the CF formation, and silk acts as insulating switching layer. b Sectional (left) and top planar (right) SEM views of the RS device. c Illustration of the metallic CF formation between two Ag NWs. A metallic CF can be formed in response to the application of a large voltage to the electrodes. In non-volatile switching, the CF can remain in the connected state for a relatively long time until another voltage pulse induces its disconnection. On the other hand, in the case of volatile switching, the CF retracts back to the electrodes immediately after set transition. d I–V characteristics for non-volatile switching for a high compliance current I = 10 mA. When a positive sweep voltage is applied, the current increases sharply, indicating the formation of the metallic CF. The compliance current I across the device controls the size of the formed CF. After the positive voltage sweeps back to zero, the device still remains in the low resistance state. As a negative voltage is applied, the device switches to the high resistance state indicating CF disruption. e I–V characteristics for volatile switching of the device at low I . When a positive sweep voltage is applied, the current increases sharply indicating CF formation. However, the device quickly switches back to its original high resistance state after the forcing voltage is swept to zero. Bidirectional volatile switching is observed, as the application of a negative voltage also generates a metastable CF. f Probability for volatile switching (VS) as a function of I , indicating the transition from volatile switching to non-volatile switching at increasing I C C According to MD simulations, the metallic CF can sponta- in the CF and on the host dielectric materials. For simplicity, we neously break as a result of atomic surface diffusion driven by the assume that the CF shape is obtained from the revolution of a minimization of the system energy. The atomic surface diffusion curve ρ(z) as shown in Fig. 2f. The normal distance dn traveled by originates from the gradient of surface atomic vacancy concen- a surface element ∂s during the time increment dt is thus given 30 33 tration or the gradient of the surface atomic chemical potential , by , resulting in a tendency to minimize the surface energy . Atoms dn B ∂ ∂κ in the bulk of the CF instead remain fixed in their lattice sites of ¼ ρ ð2Þ the crystal (Fig. 2d, e, and see Supplementary Fig. 2–3 and dt ρ ∂s ∂s Supplementary Note 2 for more details), as confirmed by recent 21,27 observations by in situ TEM . Based on the Gibbs-Thomson where B = D γδ /kT is a parameter which strongly depends on effect, the surface atomic flux J along an arbitrary surface can be the type of CF atom, on temperature and on the surrounding host modeled by assuming isotropic surface diffusion, leading to : materials. Figure 3 shows the simulation results for the morphological D γδ J ¼ ∇ κ; ð1Þ evolution of two Ag CFs with the same length h = 10 nm and s s kT different initial diameters, namely d = 2 nm (Fig. 3a) and d = 0 0 0.4 nm (Fig. 3b). More details about the simulation method and where D is the surface diffusion coefficient, γ is the surface results are reported in the Supplementary Fig. 4–7, Supplemen- energy, δ is the interatomic distance, k is Boltzmann’s constant, tary Note 3 and Supplementary Movies 3–8. The parameter B for −34 4 T is the temperature, and κ is the surface curvature, given by κ = Ag is estimated to be 10 m /s at room temperature 1/r + 1/r , where r and r are the principal radii of the (Supplementary Note 4–5 and Supplementary Table 1). Surface 1 2 1 2 curvature. Note that the driving force for the surface diffusion in diffusion leads to a segmentation of the CF and the formation of Eq. (1) is the gradient of the surface curvature κ, which is also the one or more intermediate clusters, as shown in Fig. 3b for t = 1 key parameter controlling the Gibbs-Thomson effect. The ms (see also Supplementary Movie 4 and Supplementary coefficient D for surface diffusion is thermally-activated accord- Movie 7). A similar ovulation effect has been recently reported 17,26,34 ing to D ¼ D′expðQ =kTÞ, where the pre-factor D′ and the by in situ TEM observations as the by-product of Ag nano- s s s s diffusion barrier Q mainly depend on the type of migrating atom filament clustering in an insulating material. Note that the specific NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications 3 Current (A) Current (A) Probability of VS (%) ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ab c 0 s 100 ps 200 ps de f A ds B B E 5 =  (z) 4 F Crystalline state 0 50 100 150 200 250 Time (ps) Fig. 2 MD simulation of surface diffusion. a–c MD simulation results of a Ag nanoscale CF between two electrode plates at increasing times, namely t = 0, 100 ps, and 200 ps (Supplementary Movies 1–2). The color indicates the free energy per atom with lighter blue representing atoms with higher free energy, hence higher diffusivity. To accelerate the surface diffusion process, the system temperature is set to 800 K, which is still below melting temperature of Ag. d Cross-section view of the CF at 100 ps, indicating stable bulk atoms with low free energy and crystalline states, hence negligible diffusion, whereas surface atoms show higher energy and diffusivity, thus resulting in the morphological evolution and rupture of the filament. e Typical traces of individual atoms along z direction for bulk atoms (A, C), surface atoms (B, D), and bottleneck atoms (E, F) in d. Bulk atoms show constant positions, while the surface atoms migrate toward their closest electrodes. Atoms in the CF bottleneck region also show a high tendency to migration to either the top or bottom electrode. (see Supplementary Note 2 and Supplementary Fig. 2 for more analysis). f CF geometry considered in the model of the surface diffusion. For simplicity, isotropic surface diffusion and axisymmetric (along z) CF surface are assumed. ρ(z)defines the geometry of the filament surface by rotating around the z axis, and n defines the surface evolution of a surface piece ds in unit time in outward normal direction morphological evolution of the filament is affected by the mechanism, see Supplementary Note 7). The power law for thin 30 4 hydrophobicity between filament and electrode materials, initial CFs (d < 5 nm) is consistent with the Herring’slaw s = λ , 0 τ filament shape (Supplementary Note 6, Supplementary Fig. 8–10 where s is the scaling of lifetime with the shape dimension scaling and Supplementary Movies 4–8), and anisotropy of the filament of λ, thus describing the lifetime τ as a function of the size of crystal. However, the generic isotropic simulation shown in Fig. 3 equally-shaped particles (see Supplementary Note 8). Note in fact can provide us a general rule of the size-dependent stability of the that the fixed length has negligible effect on the lifetime for d << h. CF. The steep increase for higher d marks the onset of the CF stability, hence non-volatile switching, which corresponds to the equivalence of thetwo principleradii of surfacecurvature (Fig. 4b inset), similar Size-dependent lifetime.We define the lifetime τ of the CF as the to the liquid capillary bridge between two plates . first opening of a depleted gap according to the numerical solution Results in Fig. 4b provide quantitative criteria for discriminat- of Eq. (2)(seeFig. 3). Reducing the diameter of the CF by 5 times ing volatile and non-volatile RS depending on the CF size. For (from Fig. 3atoFig. 3b) results in a reduction of the lifetime by instance, a one-atom-wide CF with d ≈ 0.2 nm shows a lifetime about 150 times, as shown by the simulated gap length in Fig. 4a, τ ≈ 10 μs, resulting in volatile switching for possible applications due to the larger surface curvature κ controlling the surface diffu- as selector device in crossbar arrays or neuromorphic elements. sion rate (Eq. (1)) and the CF morphological evolution rate On the other hand, the simulation results project that a CF with (Eq. (2)). The dependence of lifetime on the initial CF diameter can d ≈ 14 nm can have a lifetime τ ≈ 5×10 s, corresponding to explain the transition from volatile switching (Fig. 1e) to non- about 16 years at room temperature, which is thus compatible volatile switching (Fig. 1d) at increasing I , where a larger com- with non-volatile memory applications. pliance current leads to a larger CF diameter with longer lifetime. The calculated quantitative timescale of the geometrically To highlight the size-dependent lifetime, Fig. 4b summarizes the CF identical shape evolution process identified by d /h can be lifetime as a function of the initial CF diameter d with a constant extrapolated by Herring’s scaling law to interpret some general CF length h= 10 nm being assumed. The lifetime increases with the observations. For instance, a filament with initial diameter d = CF size according to a power law τ  d , then increases asymp- 0 80 nm and filament length h = 4 μm will have the same shape totically as it approaches a stable size d ≈ 14 nm. The power law evolution (e.g., resulting in egg-shaped cluster segmentation) of a with exponent 4 in our surface-diffusion model arises from Eq. (2), filament with initial diameter d = 0.2 nm and filament length h where the filament surface evolution rate dn/dt is proportional to 0 = 10 nm, except for their dimension scaling of λ = 400 and the second-order derivative of the curvature κ in Eq. (2), which in lifetime scaling of s = 2.56 × 10 . As a result of the dimensional turn is a second-order derivative of the surface profile ρ in Eq. (1) τ scaling, the lifetime scales from 10 μs for the filament with (based on similar analysis, we also exclude other possible 4 NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications z (nm) 0 1 –1 NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ARTICLE t = 0 s 24 ms 30 ms 60 ms 10 10 10 10 8 8 8 8 1.5 6 6 6 6 d = 2 nm 4 0 4 4 0.5 2 2 2 2 0 0 0 0 2 2 2 2 –0.5 2 2 2 0 2 0 0 0 0 0 0 0 –2 –2 –2 –2 –2 –2 –2 –2 (nm) (nm) 10 10 10 10 10 10 8 8 8 8 8 8 6 6 6 6 6 d = 0.4 nm 4 4 4 4 4 2 2 2 2 2 2 0 0 0 0 0 0 –2 0 1 0 1 0 1 1 0 1 0 0 0 –1 –1 0 0 0 –1 –1 –1 (nm) (nm) t = 0 s 40 μs 0.13 ms 0.4 ms 0.6 ms 1 ms Fig. 3 Morphological changes induced by surface diffusion. a Simulation results of the surface diffusion equations, indicating the rearrangement of a Ag CF with initial diameter d = 2 nm at increasing times, namely t = 0, 24 ms, 30 ms, and 60 ms. b Same as a, but for a CF with an initial diameter d = 0.4 nm at 0 0 times t = 0, 40 μs, 0.13 ms, 0.4 ms, 0.6 ms, and 1 ms. For both cases, the CF length is 10 nm, equivalent to the thickness of the insulating layer between two planar electrodes. The color in the figures indicates the surface curvature, where surface points with higher curvature are more likely to induce surface diffusion, thus providing a suitable spot for CF rupture. The CF lifetime decreases from around 20 ms (a) to about 0.13 ms (b)as d is reduced from 2 nm to 0.4 nm. The ovulation effect in b, where nano-clusters result from the disconnection of a thin CF, is consistent with in situ TEM observations of Ag nano- 17,26,34 clusters evolving from Ag nanoscale CFs 5 39–43 d = 0.2 nm and h = 10 nm, to 2.56 × 10 s (about 3 days, in line reporting data of sub-10 nm scale filaments for both Cu and 36 17,23,44,45 with the measured lifetime of AgNWs ) for the filament with Ag from the literatures (more details in the Supple- d = 80 nm and h = 4 μm. mentary Table 2–3). Compared to Ag, Cu-based RS devices show a stronger tendency to non-volatile switching due to its higher surface activation energy Q and, hence, smaller B (estimated as −47 4 Universal model of volatile and non-volatile switching.To 10 m /s at room temperature, see Supplementary Note 4). further validate our model, we conducted time-resolved experi- Note the large variation of lifetime, which might originate from ments to measure the lifetime of Ag CFs as a function of I . The C anisotropic surface diffusion along different crystalline directions, CF was obtained by applying an excitation pulse at relatively large or inaccurate control of the CF size by I . Different types of voltage, followed by a monitor voltage at relatively low voltage dielectric materials would also impact on the lifetime by affecting V = 0.1 V to monitor the conductance of the device in real read parameter B in Eq. (2). Despite these variations, the surface dif- time. Figure 5a shows the setup of applied voltage pulse, while the fusion model accounts for the size dependence of lifetime over a inset shows the measurement configuration, consisting of a RS broad range of experimental conditions and samples. The tem- device connected to a load resistance R in serial. The R aimed at perature dependent lifetime also relies on the surface activation L L limiting the current during the set transition. By changing the energy Q . For the estimations of the parameter B and the pre- value of R from 1 MΩ to 100 Ω, the CF size could be varied to dicted size-lifetime lines at different temperatures in Fig. 5c, the study the size-dependent lifetime. Figure 5b shows the monitored surface activation energy Q for Cu and Ag was assumed to be conductance for various I from 1 μΑ to 10 mA, where the initial 1.1 eV and 0.52 eV, respectively. This is consistent with the data conductance G shows a linear increase with I in agreement with 0 C projected from the temperature dependent retention times in Cu field- and temperature-controlled switching in RS devices . The and Ag RS devices by fitting with the Arrhenius rule, which gives variable initial conductance is mapped into an initial CF diameter the value of Q in the range of 1.3 ~ 1.4 eV and 0.5 ~ 0.7 eV for Cu 43–45 d according to G ¼ πσd =ð4hÞ, where σ is the CF conductivity 0 and Ag, respectively . 0 0 37,38 considering the enhanced scattering effects in nanoscale CFs (Supplementary Note 9 and Supplementary Fig. 11). The figure also shows the calculated conductance evolution G(t) from Discussion Eq. (2), indicating a good agreement with data. Figure 5c shows Surface self-diffusion effect was first observed in vacuum tube the measured and calculated lifetime as a function of d , also electronic devices, as responsible for the blunting of a sub-mm NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications 5 (nm) (nm) –1 Curvature (nm ) –1 Curvature (nm ) ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 least two evidences: first, recent TEM observations reveal the presence of Ag or Cu clusters rather than homogeneously dis- d = 2 nm tributed Ag within the doped silicon-oxide layer. This was shown 17 26 d = 0.4 nm 0 for Ag-doped SiO (x <2) , Cu-doped SiO (x <2) , and Ag- x x 27,34 ≈130 μs doped SiO . All these results indicate that Ag and Cu have ≈ 20 ms relatively low solubility in silicon oxide, thus resulting in the clustering of Ag or Cu atoms. The low solubility of Ag and Cu in –6 –5 –4 –3 –2 –1 0 the host materials can be understood as the result of the low 10 10 10 10 10 10 10 reactivity of Ag and Cu elements and the strong chemical stability Time (s) of Si-O valence bond (see Supplementary Note 7 for extended 10 discussion). Second, experimental data are consistent with Her- ring’s scaling law τ  d , while one would expect a dependence 10 τ  d for out-diffusion as reported by our analysis in the Sup- 0.1 50,51 plementary Note 7, in agreement with previous results . Out- r < 0 6 5 10 0 diffusion might be non-negligible when the metal has a relatively large solubility in the host materials, such as Ag in Ag S and Cu 0 2 –0.1 10 10 in CuS . 0 5 –5 –10 (nm) –10 (nm) The volatile switching in RS devices has previously been interpreted as the consequence of the atomic clustering to minimize the Gibbs-Thomson energy at the interface between the 17–19,54 filament and the host material . Our interpretation of –2 filament shape evolution induced by surface diffusion also has Slope = 4 roots in the Gibbs-Thomson effect, given the dependence on –4 surface curvature radii in Eq. (1). Another common phenomenon 55–58 induced by Gibbs-Thomson effect is Ostwald ripening , –6 which has been proposed to control the evolution of the particles –1 0 1 10 10 10 obtained by filament fragmentation . According to our model, d (nm) surface diffusion might control the initial stages of the filament disconnection, which also dictates the filament lifetime according Fig. 4 CF size-lifetime scaling law. a Filament gap length as a function of the to the Herring’s law. Ostwald ripening instead may be responsible relaxation time. The increase of the gap length from zero marks the for the post-lifetime evolution of the filament particles. In any moment of CF disruption which we defined as lifetime τ. b Filament case, the driving force for the surface diffusion and Ostwald disruption time as a function of initial filament diameter d . The size-time ripening both can be traced back to the Gibbs-Thomson effect scaling for thin filament (d ≪ 10 nm, h = 10 nm) well agrees with Herring’s (see Supplementary Note 10 and Supplementary Fig. 12 for more law τ  d with a slope of 4, while, on the other hand, for thick filament (d discussion). > 10 nm), the lifetime more rapidly increases with the lateral size as a stable In RS devices, CFs of various sizes can be electrically formed, capillary bridge is formed, marking an increase of the lifetime from resulting in a large range of electrically measurable lifetime. microseconds to years with increasing filament diameter. Inset: snapshot of According to our surface diffusion model, the ultimate stability of a stable capillary bridge formed from filament with initial diameter d = the CF for non-volatile switching arises from a stable capillary 14 nm. The stability of this shape originates from the two principle radii of bridge between the top and bottom electrodes. Note that this surface curvature having equal modulus and opposite signs. In the condition might result in a relatively large CF, which conflicts bottleneck point, the horizontal radius of the surface curve r > 0, whereas with other requirements of RS devices for practical applications in the vertical radius r < 0, resulting in the surface curvature κ tending to zero non-volatile memories. For instance, RS devices should also be easily erasable at relatively low current, which is necessary to minimize the IR voltage drop across lines in crosspoint arrays. An filamentary field-emission cathode operating at elevated tem- excessive voltage drop, in fact, would lead to unwanted disturbs to perature (~1000 K) . The lifetime of this type of filament, unselected cells. The tradeoff between small operating currents which controls the vacuum tube lifetime, is generally in the and CF stability requires careful device and materials optimiza- range of hundreds of hours. At nanoscale dimensions, the tion, toward the minimization of the free energy at the CF sur- morphological changes driven by the minimization of surface face. Note that experimental data show no tradeoff between energy are highly accelerated to the range of observable time endurance and operation current (see Supplementary Note 11 for scale at room temperature, which is at the origin of a liquid-like more discussion). Conversely, minimization of the lifetime in the pseudoelasticity observed in situ. Surface diffusion effects also range of few ns might enable the operation of RS device as fast 20,59 control general properties in nanoscale world, such as the lack and efficient selector device for crosspoint arrays . The fast of sharp tipped metal coated probes for atomic force micro- recovery of the off-state is essential in this case to enable random scopy compared to the covalent bonded crystallized silicon or access within the array, where each memory must appear unse- diamond probes , and the instability of ultrathin metallic lected immediately after access for read or set/reset. Materials NWs, e.g., Ag NWs with diameter less than 40 nm . engineering should guide the selection of CF materials for selector In this work, we provide evidence for surface diffusion being technology to enhance the surface energy and the related surface the fundamental mechanism for the filament rupture in RRAM diffusion effects . devices. Other works have previously proposed that out-diffusion, In summary, we propose a universal surface diffusion rather than surface diffusion, acts as the leading dissolution mechanism for the spontaneous rupture of metallic CFs in fila- process in other materials systems, such as Ni in NiO . We note, mentary RS devices. Surface diffusion consistently accounts for however, that out-diffusion is not expected to play a major role in the transition from volatile to non-volatile switching observed in the materials systems considered in our work, namely Ag or Cu in nanoscale RS devices, where the lifetime of sub-10 nm CFs can silk and oxide compounds. This is independently supported by at span from microseconds to years. Results provide a general 6 NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications Lifetime,  (s) Gap (nm) –1 Curvature (nm ) (nm) NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ARTICLE ac Oscilloscope 300K Switch pulse 2 L 400K Cu 10 years RS device Resistor 10 500K Monitor voltage 300K 358K 10 358K 473K 473K –3 498K 473K Time (s) × 10 498K 498K 300K 2 523K 473K 523K Ag 523K 498K 400K 523K 300K 300K –2 Ag: Data. –2 10 Ag: Z. Wang et. al., 2016. Ag: J. Yoo et. al., 2017. Ag: S. Ambrogio et. al., 2014. –4 Ag: A. Bricalli et. al., 2018. –4 300K Cu: J. Yoon et. al., 2009. Cu: L-M. Lin et. al., 2017. 298K –6 Cu: C-Y. Liu et. al., 2011. Data –6 Cu: Y. Yang et. al., 2011. 373K Cu: J. Park et. al., 2010. Calculation –8 –1 0 1 2 –5 0 5 10 10 10 10 10 10 10 d (nm) Time (s) 0 Fig. 5 Universal explanation for volatile and non-volatile switching. a Illustration of the experimental setup for the measurement of the lifetime of Ag filament. The Ag NWs resistive device with conductance G is serially connected with a load resistance R which limits the current to a maximum value I .A L C voltage pulse (2.5 V, 100 μs) is applied to create the Ag filament, followed by a relatively low monitor voltage (0.1 V) to probe the filament evolution. b Measured and calculated conductance for the resistive switching device for different filament sizes. As I increases, the lifetime of the Ag filament increases as a result of the size-dependent surface diffusion. The largest I ~10mA results in a stable conductance, corresponding to a stable capillary bridge 39–43 17,23,44,45 with a large diameter. c Measured and calculated CF lifetime for devices with electrode made of Cu and Ag as a function of the initial −34 4 −47 4 diameter d . At room temperature, the parameter B was estimated as 10 m /s and 10 m /s for Cu and Ag filaments, respectively. The values of the surface activation energy Q was estimated as 1.1 eV and 0.52 eV for Cu and Ag, respectively. Calculations at various temperatures are also shown. The results account for the transition from volatile switching to non-volatile switching in RS devices (Fig. 1d–f) based on the size-dependent lifetime framework for understanding the stability of nanoscale structures, Numerical simulation of the filament shape evolution. The simulations of morphological evolutions were performed using Matlab©R17b with self-design and designing RS devices for a wide range of applications, e.g., codes. Isotropic surface diffusion and the CF surface of revolution by Eq. (2) were non-volatile memories with high stability for digital data storage, assumed. The morphological evolutions of the CF geometry are simulated in volatile switching for selector devices in crosspoint arrays, and 33 dimension-less form . To this purpose, we defined dimension-less variables H = tunable-lifetime RS synapses for neuromorphic computing with h/l, D = d /l, K = κl, and Γ = Bt/l , where h is the CF length, equivalent to the 0 0 thickness of the insulating layer in the RS device, d is the initial CF diameter, t is short/long-term plasticity. 0 time, and H, K, Γ are their dimensionless representations. The constant l (unit: m) is the scaling ratio between the CF size and the dimensionless one, defining the spatial dimension of the filament. For each step, the curvatures of the filament surface for each segment were calculated, thus the changes of the morphological Methods Device fabrication and characteristics. Silver nanowires (length: 10 µm, dia- profile were obtained from Eq. (2) and the surface profile was updated accordingly. A finite differential method was used to calculate the differential values of surface meter: 60 nm; concentration: 0.5% wt) were purchased from Sigma-Aldrich. The aqueous solution of silk fibroin for fabricating the device was prepared according curvatures and morphological change rates. The output of the computation was converted back to real space/time variables from dimensionless variables. For to the reported method . Firstly, a 5/70 nm-thickness Cr/Au layer was deposited instance, the real-time value can be obtained by t = Γl /B. The source code is on silicon substrate as the bottom electrode. Then, 0.1 ml Ag NWs solution was available from the authors upon request. added into 1 ml silk fibroin solution (2% wt) to form the blended solution. The resultant solution was spin-coated onto the bottom electrode at 1000 rpm for 45 s, and then evaporated for 2 h at room temperature. Finally, a 70 nm-thickness Au Data availability pad with the size of 100 µm × 100 µm was evaporated as the top electrode. For this The data that support the findings of this study are available from the corre- device, the effective active electrodes are equivalent to two adjacent AgNWs in the sponding author upon reasonable request. composite film or one Au electrode and one Ag NW electrode. Keithley 4200 semiconductor parameter analyzer was employed to measure the DC elec- trical characteristics. Arbitrary waveform generators (Agilent 33220A) and oscil- Received: 2 August 2018 Accepted: 2 December 2018 loscope (Tektronix DPO5054B) were used for lifetime measurement under pulse mode. MD simulation. 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Surface diffusion-limited lifetime of silver and copper nanofilaments in resistive switching devices

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Abstract

ARTICLE https://doi.org/10.1038/s41467-018-07979-0 OPEN Surface diffusion-limited lifetime of silver and copper nanofilaments in resistive switching devices 1 2 1 1 1 1 Wei Wang , Ming Wang , Elia Ambrosi , Alessandro Bricalli , Mario Laudato , Zhong Sun , 2 1 Xiaodong Chen & Daniele Ielmini Silver/copper-filament-based resistive switching memory relies on the formation and dis- ruption of a metallic conductive filament (CF) with relatively large surface-to-volume ratio. The nanoscale CF can spontaneously break after formation, with a lifetime ranging from few microseconds to several months, or even years. Controlling and predicting the CF lifetime enables device engineering for a wide range of applications, such as non-volatile memory for data storage, tunable short/long term memory for synaptic neuromorphic computing, and fast selection devices for crosspoint arrays. However, conflictive explanations for the CF retention process are being proposed. Here we show that the CF lifetime can be described by a universal surface-limited self-diffusion mechanism of disruption of the metallic CF. The surface diffusion process provides a new perspective of ion transport mechanism at the nanoscale, explaining the broad range of reported lifetimes, and paving the way for material engineering of resistive switching device for memory and computing applications. 1 2 Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano and IUNET, Piazza L. da Vinci, 32-20133 Milano, Italy. Innovative Centre for Flexible Devices (iFLEX), School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore. Correspondence and requests for materials should be addressed to X.C. (email: [email protected]) or to D.I. (email: [email protected]) NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications 1 1234567890():,; ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 esistive switching (RS) memory, technically referred as positive voltage, followed by a reset transition, or CF dis- resistive random-access memory (RRAM), is a two- connection, at negative voltage. The formed CF usually shows a Rterminal device that can change its resistance in response non-volatile behavior, namely it remains stable after set tran- to the electrical stimulus by a voltage pulse, as a result of the sition if no further voltage excitation is applied, which forms formation and disruption of a nanoscale conductive filament (CF) the basis for the memory operation. Set operation at negative with relatively high conductance due to the high concentration of voltage and reset operation at positive voltage can also take defects. Defects can originate from the host material, such as place, thanks to the symmetric structure of the nanocontact oxygen vacancies in a metal oxide based memory , or from the device where Ag is present in both electrodes (Supplementary electrodes via ionic migration across the insulating material, e.g., Fig. 1and SupplementaryNote1). Thelifetimeof the CF copper (Cu) or silver (Ag) in the so-called conductive bridge should be longer than ten years for a practical memory appli- random-access memory (CBRAM) . Depending on the specific cation where data must be stored reliably. However, volatile application, the formed CF has a lifetime, or retention time, switching can also occur, where the CF spontaneously ruptures ranging from few microseconds to several months, or even years. after formation with a lifetime as short as few microseconds. For example, RS device finds application in non-volatile mem- Volatile and non-volatile switching can coexist within the same ories, where the formed CF must have a lifetime in the range of 10 device structure, with the transition between the two switching 1,3 years . RS device also finds application as a volatile switch which modes being controlled by the compliance current I ,namely is characterized by a short lifetime in the range of microseconds the maximum current allowed to flow across the device during 21–23 to milliseconds, providing a feasible technology for fast selection the set transition .Figure 1eshows typical I-V curves 4,5 devices in crosspoint arrays of memory or sensor devices . The for the same device in Fig. 1doperated atlower I :the RS tunable lifetime of the CF in the volatile RS device also mimics device shows non-volatile switching for I = 10 mA, while a 6,7 the short term plasticity of biological synapses , enabling a burst lower I leads to volatile switching where the CF disconnects of novel applications for brain-inspired neuromorphic comput- spontaneously as the voltage is reduced to zero after the set 8–11 ing . Recently, the coexistence of volatile and non-volatile RS transition. Bidirectional volatile switching, where the set tran- within the same device depending on the compliance current sition can take place at either positive or negative voltage, is 12–14 23 during the CF formation has been extensively reported . usually demonstrated . The value of the compliance current I However, conflicting explanations are being proposed for the CF controls the device behavior, where switching become lifetimes in non-volatile and volatile RS phenomena. In non- increasingly volatile as I is decreased (Fig. 1f). Since volatile volatile switching, the rupture of metallic filament is usually and nonvolatile switching solely differ by the lifetime of their attributed to the out-diffusion of the metallic atoms from the CF CFs, it is reasonable to attribute the two switching modes to the 15,16 to its host dielectric material . On the other hand, lifetime in same mechanism. Since a higher I generally corresponds to a 1,24 volatile switching is interpreted as the consequence of the atomic thicker CF , it is also plausible to explain the volatile and 17–19 clustering to minimize the CF-dielectric interfacial energy .A non-volatile behaviors to a strong size dependence of CF life- comprehensive physical understanding of CF lifetime in volatile time. In fact, the nanocontact effect between Ag NWs and non-volatile RS device may enable a stronger ability to (Fig. 1c) in our demonstrated device enable a fine control of the engineer the device materials and operation toward application- filament size by I since the limited Ag atoms source and based optimization of RS device. confined electric field eliminate a common overshoot issue Here, we show that metallic CF lifetime is strongly affected by during the operation of RS devices . surface atomic self-diffusion. The gradient of surface atomic Given the random nature of the Ag NW network in the host vacancy concentration induces the migration of atoms on the CF material, the distance between the two electrodes in the switching surface toward the minimization of the surface area, leading to region might be affected by variability. Each device might in fact clustering of metal atoms and eventually to CF disruption. The- have a different distance between the active NWs, thus resulting oretical analysis predicts that the surface diffusion effect is only in a variation of threshold voltage from device to device. Even dominant in the sub-10 nm scale at room temperature, due to the within the same device, the weakest point where the filament is high surface-to-volume ratio. The lifetime for disruption of a formed might change location or distance at each cycle, thus typical CF can span from microseconds to years for the CF size resulting in a cycle-to-cycle variation of threshold voltage. The (diameter) changing from <1 nm size to 14 nm size. The size- threshold voltage distribution of our devices were shown to have dependent lifetime is experimentally validated with a broad range a relatively good uniformity both from cycle to cycle, and from of data for various types of both non-volatile and volatile RS device to device , thus indicating a relatively small variation of devices. This work provides a new perspective of ion transport the distance between Ag NWs. mechanism in nanoscale, paving the way for structural and material engineering of nanoionic devices. Surface-diffusion effects. Recent in situ transmission electron 17,26 microscope (TEM) observations of metallic CFs revealed that Results Ag and Cu atoms from the CF tend to form clusters rather than Volatile and non-volatile switching.Figure 1ashows aRS out-diffuse toward the host dielectric material. The clustering of device based on a metal-insulator-metal (MIM) structure with the metal atoms leads to the formation of nanoclusters and nano- Au electrodes and a dielectric layer of silk-Ag nanowires (Ag spheres . To highlight the clustering-induced CF rupture, we run NWs) composite. Ag NWs are buried in the silk layer ,as a molecular dynamics (MD) simulation by using the LAMMPS shown by the scanning electron microscope (SEM) sectional program adopting an embedded-atom-method (EAM) poten- and planar views in Fig. 1b. Ag NWs serve as reservoirs for tial to describe the interactions between Ag atoms. We set the metallic atoms for the formation of a nanoscale CF which system temperature to 800 K to accelerate the CF morphological electrically connects the two electrodes under the application of change to a reasonable simulation time. Figure 2a–c shows the an external voltage (Fig. 1c). To erase the memory state, the CF time evolution of the simulated Ag CF between the two electro- can be ruptured by a second external stimulus. These processes des, which might represent two Ag NWs in the structure of are shown by the electrical current-voltage (I–V) characteristics Fig. 1c, or two planar Ag electrodes in a vertical MIM 4,23 in Fig. 1d, indicating a set transition, or CF formation, at structure . 2 NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ARTICLE ab c Au 5 μm AgNW Au Silk Silk-AgNWs Ag filament V AgNWs Au Au AgNW AgNWs AgNW Au 200 nm de f l = 10 mA l = 1 mA c c –2 –2 10 10 –4 –4 10 10 –6 –6 10 10 10 μA –8 –8 10 10 –10 –10 20 –12 –12 10 10 –1.5 –1 –0.5 0 0.5 1 1.5 –1.5 –1 –0.5 0 0.5 1 1.5 –7 –6 –5 –4 –3 –2 –1 10 10 10 10 10 10 10 Voltage (V) Voltage (V) l (A) Fig. 1 Volatile and non-volatile switching of RS devices. a Schematic structure of a RS device based on Ag NWs. Bottom and top Au layers act as contact pads, Ag NWs act as effective bottom and top electrodes for the CF formation, and silk acts as insulating switching layer. b Sectional (left) and top planar (right) SEM views of the RS device. c Illustration of the metallic CF formation between two Ag NWs. A metallic CF can be formed in response to the application of a large voltage to the electrodes. In non-volatile switching, the CF can remain in the connected state for a relatively long time until another voltage pulse induces its disconnection. On the other hand, in the case of volatile switching, the CF retracts back to the electrodes immediately after set transition. d I–V characteristics for non-volatile switching for a high compliance current I = 10 mA. When a positive sweep voltage is applied, the current increases sharply, indicating the formation of the metallic CF. The compliance current I across the device controls the size of the formed CF. After the positive voltage sweeps back to zero, the device still remains in the low resistance state. As a negative voltage is applied, the device switches to the high resistance state indicating CF disruption. e I–V characteristics for volatile switching of the device at low I . When a positive sweep voltage is applied, the current increases sharply indicating CF formation. However, the device quickly switches back to its original high resistance state after the forcing voltage is swept to zero. Bidirectional volatile switching is observed, as the application of a negative voltage also generates a metastable CF. f Probability for volatile switching (VS) as a function of I , indicating the transition from volatile switching to non-volatile switching at increasing I C C According to MD simulations, the metallic CF can sponta- in the CF and on the host dielectric materials. For simplicity, we neously break as a result of atomic surface diffusion driven by the assume that the CF shape is obtained from the revolution of a minimization of the system energy. The atomic surface diffusion curve ρ(z) as shown in Fig. 2f. The normal distance dn traveled by originates from the gradient of surface atomic vacancy concen- a surface element ∂s during the time increment dt is thus given 30 33 tration or the gradient of the surface atomic chemical potential , by , resulting in a tendency to minimize the surface energy . Atoms dn B ∂ ∂κ in the bulk of the CF instead remain fixed in their lattice sites of ¼ ρ ð2Þ the crystal (Fig. 2d, e, and see Supplementary Fig. 2–3 and dt ρ ∂s ∂s Supplementary Note 2 for more details), as confirmed by recent 21,27 observations by in situ TEM . Based on the Gibbs-Thomson where B = D γδ /kT is a parameter which strongly depends on effect, the surface atomic flux J along an arbitrary surface can be the type of CF atom, on temperature and on the surrounding host modeled by assuming isotropic surface diffusion, leading to : materials. Figure 3 shows the simulation results for the morphological D γδ J ¼ ∇ κ; ð1Þ evolution of two Ag CFs with the same length h = 10 nm and s s kT different initial diameters, namely d = 2 nm (Fig. 3a) and d = 0 0 0.4 nm (Fig. 3b). More details about the simulation method and where D is the surface diffusion coefficient, γ is the surface results are reported in the Supplementary Fig. 4–7, Supplemen- energy, δ is the interatomic distance, k is Boltzmann’s constant, tary Note 3 and Supplementary Movies 3–8. The parameter B for −34 4 T is the temperature, and κ is the surface curvature, given by κ = Ag is estimated to be 10 m /s at room temperature 1/r + 1/r , where r and r are the principal radii of the (Supplementary Note 4–5 and Supplementary Table 1). Surface 1 2 1 2 curvature. Note that the driving force for the surface diffusion in diffusion leads to a segmentation of the CF and the formation of Eq. (1) is the gradient of the surface curvature κ, which is also the one or more intermediate clusters, as shown in Fig. 3b for t = 1 key parameter controlling the Gibbs-Thomson effect. The ms (see also Supplementary Movie 4 and Supplementary coefficient D for surface diffusion is thermally-activated accord- Movie 7). A similar ovulation effect has been recently reported 17,26,34 ing to D ¼ D′expðQ =kTÞ, where the pre-factor D′ and the by in situ TEM observations as the by-product of Ag nano- s s s s diffusion barrier Q mainly depend on the type of migrating atom filament clustering in an insulating material. Note that the specific NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications 3 Current (A) Current (A) Probability of VS (%) ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ab c 0 s 100 ps 200 ps de f A ds B B E 5 =  (z) 4 F Crystalline state 0 50 100 150 200 250 Time (ps) Fig. 2 MD simulation of surface diffusion. a–c MD simulation results of a Ag nanoscale CF between two electrode plates at increasing times, namely t = 0, 100 ps, and 200 ps (Supplementary Movies 1–2). The color indicates the free energy per atom with lighter blue representing atoms with higher free energy, hence higher diffusivity. To accelerate the surface diffusion process, the system temperature is set to 800 K, which is still below melting temperature of Ag. d Cross-section view of the CF at 100 ps, indicating stable bulk atoms with low free energy and crystalline states, hence negligible diffusion, whereas surface atoms show higher energy and diffusivity, thus resulting in the morphological evolution and rupture of the filament. e Typical traces of individual atoms along z direction for bulk atoms (A, C), surface atoms (B, D), and bottleneck atoms (E, F) in d. Bulk atoms show constant positions, while the surface atoms migrate toward their closest electrodes. Atoms in the CF bottleneck region also show a high tendency to migration to either the top or bottom electrode. (see Supplementary Note 2 and Supplementary Fig. 2 for more analysis). f CF geometry considered in the model of the surface diffusion. For simplicity, isotropic surface diffusion and axisymmetric (along z) CF surface are assumed. ρ(z)defines the geometry of the filament surface by rotating around the z axis, and n defines the surface evolution of a surface piece ds in unit time in outward normal direction morphological evolution of the filament is affected by the mechanism, see Supplementary Note 7). The power law for thin 30 4 hydrophobicity between filament and electrode materials, initial CFs (d < 5 nm) is consistent with the Herring’slaw s = λ , 0 τ filament shape (Supplementary Note 6, Supplementary Fig. 8–10 where s is the scaling of lifetime with the shape dimension scaling and Supplementary Movies 4–8), and anisotropy of the filament of λ, thus describing the lifetime τ as a function of the size of crystal. However, the generic isotropic simulation shown in Fig. 3 equally-shaped particles (see Supplementary Note 8). Note in fact can provide us a general rule of the size-dependent stability of the that the fixed length has negligible effect on the lifetime for d << h. CF. The steep increase for higher d marks the onset of the CF stability, hence non-volatile switching, which corresponds to the equivalence of thetwo principleradii of surfacecurvature (Fig. 4b inset), similar Size-dependent lifetime.We define the lifetime τ of the CF as the to the liquid capillary bridge between two plates . first opening of a depleted gap according to the numerical solution Results in Fig. 4b provide quantitative criteria for discriminat- of Eq. (2)(seeFig. 3). Reducing the diameter of the CF by 5 times ing volatile and non-volatile RS depending on the CF size. For (from Fig. 3atoFig. 3b) results in a reduction of the lifetime by instance, a one-atom-wide CF with d ≈ 0.2 nm shows a lifetime about 150 times, as shown by the simulated gap length in Fig. 4a, τ ≈ 10 μs, resulting in volatile switching for possible applications due to the larger surface curvature κ controlling the surface diffu- as selector device in crossbar arrays or neuromorphic elements. sion rate (Eq. (1)) and the CF morphological evolution rate On the other hand, the simulation results project that a CF with (Eq. (2)). The dependence of lifetime on the initial CF diameter can d ≈ 14 nm can have a lifetime τ ≈ 5×10 s, corresponding to explain the transition from volatile switching (Fig. 1e) to non- about 16 years at room temperature, which is thus compatible volatile switching (Fig. 1d) at increasing I , where a larger com- with non-volatile memory applications. pliance current leads to a larger CF diameter with longer lifetime. The calculated quantitative timescale of the geometrically To highlight the size-dependent lifetime, Fig. 4b summarizes the CF identical shape evolution process identified by d /h can be lifetime as a function of the initial CF diameter d with a constant extrapolated by Herring’s scaling law to interpret some general CF length h= 10 nm being assumed. The lifetime increases with the observations. For instance, a filament with initial diameter d = CF size according to a power law τ  d , then increases asymp- 0 80 nm and filament length h = 4 μm will have the same shape totically as it approaches a stable size d ≈ 14 nm. The power law evolution (e.g., resulting in egg-shaped cluster segmentation) of a with exponent 4 in our surface-diffusion model arises from Eq. (2), filament with initial diameter d = 0.2 nm and filament length h where the filament surface evolution rate dn/dt is proportional to 0 = 10 nm, except for their dimension scaling of λ = 400 and the second-order derivative of the curvature κ in Eq. (2), which in lifetime scaling of s = 2.56 × 10 . As a result of the dimensional turn is a second-order derivative of the surface profile ρ in Eq. (1) τ scaling, the lifetime scales from 10 μs for the filament with (based on similar analysis, we also exclude other possible 4 NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications z (nm) 0 1 –1 NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ARTICLE t = 0 s 24 ms 30 ms 60 ms 10 10 10 10 8 8 8 8 1.5 6 6 6 6 d = 2 nm 4 0 4 4 0.5 2 2 2 2 0 0 0 0 2 2 2 2 –0.5 2 2 2 0 2 0 0 0 0 0 0 0 –2 –2 –2 –2 –2 –2 –2 –2 (nm) (nm) 10 10 10 10 10 10 8 8 8 8 8 8 6 6 6 6 6 d = 0.4 nm 4 4 4 4 4 2 2 2 2 2 2 0 0 0 0 0 0 –2 0 1 0 1 0 1 1 0 1 0 0 0 –1 –1 0 0 0 –1 –1 –1 (nm) (nm) t = 0 s 40 μs 0.13 ms 0.4 ms 0.6 ms 1 ms Fig. 3 Morphological changes induced by surface diffusion. a Simulation results of the surface diffusion equations, indicating the rearrangement of a Ag CF with initial diameter d = 2 nm at increasing times, namely t = 0, 24 ms, 30 ms, and 60 ms. b Same as a, but for a CF with an initial diameter d = 0.4 nm at 0 0 times t = 0, 40 μs, 0.13 ms, 0.4 ms, 0.6 ms, and 1 ms. For both cases, the CF length is 10 nm, equivalent to the thickness of the insulating layer between two planar electrodes. The color in the figures indicates the surface curvature, where surface points with higher curvature are more likely to induce surface diffusion, thus providing a suitable spot for CF rupture. The CF lifetime decreases from around 20 ms (a) to about 0.13 ms (b)as d is reduced from 2 nm to 0.4 nm. The ovulation effect in b, where nano-clusters result from the disconnection of a thin CF, is consistent with in situ TEM observations of Ag nano- 17,26,34 clusters evolving from Ag nanoscale CFs 5 39–43 d = 0.2 nm and h = 10 nm, to 2.56 × 10 s (about 3 days, in line reporting data of sub-10 nm scale filaments for both Cu and 36 17,23,44,45 with the measured lifetime of AgNWs ) for the filament with Ag from the literatures (more details in the Supple- d = 80 nm and h = 4 μm. mentary Table 2–3). Compared to Ag, Cu-based RS devices show a stronger tendency to non-volatile switching due to its higher surface activation energy Q and, hence, smaller B (estimated as −47 4 Universal model of volatile and non-volatile switching.To 10 m /s at room temperature, see Supplementary Note 4). further validate our model, we conducted time-resolved experi- Note the large variation of lifetime, which might originate from ments to measure the lifetime of Ag CFs as a function of I . The C anisotropic surface diffusion along different crystalline directions, CF was obtained by applying an excitation pulse at relatively large or inaccurate control of the CF size by I . Different types of voltage, followed by a monitor voltage at relatively low voltage dielectric materials would also impact on the lifetime by affecting V = 0.1 V to monitor the conductance of the device in real read parameter B in Eq. (2). Despite these variations, the surface dif- time. Figure 5a shows the setup of applied voltage pulse, while the fusion model accounts for the size dependence of lifetime over a inset shows the measurement configuration, consisting of a RS broad range of experimental conditions and samples. The tem- device connected to a load resistance R in serial. The R aimed at perature dependent lifetime also relies on the surface activation L L limiting the current during the set transition. By changing the energy Q . For the estimations of the parameter B and the pre- value of R from 1 MΩ to 100 Ω, the CF size could be varied to dicted size-lifetime lines at different temperatures in Fig. 5c, the study the size-dependent lifetime. Figure 5b shows the monitored surface activation energy Q for Cu and Ag was assumed to be conductance for various I from 1 μΑ to 10 mA, where the initial 1.1 eV and 0.52 eV, respectively. This is consistent with the data conductance G shows a linear increase with I in agreement with 0 C projected from the temperature dependent retention times in Cu field- and temperature-controlled switching in RS devices . The and Ag RS devices by fitting with the Arrhenius rule, which gives variable initial conductance is mapped into an initial CF diameter the value of Q in the range of 1.3 ~ 1.4 eV and 0.5 ~ 0.7 eV for Cu 43–45 d according to G ¼ πσd =ð4hÞ, where σ is the CF conductivity 0 and Ag, respectively . 0 0 37,38 considering the enhanced scattering effects in nanoscale CFs (Supplementary Note 9 and Supplementary Fig. 11). The figure also shows the calculated conductance evolution G(t) from Discussion Eq. (2), indicating a good agreement with data. Figure 5c shows Surface self-diffusion effect was first observed in vacuum tube the measured and calculated lifetime as a function of d , also electronic devices, as responsible for the blunting of a sub-mm NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications 5 (nm) (nm) –1 Curvature (nm ) –1 Curvature (nm ) ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 least two evidences: first, recent TEM observations reveal the presence of Ag or Cu clusters rather than homogeneously dis- d = 2 nm tributed Ag within the doped silicon-oxide layer. This was shown 17 26 d = 0.4 nm 0 for Ag-doped SiO (x <2) , Cu-doped SiO (x <2) , and Ag- x x 27,34 ≈130 μs doped SiO . All these results indicate that Ag and Cu have ≈ 20 ms relatively low solubility in silicon oxide, thus resulting in the clustering of Ag or Cu atoms. The low solubility of Ag and Cu in –6 –5 –4 –3 –2 –1 0 the host materials can be understood as the result of the low 10 10 10 10 10 10 10 reactivity of Ag and Cu elements and the strong chemical stability Time (s) of Si-O valence bond (see Supplementary Note 7 for extended 10 discussion). Second, experimental data are consistent with Her- ring’s scaling law τ  d , while one would expect a dependence 10 τ  d for out-diffusion as reported by our analysis in the Sup- 0.1 50,51 plementary Note 7, in agreement with previous results . Out- r < 0 6 5 10 0 diffusion might be non-negligible when the metal has a relatively large solubility in the host materials, such as Ag in Ag S and Cu 0 2 –0.1 10 10 in CuS . 0 5 –5 –10 (nm) –10 (nm) The volatile switching in RS devices has previously been interpreted as the consequence of the atomic clustering to minimize the Gibbs-Thomson energy at the interface between the 17–19,54 filament and the host material . Our interpretation of –2 filament shape evolution induced by surface diffusion also has Slope = 4 roots in the Gibbs-Thomson effect, given the dependence on –4 surface curvature radii in Eq. (1). Another common phenomenon 55–58 induced by Gibbs-Thomson effect is Ostwald ripening , –6 which has been proposed to control the evolution of the particles –1 0 1 10 10 10 obtained by filament fragmentation . According to our model, d (nm) surface diffusion might control the initial stages of the filament disconnection, which also dictates the filament lifetime according Fig. 4 CF size-lifetime scaling law. a Filament gap length as a function of the to the Herring’s law. Ostwald ripening instead may be responsible relaxation time. The increase of the gap length from zero marks the for the post-lifetime evolution of the filament particles. In any moment of CF disruption which we defined as lifetime τ. b Filament case, the driving force for the surface diffusion and Ostwald disruption time as a function of initial filament diameter d . The size-time ripening both can be traced back to the Gibbs-Thomson effect scaling for thin filament (d ≪ 10 nm, h = 10 nm) well agrees with Herring’s (see Supplementary Note 10 and Supplementary Fig. 12 for more law τ  d with a slope of 4, while, on the other hand, for thick filament (d discussion). > 10 nm), the lifetime more rapidly increases with the lateral size as a stable In RS devices, CFs of various sizes can be electrically formed, capillary bridge is formed, marking an increase of the lifetime from resulting in a large range of electrically measurable lifetime. microseconds to years with increasing filament diameter. Inset: snapshot of According to our surface diffusion model, the ultimate stability of a stable capillary bridge formed from filament with initial diameter d = the CF for non-volatile switching arises from a stable capillary 14 nm. The stability of this shape originates from the two principle radii of bridge between the top and bottom electrodes. Note that this surface curvature having equal modulus and opposite signs. In the condition might result in a relatively large CF, which conflicts bottleneck point, the horizontal radius of the surface curve r > 0, whereas with other requirements of RS devices for practical applications in the vertical radius r < 0, resulting in the surface curvature κ tending to zero non-volatile memories. For instance, RS devices should also be easily erasable at relatively low current, which is necessary to minimize the IR voltage drop across lines in crosspoint arrays. An filamentary field-emission cathode operating at elevated tem- excessive voltage drop, in fact, would lead to unwanted disturbs to perature (~1000 K) . The lifetime of this type of filament, unselected cells. The tradeoff between small operating currents which controls the vacuum tube lifetime, is generally in the and CF stability requires careful device and materials optimiza- range of hundreds of hours. At nanoscale dimensions, the tion, toward the minimization of the free energy at the CF sur- morphological changes driven by the minimization of surface face. Note that experimental data show no tradeoff between energy are highly accelerated to the range of observable time endurance and operation current (see Supplementary Note 11 for scale at room temperature, which is at the origin of a liquid-like more discussion). Conversely, minimization of the lifetime in the pseudoelasticity observed in situ. Surface diffusion effects also range of few ns might enable the operation of RS device as fast 20,59 control general properties in nanoscale world, such as the lack and efficient selector device for crosspoint arrays . The fast of sharp tipped metal coated probes for atomic force micro- recovery of the off-state is essential in this case to enable random scopy compared to the covalent bonded crystallized silicon or access within the array, where each memory must appear unse- diamond probes , and the instability of ultrathin metallic lected immediately after access for read or set/reset. Materials NWs, e.g., Ag NWs with diameter less than 40 nm . engineering should guide the selection of CF materials for selector In this work, we provide evidence for surface diffusion being technology to enhance the surface energy and the related surface the fundamental mechanism for the filament rupture in RRAM diffusion effects . devices. Other works have previously proposed that out-diffusion, In summary, we propose a universal surface diffusion rather than surface diffusion, acts as the leading dissolution mechanism for the spontaneous rupture of metallic CFs in fila- process in other materials systems, such as Ni in NiO . We note, mentary RS devices. Surface diffusion consistently accounts for however, that out-diffusion is not expected to play a major role in the transition from volatile to non-volatile switching observed in the materials systems considered in our work, namely Ag or Cu in nanoscale RS devices, where the lifetime of sub-10 nm CFs can silk and oxide compounds. This is independently supported by at span from microseconds to years. Results provide a general 6 NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications Lifetime,  (s) Gap (nm) –1 Curvature (nm ) (nm) NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ARTICLE ac Oscilloscope 300K Switch pulse 2 L 400K Cu 10 years RS device Resistor 10 500K Monitor voltage 300K 358K 10 358K 473K 473K –3 498K 473K Time (s) × 10 498K 498K 300K 2 523K 473K 523K Ag 523K 498K 400K 523K 300K 300K –2 Ag: Data. –2 10 Ag: Z. Wang et. al., 2016. Ag: J. Yoo et. al., 2017. Ag: S. Ambrogio et. al., 2014. –4 Ag: A. Bricalli et. al., 2018. –4 300K Cu: J. Yoon et. al., 2009. Cu: L-M. Lin et. al., 2017. 298K –6 Cu: C-Y. Liu et. al., 2011. Data –6 Cu: Y. Yang et. al., 2011. 373K Cu: J. Park et. al., 2010. Calculation –8 –1 0 1 2 –5 0 5 10 10 10 10 10 10 10 d (nm) Time (s) 0 Fig. 5 Universal explanation for volatile and non-volatile switching. a Illustration of the experimental setup for the measurement of the lifetime of Ag filament. The Ag NWs resistive device with conductance G is serially connected with a load resistance R which limits the current to a maximum value I .A L C voltage pulse (2.5 V, 100 μs) is applied to create the Ag filament, followed by a relatively low monitor voltage (0.1 V) to probe the filament evolution. b Measured and calculated conductance for the resistive switching device for different filament sizes. As I increases, the lifetime of the Ag filament increases as a result of the size-dependent surface diffusion. The largest I ~10mA results in a stable conductance, corresponding to a stable capillary bridge 39–43 17,23,44,45 with a large diameter. c Measured and calculated CF lifetime for devices with electrode made of Cu and Ag as a function of the initial −34 4 −47 4 diameter d . At room temperature, the parameter B was estimated as 10 m /s and 10 m /s for Cu and Ag filaments, respectively. The values of the surface activation energy Q was estimated as 1.1 eV and 0.52 eV for Cu and Ag, respectively. Calculations at various temperatures are also shown. The results account for the transition from volatile switching to non-volatile switching in RS devices (Fig. 1d–f) based on the size-dependent lifetime framework for understanding the stability of nanoscale structures, Numerical simulation of the filament shape evolution. The simulations of morphological evolutions were performed using Matlab©R17b with self-design and designing RS devices for a wide range of applications, e.g., codes. Isotropic surface diffusion and the CF surface of revolution by Eq. (2) were non-volatile memories with high stability for digital data storage, assumed. The morphological evolutions of the CF geometry are simulated in volatile switching for selector devices in crosspoint arrays, and 33 dimension-less form . To this purpose, we defined dimension-less variables H = tunable-lifetime RS synapses for neuromorphic computing with h/l, D = d /l, K = κl, and Γ = Bt/l , where h is the CF length, equivalent to the 0 0 thickness of the insulating layer in the RS device, d is the initial CF diameter, t is short/long-term plasticity. 0 time, and H, K, Γ are their dimensionless representations. The constant l (unit: m) is the scaling ratio between the CF size and the dimensionless one, defining the spatial dimension of the filament. For each step, the curvatures of the filament surface for each segment were calculated, thus the changes of the morphological Methods Device fabrication and characteristics. Silver nanowires (length: 10 µm, dia- profile were obtained from Eq. (2) and the surface profile was updated accordingly. A finite differential method was used to calculate the differential values of surface meter: 60 nm; concentration: 0.5% wt) were purchased from Sigma-Aldrich. The aqueous solution of silk fibroin for fabricating the device was prepared according curvatures and morphological change rates. The output of the computation was converted back to real space/time variables from dimensionless variables. For to the reported method . Firstly, a 5/70 nm-thickness Cr/Au layer was deposited instance, the real-time value can be obtained by t = Γl /B. The source code is on silicon substrate as the bottom electrode. Then, 0.1 ml Ag NWs solution was available from the authors upon request. added into 1 ml silk fibroin solution (2% wt) to form the blended solution. The resultant solution was spin-coated onto the bottom electrode at 1000 rpm for 45 s, and then evaporated for 2 h at room temperature. Finally, a 70 nm-thickness Au Data availability pad with the size of 100 µm × 100 µm was evaporated as the top electrode. For this The data that support the findings of this study are available from the corre- device, the effective active electrodes are equivalent to two adjacent AgNWs in the sponding author upon reasonable request. composite film or one Au electrode and one Ag NW electrode. Keithley 4200 semiconductor parameter analyzer was employed to measure the DC elec- trical characteristics. Arbitrary waveform generators (Agilent 33220A) and oscil- Received: 2 August 2018 Accepted: 2 December 2018 loscope (Tektronix DPO5054B) were used for lifetime measurement under pulse mode. MD simulation. 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D.I. supervised the research. 35590–35597 (2017). 8 NATURE COMMUNICATIONS | (2019) 10:81 | https://doi.org/10.1038/s41467-018-07979-0 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-07979-0 ARTICLE Additional information Open Access This article is licensed under a Creative Commons Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467- Attribution 4.0 International License, which permits use, sharing, 018-07979-0. adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Competing interests: The authors declare no competing interests. Commons license, and indicate if changes were made. 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