This is the accepted version of the article: Aguirre, Fernando Leonel; Rodríguez Fernández, Alberto; Pazos, Sebastián Matías; [et al.]. «Study on the Connection Between the Set Transient in RRAMs and the Progressive Breakdown of Thin Oxides». IEEE Transactions on Electron Devices, Vol. 66, Issue 8 (August 2019), p. 3349-3355. DOI 10.1109/TED.2019.2922555 This version is avaible at https://ddd.uab.cat/record/215344 under the terms of the license 1 Study on the connection between the set transient in RRAMs and the progressive breakdown of thin oxides Fernando Leonel Aguirre, Member, IEEE, Alberto Rodriguez-Fernandez, Sebastián Matı́as Pazos, Member, IEEE, Jordi Suñé, Fellow, IEEE, Enrique Miranda, Senior Member, IEEE, Félix Palumbo, Member, IEEE Abstract—In this paper, the transition rate (TR) from the the temperature increase associated with Joule heating [10]. high to the low resistance state of a HfO2 -based Resistive Ion migration is modeled by diffusion and drift components, Random Access Memory (RRAM) is investigated. TR is sta- where both rely on hopping mechanisms. Ions move along an tistically characterized by applying constant voltage stresses in the range from 0.45V to 0.65V. It is found that TR follows energy landscape of potential wells, which provide states for a voltage dependence that closely resembles that exhibited by ion localization [11], [12]. MIS/MIM structures when subjected to constant electrical stress but with remarkably different fitting parameters. This result suggests a common underlying mechanism in both evolutionary On the other hand, the main physical mechanism behind behaviors. Furthermore, the investigation provides additional the BD dynamics of ultra-thin dielectrics (Al2 O3 , HfO2 , SiO2 , evidence supporting the micro-structural changes in the oxide Si2 N4 ) used in CMOS technology was recently identified [13], after the forming step as well as the role played by the atomic [14]. Briefly, the energy transfer from the CF to its surround- species during the SET event. ings promotes the diffusion of the fastest atomic species, Index Terms—RRAM, Resistive-Switching, High-k, Progressive which gradually enlarges the CF connecting the electrodes oxide breakdown of the stack causing a progressive increase in the leakage current. Remarkably, SET and BD events show the same I. I NTRODUCTION statistical behavior [9], and similar micro structural changes Resistive-switching random access memory (RRAM) is in the dielectric [15]–[19]. Several authors [15]–[17] showed attracting a considerable interest as a promising future tech- that the BD spot is characterized by the formation of a Si- nology for scalable memory [1] and neuromorphic computing rich (for poly-Si/SiOx Ny /Si stacks) or a metal-rich region (for systems [2]. RRAM relies on the formation and dissolution of metal gate/high-K/Si stacks) in the gate dielectric. In this a nanoscale conductive filament (CF) spanning an insulating regard, Privitera et al. [18] have shown the presence of metallic layer, typically a binary transition-metal oxide such as NiO species in the oxide for the case of HfO2 -based RRAM MIM [3], TiOx [4], HfOx [5], TaOx [6], among others. The CF is devices after forming. initially generated by a forming operation, namely, a controlled dielectric breakdown (BD) of the insulating layer using an In particular, a huge amount of research has been carried appropriate current compliance level [7]. A small gap in the out regarding the static I-V characteristics of the RRAMs. localized CF, which is responsible for the low-resistance state However, the time evolution of the switching phenomenon is (LRS) in the memory device, is then opened through a RESET not completely understood yet. In this context, it is clear that operation causing the transition from the LRS to the high despite the recent advances regarding the modelling of the resistance state (HRS), and closed with a SET operation (HRS current-voltage behaviour of the RS devices [9], [20], more to LRS transition). SET/RESET operations can be achieved information about the SET event in RRAM devices is needed. via electrical pulses of the same or opposite polarities (unipo- A detailed knowledge of the evolution of the CF morphology lar/bipolar switching modes, respectively). The RS mecha- during forming and SET transitions as well as the correspond- nism has been widely studied in the last years [1]–[12], and ing shape of the I–V curves are needed for accurately model many authors claim that SET/RESET processes are described the switching phenomena and to make reliability predictions. through ion migration induced by the local electric field and Ultimately, the study of the voltage-time dependence of RS is needed to estimate the minimum time required for writing (Corresponding author: F. Palumbo) F. L. Aguirre, S. M. Pazos and F. Palumbo are with the Unidad de a bit in a RRAM cell [21]. In this paper, the HRS to LRS Investigación y Desarrollo de las Ingenierı́as, Facultad Regional Buenos transition is studied as a function of time and switching voltage Aires, Universidad Tecnológica Nacional, Medrano 951 (C1179AAQ), Buenos using a large number of measurements. Based on a physical Aires, Argentina, and with Consejo Nacional de Investigaciones Cientı́ficas y Técnicas, Godoy Cruz 2290 (C1425FQB), Buenos Aires, Argentina. (aguir- description of the BD dynamics in dielectrics of common use ref@ieee.org, spazos@frba.utn.edu.ar and felix.palumbo@conicet.gov.ar) in CMOS processes and the aforementioned similarities to the A. Rodriguez-Fernandez, J. Suñé and E. Miranda are with the Departament SET event in RRAM, a model for the time evolution of the d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Cerdanyola del Vallès 08193, Spain. (alberto.rodriguez@uab.cat, jordi.sune@uab.cat and resistive state of the RRAM as a function of the switching enrique.miranda@uab.cat) voltage is proposed. 2 10−4 RESET VDD with the literature [7], [9], [10], [25] whose duration shows a strong voltage dependence and dispersion. Such dispersion RRAM will be discussed in Sec. IV-A. The maximal current growth Current [A] 10−5 LRS rate is limited by the bandwidth of the equipment. Figures 2c VGS to 2g show the initial (Iinit , empty symbols) and end (Iend , HRS 10−6 1stcycle filled symbols) currents of the acquired transients, including Avg. cycle those shown in Fig. 2a and 2b. It is worth mentioning that the SET region 50 cycles (0.45 to 0.65 V) initial current matches the I-V data shown in Fig. 1, where 10−7 −1 −0.5 0 0.5 1 1.5 2 the SET region shows initial currents around 10 µA. Iend Voltage [V] current represents the level from which the acquired transient Fig. 1. I-V characteristics for the samples under test (50 curves). The red exhibits a jump to the compliance level (see Fig. 2), leaving solid line is the average curve and the blue dashed one stands for the 1st the sample in LRS. The time evolution of the HRS to LRS cycle. The inset in the right side shows the 1T1R assembly, comprising the transition is quantified by the slope dIT r /dt, as defined in Ref. RRAM structure and its driving N-MOS transistor. [13], [26], [27]. Such metric will be subsequently referred to as Transition Rate (TR) [A/s]. TR values were experimentally II. E XPERIMENTAL evaluated through measurements such as those of Fig. 2a and 2b and it is reported for approx. 100 measurements for each Experimental data were obtained from HfO2 -based RRAM voltage value (see Fig. 2h). The comparison between the TR cells. The MIM structure consists in a 10 nm thick atomic in Figs. 2a and 2b and the trend in Fig. 2h suggest a strong layer-deposited HfO2 film sandwiched between Ti and TiN voltage dependence, as the TR increases almost four orders of electrodes. The cell is connected in series with an n-type MOSFET, embedding a 1 Transistor - 1 Resistor (1T1R) structure, as shown in the inset of Fig. 1. The transistor controls the maximum current that can flow through the CVS 450 mV CVS 650 mV (a) (b) memory cell which in turn determines the resistance window 10−4 ≈ 4.3x10−3 ≈ 8.4x100 of the device [7], [22]. All the measurements where performed A/sec Current [A] 3 A/sec by applying a gate-source voltage (VGS ) of 1.2V. Quasi-static I-V-t measurements were performed using a Keithley 4200- SCS equipped with a Fast Measurement and Pulse Generator Unit (4225-RPM) capable of providing an appropriate time 1 2 ≈ 2.8x10−4 ≈ 4.8x100 resolution (down to 200 ns in Fig. 2b). As reported in a 10−5 A/sec A/sec previous work considering similar samples [20], the forming 10−3 10−2 10−1 10−7 10−6 10−5 Time [s] Time [s] event takes place at ≈ 3.8V and the devices exhibit bipolar switching characteristics. Notice that the average SET and RESET voltages are almost symmetric (≈ ±0.5V). This −4 log10 (Current) [A] indicates voltage controlled processes for HfO2 in agreement with previously reported results [23]. Further details about the −4.5 devices and experimental setup can be found in Ref. [9]. −5 (c) (d) (e) (f) (g) III. R ESULTS 20 80 20 80 20 80 20 80 20 80 In order to study the SET event, the whole process including Ci [#] Ci [#] Ci [#] Ci [#] Ci [#] the wear-out phase and the transition from HRS to LRS must 103 Fast BD RA happens at (h) be explored. Therefore, current-time (I-t) measurements at ≈ 10 − 100 µA 101 constant bias were performed using the high-bandwidth setup for all samples TR [A/sec] mentioned in Sec. II until the fast HRS to LRS transition 10−1 occurred or in other words, until the current through the device reaches the compliance limit (∼ 100 µA). I-t measurements 10−3 HRS → LRS ≈ 100 were performed under Constant Voltages Stress (CVS) of 450 points for each voltage Data for Hf O2 mV, 500 mV, 550 mV, 600 mV and 650 mV. For clarity, 10−5 0.3 0.4 0.5 0.6 0.7 only the transients corresponding to the 450 mV and 650 mV Voltage [V] stresses are shown in Figs. 2a and 2b. Such stress voltages Fig. 2. Current transient of the DUTs under CVS. For clarity, (a) the lowest were applied in the HRS state and were chosen after the I-V -450 mV- and (b) highest -650 mV- voltages are shown. Ball markers 1,2 and 3 point out the initial current (Iinit ), the onset of the progressive increase of curves depicted in Fig. 1, where the HRS to LRS transition current (Ion ) and the final jump to the compliance level (Iend ), respectively. occurs for voltages ranging from 0.45 to 0.65 V. Initial currents (empty markers) and end currents (Iend ) (filled markers) at (c) Current through the MIM stack during the HRS to LRS 450 mV, (d) 500 mV, (e) 550 mV, (f) 600 mV and (g) 650 mV. Ci in figs (c) to (g) stands for the cycle number. (h) Transition Rate (TR, dIT r /dt) of the transition (IT r ) increases gradually with time [24], evidencing samples under test. Approx. 100 transients and the mean value are reported the progressive nature of the SET event (see Figs. 2a and for each voltage condition (450, 500, 550, 600 and 650 mV). The mean value 2b). It is a noisy and progressive process well in agreement increases roughly 1 order of magnitude every 50 mV. 3 magnitude in between these two cases. Similar measurements Fresh T iN LRS S T iN HRS of the HRS-LRS transition have been previously reported [25], T iN showing a comparable voltage dependence (TR increases as HK F VOs tgap tgap the applied voltage increases). tox tox R tox HK HK Ti (a) Ti (b) Ti (c) IV. A NALYSIS AND DISCUSSION It has been experimentally shown that both the SET and −3 (e) 3.2 Iset model log10 (Temperature) [◦ K] Iset model (d) forming event in RRAM devices [9], [25] and the dielectric −4 log10 (Current) [A] data f2 ≈ 1 BD of gate oxides [13], [14] share some common aspects. −4 f2 ≈ 0.5 3 Aside from the noisy and progressive increase of the leakage −5 f2 ≈ 0.25 2.8 current, whose increase rate depends on the stressing voltage, α = 0.47 f2 ≈ 0.1 V1 = 0.8mV further insight into these events reveals a few other common −5 V2 = 0.6V −6 2.6 points. Previously reported current compliance studies have I1 = 150nA shown a clear dependence of the CF characteristics on the I2 = 50µA f2 −7 −6 2.4 maximal current flowing through the device, both for the BD 0 0.2 0.4 0.6 0 0.2 0.4 0.6 of gate oxides [7] and the SET event in RRAM devices [22]. Voltage [V] Voltage [V] In addition, TEM imaging of Si-based MOS capacitors prior to Fig. 3. Representation of the tox reduction due to the appearance of a gap in and post dielectric BD [15]–[17] and HfO2 -based RRAM cells the CF: (a) Before forming step, (b) LRS and (c) HRS. Blue balls represent the electrode’s atomic species, and red balls stands for the oxygen vacancies after forming and cycling [18], [19] show comparable micro- (VOs). (d) ISET model described by Eq. 2 vs. measurements. (e) Temperature structural changes in the oxide, suggesting the diffusion of the calculations as function of voltage and the energy loss in the CF constriction. anodic atomic species into the oxide layer during both events. In both (d) and (e) plots the red shaded zone indicates the voltages employed for the CVS (0.45 to 0.65 V) Thus, there are not only similar electrical characteristics between the SET event and the gate oxide BD, but also com- parable micro-structural changes and the combination of both be given in the following sections, as well as an explanation points towards a common underlying physical mechanism. In about the parameters’ change from the gate oxide BD to the such scenario, we propose to model the results for the SET SET event case. event in RRAM devices similarly to the gate-oxide BD in MOSFETs. In this regard, Palumbo et al. have presented in Ref. [13] a model describing the gate oxide BD phenomenon A. Model of the Transition Rate (TR) for HRS to LRS as in ultra-thin, bulk dielectrics considering SiO2 and various function of voltage high-k dielectrics with different thermal conductivities de- Based on the experimental results and the common under- posited on III-V and Si substrates as well as in 2D layered ma- lying physical mechanism that seems to governs both SET terials [28], providing good understanding of the experimental and oxide BD, a diffusion phenomenon driven by the energy data. Such model accounts for the progressive nature of the transfer from the CF to its surroundings is proposed, including BD event and quantifies it in terms of dIBD /dt (namely the the voltage and oxide thickness dependence. In this context, Degradation Rate, DR), where IBD is the current through the and considering the model reported in Ref. [13] for the BD device during the Progressive Breakdown (PBD). Regarding transient, it is possible to express the TR for the HRS to LRS the physics behind this evolution, the model assumes that the as in Eq. 1 BD process is closely linked to the energy transfer from the dIT r qV f1 CF itself to its surrounding atomic network. According to TR = = DISET (1) dt kB T t2ox this idea, the high temperature associated with the localized current flow (current density of a few MA/cm2 through a BD where tox is the oxide thickness, T is the temperature at the spot area of 1-50 nm2 [13], [15], [16]) would promote the gap in the CF (see Fig. 3c), kB is the Boltzmann constant, D is electromigration of the fastest available atomic species, thus the diffusion constant of the atomic species responsible for the contributing to the enlargement of the BD filament connecting HRS to LRS transition, V is the applied voltage, ISET is the the electrodes of the stack. Such electro-migration phenomena current level at the onset of the HRS to LRS transition (SET have been shown to exist in RRAM by Tang et al. [29]. event) as expressed in Eq. 2 and f1 = ne λe σe , with being ne This interpretation of the BD phenomena accounts for the the electron density, λe the electron mean free path and σe the dependence of the CF features on the current compliance and cross-section for the electron-atom collision (responsible for the presence of the anodic species in the oxide layer after the momentum transfer). f1 is around the unity value since the BD, and therefore, it could be used to model the SET event defect concentration in the CF is most likely very high [18]. in RRAMs. From Eq. 1, dIT r /dt is proportional to D × ISET . This It is worth pointing out that TR shows an evident voltage means that the CF growth rate increases either by increasing dependence (four orders of magnitude in 200 mV) much ISET , the electron current, or the dominant diffusivity D. stronger than the DR reported for the BD event (dIBD /dt, 3-5 There is also a dependence on tox , V and T . So, to use Eq. orders of magnitude per volt) [13]. To understand such a big 1 we need to model ISET and D. Additionally, the effective difference, a detailed explanation of the proposed model will value of tox as well as the atomic species involved in the HRS 4 to LRS transition will be further discussed in Sections IV-B 2 4 log10 (Temperature) [◦ K] 0.65 V 0.60 V 2nm 10nm and IV-C, respectively. Weibit (ln(-ln(1-F))) 1 β∼1.31 β∼1.17 3.5 f2 ≈ 1 SET processes were shown to be controlled by the device 0 0.55 V f2 ≈ 0.1 I-V characteristics, which dictates the local temperature [13], −1 β∼1.11 f2 3 [22] and drives the completion and rupture of a nano-scale 0.50 V −2 CF through the insulating layer [10] (see Figs. 3b and 3c). β∼1.02 2.5 This accounts for the compliance current used to control the −3 0.45 V ∆T = f2 V ISET (b) β∼1.14 (a) 2πtox k resistance in the SET state [10]. ISET can be described by −4 2 −6 −4 −2 0 2 0 0.2 0.4 0.6 modeling the discontinuous CF (see Fig. 3c) as a quantum log10 (Time to SET) [sec] Voltage [V] size filament with a constriction, according to the Landauer- Fig. 4. (a) ts distributions for CVS experiments for ∼100 transitions for each Buttiker formalism [8] as we have previously reported [7]. voltage. Symbols are experimental data. Dash-dotted lines are Weibull fitting However, for simplicity we have preferred to model the results. (b) Temperature in the CF constriction versus the stressing voltage, the resulting tox and the energy loss; the red shaded zone indicates the stressing ISET − V characteristic of the CF in HRS by assuming an voltage range (0.45-0.65 V). interpolation equation (Eq. 2) [13], [28]. This avoids the use of more parameters. The fitting of our experimental data is shown in Fig. 3d. I1 ,V1 and I2 ,V2 represents two points in helpful to explain the remarkable dispersion shown in Figs 2a the experimental ISET − V curve (see HRS curves in Fig. and 2b. If for example f2 has a 20% dispersion, then TR may 1) at low and high voltages, respectively, while α is a fitting present a standard deviation of up to 2 orders of magnitude. constant.    α  I2 V − V1 −Eact ISET = I1 exp log (2) D = D0 e kB T (4) I1 V2 − V1 To model D we need first to model the temperature T in the constriction/discontinuity of the CF. To do so the heat B. Effect of the tox reduction after the forming step diffusion equation was solved. We assumed a simplification of spherical symmetry around the CF constriction and considered To implement this model for the SET event, the thickness of the source power density to be constant over the inner surface the dielectric needs to be considered in detail. In a first step, the of the sphere. The result is Eq. 3, where f2 is the fraction of the CF is created through the fresh insulating layer (HfO2 in Fig. energy qV per electron lost at the constriction, the dissipated 3a) by a forming operation (a controlled dielectric BD, Fig. power at the CF constriction is proportional to ISET × V , 3b). Then, the switching mechanism relies on the creation of a Tamb the room temperature and k is the thermal conductivity gap (RESET) and the restoration of the CF (SET). The width of the dielectric. (tgap ) of such gap is independent of the oxide layer thickness f2 V ISET (tox ) (see Fig. 3c) but dependent on the current compliance T = + Tamb (3) 2πtox k used during the SET event [11], [12], [15]. The assumption of power dissipation taking place inside the In a dielectric layer, BD is attributed to the formation of dielectric layer is reasonable. It has been shown by Takagi a percolative path between anode and cathode due to the et al. [30] for the case of gate oxide BD in MOSFETs generation of defects of size of ∼1 nm [15], and it is sta- that electrons tunneling through defects responsible for stress tistically described using the Weibull distribution, an extreme- induced leakage current (SILC) in thin oxynitrides do lose value distribution appropriate for a weakest-link problem such a large fraction of their energy in the oxide, which suggests as dielectric BD. Being the probability of forming such a path an inelastic process. This behavior has been explained to be throughout the oxide bulk dependent of the oxide thickness a consequence of defect relaxation [31] and was recently [34], it is possible to use the statistics of the SET switching confirmed by Lombardo et al. [32] for ultra-thin MOS devices. time (ts ) (i.e. the time to complete the HRS to LRS transition) f2 represents the fraction of energy qV lost by the carriers under constant bias to estimate the effective thickness of the injected into the dielectric, which ranges from 0 to 1. While oxide layer after the forming event (tgap ). Figure 4a shows at a large applied voltage, f2 tends to 1 in agreement with the Weibull plots for ts , where the slope (marked as β, and the electron’s high energy loss, for low voltages f2 decreases, constant through out all the voltages considered) is ∼1.2. This tending to zero for V =0. f2 also depends on the temperature, suggests a HfO2 film of ∼2 nm from its comparison with mainly because of phonon-electron scattering [32]. Therefore, literature [34], [35]. From the model viewpoint, this can be f2 is a function of voltage and temperature whose behavior regarded in Eq. 1 as a reduction in the physical thickness tox , is found by a best fit procedure. The influence of f2 on the as illustrated in Figs. 3a and 3c. From Eq. 3, it is clear that such temperature is shown in Fig. 3e for different f2 values. tox reduction causes a significant increase in the temperature Once T at the CF constriction is estimated, then the dif- at the CF constriction, as shown in Fig. 4b by the dashed and fusivity D can be modeled by the exponential law given by solid lines for the case of tox ≈ 10 nm (fresh device) and Eq. 4 where D0 is a pre-exponential term and Eact is the tox ≈ tgap ≈ 2 nm. It is worth mentioning that the local diffusion activation energy. It is worth noting that as shown reduction of the thickness caused by the creation of a metal by Lombardo et al. [32] substituting Eq. 4 and 3 into 1, an rich region in the oxide has been observed using cross section exponential dependence of TR on f2 shows off. This may be HRTEM [17], [18], [36]. 5 −10 The sample is then in HRS, with a ruptured CF that consists Cu:SiO2 Oxygen vac. D Data from33 mainly of the anodic atomic species (blue balls) that diffused −12 SiO2 2nm - during the forming. Under such scheme, the SET event is Model13 explained as the completion of the gap due to the migration  log10 (D) cm2 /sec −14 Al2 O3 9nm - Model13 of O2− ions towards the TE through a field-assisted and −16 HfO2 10nm - thermally-activated effect, which creates the oxygen vacancies  A Model13 that fill the gap within the CF (see Fig. 3b) [20], [38], [39]. −18 Metal spec. HfO2 4nm - This is quite a relevant point to notice, as the diffusivity of Data from37 oxygen vacancies (VOs), or equivalently the O2− ions, in a −20 B HfO2 3.5nm - Room Data from37 HfO2 layer of thickness similar to tgap spread over a range Temp. C similar to the fitted diffusivity for the TR [37] (see curve D −22 Best fit D for TR in Fig. 5). Therefore it might, altogether with the mentioned 0 1 2  3 4 1000/T K−1 ”reduction” of tox , explain the higher TR for these samples. Fig. 5. Diffusivity of the dominant atomic species in the CF vs. reciprocal of temperature. VOs diffusivity [37] is ∼ 104 times higher than for the metallic D. Fitting results species [13]. Eact ranges from 0.3 to 0.7 eV. The diffusivity D required for fitting the TR results is shown to be in the same range as the VOs diffusivity. The fitting results for TR as function of the applied voltage obtained with the proposed model in Eqns. 1-4 are illustrated in Fig. 6 (see curve n◦ 1). These results have been superim- C. Increase in the diffusivity of the species involved posed to the scatter plot of the experimental TR data (see the square symbols), showing good agreement with the mean In the model proposed by Palumbo et al. in Ref. [13] the value for each voltage (indicated by the ball markers). The creation and growth of the CF connecting anode and cathode proposed fit accounts for both the tox reduction (tox considered (Progressive BD) are due to the diffusion of the anode/cathode is equal to tgap ∼2 nm) and the increase in diffusivity (D0 is in atomic species into the gate dielectric, creating a metallic the order of ∼10−6 cm2 /sec as other species are considered filamentary path. This has been shown [13] by fitting the to complete the CF, i.e. oxygen vacancies). The rest of the DR observed in both SiO2 - and High-K stacks with Eq. parameters involved remain as previously mentioned (Eact ∼ 1 and evaluating the required diffusivity D as function of 0.3-0.7 eV, f2 ∼0.1 and f1 ∼1). temperature with Eq. 4 as presented in Fig. 5 (see curves A, B In order to make clear the impact of both the tox reduction and C). Although quite large (of the order of 10−13 cm2 /sec at and the diffusivity increase (D0 ), alternative fitting values 1000 ◦ K, with low activation energies ranging from 0.7 to 0.3 are used to plot curves n◦ 2, n◦ 3 and n◦ 4. Curve n◦ 2 shows eV), such values are in a range compatible with the diffusivity TR as function of voltage assuming fixed tox to the nominal of metals in dielectrics for conditions similar to those adopted oxide thickness (tox ∼ 10 nm) but an increase in the atomic here (e.g. the case of Cu diffusion into SiO2 layers [33]). species diffusivity (D0 ∼ 10−6 cm2 /sec). Curve n◦ 3 presents In the same way, the diffusivity required to fit the TR vs. the resulting curve when only the tox reduction is considered voltage data has been calculated with Eq. 1-4 assuming the (i.e. tox ∼ tgap ∼ 2 nm and D0 corresponding to the metal same values for the fitting parameters [13] (Eact ranging from 0.3 to 0.7 eV, f2 ∼ 0.1 and f1 ∼ 1) and is also plotted against the temperature in Fig. 5 (Curve D). The obtained 104 2 D0 ≈ 3x10−6 cm tox ≈ 10 nm value for D is quite larger (∼ 10−6 cm2 /sec at 1000 ◦ K) than Eact ≈ 0.52 eV sec Eact ≈ 0.52 eV the fitted diffusivities for the case of gate oxide BD. It should 101 tox ≈ 2 nm D0 ≈ 3x10−6 cm 2 sec Transition Rate [A/sec] be mentioned that even in an unlikely scenario in which 100% 1 2 of the electron’s energy is lost at the BD spot (i.e.: f2 = 1), 10−2 the required diffusivity to fit the TR data is significantly higher than the diffusivity obtained from fitting the progressive BD tox ≈ 10 nm of gate oxides (for clarity, such fitting results are not shown). 10−5 Eact ≈ 0.52 eV 2 D0 ≈ 5x10−13 cm2 D0 ≈ 5x10−13 cm At this point it is worth recalling that the transition from sec sec HRS to LRS has been explained as the vanishing of the Eact ≈ 0.52 eV 4 10−8 tox ≈ 2 nm gap in the filamentary path. During the forming operation, 3 the CF is jointly created by the migration of the conductive Data Hf O2 10−11 species from the electrodes (blue balls) into the dielectric 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 and the dissociation of oxygen ions (O2− ), which drift to the Voltage [V] top electrode generating positively charged oxygen vacancies Fig. 6. TR data (square markers -ball markers stands for the mean value-) (red balls) in the oxide layer and a reservoir of O2− ions fitted assuming oxygen vacancies and tgap = tox (cyan dashed line -curve in the Top Electrode (TE) (see Figs. 3a and 3b) [12], [38]. n◦ 1-). Additionally, TR assuming the values reported in the literature for tox and D is plotted -curves n◦ 2, 3 and 4-. TR increases almost one order Then, the RESET process opens a gap in the CF due to the of magnitude for every 50 mV step, with a mean value of 2x10−3 A/sec, recombination of the oxygen vacancies in the CF with the O2− 1.4x10−2 A/sec, 2.1x10−1 A/sec, 1.8x100 A/sec and 1x101 A/sec for 450 ions that diffuses back from the TE into the oxide (Fig. 3c). mV, 500 mV, 550 mV, 600 mV and 650 mV, respectively 6 diffusion in oxides ∼ 10−13 cm2 /sec). Finally, curve n◦ 4 VI. ACKNOWLEDGEMENTS presents TR as function of the applied voltage considering This work has been funded by both Argentinean the same parameter values as in the gate oxide BD transients, and European institutions. Argentine funding was i.e. diffusivity of metals in oxide layers (D0 ∼ 10−13 cm2 /sec) provided by MINCyT (Contracts PICT2013/1210, and no tox reduction (tox ≈ 10 nm). This coincides with the PICT2016/0579 and PME2015-0196), CONICET (Project DR for gate oxide BD. PIP-11220130100077CO) and UTN.BA (Projects PID-UTN The comparison of curves n◦ 1 and n◦ 4 evidences that TR EIUTIBA4395TC3, CCUTIBA4764TC, MATUNBA4936 and is significantly higher than the DR expected for the voltage CCUTNBA5182). On the other hand, the participation of range considered. It is also worth noticing that TR calculated E.M. and J. S. in this work has been developed within the considering only a tox reduction or an increase in diffusivity WAKeMeUP 783176 project, co-funded by grants from the (D0 ) cannot meet the experimental data (see curve n◦ 1 vs. Spanish Ministerio de Ciencia, Innovación y Universidades curve n◦ 3 and curve n◦ 1 vs. curve n◦ 2, respectively). This and the ECSEL EU Joint Undertaking. E.M. acknowledges suggests that TR as function of voltage is jointly determined C. Cagli for data provision and discussion. by a combination of both effects, as none of them can fit the results independently. R EFERENCES [1] R. Waser, R. Dittmann, G. Staikov, and K. Szot, “Redox-Based Re- sistive Switching Memories - Nanoionic Mechanisms, Prospects, and V. S UMMARY Challenges,” Advanced Materials, vol. 21, no. 25-26, pp. 2632–2663, jul 2009, doi: 10.1002/adma.200900375. In this work, we showed that the High-Resistance-State [2] Y. Shi, X. Liang, B. Yuan, V. Chen, H. Li, F. Hui, Z. Yu, F. Yuan, E. Pop, H.-S. P. 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