Filamentary TaOx/HfO2 ReRAM Devices for Neural Networks Training with Analog In‐Memory Computing

The in‐memory computing paradigm aims at overcoming the intrinsic inefficiencies of Von‐Neumann computers by reducing the data‐transport per arithmetic operation. Crossbar arrays of multilevel memristive devices enable efficient calculations of matrix‐vector‐multiplications, an operation extensively called on in artificial intelligence (AI) tasks. Resistive random‐access memories (ReRAMs) are promising candidate devices for such applications. However, they generally exhibit large stochasticity and device‐to‐device variability. The integration of a sub‐stoichiometric metal‐oxide within the ReRAM stack can improve the resistive switching graduality and stochasticity. To this purpose, a conductive TaOx layer is developed and stacked on HfO2 between TiN electrodes, to create a complementary metal‐oxide‐semiconductor‐compatible ReRAM structure. This device shows accumulative conductance updates in both directions, as required for training neural networks. Moreover, by reducing the TaOx thickness and by increasing its resistivity, the device resistive states increase, as required for reduced power consumption. An electric field‐driven TaOx oxidation/reduction is responsible for the ReRAM switching. To demonstrate the potential of the optimized TaOx/HfO2 devices, the training of a fully‐connected neural network on the Modified National Institute of Standards and Technology database dataset is simulated and benchmarked against a full precision digital implementation.


Introduction
The volume of data created by modern society grows rapidly, driven by the increase of digitalization across a wide range of business and consumer applications. [1,2] Artificial Intelligence Among a wide range of available memristor technologies, the two-terminal phase change memory (PCM) and resistive random-access memory (ReRAM) have raised vivid interest. Both can be integrated in dense arrays, are scalable, support fast write/read operations, multi-level cell (MLC) programming, low-power operations, have high-endurance, and are CMOS compatible. [14,[18][19][20] PCMs are characterized by G updates with accumulative behavior only in the direction of lower resistances, [21] making them well-suited for ANNs inference applications. For the training of neural networks, where, instead, granular monotonic G updates are required in both directions, [22] ReRAM-based synapses are potentially more suited. [13]

From the Metal-Insulator-Metal to the Oxide Bilayer ReRAM
The conventional ReRAM structure is a metal-insulator-metal (MIM) stack, typically a transition metal oxide (TMO) encapsulated between an inert electrode (IE) [23] and a reactive one (RE). In this technology, the application of a sufficiently large electric field generates anion (O 2− ) migration, forming a conductive filament of oxygen vacancies (Vo .. in the Kröger-Vink notation [24] ). [25] This process is known as the forming. The subsequent resistive switching operations are determined by the modulation of the Vo .. density profile in the TMO. [25] The selection of the electrodes and TMO materials is of fundamental importance for these processes as they determine the energy of formation of the oxygen vacancies. [26] This directly Figure 1. a,b) Circuit schematics of a passive and of a 1T1R crossbar array, respectively. c) Reset process, involving the depletion of Vo .. from a filament region next to a TMO/electrode interface. At V = V reset , the voltage divider on the depleted region increases as long as its equivalent resistance R switch dynamically increases, resulting in an abrupt reset. d) Set process, determined by the growth of the Vo .. density in the formerly depleted filament region.
The device resistance drops abruptly, until the voltage divider on the ESR becomes relevant.

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impacts the electrical performances of the device, such as the forming voltage, the on/off ratio and the writing reliability. [27] Moreover, the electrodes' oxygen affinity, the electrodes' work functions (WFs) and the voltage polarity of the forming process can influence the switching polarity. [28] In filamentary MIM devices, the switching process in the direction of higher resistances, the reset, is generally a gradual process, where the device resistance increases upon increasing the applied voltages. [29] Vice versa, the switching process in the direction of lower resistances, the set, is a self-accelerated [29] process, where the device resistance drops abruptly. The asymmetry between the set and the reset does not fit the requirements indicated for the training of memristor-based synapses. [22] However, in the next lines we explain how to improve the switching symmetry, by exploiting dedicated resistive regimes where the self-acceleration of the set is relaxed and the onset of the reset is accelerated.
We can assume the device to be represented by an equivalent circuit of two resistances in series, as depicted in Figure 1c,d. One resistance represents the switching region (R switch ) of the device; the other one represents the passive equivalent series resistor (ESR) of the device, made of the electrodes' contacts and a portion of the filament remaining unchanged upon switching, named filament "plug". [30] The acceleration of the reset occurs when R switch and ESR are comparable. In this case, while R switch increases, the voltage divider between R switch and ESR changes, with the voltage drop on R switch increasing and the voltage drop on ESR decreasing. This positive-feedback process ends when the voltage drop on ESR becomes negligible compared to the one on R switch . This phenomenon, described in Figure 1c, determines a sharp reset onset.
On the other hand, during the set, R switch decreases abruptly approaching the ESR value. When ESR is no more negligible compared to R switch , the decrease of R switch consequently reflects into an increase of the voltage drop on ESR and a decrease of the voltage drop on R switch . This phenomenon, described in Figure 1d, determines a gradual continuation of the set, after the initial abrupt onset.
The integration of a sub-stoichiometric oxide within the MIM-ReRAM stack, to create an oxide bilayer, can increase the ESR value, improving the symmetry between set and reset. In Hardtdegen et al., [31] a HfO 2 -MIM ReRAM is compared to a TiO x /HfO 2 bilayer ReRAM. The forming generates a conductive filament across the whole bilayer. The portion of the filament in the TiO x gives an additional contribution to the ESR, compared to the other device. The increase of the ESR value enhances the mechanisms described in Figure 1c,d, leading to a more gradual set and a more abrupt reset. [31] By operating at intermediate resistive states, where the set acceleration is attenuated and the reset remains a gradual process, the bilayer shows bidirectional gradual resistive switching. [32] However, there is a trade-off against the available resistive window.
In Woo et al., [33] the improved switching symmetry and graduality observed in a AlO x /HfO 2 bilayer ReRAM are attributed to the different mobility of the Vo .. in the two metal-oxides, which allow to electrically modulate the width of the conductive filament in both directions, avoiding the formation of a highly resistive filament gap. The presence of an additional metal-oxide in the device stack, making the ReRAM an oxide bilayer, can also improve the stability of the resistive states, [31] the endurance, [34] the reliability, [27,35] and the switching stochasticity, [27] by acting at the origin of the electronic-ionic mechanisms responsible for resistive switching. [36] A potential disadvantage introduced by the oxide bilayer concept is the increase of the forming voltages, determined by the series of two insulating materials. To reduce this effect, while keeping the improved symmetry introduced by the bilayer concept, a conductive metal-oxide (CMO) can be stacked onto the insulating TMO. With this solution, the voltage applied during the forming mainly drops on the TMO. On the other hand, if the resistivity of the CMO is higher than the resistivity of a metallic electrode, the device ESR increases with a positive impact toward the suppression of the set self-acceleration, as modeled in Zhao et al. [37] In Wu at al., [38] the graduality of the set in the CMO/TMO bilayer is explained by a different effect. The heat confinement determined by the low thermal conductivity of the CMO leads to the formation of multiple weak filaments in the TMO. Each weak filament partially contributes to the total switching of the device, resulting in a gradual process.
Differently from previous works where gradual bidirectional switching is observed in cells of HfO 2 -based bilayer devices with fixed stack materials (AlO x /HfO 2 in Woo et al., [33] TaO x / HfO 2 in Yao et al., [13] and Kim et al., [39] TiO x /HfO 2 in Cuppers et al. [32] ), here we present a solution to further optimize the analog response of the device, toward an increased number of multilevel states and reduced power consumption. Through a material engineering work, we studied the impact of the electrodes' work functions and of the conductive-metal-oxide' thickness and resistivity on the electrical response of the device. This investigation led us to understand the origin of the anomalous analog set property and to optimize the device' accumulative pulse response. We also verified the independence of the resistive states from the scaling of the cell area, to strengthen the hypothesis of filamentary-based switching.
By reactive sputtering, it is possible to deposit various substoichiometric TaO x films, [40,41] corresponding to different resistivities. Such layers can be exploited to experimentally determine how different CMO resistivities impact the device switching properties.
First, we will describe the TaO x materials development and structural characterization. Then, we present and discuss the electrical characteristics of a device made of the TaO x / HfO 2 bilayer, sandwiched between TiN electrodes, to create a CMOS-compatible ReRAM. A Ti/HfO 2 /TiN baseline device was fabricated to benchmark the upgraded switching properties exhibited by the oxide bilayer. [39] To investigate the impact of the electrodes' WFs on the device switching properties, we fabricated a new oxide bilayer with a Pt bottom electrode (BE), instead of TiN. Guided by the observations collected from a step-by-step electrical characterization (forming, first set, first reset), we propose a microscopical interpretation of the resistive switching mechanisms, valid for both the oxide bilayers with a Pt BE and with a TiN BE.
To improve the device power consumption, reduce weight update noise and improve potentiation/depression symmetry, we optimized the TaO x material by tuning its thickness and resistivity. Finally, we extracted the analog device model best www.advelectronicmat.de fitting the optimized TaO x /HfO 2 ReRAM pulse response. [42] Using this model, we simulated the training of a fully-connected neural network of analog devices on the modified National Institute of Standards and Technology database (MNIST) dataset. [43]

Material Development
To find the sputtering conditions for depositing a conductive TaO x , we realized several TaO x films for structural characterization. All these films were deposited onto HfO 2 /TiN substrates, to enforce the same growth conditions as in the ReRAM devices. The sputtering chamber conditions, such as power, duration, and (O 2 , Ar) mixture stream were kept fixed in all the depositions (see "Experimental Section" for details). The chamber pressure was varied from 6-11 µbar, in steps of 1 µbar between samples.
Grazing incidence X-ray diffraction (GIXRD) characterization provides information about the structure and the stoichiometry of the deposited suboxides. The GIXRD profiles of the TaO x / HfO 2 /TiN stacks, obtained by scanning at an incidence angle of 0.65°, are shown in Figure 2a. The peak at 42.5° is characteristic for the (200) TiN. [44] The broad TaO x peaks are shaped by the superposition of multiple contributions: in the figure we indicated only the crystallographic peaks accounting for more than 30% of the intensity. Their deconvolution (reported in Figure S1, Supporting Information) reveals the coexistence of multiple stoichiometries of TaO x and the Ta metal, indicating that the grown material does not have a unique composition, but rather is a complex phase.
With increasing sputtering pressures, a clear change in the broad TaO x peak shape is identified, due to the change of the relative intensity of the contributing peaks: the oxidized components increase, at the expenses of the pure Ta one. These findings indicate that more oxygen is incorporated in the Ta lattice when sputtering at higher pressures. [40] We extracted the film thicknesses and densities from X-ray reflectivity (XRR) measurements (see Figure S3, Supporting Information, for details) and summarized their values in Figure 2b. The deposition rate is constant at ≈0.15 nm s −1 for all the depositions, except for a chamber pressure of 11 µbar, where it falls to ≈0.03 nm s −1 . The fit of the XRR scans revealed the formation of a ≈2 nm thick TaO x interface layer at the boundary with the HfO 2 , with lower density than the bulk TaO x . For increasing chamber pressures, the bulk TaO x density gradually decreases from 11.6 g cm −3 at 6 µbar, to 10.7 g cm −3 at 10 µbar, and 9.9 g cm −3 at 11 µbar.
The characterization of the films' resistivity was performed by circular transmission line measurements (CTLM). The measured sheet resistances (Ω □ −1 ) are reported as function of the chamber pressure in Figure 2c. The materials resistive window spans over more than one order of magnitude, from a few kΩ □ −1 up to values larger than 100 kΩ □ −1 .
We converted the sheet resistances into resistivities (r) and report the values in Figure 2b. For the film deposited at 11 µbar  [45] with the correspondent space group. b) Table summarizing TaO x films thicknesses, densities, and resistivities, respectively, determined by XRR and CTLM. c) Measured sheet resistance values plotted as a function of the sputtering chamber pressure.

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it was not possible to quantify the resistivity, because the measured sheet resistance exceeded the tool maximum measurable limit of ≈10 GΩ □ −1 .
The characterization of the material stack was complemented by transmission electron microscopy (TEM) analysis of a pristine TiN/ TaO x / HfO 2 / TiN ReRAM with a ≈20 nm thick TaO x film deposited at 9 µbar. Figure 3a shows the scanning-TEM (STEM) image of a device in bright field (BF) mode. The contrast is sufficient to identify a thin, dense, amorphous layer at the TaO x /HfO 2 interface. Its thickness is estimated to be ≈3 nm. Also, at the HfO x bottom interface with TiN, a thin oxidized TiO x film grows, where a thickness of ≈1.5 nm can be recognized. The oxidation of the TiN surface is attributed to the deposition of HfO 2 , which takes place in an O 2 plasma atmosphere at 290 °C. [46] Figure 3b shows the energy-dispersive spectroscopy (EDS) analysis performed by scanning from the bottom to the top TiN to study the composition across the full stack. This analysis confirms the presence of a more oxidized TaO x phase below the crystalline TaO x bulk, as the Ta counts in the material decrease, while the O 2 counts keep constant. The pillar growth of the TiN is believed to be responsible for the projection of the TiN roughness to the morphology of the rest of the stack, causing an overlap of the Hf and Ta counts at the TaO x /HfO 2 interface, and of the Hf and Ti counts at the HfO 2 /TiN interface. Moreover, interdiffusion can not be excluded.
Please note that during the scanning TEM (STEM) acquisitions we could not acquire sufficiently high-resolution images to classify the crystallinity properties of the bulk TaO x . This limitation was caused by the small size of the grains identified (<6 nm, as reported in Figure S4, Supporting Information).

DC I-V Characteristics of the Oxide Bilayer ReRAM
In this section we present the DC I-V characteristics of a bilayer TiN/TaO x /HfO 2 /TiN ReRAM device. The thicknesses of the TaO x , HfO 2 , and TiN electrodes are ≈30, ≈6, and ≈20 nm, respectively. The resistivity of the TaO x layer is r x TaO ≈0.25 Ω cm. In parallel, we show the DC I-V characteristics of a baseline MIM stack, with the RE/TMO/IE structure, for comparison. Its structure is Ti/HfO 2 /TiN, with a ≈10 nm thick Ti layer.
In Figure 4a,b we compare their DC I-V forming characteristics, obtained by applying a positive voltage sweep. They show substantial differences: at 2 V, a leakage current of 100 pA is measured in the bilayer device, while in the baseline structure it is as large as ≈800 nA, close to the critical values required for the onset of the forming (I forming ≈3 µA). The forming voltage in the baseline device is ≈2.5 V, while in the bilayer configuration it can be as high as ≈5.5 V.
The higher pristine resistance of the bilayer structure can be explained by two main reasons. First, we know that even a pure Ta electrode would scavenge less O 2 from the HfO 2 layer, compared to a Ti one, due to their different oxygen affinities. [27] Moreover, it is likely that our conductive TaO x has a poor scavenging effect on the HfO 2 layer, [47] since it was already partially oxidized as deposited by the O 2 plasma environment.
After the forming, the application of a negative voltage sweep generates opposite effects on the two ReRAM devices, as reported in Figure 4c,d: the baseline configuration shows a reset transition, the bilayer a set one.
The subsequent application of a positive voltage sweep resets the bilayer device back to higher resistances, while the same polarity sets the baseline device to lower resistances.
Another difference between them is about the onsets of the resistive switching mechanisms: while in the baseline most of the device conductance change occurs abruptly as soon as the physical conditions for switching are reached, in the bilayer it is a rather gradual process sustained by the increase of the applied voltages.
We repeated the same bipolar DC write/erase cycle five times on both samples. The corresponding I-V characteristics are displayed in Figure 4e,f. The baseline shows a certain variability of the V set , which is attributed to the reset process stochasticity. [48] This is accompanied by a large variability of the programmed high resistive states (HRS). Contrarily, the bilayer Despite having improved the resistive switching graduality and stochasticity, the bilayer structure shows higher pristine resistances compared to the baseline stack, leading to a large increase of the V forming values. This effect hinders the device compatibility with the most advanced CMOS technologies. To address this point, future works will focus on the engineering of a sub-stoichiometric HfO x layer to reduce the V forming , [49] without compromising the analog and low-stochastic switching properties.

Interpretation of the Resistive Switching Mechanisms in the Oxide Bilayer ReRAM
In the filamentary ReRAM devices, the polarity of the resistive switching mechanisms depends, among other factors, on the WFs of the electrodes. [28,50] Their role was investigated in the MIM structures made of an n-type TMO, encapsulated between a high and a low WF electrode. [51,52] The high WF electrode/ TMO interface can be modeled as a Schottky barrier, while the low WF electrode/TMO interface is a low-impedance Ohmic contact. In such a structure, after forming a conductive filament of Vo .. in the TMO, these defects can be either repelled from the TMO region next to the Schottky barrier, or accumulated there, depending on the applied voltage polarity. [28] The local depletion of Vo .. increases the device resistance, while their accumulation decreases it. [28] The WF asymmetry can also affect the on/off switching ratio [50] and the reliability of the bipolar switching, [53,54] with both properties degrading for low WF asymmetries.
To verify whether the WF asymmetry plays a role in the reverse switching polarity of our baseline and bilayer structures, we investigate this aspect in more detail. In the baseline device, there is a clear asymmetry between the Ti electrode (WF Ti ≈ 4.33 eV [55] ) and the TiN electrode (WF TiN ≈ 4.7 ÷ 4.9 eV [56] ). For the bilayer device, we did not find in literature a referential WF value for our conductive TaO x layer. We found references for the Ta, whose WF can range from 4 to 4.8 eV, [55] and for the Ta 2 O 5 (WF Ta O 2 5 ≈ 4.05 eV [57] ). However, with such references we cannot claim with certainty the direction of the WF asymmetry in the bilayer stack, which would rather require dedicated measurements.
We decided to test our hypothesis with an alternative approach. We fabricated a bilayer device with a Pt BE, because Pt has the largest WF among metals (WF Pt ≈ 5.65 eV [58] ) and therefore mandatorily forces a WF asymmetry in the same direction as the one of the baseline. However, as displayed in Figure 5, the bilayer stack with the Pt BE shows the same switching polarity as the one of the TiN-BE bilayer device. We conclude that the reverse switching polarity between the bilayer and the baseline ReRAMs cannot be attributed to an inversion of the WF asymmetry.
As a next step, we will interpret the switching mechanisms based on the exhibited DC I-V characteristics. In Figure 5, the forming, set, and reset operations are shown. For each process, we provide a tentative description of the microscopic mechanisms involved. As an example, Figure 5a shows the I-V characteristics of the forming process and Figure 5b below depicts it at the nanoscale. The applied forming voltage generates a conductive filament of Vo .. across the HfO 2 layer, by driving a migration of O 2− anions toward the interface with the TaO x . [25] The abrupt increase of the current upon forming the filament www.advelectronicmat.de induces a local high temperature increase, which, combined to Coulomb repulsion, make the O 2− diffuse radially. [25] A more oxidized region (TaO y>x ) is obtained, dominating the device resistance after forming. This is the post-forming resistance (R pf ), correspondent to the device HRS. Now the device is formed and can be set to a low resistive state (LRS) upon the application of a negative voltage sweep, as shown in Figure 5c. We imposed a compliance of 100 µA to avoid that excessive currents could lead to very large resistance drops. In Figure 5d we depict the redox processes causing the decrease of the device resistance. Activated by the negative voltage applied, the O 2− formerly diffused in the TaO y region during the forming process migrate back to the HfO 2 layer. Consequently, the volume of the O-rich TaO y region shrinks, contributing to a decrease of the device resistance, while the Vo .. in the HfO 2 filament recombine with the incoming O 2− , contributing to an increase of the device resistance. Since we measure a drop of the total device resistance, among these two counteracting processes the reduction of the TaO y dominates over the oxidation of the filament tip. Subsequently, as shown in Figure 5e, upon the application of a positive voltage sweep, the device can reset to a HRS. In Figure 5f we describe the correspondent redox processes, where the O 2− migrating from the filament gap toward the TaO x layer gradually oxidize it, while the filament gap gradually reduces, upon increasing voltage amplitudes. In this case, since we measure an increase of the device resistance, the dominant resistive switching process is given by the local oxidation of the TaO x .
Under these hypotheses, we conclude that after the forming process, the current bottleneck in the device is the TaO x layer, both in the LRS and in the HRS, and not the filament in the HfO 2 .
The main difference observed between the Pt-BE and the TiN-BE bilayer devices is in the set mechanism, which is abrupt in the first case and gradual in the second. To explain this difference, we will first compare the voltage amplitudes required in the two samples to activate the set process and then we will discuss the role of the local electric field (F) and temperature (T) at the filament/TaO x interface.
The bilayer stack with the Pt BE shows higher set voltages and higher R pf values too compared to the TiN-BE one (R pf,Pt−BE ≈ 305 kΩ and R pf, TiN−BE ≈ 99 kΩ, from Figures 5a and 4a; |V set,Pt−BE | ≈ 0.96 V and |V set, TiN−BE | ≈ 0.50 V, from Figures 5c  and 4c). The requirement of higher voltages to activate the set mechanism when the devices are programmed in higher HRSs was already observed in MIM filamentary ReRAMs [29] and in bilayer structures too. [32] For the latter, it was also shown that the combination of higher HRSs and onset voltages makes the set process sharper. [32] In the next lines, we tentatively describe the physical origin for such phenomenon, based on the switching model derived for our bilayer structures.
While the set mechanism evolves (Figure 5d), the O-rich TaO y region shrinks, but keeps the dominant contribution to the device resistance. Therefore, we can expect that most of the applied |V set | will keep being distributed on the shrinking TaO y , hence leading to a local F enhancement. In parallel, the current increase leads to a T growth in the same TaO y region, due to Joule heating. The (F,T) enhancement promotes further O 2− migration, which ultimately installs a positive (F,T) feedback loop, resulting in an abrupt set process. [29] A gradual set transition can be restored by relaxing the (F,T) enhancement in the TaO y region with the introduction of an external series resistor. Its effect is to reduce the power dissipated in the device during the circuital transients that follow the onset of the set process, [59] preventing the thermal runaway responsible for the abrupt switching.
The non-linearity of the HRS makes a 1 kΩ series resistor sufficient for this purpose, without compromising the resistive

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switching window, as displayed in Figure 5g,h, where an on/off ratio of ≈1 order of magnitude is achieved by applying a maximum V stop = +1.4 V.
Differently from the filamentary-type devices, which generally show abrupt set mechanisms, the interface-type devices are characterized by a bidirectional gradual resistive switching, [60] typically showing area-dependent resistive states. [60] Therefore, to confirm the hypothesis of filamentary switching for our bilayer ReRAMs, we studied the area-dependency of their resistive states, including (6 µm) 2 , (12 µm) 2 , (30 µm) 2 , and (60 µm) 2 devices in the statistics. For each area, we applied 10 bipolar voltage sweeps up to the stop values −1.2 V and +1.6 V.
The median LRS and HRS were grouped in boxplot graphs and plotted against the device area, as shown in Figure 6. We observe that neither the HRS nor the LRS scale with the area. The fluctuations between the different cell areas can be attributed to the device-to-device variability and to the relatively small size of the collected statistics.
These results support the hypothesis that the switching mechanisms are filamentary based, even if they become gradual in both directions when a 1 kΩ series resistor is introduced.

Impact of the TaO x Resistivity on the Switching Properties of the Oxide Bilayer ReRAM
To explore the role of the TaO x resistivity on the switching properties of the bilayer devices, we compare two ReRAM types fabricated using TaO x layers with resistivities of r x TaO ≈ 0.01 Ω cm and r x TaO ≈ 0.25 Ω cm. In both cases, the TaO x film is ≈30 nm thick and the BE material is TiN.
In Figure 7a,b we compare their post-forming DC I-V characteristics. Both devices similarly show low-stochastic, gradual bidirectional switching transitions, making the current curves almost overlapping over 20 subsequent cycles. Moreover, the switching processes require low voltages (<1 V) to be activated. The main difference between the two types of ReRAM is that only the device with the more resistive TaO x can reset to HRS values >10 kΩ.
To validate this result from a statistical point of view, we measured 10 devices per each TaO x type, using the same stop voltages. In Figure 7c,d we compare the cumulative distributions  www.advelectronicmat.de of their resistive states. Each device is represented by a pair of lines of the same color, one for the LRS and the other one for the HRS. The statistics confirms that the more resistive TaO x improves the HRS values beyond 10 kΩ and the on/off ratio too, which increases up to ≈ 1 order of magnitude. However, the resistive states increase comes at the cost of a broader deviceto-device variability (cumulative distributions more distanced), as well as a larger cycling variability (cumulative distributions more oblique).
The gradual resistive switching properties are enhanced at high bandwidth. In Figure 7e,f we compare the ReRAMs with different TaO x types by applying short programming pulses. In both cases the programming sequence consists in alternating 200 identical set and reset pulses. This sequence is iterated ten times to check the stability of the potentiation/depression characteristics. The duration and the amplitudes of the voltage pulses are selected to maximize the number of conductive states (NoS), which improves when G is updated in small steps, but covers a large window too.
For the ReRAM with the low-resistive TaO x , a pulse duration of 150 ns and pulse amplitudes of +1.25 V and −0.95 V were used for depression and potentiation, respectively. Instead, 400 ns pulses of amplitudes +1.30 V and −1.00 V were used for the ReRAM with the more resistive TaO x .
The methodology used for determining the NoS is detailed in the Paragraph S6, Supporting Information. The device with the low-resistive TaO x layer has 13 and 9.5 average NoS for potentiation and depression, respectively. The other device has an average NoS of 9.5 and 11.2.

Impact of the TaO x Thickness on the Switching Properties of the Oxide Bilayer ReRAM
In previous studies, it was shown that in MIM ReRAMs with a RE/TMO/IE structure, the thickness of the RE affects the O 2 scavenging reactions at the interface with the TMO, impacting the device switching properties. [27,47,61,62] For RE thicknesses between 1 and 5 nm, the O 2 scavenging process is enhanced by greater thicknesses, causing a decrease of the forming voltages. [61,62] Instead, for REs thicker than 5 nm, the forming voltages stop decreasing, [61] due to the saturation of the O 2 scavenging reactions. [61] In this study, we fabricated three variations of TiN-BE bilayer devices, where we changed the TaO x thickness to understand its impact on the device switching properties. The thickness variations are ≈ 20, ≈50, and ≈60 nm of the highly resistive TaO x material (r x TaO ≈ 0.25 Ω cm). Figure 8d shows that for increasing TaO x thicknesses, the forming voltages do not decrease. Therefore, we conclude that the O 2 scavenging processes at the TaO x /HfO 2 interface have similarly saturated in all the examined samples.
In Figure 8a-c, we compare their post-forming DC I-V characteristics. The 20 nm thick TaO x device exhibits gradual bidirectional resistive switching transitions, similarly to the one with a 30 nm thick TaO x layer, shown in Figure 7b. Vice versa, the device with the 50 nm thick TaO x displays an abrupt set transition, and the one with the 60 nm thick TaO x shows multiple abrupt set transitions. Moreover, we can highlight that the HRS values tend to decrease for increasing TaO x thicknesses.

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To understand the origin of this latter trend, we first correlate the distributions of the HRSs to the R pf values, plotting them all against the TaO x thickness, as displayed in Figure 8e. We clearly observe that also the R pf values decrease for increasing TaO x thicknesses, indicating that the trend originates from the forming process itself.
To understand why thicker TaO x layers result into lower R pf values, we include in the discussion some additional considerations concerning the thermal properties of the TaO x layer and their impact on the forming process.
The thermal coefficient of a conductive TaO x film depends on its resistivity. [63] Since our TaO x material is characterized by the resistivity r x TaO ≈ 0.25 Ω cm, we can assume a low thermal coefficient ≲ 1 W mK −1 . [63] For this reason, in our devices, the TaO x acts as heat confinement layer. [38,64] The impact of this effect on the forming process becomes clear if we resume the nanoscale model depicted in Figure 5a. When the filament begins to form, the heat confinement effect induces high T at the TaO x /filament interface, promoting the ion mobility. This favors the O 2 − migration from the HfO 2 to the TaO x layer, enhancing the generation of conductive Vo .. in the HfO 2 layer. The high conductivity of the TaO x layer makes the voltage drop insufficient to sustain the vertical drift of the O 2 − in the TaO x layer too. Instead, the high T generated upon forming the filament favor the lateral diffusion of the O 2 − in the TaO x layer. [41,65] Thicker thicknesses of the TaO x layer further enhance the heat confinement effect, due to the increasing distance between the hot TaO x /filament interface and the thermally conductive TiN-TE. With higher T, the thermal diffusion is promoted, extending the highly oxidized TaO y>x region depicted in Figure 5b more laterally than vertically.
Since the device resistance is measured vertically, the formation of a more conductive filament in the HfO 2 and the enhanced lateral diffusion of the O 2 − in the TaO x layer concur toward a reduction of the R pf values.
The enhanced heat confinement effect can also explain the origin of the sharper set mechanisms observed in the bilayer devices with thicker TaO x layers. The set process was modeled in Figure 5c as a redox reaction, where the reduction of the O-rich TaO y>x region dominates the device resistance change, over the oxidation of the filament tip. During this process, the evolution of the T at the TaO x /filament interface is critical for the switching graduality, as already discussed.
We conclude that the abrupt set transitions observed in the devices with 50 and 60 nm thick TaO x layers are driven by an enhanced heat confinement effect, overcoming the typical switching graduality observed in the devices with thinner TaO x layers.
A particular case is the ReRAM with the 60 nm thick TaO x , characterized by multi-step abrupt set transitions, as displayed in the magnified corner of Figure 8c. This phenomenon could be attributed to the formation of multiple filaments, as explained by Wu et al. [38]

The Oxide Bilayer ReRAM with the Optimal TaO x Material-Pulsed Characterization
The comparison between ReRAMs with different TaO x resistivities and thicknesses indicated that thinner and more resistive TaO x layers improve the device resistances and the gradual bidirectional switching properties, without degrading the forming voltages, nor the set and reset stop voltages.
In particular, the devices with a 20 nm thick TaO x layer and x ρ TaO ≈ 0.25 Ω cm show high R pf values of ≈100 kΩ. However, we observed in Figure 8e that the DC operations degrade the HRS values by a factor ≈3x compared to the departing R pf values, due to the strong electrical stress induced by the first DC set voltage sweep.
To prevent it, we rather apply sub-µs programming pulses directly after the forming process is over. Figure 9a shows the potentiation/depression curves obtained from the application of 200 pulses of amplitudes V − = −0.95 V and V + = +1.25 V per each direction and duration 250 ns. The sequence was iterated three times to check the states' stability over cycling.
While the potentiation trace is almost analog, the depression shows an initial abrupt jump, where the device resets close to the departing high resistances.
To get more balanced potentiation/depression characteristics, we reduced the amplitude of the reset pulses down to V + = +1.10 V and we shifted the operational regime of the device toward higher conductances. In Figure 9b we show ten subsequent potentiation/depression curves obtained using the modified pulse scheme with more balanced amplitudes for set and reset. The G trace spans between 60 and 240 µS, defining a G max /G min ratio ≈ 4, and it nicely mimics a biological analog synapse, as displayed in Figure 9c.

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We can estimate the relative NoS as detailed in y Paragraph S6, Supporting Information. We get an average NoS of 14.5 and 21.3 for potentiation and depression, respectively.

Training Simulation of a Fully Connected Network of Analog Devices
In the long term, our goal is to exploit filamentary memristors to compute ANNs and other AI workloads. To validate our bilayer devices, we use the publicly accessible "IBM aihwkit", [42] which allows to simulate our devices in real world applications. This simulation framework provides different device models, of which the "PowStepDevice" is the most suitable for the oxide bilayer, and which can be extracted from the measured potentiation/depression traces of Figure 9b. It provides a pulse-to-conductance response following a power-law. The model follows a series of update rules as shown in the following equations: where w ij is the weight to be updated, w min (w max ) the lower (upper) bounds, dw min the linear update parameter, β its skew between the up/down directions, γ the exponential update parameter and β pow its skew between the up/down directions. The individual measurement traces were averaged and then normalized to (−1,+1). We employed a lmfit-based algorithm [66] to automatically fit our measurements to the aihwkit "PowStep-Device" model. The fit is depicted in Figure 10a.
As a test-vehicle for our real world validation, we selected the character recognition task on the MNIST dataset. [67] As an architecture, we selected a fully-connected four layer network with a 784 node input layer, two hidden layers with 200 and 64 nodes, respectively, and the output-layer with ten nodes. We trained the same architecture with the analog device model and, as a benchmark, using 32-bit floating point arithmetic.
The simulation keeps into account the measured cycle-to-cycle variability, but not the device-to-device variability yet. Figure 10b shows a comparison between the training convergences of the analog and of the digital model, with a crossentropy objective function. [68] The digital model converges faster to lower losses and shows a better accuracy (96%) compared to the one of the analog model (82%). This ≈15% drop in accuracy is not unexpected, since the analog device model itself already contains non-idealities in the weight update symmetry, linearity and minimum step size. [22] To fully exploit the analog devices' potential, it will be crucial to modify the standard training algorithms, based on stochastic gradient descent (SGD), taking into account the specific nonideal properties of our analog devices. As an example, the Tiki-Taka algorithm [69] can achieve excellent accuracies even with non-simmetric devices. [69] Training simulations based on this algorithm will be presented in future works.

Conclusion
In this work we designed, fabricated, and optimized a CMOS-compatible electrical synapse for in-memory computing applications.
The integration of a conductive TaO x within the ReRAM stack, which creates a TaO x /HfO 2 bilayer, improves the resistive switching stochasticity compared to a baseline ReRAM Ti/HfO 2 .
The new devices, despite having a filamentary-based physics, show anomalous but excellent gradual bidirectional resistive switching properties. Moreover, they can be programmed with fast (<200 ns) and low voltage (<1.5 V) pulses to cover an analog conductive window with a maximum-to-minimum ratio >4.
We found that thinner and more resistive TaO x layers improve the device power consumption during its operations and the number of multilevel states.
To explain the peculiar resistive switching properties of our devices, in particular the reversed polarity compared to the baseline ReRAMs, we propose a microscopical interpretation of the forming, set and reset operations. We account for a localized O 2− exchange at the interface between the HfO 2 and the TaO x . The redox reactions in the TaO x layer are responsible for the device resistive switching.

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To validate the performances in real world applications, we simulated the handwritten character recognition task with the MNIST dataset, using the IBM analog hardware acceleration kit (aihwkit). We found an accuracy drop compared to the benchmark model of only ≈15%, using SGD and backpropagation. More disruptive training algorithms such as Tiki-Taka [69] are expected to further compensate for the asymmetric properties of our devices and yield a performance comparable to the benchmark simulation.
Future work will focus on product-level integration of the bilayer ReRAM into the CMOS stack to better control the forming process. This solution is expected to reduce the current overshoots during resistive switching, [70] leading to higher resistance values and hence further reduced power consumptions.
Nonetheless, our TaO x /HfO 2 -based ReRAM already represents an attractive and flexible memory element for large-scale integration, considering its excellent granular switching properties and CMOS compatibility.

Experimental Section
Fabrication: The presented ReRAM devices were vertical, sharing a common bottom contact of n-doped Si. The 20 nm thick Pt BE was deposited by evaporation at room temperature; the 20 nm thick TiN BE was deposited by plasma-enhanced atomic layer deposition (PE-ALD) at 300 °C using a tetrakis-(dimethylamino)titanium (TDMAT) precursor and (N 2 , H 2 ) plasma. The 6 nm thick HfO 2 layer was deposited by PE-ALD at 290 °C using a tetrakis-(ethylmethylamino)hafnium (TEMAH) precursor and O 2 plasma. In the bilayer devices, the controlled sputtering parameteres for the deposition of the TaO x films were: DC power = 50 W; (O 2 , Ar) stream ratio = (1 sccm, 40 sccm); deposition time = 200 s to grow a ≈30 nm thick film. The TaO x thickness variations were realized by linearly changing the sputtering duration.
STEM and EDS were used to check the ≈20 nm thickness, XRR for the ≈30 nm one, and SEM for the ≈50 nm and ≈60 nm ones (see Figures S8 and S9, Supporting Information).
In the baseline, the 10 nm thick Ti capping of the HfO 2 was DC sputtered. The 20 nm thick TiN TE was deposited by RF sputtering of a TiN target in a mixed (Ar, N 2 ) plasma. A 50 nm W layer was sputtered on top. The sputtering of the W/TiN/TaO x (W/TiN/Ti in the baseline) proceeded without vacuum breaking between the deposition of the different layers, to avoid uncontrolled oxidation at the reactive interfaces. The patterning of the device geometry was performed through inductively coupled plasma etching of the W/TiN/TaO x (W/TiN/ Ti in the baseline) stack, using a mixed CHF 3 and SF 6 plasma, which stopped at the HfO 2 layer. A passivation layer of 100 nm thick SiN x was grown by plasma-enhanced chemical vapor deposition (PECVD). The via to access the device TE was etched with a mixed CHF 3 and O 2 plasma by reactive-ion etching (RIE). 100 nm of W were sputtered and then RIE etched to define the device pads.
The described process flow avoids any lift-off steps, which could not be performed in foundries.
Structural Characterization: The X-ray characterization, which included the GIXRD and XRR scans, was performed using a Bruker D8 Discover diffractometer, equipped with a rotating anode generator.
The lamella preparation for the TEM analysis was conducted with the FEI Helios NanoLab 450S focused ion beam. The TEM analysis was carried out with a double spherical aberration corrected JEOL ARM200F operated at 200 kV. The EDS scans were performed using a liquidnitrogen-free silicon drift detector.
Electrical Characterization: The CTLM characterization of the TaO x layers and the DC characterization of the bilayer ReRAM with Pt BE were performed with a B1500 parameter analyzer. The DC characterization of the baseline and the bilayer with TiN BE was performed with an Agilent 4155C parameter analyzer.
To simulate DC conditions, the quasi-static measurements were performed by dividing the applied voltage sweeps into 100 equal steps, lasting 100 ms each. The read of the device resistive state was done by performing a voltage sweep up to +250 mV and extracting the resistance at +200 mV.
External series resistors were introduced by mounting an SMD resistor in series to the probe tip biasing the device pads. All the bilayer devices were formed with a 10 kΩ external series resistor, to reduce the power dissipated through them during the transients following the resistive switching and limit the steady state current.
The pulsed characterization was performed using a NI PXIe-5451 arbitrary waveform generator to source the generated pulses to the device TE, and an oscilloscope NI PXIe-5164 to read the current signal flowing through the device BE. The pulsed read scheme consisted of alternating a positive and a negative pulse with amplitudes of ± 200 mV and a duration of 10 µs, to cancel out any eventual measurement offset.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.