Highly reproducible and CMOS-compatible VO2-based oscillators for brain-inspired computing

With remarkable electrical and optical switching properties induced at low power and near room temperature (68 °C), vanadium dioxide (VO2) has sparked rising interest in unconventional computing among the phase-change materials research community. The scalability and the potential to compute beyond the von Neumann model make VO2 especially appealing for implementation in oscillating neural networks for artificial intelligence applications, to solve constraint satisfaction problems, and for pattern recognition. Its integration into large networks of oscillators on a Silicon platform still poses challenges associated with the stabilization in the correct oxidation state and the ability to fabricate a structure with predictable electrical behavior showing very low variability. In this work, the role played by the different annealing parameters applied by three methods (slow thermal annealing, flash annealing, and rapid thermal annealing), following the vanadium oxide atomic layer deposition, on the formation of VO2 grains is studied and an optimal substrate stack configuration that minimizes variability between devices is proposed. Material and electrical characterizations are performed on the different films and a step-by-step recipe to build reproducible VO2-based oscillators is presented, which is argued to be made possible thanks to the introduction of a hafnium oxide (HfO2) layer between the silicon substrate and the vanadium oxide layer. Up to seven nearly identical VO2-based devices are contacted simultaneously to create a network of oscillators, paving the way for large-scale implementation of VO2 oscillating neural networks.

the different annealing parameters applied by three methods (slow thermal annealing, flash annealing, and rapid thermal annealing), following the vanadium oxide atomic layer deposition (ALD), on the formation of VO2 grains is studied and an optimal substrate stack configuration that minimizes variability between devices is proposed.Material and electrical characterizations are performed on the different films and a step-by-step recipe to build reproducible VO2-based oscillators is presented, which is argued to be made possible thanks to the introduction of a hafnium oxide (HfO2) layer between the silicon substrate and the vanadium oxide layer.Up to seven nearly identical VO2-based devices are contacted simultaneously to create a network of oscillators, paving the way for large-scale implementation of VO2 oscillating neural networks.

(INTRODUCTION)
With phenomenal computing and learning capabilities far beyond the fastest chips, the brain remains today the most power-efficient computational system.Implementing brain-like circuitry for faster less power-hungry massive data processing drives the industry to downscale CMOS technology and innovate towards new 'neurmorphic' materials.Research surrounding phasechange materials has demonstrated their ability to mimic some of the brain's elemental operations, both synaptic and neuronal.For example, the most recent work on Ge2Sb2Te5 memories enables vector-matrix multiplication for in-memory computing, implemented in a spiking neural network (SNN).[8] This type of phase-change spiking system is ideal both for powering biologicallyrealistic AI applications and for its technological potential in terms of integration at the back-endof-the-line.Recently, an analogous computing technique based on another phase-change material system offering comparable benefits has sparked a growing interest among several research groups.[2,9,10] The ambition is to unravel further the potential of phase-change materials by using oscillation-based computing, inspired by the rhythmic patterns of action potentials exhibited by neurons during the learning phase.[11] This approach provides new computational paradigms for bio-inspired applications.
In an oscillating neural network (ONN), the information is carried in the phase relations between coupled oscillators rather than in the amplitude of the signals, making them intrinsically resistant to voltage-scaled noise and typical input pattern distortion problems in Machine Learning (ML).[6] This method has demonstrated the potential to perform all types of arithmetic computation and shows the promise of major computational improvements, especially for optimization tasks, Boolean satisfiability (3-SAT) problems, and Ising machine problems.[5,9,10,11,12] Typically, finding the best solution to optimization tasks in traditional computers demands a tremendous amount of power and far larger computing times.A lightweight hardware design with phasechange material electronics offering moderate accuracy performed locally in-memory is often sufficient to find a suitable solution to common industrial operations.[10] Additionally, computing with ONNs avoids the von Neumann bottleneck energy costs arising from data transfer from the memory unit to the processor by embracing the fundamental principle of in-memory computation: "let physics do the computing".[10,12,13] Consequently, an ONN architecture built with nanoscale oscillators and compact high-fanout interconnections should be favored to allow for a richer representation of information while avoiding long-range power-hungry coupling between devices.[2,7,14] Assembling an ONN depends on the successful fabrication of individual oscillators with predictable and reproducible behavior.An ideal oscillator needs to be scalable, offering easy integration on a Silicon (Si) platform, power-efficient, endurant, and operable at high frequency.
Niobium oxide (NbO), magnesium-oxide-based magnetic tunnel junction (MgO-based STO), and vanadium dioxide (VO2) all exhibit oscillatory capabilities, with the latter being the leading candidate thanks to the low power required to trigger a high-frequency resistive switching near room temperature (68 ˚C).[1,15] The source mechanisms behind VO2's switching behavior are still being debated in the research community.For most studies, it originates between a Peierls and a Mott phase transition.[16] This little understanding on VO2's intrinsic phase-transition nature as well as the complexity required to connect several devices for the integration of a large-scale ONN has limited most of the research to simulation-based results or generally, to the study of only two coupled VO2-based oscillators.[15,17] In addition, the high variability between VO2-based oscillators, originating from the multitude of metastable vanadium oxide oxidation states generated during fabrication, has been reported to be a main limiting factor for advancing full hardwarebased ONN approaches.For example, in ref [18] and ref [19], it is demonstrated that even the highly controllable magnetron sputtering deposition technique encounters challenges in growing pure VO2 on a silicon dioxide (SiO2) substrate.In fact, the variable VO2 transition temperatures obtained in ref [19] make devices fabricated by magnetron sputtering difficult to scale to nanodimensions and unfit for the large circuit implementation we are targeting.Other studies [3,4,9,20,21] also established that the fabrication of VO2 layers on amorphous substrates through pulsed laser deposition, chemical vapor deposition, sputtering, and ALD tends to result in polycrystalline films with granular structure and considerable surface roughness.[22] This morphology is responsible for the undesired variability among electrical VO2-based oscillating devices.[23] In an effort to mitigate this variability and produce CMOS process-compatible vanadium-oxide oscillators to build ONNs, we study the advantages of several annealing techniques post-ALD deposition on different stacks where we fine-tune their respective parameters.[4] The fabrication challenges are the same ones associated with magnetron sputtering and PLD-deposition [19] of VO2; namely, the existence of several compositions, such as the Magneli (VnO2n−1, where 3 ≤ n ≤ 9) and the Wadsley (VnO2n+1, where n = 1-6) phases that are all -including VO2 -intermediary phases towards the most thermodynamically stable stoichiometry of V2O5.[19,24] In this work, we investigate the influence of the annealing parameters on the VO2's nanoscale structure and composition through Atomic Force Microscopy (AFM), Raman Spectroscopy, and X-ray reflectometry (XRR), as well as the VO2's resulting electrically prompted crystalline phase transition.Our goal is to obtain a granular film of high quality, which we define as a dense layer of compact grains with smooth surface roughness, uniform and reproducible electrical behavior showing a sharp and narrow resistance-temperature (R-T) hysteresis.[20] Finally, we also exploit the properties of different metal-oxides to study, influence, and engineer the crystalline phasechange temperature, opening the door for wider industrial applications where the thermal budget caused by the heat of the operating peripheral circuitry is limited.[25]

Vanadium Oxide Film Deposition
Vanadium oxide can be synthesized through numerous methods, including gas-phase techniques like pulsed laser deposition (PLD), chemical vapor deposition (CVD), sputtering, and atomic layer deposition (ALD) as well as solution-based methods, such as sol-gel processes and hydrothermal synthesis.While magnetron sputtering is a widely-used deposition technique, the high energy of the deposited particles leads to limited results for vanadium oxide films below 100 nm.[26] To achieve scalable ultrathin films suitable for low-power applications, gas-phase techniques offer better results.[26] These methods are well-suited for forming thin layers directly on a heated substrate in the presence of an appropriate process gas or in a two-step process with an annealing step following the deposition.
We use ALD for our depositions, as it provides uniform growth on high aspect ratio nanostructures, homogeneous deposition over a large area, and CMOS compatibility with the possibility to co-integrate the grown material on top of underlying pre-existing circuitry.[27,28] We apply the novel Tetrakis[ethylmethylamino] vanadium (TEMAV) reaction on a Si platform, which calls for the presence of an inert carrier gas (Argon) and an oxidation agent (water) to coat uniformly and quickly.[28] We prefer a dense water-grown film over an ozone-grown layer, as it was shown to more likely give rise to VO2 grains in the M1 crystallization phase after a postannealing treatment.[28,29] Our process occurs at 150 ˚C to prevent the material from being too volatile at low temperatures or from thermal decomposition at temperatures higher than 175 ˚C.
[28] The in-house recipe deposition rate is about 0.5 Å per cycle.The final thickness of the layer is 60 nm, as confirmed by XRR measurements (Table 4).
After the ALD process, a post-deposition treatment at temperatures above 420 ˚C is necessary to transform the film into the desired oxidation state (VO2).[28] The ALD process alone provides a highly homogeneous vanadium-oxide layer but lacks sufficient control over crystallinity, stoichiometry, and phase required for the devices.[28] The necessary post-deposition annealing step typically degrades the film's morphology, and the effect is even stronger in thin films where the impact is directly measurable on the metal-to-insulator temperature (MIT) and on the properties of the VO2.[30] Our aim is to reduce the rough morphology obtained after annealing, which can be attributed to a volume change associated with the de-wetting process of the dielectric surfaces during annealing.[28] Slow Thermal Annealing (STA) The Neocera Combinatorial 180 PLD system used for this method offers a precise control over the oxygen pressure with heating and cooling temperature ramps limited to a maximum of 25 ˚C min -1 .The films were brought to a set temperature of 520 ˚C at the sample holder, corresponding to a temperature of about 420 ˚C in the sample, with an oxygen flow defined to keep the pressure at 5 Pa at the highest temperature setpoint.Increasing the temperature beyond this point induces the crystallization of large grains and can raise the final oxidation state.[28] Upon reaching the set temperature of 520 ˚C, the samples were kept in the heating chamber for 5 to 10 minutes, before being cooled back down to room temperature.

Flash Annealing
High heating and cooling rates during the annealing process offer increased control over the grains' nanostructure.[31] In the early stages of phase formation, nucleation occurs, and a rapid heating rate within the sample affects both grain growth and density, resulting in a smoother film with small compact structures.[31] Other experiments have also shown that a flash annealing step could improve the film smoothness and transition sharpness.[32] Using the flash lamp FLA-50AS, Dresden Thinfilm Technology, we investigate the possibility of growing small grains with the energy of a flash only.The flash is 20 ms long, with a power between 90 and 110 J cm -2 .The samples were preheated with a thermally regulated Si carrier wafer at a fixed temperature, ranging between 140 ˚C and 330 ˚C.This tool provides heating and cooling rates orders of magnitude faster than the STA, where exact values can only be estimated.The tool allows for oxygen pressure to be constrained within the range of 1.33 Pa to 66.66 Pa.

Rapid Thermal Annealing (RTA)
To achieve control over the grains' structure through rapid thermal rates, while still maintaining atmospheric conditions suitable for VO2 growth, we used the ANNEALSYS AS-Micro RTP-System to explore rapid thermal annealing.[24,31] The samples were placed in a chamber and stabilized to a temperature of 300 ˚C, before being rapidly brought up to the final annealing temperature.The oxygen partial pressure, between 5 Pa and 25 Pa, was maintained through a continuous flow, and annealing times varied from 30 s to 600 s.This last technique combines the benefits of the STA and Flash annealing techniques by offering ultralow partial pressures with a heating rate of 18 ˚C s -1 .

Device Configuration
A planar configuration (see schematic in Ra), with corresponding scanning electron microscopy (SEM) image in c) was chosen for the fabrication of rectangular test structures with active region dimensions varying between 400 um × 400 um × 60 nm and 2000 um × 2000 um × 60 nm.The zoomed schematic of Figure 1b reveals the irregularity of the grains at the nanoscale and show how they can define a preferential current path in the device, as observed by X-Ray diffraction (XRD) nanoimaging in ref [21].The advantage of this device geometry consists in few processing steps, offering a top view of the grains involved in the phase transition.However, this implies that a different preferential current path is created in each device, which is the source of significant variability.These tests structures are convenient to verify the reliability of our annealing process and to perform material characterization with a fast turnaround.To achieve coupling between oscillators, the crossbar configuration shown in Figure 1d and e is preferable, as it confines the current path within the intersection of the cross-section between a top and a bottom electrode.
The thickness of the VO2 layer defines a current path and the amount power required to induce the phase transition.A 50 nm thick bottom electrode (3 nm Titanium (Ti) / 47 nm Platinum (Pt)) was embedded into the substrate if it was at least 50 nm thick through an e-beam lithography step followed by a dry etch.In the case of a thin substrate (SiO2 < 50nm), the bottom electrodes were deposited directly on the substrate.

RESULTS
Different annealing techniques are explored to achieve high VO2 granular quality.Synthesizing films in the VO2 oxidation state only is limited by a fine window of homogeneity and a high sensitivity to the oxygen partial pressure during the thermal treatment.[33] These challenges have a direct impact on the reproducibility of the film's granular composition and surface roughness that affects the overall electrical performance.[33] A compact and dense layer of small grains favors low variability between devices.[20] Synthesizing this reproducible VO2 layer with small and compact grains relies on precise control of annealing parameters, including temperature, time, heating/cooling rates, and oxygen partial pressure.Decoupling the effect of each parameter proves difficult due to the complex chemical and physical mechanisms happening during annealing.Therefore, we assess the overall impact of these parameters on the grains' morphology, oxidation phase, and surface roughness ex-situ and post-treatment through XRR, Raman, and AFM measurements.
We investigate the potential of three post-deposition annealing techniques to grow polycrystalline VO2 for our oscillators.These techniques provide varying degrees of control over the annealing parameters.

VO2 Grown By Slow Thermal Annealing (STA)
The AFM micrographs shown in Figure 2 (scan area 1 × 1 µm 2 ) correspond to VO2 samples A, B, and C grown directly on a 500 nm thick SiO2 substrate.Various annealing treatments applied to the samples lead to nanoscale VO2 grains of different dimensions (see Table 1).Samples A, B and C were annealed at 520 ˚C , 520 ˚C, and 540 ˚C for 5 minutes, 10 minutes, and 5 minutes, respectively.Samples annealed at temperatures below 520 ˚C did not grow VO2 grains.The conditions that lead to the smoothest film with the lowest surface roughness value (RMS) involve a short annealing time of 5 minutes at a set temperature of 520 ˚C, achieved with a ramp rate of 25 ˚C min -1 under an oxygen partial pressure of 5 Pa.In addition to these conditions, our findings from Figure 2 and Table 1 reveal that VO2 grows a rougher surface when there is an increase in annealing temperature or time, due to the formation of larger grains.This is consistent with similar results found in refs [24,31,34].

VO2 Grown By Flash Annealing (FLA)
Figure 4a shows the Raman spectra of films annealed with a flash power of 90 J cm -2 and an oxygen pressure of 20 Pa at chuck temperatures ranging from 185 ˚C to 250 ˚C.The results indicate that pre-heating the sample at least to 215 ˚C is necessary to measure the characteristic VO2 Raman peaks at 193 cm -1 and 223 cm -1 .[35] As the chuck temperature is raised above 215 ˚C before flashing, the intensity of the Raman peaks grows, indicating a greater amount of the initially amorphous material successfully crystallizes into VO2 grains.A lower ratio of the intensity of the main Raman peaks (193 cm -1 and 223 cm -1 ) relative to the intensity of the weakest peaks (389 cm - 1 , 497 cm -1 , 612 cm -1 , …) in VO2 is also associated with an increase in surface roughness in our samples.[36] The presence of V2O5 is detected (145 cm -1 ) when the pre-heating temperature is 250 ˚C or higher.
In Figure 4b, the average grain diameter size and mean surface roughness (RMS) values extracted from AFM are plotted against the chuck temperature before flash annealing.The grain size remains stable around 25 nm across all temperatures, while the surface roughness consistently increases with the substrate temperature.These trends suggest that only the surface roughness is influenced by an increase in substrate temperature.This observation is also supported by the sharper peaks measured by Raman spectroscopy at higher chuck temperatures (see Figure 4a).
Comparing results in Figure 4b to Figure 2 and Table 1 indicates that flash annealing reduces surface roughness by over 50% compared to STA-annealed samples.A change in resistivity of nearly 1.5 orders of magnitude is observed in Figure 4c, with a hysteresis width of 6 ˚C and an IMT at 58 ˚C.This temperature is considerably lower than the typical 68 ˚C for VO2 prepared by STA.This difference is attributed to the presence of defects, usually associated with higher annealing temperatures, which can induce the phase transition at lower temperatures.[37] The R-T measurements in Figure 4c also reveal a substantial variation in the resistivities (both insulator-and metallic-state) among samples 1 and 2 flash annealed under the same conditions, indicating a low level of reproducibility for this annealing technique.
Although flash annealing significantly reduces surface roughness (Figure 4b) compared to samples grown by STA (see Figure 3), the variability in grain dimensions, oxidation states, transition temperature, and electrical response between identically treated samples renders flash annealing unsuitable for the fabrication of uniform VO2-based oscillators.

VO2 Grown By Rapid Thermal Annealing (RTA)
The RTA tool offers O2 pressure control at a level as low as the STA tool while providing much faster heating and cooling ramps.Table 2 provides a summary of the various tested recipes, emphasizing whether they meet the required specifications to obtain high-quality VO2 films for our oscillators.These specifications include the presence of VO2 stoichiometry confirmed by Raman spectroscopy, layer uniformity, and sample reproducibility.The AFM measurements in Figure 5a indicate that the highly reproducible annealing recipe highlighted in blue in Table 2 results in grains as small as those obtained with the slow annealer (see Figure 2 and Table 1).Additionally, the surface is nearly as smooth as in samples subjected to flash annealing (Figure 4b) and the main Raman peaks of VO2 (193 cm -1 and 223 cm -1 ) are detected using this recipe (Figure 5b).[35] Figure 5b shows that the ratio of the intensities of the main Raman peaks to the weaker ones (389 cm -1 , 497 cm -1 , 612 cm -1 , is higher compared to those obtained with flash annealing (Figure 4a).[35] This suggests a reduced surface roughness, which is confirmed by the measurements in Figure 5a [35] This annealing technique with the highlighted conditions in Table 2 was selected to realize the VO2-based oscillators.
Figure 5c shows the R-T characteristics of crossbar devices of identical dimensions (active area of 750 nm × 750 nm × 60 nm) fabricated on a chip with these conditions.Despite the ideal structural composition of the film and the sharp, smooth transitions seen in the hysteresis curves, the devices show variability in their electrical properties.The measured resistivities range from substrate.By leveraging the diverse surface energies of these interlayers, we want to take advantage of the de-wetting angles created between the VO2 grains and the underlying surface.

VO2 On Metal Oxides
Figure 6a shows the normalized R-T characteristics of VO2 layers in stacks embedding HfO2, Ti3O5, Al2O3, or WOx interlayers (red, green, blue, and orange curve, respectively) annealed for 45 minutes at 520 ˚C, along with a reference sample of VO2 on 500 nm of SiO2 (black curve).
These materials were selected due to their widespread availability in a semiconductor fab environment and their higher surface energies compared to silicon.The longer 45-minute annealing ensures the formation of de-wetted VO2 grains on the interlayers.The presence of a thin 10 nm interlayer significantly alters the R-T characteristics compared to the reference sample (black curve).The VO2 layer deposited on WOx exhibits a less steep transition compared to typical samples on SiO2.On Al2O3, the VO2 layer displays similar hysteretic characteristics to the reference SiO2 sample, but with a slight shift towards higher temperatures, suggesting it requires higher voltages to trigger its phase transition.Similarly, the Ti3O5 interlayer results in an even higher transition temperature accompanied with a narrower hysteresis width.To achieve lowpower operation, we discarded Al2O3 and Ti3O5 as suitable interlayers for the oscillators.
Interestingly, the sample with VO2 on HfO2 annealed for 45 minutes shows an increase in the transition temperature of the IMT (80 ˚C) while keeping the MIT around 68 ˚C.
Figure 6b shows the Raman spectra corresponding to the samples with different interlayers.In samples with Al2O3 or Ti3O5 interlayer, a shift of either one of the two major peaks of VO2 is observed, suggesting the presence of strain across the VO2 layer.The characteristic VO2 Raman peaks at 193 cm -1 and 223 cm -1 are sharp and more pronounced with the HfO2 interlayer, indicating superior stabilization into the VO2 oxidation state and more uniform crystallization compared to other interlayers.[35] This is an important finding showing that the incorporation of a 10 nm HfO2 interlayer with high surface energy prevents the complete separation of VO2 into individual nanocrystals during the annealing process, as observed in previous studies.[6,38] The results in Figure 6 indicate that long annealing times at high temperatures can be employed to tune the intrinsic properties of VO2 layer when combined with a metal-oxide interlayer.To link the differences in R-T characteristics between samples to possible structural differences, we compared the SEM images of the VO2 on HfO2, Al2O3, Ti3O5, and WOx samples in Figure 6c.
These images, along with the corresponding AFM measurements, reveal similar grain size and surface roughness in all samples with various interlayers, suggesting that the observed R-T differences in Figure 6a might be attributed to variations in the vanadium oxide layer at the interface with the underlying substrate.
To confirm this theory, we investigate the VO2 to HfO2 interface for the sample annealed for 45 minutes at 520 ˚C, as it shows the largest variation in transition temperature compared to the reference sample on SiO2 substrate (Figure 6a, red and black lines, respectively).In Figure 7a  This interplay is a possible cause for the increased IMT (red curve in Figure 6a), bringing more evidence that metal-oxides such as HfO2 can be combined with long annealing times at high temperatures to engineer the crystalline phase-transition of VO2.While this constitutes an interesting finding, the primary focus remains on minimizing variability among insulating-and metallic-state resistances, as illustrated in Figure 3, Figure 4c, and Figure 5c.  Figure 8c shows the R-T characteristics of VO2 annealed for 10 minutes on a HfO2 interlayer and of a reference sample with no interlayer.With this short annealing time, the presence of HfO2 does not influence the hysteretic width or transition temperatures of VO2.More importantly, the variability in resistivities observed on the samples grown directly on SiO2 (reported in Figure 3, Figure 4c, and Figure 5c) is greatly reduced across the VO2 layer when an HfO2 interlayer is present.This leads to the reproducible characteristics presented in the following section.The AFM measurements in Figure 8a show that the average grain size (38 nm) remains small and the surface, smooth (2.4 nm) in the presence of HfO2; a finding also reported in ref [39].
In summary, HfO2 is the material with the most interesting effect on the formation of VO2.It preserves its fundamental switching properties in the case of short annealing times (10 minutes) while achieving high crystalline quality across the entire layer, even without using the optimized RTA annealing technique.In the next section, we perform an XRR and TEM study to explore the reasons why incorporating HfO2, along with a very thin SiO2 layer, reduces variability, and thus constitutes the way forward to successfully attain the level of uniformity required to couple VO2based oscillators.4. For the as-deposited sample D, vanadium oxide does not grow as a single uniform layer.A VOx layer with a density of 3.9 g cm -3 , consistent with amorphous vanadium oxide densities, is followed by a second layer with an even lower density of 3.2 g cm -3 directly in contact with the SiO2.[40] Following the annealing of sample D, the XRR analysis of sample E shows that, while it crystallized into grains (as evidenced by the increase in density to 4.6 g cm -3 in the top layer), the unwanted spurious layer persists and grows thicker, with its density slightly increasing from 3.2 g cm -3 (prior to annealing) to 3.9 g cm -3 .[40] This can be attributed to a non-uniform clustering of the material at the VO2/SiO2 interface to form grains of VO2.The lower density layer cannot be visualized sharply when imaging the samples with the local TEM technique shown in Figure 10ac, but it is reflected in several Fast Fourier transform (FFT) plots captured at the interface between the substrate and the VO2 grains (Figure 10e and f).Despite the layer being found in a single orientation crystallization in Figure 10d and g, amorphous material can still be found at the grain boundaries.The XRR measurement, which measures a wider portion of the sample, suggests that the amorphous material at the grain boundaries extends on average across the whole VO2/SiO2 interface.These findings consistently extend to similar samples with intermediate SiO2 thicknesses down to 50 nm, as discussed in SI.The introduction of an HfO2 interlayer between VO2 and SiO2, as in sample F, results in more uniform growth of VO2 grains across the entire film thickness, as

Substrate Thickness Dependence Study
shown by XRR analysis in Table 4.This observation is consistent with previous studies [39,41] suggesting that HfO2 can regulate VO2 crystallinity by promoting the nucleation of grains and reducing boundary defects.Interestingly, in VO2 films grown on ultrathin (≤10 nm) SiO2 layers on Si substrates, no spurious interfacial layers are detected and the structural properties of the crystallized VO2 layer compare well with the sample presenting the HfO2 interlayer.The results are summarized in SI.The cloud-shaped rings around the origins of the FFT plots in e) and f) reveal the presence of leftover amorphous vanadium-oxide material.
The absence of this spurious interfacial layer leads to a low variability between devices, measured in Figure 11c in comparison with those in Figure 11b.In the Raman spectra of Figure 11a, characteristic VO2 peaks are observed on both thin (≤10 nm) or thick (500 nm) SiO2 substrates.However, only devices fabricated on thin SiO2 or with a HfO2 interlayer, without any additional amorphous spurious layers, demonstrate reproducible and uniform electrical properties (see Figure 8c and Figure 11c).This suggests that by biasing the VO2 grains in such devices, a preferential current path will be established from the top to the bottom electrodes, avoiding any interference from the spurious layer, effectively removing variability between devices observed in Figure 3, Figure 4c, Figure 5c, and Figure 11b.
In the crossbar configuration, favored for precisely defining the current path in the device, a thin (≤10 nm) SiO2 is not recommended, as it may result in the electrodes coming into contact with the semiconducting Si substrate after patterning.This can be avoided by using HfO2 as an etch-stop layer.Therefore, the role of the HfO2 interlayer is threefold: 1.It acts as a barrier to avert the formation of this undesired spurious layer, responsible for creating variability among VO2-based crossbar devices, 2. It preserves VO2's structural and phase-transition properties, while 3. acting as an etch-stop layer between the semiconducting Si substrate and the VO2 grains for further processing and ohmic contacts.

VO2 Devices Relaxation Oscillators
The material development leads to these findings: the highest quality of VO2 layer is obtained with a thin SiO2 (≤10 nm)-HfO2 (10 nm)-VO2 stack annealed under the conditions described in Table 2.The reproducibility of these devices makes them the best choice to build relaxation oscillators.The crossbar oscillators are designed with 50 nm thick Ti/Pt top and bottom electrodes.
The active area has dimensions between 100 nm × 100 nm × 60 nm and 300 nm × 300 nm × 60 nm.HfO2 (10 nm) stack annealed under the conditions highlighted in Table 2. Figure 11b shows the corresponding I-V characteristics where VDD was swept from 0 V to 10 V, with a series resistor of 40 kΩ connected to the bottom electrode, and no external load capacitor.When the voltage across each device reaches their respective insulator-to-metal transition point, i.e. when the material's temperature has reached 68 ˚C, the current and the conductivity increase abruptly.We can conclude from our measurements in Figure 12 and in SI that the insulator-and metallic-state resistivities are nearly identical for all devices, with transition voltages VIMT varying by less than 7%.These results confirm the mitigated variability between the oscillators achieved with our material and stack optimization.with our annealing technique and material stack optimization investigations.[42] In Figure 12c, the repeatability in the R-T and I-V measurements shown in Figure 11a and b is demonstrated across several cycles of seven samples, revealing their similar oscillatory behaviors.The oscillation amplitude varies by less than 3.5% over 250 cycles within the same device, while the transition voltages show variations of up to 10% from one device to another.This degree of variability is at the boundaries of tolerance required for device coupling and enabling ONN-based computing.[42] In order to effectively realize an ONN, we opt for crossbars with device-to-device variability below 5%, as they tend to synchronize more easily.Designing such a network was not feasible with the characteristics of the devices shown in Figure 3.In the case of high variability among the oscillators, they would either ignore each other in the case of weak coupling and not lock in frequency, or exchange too much current when coupled strongly, often leading to oscillation failure or the hard breakdown of one of the devices.An example is shown in SI.

DISCUSSION
Here, we discuss the role of interlayers and grain boundaries on the electrical performance of the oscillators.The TEM micrographs and EDS scan shown in Figure 10 reveal a possible interdiffusion mechanism occurring between the interlayer and the VO2 at temperatures above 400 ˚C.Among the tested interlayers, WOx is the only one with a higher Free Energy of Formation than vanadium-oxide at the annealing temperatures.[43,44] In this case, VO2 acts as a scavenging material, absorbing oxygen both from the WOx interlayer and the chamber.This interaction with a dopant or a substrate material can promote the formation of undesirable VO2 crystal states (e.g.VO2(B)) or the stabilization of uncontrolled oxidation states, leading to the degradation or suppression of the film's transition temperature (see Figure 6a).Similar results were also observed in ref [22].Interestingly, the same failure mechanism observed with the WOx interlayer is not seen for samples with HfO2 or Al2O3 interlayers under long annealing (see Figure 6).According to refs [28,29,30,33], treating the film with such conditions have stabilized the films in the V2O5 stoichiometry.Instead, we observed that doping VO2 with HfO2 or Al2O3 interlayers combined with long annealing produces phase-change materials with higher transitions temperatures.Our results presented in Figure 6 indicate that a broad range of substrates with various thicknesses can be harnessed to engineer the IMT in VO2 films.[37] This opens new possibilities for engineering and tuning VO2's transition temperature, particularly for applications requiring a higher thermal budget.However, considering the specific application targeted in this study, the incorporation of interlayers other than HfO2 or the direct growth of VO2 grains on thick SiO2 results in devices with unpredictable oscillation patterns.Due to challenges related to reproducibility, stability, and lack of configurability through external parameters (Rs and Cext), extensive measurement on these devices becomes impractical, and coupling is impossible.See SI.
We now discuss the role of oxygen in annealing stable VO2.We observed a significant reduction in sample-to-sample variability by reducing the SiO2 thickness (Figure 11c), which points to a potential oxygen diffusion mechanism between the substrate and the vanadium oxide layer during the early stages of the annealing step.[45] This diffusion process could contribute to the stabilization into the VO2 oxidation state and effectively prevent excess oxygen from forming higher oxidation states such as V2O5 crystals.In fact, when the vanadium oxide film can lose oxygen through a thin SiO2 layer and the HfO2 interlayer into the Si substrate below, our optimized RTA annealing consistently produces samples of high quality, a finding also reported in ref [28].[46] In the case of a thick SiO2 substrate with no interlayer, the oxygen, unable to diffuse into the Si substrate, may remain at the interface between the VO2 grains and the substrate.This is a meaningful discovery, as we believe that the oxygen excess at the grain boundaries near the VO2/SiO2 interface is responsible for creating the measured spurious layer (see Figure 9 and Table 4) that led to variability between samples (Figure 3, Figure 4c, Figure 5c, and Figure 11b).
Here, we explain this variability by analyzing the impact of an electric field at the nanoscale level.From a device standpoint, applying a forward or backward bias respectively generates or annihilates oxygen vacancies that trigger the heterogeneous nucleation of the phase transition, thus influencing the resistance state of the VO2 film.[20,47] In the case of devices on thick SiO2 substrate, which exhibit more defects and dislocations, the non-uniform diffusion of oxygen during annealing and/or the presence of a disordered layer with higher oxygen density at the interface, (as shown in Table 4), lead to uneven conductance at the grain boundaries of the film.Consequently, biasing VO2 on a thick SiO2 substrate results in non-uniform oxygen vacancies at the grain boundaries, which translates into the varying insulator-and metallic-state resistances (Figure 3, Figure 4c, Figure 5c, and Figure 11b).This effect is exacerbated with our dense polycrystalline layer, as the number of grain boundaries increases inversely with the size of the VO2 grains.This further motivates our choice of a thin SiO2 layer (≤10 nm)-HfO2 (10 nm) stack that effectively reduces variability in the oscillators by avoiding the formation of a spurious layer during ALD deposition (Figure 9a).This allows the current path to follow the grain boundaries of the monolayer VO2 between the top and bottom electrodes without crossing the spurious layer.As a result, the VO2 grown on this optimized stack configuration (Figure 15a) and using our best annealing technique (Table 2) leads to a more uniform generation of oxygen vacancies at the grain boundaries during electrical operation.

CONCLUSIONS
The realization of a large-scale network comprising several VO2-based oscillators has been hindered by the challenging stabilization of VO2 oxidation state, typically introducing granularities and rough morphology.This has led to degraded electrical performance and significant variability between devices, generally limiting the coupling to only two devices.To achieve the required device reliability for a neuro-inspired circuit, we investigated the role of annealing parameters using three different methods post-ALD deposition of the vanadium oxide film.Our goal was to obtain a high-quality VO2 layer with low surface roughness, densely positioned small grains, and highly reproducible current-voltage (I-V) and hysteretic R-T characteristics.
To achieve this level of quality, we employed a rapid thermal annealing technique capable of delivering a quick and uniform heat distribution across the entire vanadium oxide layer.Our findings revealed that device variability was attributed to the formation of an amorphous spurious vanadium oxide layer at the VOx/SiO2 interface when SiO2 was thick (>10 nm).This layer significantly affected the generation of oxygen vacancies during device operation, leading to an uncontrolled current path within the cross-section area of our crossbar VO2-based oscillators.
Furthermore, we studied the role of different metal-oxide interlayers placed between the Si/SiO2 substrate and the VO2.By engineering a stack that included a HfO2 interlayer, we obtained a sharper interface, resulting in mitigated device variability.By combining our highly reproducible annealing treatment with our optimized epitaxial stack SiO2 (≤10 nm) -HfO2 (10 nm) underneath the vanadium-oxide layer, we achieved excellent results, with up to 7 VO2-based oscillators simultaneously contacted on a CMOS medium.These oscillators all oscillated at precisely the same frequency with very similar voltage amplitudes between 0.3 V and 2 V.This level of uniformity and ideal electrical performance meets the requirements for successful device coupling and the realization of an oscillating neural network.Our network of VO2-based oscillators presents an attractive and scalable computing unit for hardware accelerators, offering new computational paradigms for AI applications in optimization problems and pattern recognition, thanks to its highperformance switching properties and CMOS compatibility.[5,7,11]

Figure 1 .
Figure 1.a) Schematic representation of a planar VO2 device with a preferential current path in

Figure 2 .
Figure 2. AFM measurements of an STA treated VO2 film on a 500 nm thermal SiO2 substrate

Figure 4 .
Figure 4. a) Raman spectra of vanadium-oxide samples grown on 500 nm thermal SiO2 pre-heated

Figure 4c shows 4 -
Figure4cshows 4-probe measurements performed on samples with the highest crystallized

Figure 5 .
Figure 5. a) AFM imaging and b) Raman spectroscopy of the VO2 sample RTA annealed with the

Figure 6 .
Figure 6.a) Normalized Resistivity versus temperature and b) Raman spectra for VO2 samples and b, the transmission electron microscope (TEM) micrograph and energy dispersive spectroscopy (EDS) scans measured on the sample with the HfO2 interlayer highlight the formation of a thin layer at the VO2/HfO2 interface of roughly 8 nm, where both Hafnium and Vanadium are present.

Figure 7 .
Figure 7. a) TEM image and b) EDS composition analysis at the interfaces of a sample with 500

Figure 8 .
Figure 8. a) AFM measurement of an STA treated VO2 film on a 500 nm thermal SiO2 substrate

Figure 9a and b
Figure 9a and b show the XRR patterns of samples D and E characterized by a vanadium oxide

Figure 9 .
Figure 9. XRR patterns characterized by a vanadium oxide layer deposited on 500 nm SiO2 a)

Figure 10 .
Figure 10.a) TEM image of a crossbar device with VO2 grains.Grains grow directly b) on the

Figure 11 .
Figure 11.a) Raman spectra for STA treated VO2 samples on SiO2 substrate layer grown thermally

Figure 12 .
Figure 12. a) Resistivity-Temperature characteristics of VO2 crossbar devices grown on a thin

Figure 12e shows the
Figure12eshows the circuit connections made to realize VO2-based oscillators, including a

Table 1 .
VO2 grains statistics of the samples measured in Figure2.Data analysis performed with Gwyddion (software version 2.59).

Table 2 .
Tested Rapid Thermal Annealing conditions tested to produce smooth granular VO2 film on a Si/SiO2 platform.The best reproducible results are observed for the conditions: Temp: 470 °C, O2 pressure: 5 Pa, Annealing time: 10 min.

Table 4 .
XRR fit analysis for stacks D, E, and F.