Spatially-Resolved Thermometry of Filamentary Nanoscale Hot Spots in TiO2 Resistive Random Access Memories to Address Device Variability

Resistive random access memories (RRAM), based on the formation and rupture of conductive nanoscale filaments, have attracted increased attention for application in neuromorphic and in-memory computing. However, this technology is, in part, limited by its variability, which originates from the stochastic formation and extreme heating of its nanoscale filaments. In this study, we used scanning thermal microscopy (SThM) to assess the effect of filament-induced heat spreading on the surface of metal oxide RRAMs with different device designs. We evaluate the variability of TiO2 RRAM devices with area sizes of 2 × 2 and 5 × 5 μm2. Electrical characterization shows that the variability indicated by the standard deviation of the forming voltage is ∼2 times larger for 5 × 5 μm2 devices than for the 2 × 2 μm2 ones. Further knowledge on the reason for this variability is gained through the SThM thermal maps. These maps show that for 2 × 2 μm2 devices the formation of one filament, i.e., hot spot at the device surface, happens reliably at the same location, while the filament location varies for the 5 × 5 μm2 devices. The thermal information, combined with the electrical, interfacial, and geometric characteristics of the device, provides additional insights into the operation and variability of RRAMs. This work suggests thermal engineering and characterization routes to optimize the efficiency and reliability of these devices.


S1 Fabrication of the samples
We fabricated our sample structure on top of a 300 nm SiO2/Si substrate.We deposited 30 nm of Au as the bottom electrode on top of a 10 nm thick adhesion layer by means of e-beam evaporation.Then, we deposited the 10 nm TiO2 active layer by means of atomic layer deposition (ALD) and 10 nm Ti through e-beam evaporation.After that, we deposited 30 nm Au top electrode by means of ebeam evaporation.For the purpose of electrical isolation, we capped the whole structure with a 10 nm thin Al2O3 capping layer.The details of the device layers are illustrated in Figure S1 (a).We arranged the devices in a cross-point structure with an active area size of (b) 2x2 and (c) 5x5 µm 2 .The contact pad size is 100x100 µm 2 in both cases.

S2. Electrical characterization in RRAM
For the electrical switching process of our resistive random access memory (RRAM) devices we performed electric voltage sweeps using a semiconductor parameter analyzer (SPA).Before forming the filament, we used an initial current compliance of Icc = 1 µA, in order to decrease the severity of overshooting effects.However typically we required to use higher compliances in order to form the filament completely.The forming voltage Vforming in between devices varied usually in the range of 0.5 to 2 V having a higher magnitude than the subsequent set voltage which is in line with observations in the literature. 1 After the forming process we reset the device by applying a reversed bias with a higher Icc than in the last set or forming process.To ensure the cyclability of the devices we set and reset them for at least 10 cycles before we checked them with the scanning thermal microscope (SThM).
Figure S2 (a,b) show two examples of one 2x2 µm 2 and one 5x5 µm 2 devices representing ten full cycles.During the cycles we applied a constant current compliance during the set process to achieve consistent set conditions. Figure S2 (c,d) show the electrical resistance in the high resistive state (HRS) and the low resistive state (LRS) for two devices with a cross-point area of (c) 2x2 µm 2 and (d) 5x5 µm 2 during 50 full cycles.The HRS and LRS values were read at 0.07 V before and after the switching in the set process.The results support that our devices are capable of switching for more than 50 cycles.

S3. Device-to-device (D2D) and cycle-to-cycle (C2C) variability
One of the major limitations in RRAM devices is connected with the variability of the I-V characteristics.Figure S3 (a-f) show I-V cycles in six investigated 2x2 µm 2 devices which we investigated in-operando.In all the six devices we observed a relative stable cycle-to-cycle (C2C) behavior, i.e., the curves of the various cycles matched within the same device.In all the devices we can see a clear trend going from a small slope in the I-V curves to a sharp increase at a higher voltage magnitude during the set process.However, these graphs distinguish through the steepness of their slope.
Figure S3 (g-l) show I-V cycles in six investigated 5x5 µm 2 devices which we investigated inoperando.On contrary to the 2x2 µm 2 we saw an increased C2C and D2D variability illustrated due to a decay of the current (g), variation of the set voltage and strong reset (h), change of the set slope (i) or by multiple set steps (l).On average we observed a standard deviation of the forming voltage Figure S3.Measured I-V cycle characteristics for RRAM devices with a Crosspoint area of (a-f) 2x2 µm 2 and (g-l) 5x5 µm 2 for six devices each.The blue and the red graphs symbolize the set and reset processes, respectively.The black arrows present the direction of the set and the reset process.
of 10 % for the 2x2 µm 2 and 19 % for the 5x5 µm 2 devices showing an increased C2C variability in the 5x5 µm 2 devices.
In conclusion, we saw a significant difference in the stability of the I-V cycle behavior when comparing the 2x2 and the 5x5 µm 2 devices.The distinct types of set curves of the 5x5 µm 2 devices indicate a non-uniform formation step of the conductive filaments.These results demonstrate the need of thermal characterization of our devices in order to identify the source of the variability in these devices.For the calibration of our scanning thermal microscope (SThM) probes, we used an approach as previously applied in literature. 2,3Figure S4 (a) illustrates the calibration approach which we followed for the SThM thermo-resistive probes used in this study.For the calibration sample, we deposited four 2nm Ti/50 nm Pd heater pads by means of optical lithography and e-beam evaporation.Subsequently we fabricated 2 nm Ti/30 nm Pd metal lines of different widths (50-750 nm) through ebeam lithography and evaporation.To electrically isolate the sample from the probe we further deposited a thin 10 nm Al2O3 film on top of the calibration sample using pulsed laser deposition (PLD). 3 started with electrically characterizing the different Pd metal lines by applying four-point probe measurements.Therefore, we applied an electric current through the outer heater pads while measuring the voltage drop along the Pd lines through the inner pads, as shown in Figure S4 (a) by means of a semiconductor parameter analyzer (SPA).Pd is a thermo-resistive material meaning its electrical resistance Rline is temperature dependent and its value at a temperature T described as follows:

S4
By means of equation S1 we can estimate the temperature at Rline of the line by knowing its temperature coefficient of resistance (TCR) and a reference value Rline,0 at the temperature T0.The TCR is a material specific characteristic which we determined by measuring the resistance vs power curves of the lines for different temperatures (room temperature to 340 K) using a temperature adjustable sample stage.Using the TCR we calculated the temperature increase of the line as a function of the power applied to it.A more detailed description of the electrical characterization process can be found in our previous paper. 3 the second step we scanned the non-heated and heated metal lines with our SThM probes.In operation the SThM probes were connected to a Wheatstone bridge as illustrated in Figure S4 (b).This electrical network consists of two fixed resistances R (1 kΩ), one adjustable resistance Rpot and the resistance of the probe Rprobe.In operation we applied a voltage across the bridge Vsource of 0.5 V resulting in a power of 19 µW.In contact with the sample, we nullified the signal measured along the line VSThM.Our SThM probes consists of a thin Pd resistor on top a SiN film.Thus, the resistance of the thermoresistive Pd probe correlates with the temperature of the probe.By that we measured differences in the surface temperature ΔT due to changes in VSThM during the scan.
During the fabrication step we used the nullified SThM probe to estimate the temperature rise of the heated metal lines.As an example, Figure S4 (c) shows the topography map of a 500 nm wide line.
In Figure S4 (d) and (e) we plotted two thermal maps obtained on the same line in a (d) non-heated (ΔTline = 0 K) and (e) heated case (ΔTline ≈ 10 K).In this case we still observed some minor signal variation in the non-heated case at the line, which are originated by differences in the tip to surface interaction.Therefore, we estimated the signal difference at the heated line ΔVSThM,line (ΔTline) in comparison with ΔVSThM,line (0) at a reference non-heated map to minimize the impact of topographical artefacts.Additionally, we determined the mean value of ΔVSThM,line along the line in order to reduce variation of the scan.
By following this principle, we estimated ΔVSThM,line, measured with the SThM as a function of ΔTline characterized electrically.Figure S4 (f) shows the ΔVSThM,line vs ΔTline graph for the 500 nm wide Pd line obtained for five different heating configurations.As in previous studies, we observed a linear correlation of the SThM signal at the line and its temperature. 2,3Hence, we calculated the calibration factor (CaF) of our SThM probes as a function of the line width by determining the slope of each ΔVSThM,line vs ΔTline graph.
Figure S4 (g) shows the CaF vs line width graphs for the three tips used for the measurements of this study.All of the three graphs show the characteristic saturation behavior of CaF for higher line widths as observed before. 2,3When comparing the three graphs we observed different saturation values as also differences in the cut off line width of the graphs.Therefore, it is essential to calibrate each probe in order to maximize the accuracy of the calibration process.Each of the three probes are from different patches and therefore can vary in their characteristics.
For example, we obtained that the calibration factor for tip 2 saturated at a value of CaF = 7.1 ± 0.5 mV/K for surface temperature features above 680 nm.This CaF was used to calculate the temperatures of most of the hot spots observed experimentally, e.g., for the results in Figure 1 of the main manuscript where the full widths at half maximum (FWHM) of the hot spots exceed the cut-off line width.The electrical signal in mV measured with SThM (ΔVSThM) was calculated as the difference between the heated maps and a reference map at zero power.Overall, ΔVSThM can be converted to the temperature increase (∆) in K as follows: At this point it is worth noting that a careful calibration allows this approach to be extended for the study of even smaller devices.As can be seen from the graphs in Figure S4 (g) we observe a drop in the calibration factor at a certain cut-off line width.This is related to the disc-shaped thermal exchange area between the tip and the sample.When the size of the device heating feature lies below the size of the cut-off line width, the heat exchange between the tip and device is truncated and the calibration factor decreases.However, beyond the cut-off, one should notice that the conversion factor drastically reduces.For devices or hot spots below ~50 nm determining an accurate value could be very challenging and might also involve considerable uncertainty.Therefore, additional strategies to alleviate it could be to measure in vacuum, i.e. to reduce the thermal exchange radius between the tip apex and the surface by removing heat transfer mechanisms like convection or water meniscus, 4 or to improve the signal processing techniques, like the deconvolution approach described by Deshmukh et al. 2

S5. Steady state SThM characterization
We repeated the procedure described in the main text for the thermal characterization of the hot spot for all our RRAM devices.Figure S5 (a) shows the topography map of a RRAM device with a crosspoint area of 2x2 µm 2 obtained with a SThM probe.At this point it is worth mentioning that we observed a variation in the topography roughness of our devices as can be seen when comparing the topography in Figure S5 (a) with the one in Figure 2 (a).However, we want to clarify that the position of the hot spots is localized independent from any wrinkles or surface roughness variations.Therefore, we estimate that the formation of the filament is not triggered by topographical artifacts.Figure S5 (b) shows a 3D representation of two thermal maps obtained for the same 2x2 µm 2 device.
Here we present two maps obtained for a non-heated case (P = 0 mW) and for a heated case (P = 0.57 mW).In the heated case we observed a hot spot induced by current passing through the conductive filament.Figure S5 (c) shows multiple temperature maps obtained on the same device after the device is set (blue dashed rectangular) vs reset (red dashed rectangular).In the set state we can see that the hot spot is localized at the same location and its temperature scales up as the power applied to the device increases (same set state, i.e., no cycling between images).We observed that the maximum hot spot temperature increased from 13 K at 0.21 mW to 18 K at 0.4 mW.After resetting the device, we carried out temperature maps for similar powers as in the set case but with the reversed polarity (see Figure S5 (d)).
In comparison with the results in Figure 2 of the main text the differences in between the set and reset state are relatively low.By looking at the thermal maps during the reset state we still observed an elevated heating at the initial hot spot position but less localized than in the set state.So, as also observed with a weaker effect in the 5x5 µm 2 device, the filament breakdown is not fully complete.
When comparing the set I-V curves of the two devices in Figure 1 (b) we can see that the difference before and after the set is comparable low in the 2x2 µm 2 device.Therefore, the smaller difference in between set and reset heating might originate from a less complete breakdown.

S6. COMSOL model for the characterization of the filament temperature
In order to confirm the experimentally obtained temperatures and to estimate the filament temperature we employed an electrothermal finite element method (FEM) model in COMSOL Multiphysics.We built our model on base considering the same boundary and heat flux conditions of the results obtained in a study by Deshmukh et al. 2 By means of that we replicated the structure of the 5x5 µm 2 device which results are shown in Figure 2 of the main text.Therefore, we used a 2.5 x 2.5 x 20 µm model with a cylindrical symmetry around the central axis as shown in Figure S6.We adjusted the geometry to mimic our current Si/SiO2/Ti/Au/TiO2/Ti/Au/Al2O3 as described in Section S1.As can be seen in Figure S6 we shaped the Filament on the left edge of the TiO2 using an hourglass structure, as this approach showed the best fitting.
In accordance with previous studies we estimated the thermal contact conductance in between the oxide and the top electrode GTiO2-Ti/Au using the full width at half maximum (FWHM) of our SThM scans of the hot spot as follows. 2 The thermal healing length of the hot spot is where kth,TE and tTE are the thermal conductivity and thickness of the top electrode, respectively.In our RRAM devices we can estimate FWHM ≈ 2LH given the small size of our filaments (dCF ≪ LH).Therefore, we estimated the FWHM of the hot spot temperature peaks for the three images investigated.The thickness and thermal conductivity of the top electrode as also the remaining material characteristics are assembled from the literature and the COMSOL library.Table S1 shows the fixed material and contact parameters used for this FEM simulation.It is worth noting that one can reduce the heat spreading from the filament to the surface by reducing the thickness of the top electrode.On the other hand, it is also important to take into account that another key restricting factor for this heat spreading is the thermal interface between the filament and the top electrode, as discussed by Deshmukh et al.For the characterization of the Joule heating, we adjusted the top electrode as a current source with an applied current equal to the values measured during the SThM mapping Imeasured.The bottom electrode acts as the electrical ground at which the potential is 0 V.  Table S2 shows the sweep parameter and the results of the COMSOL simulation which presented the best fit with the experimental results.Figure S7 (a) shows the corresponding simulated temperature profiles at the surface of the RRAM devices for the best fitting parameters of the three investigated SThM maps.In general, we observed a good fit of the FWHM and the potential drop in between experiments and simulation.We obtained slightly higher (10-15 %) values for the maximum temperature at the surface ΔTmax,surface from the simulation in comparison with the experimental results.Considering the error of our calibration factor and the other material parameters this temperature difference is in a reasonable range.Figure 7 (b) shows a fit of the experimentally obtained surface temperature profile (straight line) with the profile obtained from the COMSOL simulation (dashed line) for Imeasured = 280 µA.In this graph we normalized the temperature in order to take the temperature difference into account.

Table S1. Model
It is worth noting that heat dissipation depends on the device area.For wider area devices, electrodes can carry away heat more easily which leads to a decrease in the maximum surface temperature under identical thermal interfaces, filament size and electrode thermal conductivity.
In comparison to the results of Deshmukh et al. 2 we estimated a higher kth,filament, which can be originated from the difference in the material characteristics and higher thickness of the titanium oxide layer and thus the filament.Additionally, our simulations results indicate a relatively high filament diameter of around 41-44 nm, which is connected to the relatively high electric currents applied to the device.Finally, the maximum temperature increases of the filaments ΔTmax,filament is estimated to be in between 172 and 245 K, correlating with the power applied to the device.

S8. Hot spot location with cycling
For the characterization of the hot spot moveability, we repeated the steady state measurements of the devices after I-V cycling, Figure S8   S-16

S9. Characterization of the line resistance
The I-V curves we measured are the extrinsic I-V characteristics.The voltage drops not only on the memory cell but also on the series resistance, which includes the line resistance of the electrodes, the contact resistance of the probes and pads and other contributions from the device stack, as for example the vertical conduction in the electrodes.By subtracting the voltage drop over the series resistance, the intrinsic I-V characteristics can be obtained. 5Fantini et al. 5 reported that the intrinsic I-V behavior of resistive switching devices shows that the set is triggered at a certain threshold voltage and is followed by a snapback to a voltage value where the differential resistance dV/dI is approximately 0, i.e. a vertical line in the I-V characteristics.Taking this into account, the series resistance can be estimated by calculating the series resistance value that transforms the extrinsic I-V curve into the intrinsic one, exhibiting the vertical transition behavior.
We extracted the approximate value of the series resistance for 2x2 µm 2 and 5x5 µm 2 devices from the extrinsic I-V curves in Figure S9 based on the abovementioned method.During the set process, after the abrupt jump at the threshold voltage, the current shows a linear dependence with the voltage before reaching the compliance.This is caused by the series resistance.Its value can be estimated from the slope of the curve in the linear region (the red line in Figure S9).The estimated series resistance of 2x2 µm 2 and 5x5 µm 2 devices is 1 kΩ and 300 Ω, respectively.The contact resistance between the probe and the electrode is similar due to the same measurement method, therefore the line resistance and the other electrode contributions should be the dominating cause of the difference in the series resistance.To be noted, these values are not for the pristine devices, but for the devices that switched for at least 20 cycles.
Additionally, we measured the line resistance of both the top and bottom electrode for various pristine devices.Figure S9 (c) shows the measured combined line resistance Rline of the bottom and top electrode as a function of the line width.At a higher line width, we observed a relatively constant value for Rline.In these cases, we expect the contact resistance between the measuring probes and the electrode surface to be the dominating factor of Rline.For the relevant line widths (2 µm and 5 µm) we measured an increment in the line resistance based on the decreased line area.By subtracting the estimate of the contact resistance, we obtained a Rline of 123 Ω and 308 Ω for the 5x5 and 2x2 µm 2 devices, respectively.The difference from the measured line resistance and the estimated series resistance stems from the contact resistance between the lines and the active area and possible other resistances which are not included in the line resistance.

S10. STEM characterization of the layer structure in pristine and cycled devices
In order to investigate the impact of the electrical forming and cycling of the device on the material structure we employed high-angle annular dark field scanning transmission microscopy (HAADF-STEM) with an energy-dispersive X-ray spectroscopy (EDX) detector.First, we cut the samples out of the cross-point area of our RRAM devices using the focused ion beam (FIB) technique.Second, we employed transmission electron microscopy (TEM) in the cross-section direction for the characterization and evaluation of the device layer structure.By means of that we aimed to evaluate the chemical composition and distribution of the three main elements i.e., Au, Ti and O which are the building blocks for the metal/insulator/metal (Au/TiO2/Ti/Au) structure of our RRAM devices.devices before and after electrical cycling.On the one hand they observed a continuous Ti and O signal in the pristine device.On the other hand, the measurements revealed a drop in the Ti and O signal in between the TiO2 layer and the Pt top electrode in the formed devices referred to delamination.This delamination effect was claimed to be originated from the development of O2 gas during the formation of the conductive filament.
From our results we cannot make a solid conclusion about the impact of the layer delamination observed in our devices on their I-V or heating variation during cycling.However, we should emphasize that this effect might lead to a limitation in the electrical performance and variability of RRAM devices.Presumably, the delamination should lead to a reduction of the effective cross-point area of the devices.  .

Figure
Figure S1.(a) Schematic of the fabrication procedure of the investigated samples.The thickness and fabrication method of each layer is indicated in the drawing.(b,c) Schematic of the cross-point structure for the (b) 2x2 µm 2 devices and (c) 5x5 µm 2 devices.

Figure S2 .
Figure S2.(a,b) Electric current as a function of the electrical voltage during the set (blue) and reset process (red) for 10 cycles in a (a) 2x2 µm 2 and in a (b) 5x5 µm 2 device.The grey dashed curves show the forming process.(c,d) Electrical resistance in the high resistive state (HRS) in red and the low resistive state (LRS) in blue of the RRAM devices vs number of cycles for a crosspoint area size of (c) 2x2 µm 2 and (d) 5x5 µm 2 .
Figure S4.(a) Calibration sample and measurement configurations.Scanning thermal microscope (SThM) probe scans over heated palladium (Pd) lines of different widths (50-750 nm) connected to four Pd heater pads each.The thermoresistive metal lines are characterized electrically by four-Point probe measurements to determine the heating temperature of the lines.(b) Design of the Wheatstone bridge connected to the SThM probe during the scan.A constant bridge voltage Vsource is applied during the measurement and the change in temperature is read due to changes in the bridge signal VSThM.(c) Topography image of a 500 nm wide Pd line.(d,e) SThM thermal maps of the same line obtained with a temperature increase of the line ΔTline of (d) 0 K (non-heated) and (e) 10 K (heated).(Scale bar is equal to 500 nm).(f) SThM thermal Signal of a 500 nm wide Pd line ΔVSThM,line as a function of ΔTline.(g) SThM Calibration Factor (CaF) estimated by means of the slope of the ΔVSThM,line vs ΔTline graphs as a function of the line width for the three different tips we used for the thermal characterization of our devices.

Figure S5 .
Figure S5.(a) Topographic image of a device with an area of 2x2 µm 2 (scale bar 200 nm) (b) 3D SThM temperature VSThM (z-axis) map obtained for the device shown in (a) when applying a power of P = 0.57 mW and under no power applied (P = 0).The difference in SThM signal between heated vs non-heated case was converted into a temperature change by using a calibration factor of CaF = 7.1 mV/K.(c) and (d) SThM temperature maps for four different power magnitudes after (c) setting the device at a positive polarity (blue dashed rectangle) and after (d) resetting the device at the reverse negative polarity (red dashed rectangle).(scale bar 200 nm).

Figure S6 .
Figure S6.Finite element method (FEM) model geometry of the applied model for the characterization of the hot spot temperature.The model has a cylindrical symmetry around the central axis with a structure equivalent to the experimental TiO2 RRAM devices with an hourglass shaped filament.An electric current Imeasured is applied from the top electrode to the bottom electrode.

2 Figure
Figure S7.(a) Simulated temperature increase along the surface ΔTsurface of the 5x5 µm 2 RRAM device structure for three different currents Imeasured (280 µA in blue, 360 µA in green and 370 µA in red).(b) Normalized simulated (dashed line) and measured SThM (straight line) temperature increase ΔTsurface/ΔTsurface,max along the surface of the RRAM device for an electric current Imeasured of 280 µA.
(a) and(b) show two examples of heat dissipation in set devices at different stages of cyclability for a (a) 2x2 µm 2 and (b) 5x5 µm 2 device.In addition to the maps of Figure4of the main text, we observed a static hot spot position in the 2x2 µm 2 device while a shift of the hot spot occurred in the 5x5 µm 2 device.

Figure S8 .
Figure S8.3D surface temperature maps (z-axis) plotted over the 2D topography (x and y axis) of devices with an area of (a) 2x2 µm 2 and (b) 5x5 µm 2 .The 2D topographic maps at the bottom show the height differences in the scanned area (greyscale bar on the bottom right).The color scheme of the 3D plots shows the temperature increase during the steady state measurements (colored bar on the top right).Power P applied to the devices during the scans in (a) are 0.33 mW/0.32 mW/0.59mW and in (b) are 0.27 mW/0.55 mW/0.47 mW from left to right.

Figure S9 .
Figure S9.(a) and (b) Measured I-V characteristics of the 2x2 µm 2 and 5x5 µm 2 devices, respectively.The red line is the fit of the linear region.(c) Measured line resistance Rline of the bottom and top electrode as a function of the line width of the device.

Figure
FigureS10(a) and (b) show the HAADF and the EDX images obtained from a pristine, i.e., not electrically formed device.Hereby, the HAADF imaging method enables us to clearly the high atomic number Au electrodes.The remaining layers are indicated in FigureS10 (a)according to the device structure.We clearly observed a continuous Ti and O signal along the TiO2/Ti areas in between the electrodes.

Figure
FigureS10 (c) and (d)show the HAADF and the EDX images obtained of an already cycled 5x5 µm 2 device.Similar to the pristine device the EDX image shows a clear Au signal at the position of the electrodes.However, we observed a small but not continuous drop of the Ti and O signal at the transition area in between the TiO2 layer and the bottom electrode.Similar observations have been made by Carta et al.6 in a Pt/TiO2/Pt RRAM device.In their study, they investigated the material structure of their RRAM devices in pristine and in formed state.They performed HAADF-STEM measurements with an EDX detector for the characterization of the

Figure
FigureS11shows two examples of I-V graphs and the corresponding SThM-temperature logger graphs of a 2x2 µm 2 and a 5x5 µm 2 device.FigureS11(a) and (b) show the current vs voltage behavior of the devices during cycling.FigureS11 (c) and (d) show the temperature evolution at the initial hot spot location measured simultaneously during the I-V cycling for 15 and 10 full cycles, respectively.The cycling behavior of the 2x2 µm 2 device remains constant, accompanied by a consistent series of set-reset temperature evolutions in the logger graphs, indicating a static hot spot location.This can also be observed at different current compliances Icc (blue Icc = 0.5 mA vs red Icc = 0.8 mA).However, in the 5x5 µm 2 device we observe a drastic change of the temperature evolution in accordance with the variability of the I-V curves.The device still remains cyclable, but the temperature becomes lower after a certain number of cycles.These observations indicate that a new filament is eventually formed at a different location.This behavior can be extrapolated to more cycles, simply based on the reliability of the device.As we show in supporting information section S2, our devices remain cyclable after 50 switching cycles.

Figure S11 .
Figure S11.(a) and (b) I-V curves for 15 and 10 cycles for 2x2 µm 2 and a 5x5 µm 2 devices, respectively.(c) and (d) logger temperature measured for the different set and reset cycles of the devices shown in (a) and (b), respectively, at same SThM probe location.

Table S2 .
Comparison of the hot spot characteristics of the SThM measurements and the COMSOL Multiphysics simulation for the three investigated scans.Also shown are the corresponding sweep parameters that showed the best fits.