Current-induced electrical self-oscillations across out

Current-induced electrical self-oscillations across out-of-plane threshold switches based on VO2 layers integrated in crossbars geometry A. Beaumont, J. Leroy, J.-C. Orlianges, and A. Crunteanu Citation: Journal of Applied Physics 115, 154502 (2014); doi: 10.1063/1.4871543 View online: http://dx.doi.org/10.1063/1.4871543 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Sharp semiconductor-to-metal transition of VO2 thin films on glass substrates J. Appl. Phys. 114, 244301 (2013); 10.1063/1.4851655 Tuning the properties of VO2 thin films through growth temperature for infrared and terahertz modulation applications J. Appl. Phys. 114, 113509 (2013); 10.1063/1.4821846 Structural, electrical, and terahertz transmission properties of VO2 thin films grown on c-, r-, and m-plane sapphire substrates J. Appl. Phys. 111, 053533 (2012); 10.1063/1.3692391 Geometric confinement effects on the metal-insulator transition temperature and stress relaxation in VO2 thin films grown on silicon J. Appl. Phys. 109, 063512 (2011); 10.1063/1.3556756 Stability of electrical switching properties in vanadium dioxide thin films under multiple thermal cycles across the phase transition boundary J. Appl. Phys. 104, 086105 (2008); 10.1063/1.3000664

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JOURNAL OF APPLIED PHYSICS 115, 154502 (2014)

Current-induced electrical self-oscillations across out-of-plane threshold switches based on VO2 layers integrated in crossbars geometry A. Beaumont,1 J. Leroy,1 J.-C. Orlianges,2 and A. Crunteanu1,a) 1

XLIM Research Institute UMR 7252, CNRS/University of Limoges, 123 avenue Albert Thomas, 87060 Limoges, France 2 SPCTS UMR 7513, CNRS/University of Limoges, 12 rue Atlantis, 87068 Limoges, France

(Received 3 March 2014; accepted 4 April 2014; published online 15 April 2014) Electrically activated metal-insulator transition (MIT) in vanadium dioxide (VO2) is widely studied from both fundamental and practical points of view. It can give valuable insights on the currently controversial phase transition mechanism in this material and, at the same time, allows the development of original MIT-based electronic devices. Electrically triggered insulator-metal transitions are demonstrated in novel out-of-plane, metal-oxide-metal type devices integrating a VO2 thin film, upon applying moderate threshold voltages. It is shown that the current-voltage characteristics of such devices present clear negative differential resistance effects supporting the onset of continuous, current-driven phase oscillations across the vanadium dioxide material. The frequencies of these self-sustained oscillations are ranging from 90 to 300 kHz and they may be tuned by adjusting the injected current. A phenomenological model of the device and its command circuit is developed, and allows to extract the analytical expressions of the oscillation frequencies and to simulate the electrical oscillatory phenomena developed across the VO2 material. Such out-of-plane devices may further contribute to the general understanding of the driving mechanism in metal-insulator transition materials and devices, a prerequisite to promising applications in high speed/high frequency networks C 2014 AIP Publishing LLC. of oscillatory or resistive memories circuits. V [http://dx.doi.org/10.1063/1.4871543] I. INTRODUCTION

Vanadium dioxide (VO2) is a strongly electron-correlated material receiving a significant fundamental research interest over the last decades due to its peculiar and rich electrooptical non-linear properties associated with its reversible temperature-driven insulator-to-metal transition (commonly referred as MIT) occurring at moderate temperatures (around 340 K).1–4 This first-order transition induces abrupt changes in the material’s electrical, optical, and mechanical properties and can be easily triggered by several external stimuli (temperature, electrical, and optical signals or stress).5–9 The physics underlying the MIT in VO2 is still controversial, opposing a temperature-driven mechanism related to electron–phonon interactions (structural Peierls transitions—SPT)4,9 to a pure electronic one due to electron-electron correlations (Mott transitions).2,7,8,10,11 The properties of VO2 have also inspired original applications such as fast electronic switches,6,7,12,13 non-volatile memories,14 tunable and memory metamaterials,15 or voltage controlled oscillators.16–20 The electrically driven metal-insulator transition in VO2 (hereafter named as E-MIT and triggered either by current injection in two-terminal devices or by biasing them with a voltage) provides a high magnitude reversible resistive switching (103–104 changes in device resistivity). As is the case with other oxide compounds,21,22 E-MIT can be described as a threshold switching, for which the material resistance is dramatically decreasing above an applied a)

Author to whom correspondence should be addressed. Electronic mail: [email protected]

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electrical bias threshold.23 The term accounts also for the volatility of the resistive switching in MIT materials, as opposed to the non-volatile, permanent effects induced by electrical switching in memristive systems.24 First observations of threshold switching in VO2 bulk materials show that the E-MIT is described by an S-shaped current-voltage characteristic of the devices, characterized by a current controlled negative differential resistance (CC-NDR).25–28 Under a specific electrical excitation, this CC-NDR effect underlies the onset of spontaneous electrical oscillations across two-terminal devices integrating bulk VO2,26–28 with oscillation frequencies in the kHz range. Reported frequencies of 1 MHz in VO2 thin films integrated in planar two-terminal devices16–20 and even 5 MHz in WxV1xO2 nanobeams29 make such devices attractive as voltage or current-controlled oscillators, frequency modulators, or inverters in electronic circuits. However, two-terminal planar VO2 oscillators are presenting relatively high MIT voltage thresholds (in the order of tens of volts) and their integration in dense electronic circuit designs is challenging. Out-of-plane metal-VO2-metal devices in crossbars configuration offer a smaller footprint and are likely to provide a higher degree of circuit integration. At the same time, given the reduced distance between the metallic electrodes (equal to the thickness of the VO2 layer) the E-MIT in such devices can be triggered at moderately low voltages.13 Still, the fabrication of metal-VO2-metal structures is challenging since the material properties (MIT temperature and magnitude, stress, composition) are largely affected by the underlying layer30 and until now, no report was available on electrical self-oscillations in out-of-plane devices integrating the VO2 material.

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Here, we report the observation of electrically triggered insulator-metal transition with moderate applied voltages and the current-driven self-sustained phase oscillations in out-of-plane, metal-oxide-metal type (MOM) micrometersize devices integrating a VO2 thin film. Electrically tunable frequencies ranging from 90 to 300 kHz were obtained and the switching dynamics of the devices was studied in the light of an analytical model. II. EXPERIMENTAL DETAILS

In order to characterize the out-of-plane resistive switching phenomena in VO2, we fabricated MOM devices in the crossbars configuration shown in Figure 1(a). A first 70-nm thick metallic bottom electrode (BE or bit lines made of Ti/Au/Ti—10/50/10 nm) was fabricated on a c-cut sapphire substrate, followed by the deposition and the patterning of a 130-nm thick VO2 layer.31 Finally, a crossing 150-nm thick metallic top electrode (TE or word lines, Ti/Au—10/140 nm) was patterned perpendicularly to the bottom electrode using a lift-off process. The lateral dimensions of the individual VO2-based MOM devices are thus defined by the respective widths of the bottom and top electrodes. We investigated devices having square shapes (equal lengths and widths), with overall dimensions of 9 9 lm2, 5 5 lm2, and 3 3 lm2, respectively. A scanning electron microscopy image of typical 3 3 lm2 fabricated devices is presented in Figure 1(b). The current–voltage (I–V) characteristics of the devices were recorded by introducing them into a simple electrical circuit containing a series resistance (RS ¼ 50 X), and a source meter (Keithley 2612A) operating in both voltage and current modes.32 III. RESULTS AND DISCUSSIONS A. Quasi-static current-voltage characteristics

The resistance versus temperature curve of a typical 9 9 lm2 crosspoint device (designated from now on as L31) is presented in Figure 2(a). While the device temperature is raised above the insulator-to-metal transition temperature (TMIT 70 C), its low-bias (100 lA) resistance exhibits an abrupt drop and reveals a sharp hysteresis upon cooling and recovery of its initial resistance value. The current-voltage characteristic of the same device (Figure 2(b)) was obtained at room temperature by recording the current through the device while applying a ramping voltage (from 3 V to þ3 V) across the two opposite

FIG. 1. (a) Schematic of the out-of-plane MOM devices integrating a VO2 layer, highlighting a single resistive switch. (b) False-colors scanning electron micrograph of twelve 3 3 lm2 fabricated cross point devices.

FIG. 2. (a) The low-bias resistance of a typical MOM device (9 9 lm2) as the temperature is cycled between 20 C and 100 C indicating a sharp, low-hysteresis temperature-triggered MIT. (b) Current-voltage curve for the same VO2-based structure obtained by recording the current flowing through the device during voltage sweeping between 3 V and þ3 V. The I-V curve shows a symmetrical hysteresis with respect to the origin of the I-V axes and characteristic E-MIT threshold switching at Vth ¼ þ2 V and 2 V.

electrodes. The device exhibits a clear electrically triggered MIT (E-MIT) behavior12,23,31 expressed by sharp current jumps at low threshold voltages (Vth), around 2 V and þ2 V. For applied voltages above Vth, the device switches to a low-resistance state (LRS) corresponding to the metallic VO2 phase and it recovers its initial high-resistance state (HRS) as the applied voltage is swept down (corresponding to the insulating state of the VO2 material). The current-voltage curve is reversible, perfectly reproducible and has a clear hysteretic behavior for both polarities, with the hysteresis loops being pinched at the origin of the I-V axes. The values of the HRS and LRS (of 1930 X and 78 X, respectively) are very similar to the values of the device resistance at 20 C (R20 1850 X) and at 100 C (R100 77 X) during the thermally triggered MIT (Figure 2(a)). Thus, the magnitude of the E-MIT (defined as the ratio between the HRS and LRS) correlates very well with the magnitude of the thermally induced MIT (defined as the R20 /R100 ratio) and, as mentioned elsewhere,13 it offers a solid indication for a bulk-type threshold switching phenomenon during E-MIT in the VO2-based MOM devices. Similar characteristics were recorded on a collection of more than 50 MOM devices having different sizes (large— 9 9 lm2, medium—5 5 lm2, and small—3 3 lm2) for which we studied the dispersion of the parameters defining their electrical threshold switching (critical voltage at MIT and magnitude of the E-MIT). Figure 3(a) shows the


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FIG. 3. Histograms representing the dispersion of (a) the E-MIT voltage threshold values (Vth) and (b) the HRS/LRS resistivity ratios for a collection of more than 50 devices with different dimensions: 19 “large” (9 9 lm2), 18 “medium” (5 5 lm2), and 15 “small”-type devices (3 3 lm2).

FIG. 4. (a) Temperature dependency of the I-V curves for the L31 MOM device (9 9 lm2) illustrating the drop of the threshold voltage with increasing temperature. (b) Arrhenius-type plots (log(r) vs. 1/T) extracted from the curves in Figure 4(a) indicating a bias-dependent energy activated conduction mechanism in the HRS of the MOM device.

distribution of the threshold E-MIT voltage for each type of device, as an indication of their switching variability. It seems that for the small-size MOM devices the dispersion of the MIT activation voltages becomes narrower. Overall, for most of the devices, regardless of their size, the critical electrical field necessary for the E-MIT ranges from 0.6 to 3 107 V/m, in agreement with previous reports on similar out-of-plane or planar, nanometer scale two-terminal devices.12,13 The magnitude of the E-MIT (HRS/LRS resistivity ratios) was calculated for the whole device collection and the results are displayed in Figure 3(b). As observed elsewhere for out-of-plane nano-junctions on germanium or silicon conductive substrates,33 these values are rather low compared with the E-MIT magnitudes values obtained for planar thermal or electrically activated two-terminal devices where ratios ranging from 100 to 10 000 were already reported.8,12,19 Most probably, the bottom Ti/Au/Ti bottom electrode does not offer the best lattice matching for the crystalline VO2 growth and, although the VO2 devices experience clear E-MIT behavior (whose properties are influenced by the different interfaces between the VO2 grains/ nano-domains with the electrodes), the magnitude of the phase transition needs to be further improved, e.g., by optimizing the VO2 deposition parameters for a specific BE-VO2 combination.13,33 One may notice that with decreasing the size of the MOM devices, the E-MIT magnitude dispersion is also decreasing although its median value is slightly increasing. A few devices (one for each size) have a far larger resistivity ratio than the other devices. Additional data concerning the variability of the devices properties are provided in the associated supplementary material.34 The E-MIT threshold voltage of individual MOM devices depends on the ambient temperature. The Vth values are progressively decreasing and tend to zero as the temperature is increased towards the MIT transition temperature (Figure 4(a) for the 9 9 lm2 L31 device). Following the temperature-dependent I-V curves in Figure 4(a), one may differentiate between the HRS of the MOM device, corresponding to the insulating phase of the VO2 constituent (V < Vth) and the low-resistance state, associated with the metallic vanadium dioxide material (for applied voltages > Vth). In-between these two states, one may situate a highly unstable MIT transitive regime which is relevant for the onset of self-sustained oscillations across the device, as will be explained further on.

From the electrical point of view, the LRS state is clearly governed by a linear, Ohm-type conduction over the whole range of temperatures. The HRS region corresponding to insulating VO2 material presents more complex features: for temperatures far below the TMIT and voltages lower than 0.5 V, the current follows a linear dependence on the applied voltage suggesting an ohmic conduction mechanism; however, for intermediate applied voltages (between 0.5 and 2 V) and temperatures below TMIT, the I-V curve follows a clear non-linear conduction mechanism profile.32,33 The I-V curves in Figure 4(a) were used to extract the temperature-dependent conductivity (r) of the L31 device in its HRS state, at four different bias voltages (Figure 4(b)). As reported earlier,3 the conductivity of the VO2 in the insulating state is dominated by the electron conduction and the thermally assisted conductivity can be simply expressed as r ¼ elNc expðEA=kTÞ, where l is the electron mobility, NC is the effective conduction band density of state, EA is the energy separation of the Fermi level from the conduction band edge, k is Boltzmann’s constant, and T is the temperature. The Arrhenius plots (log(r) vs.1/T) presented in Figure 4(b) show a good alignment of data points for each voltage, indicating that an energy activated conduction mechanism is likely to take place in the insulating state of the VO2 and that the activation energies are bias-dependent. The activation energies are declining from 0.205 eV to 0.181 eV as the bias applied to the MOM device is increasing from 0.2 V to 0.8 V. More likely, as the applied bias increases, the current through the device increases accordingly, giving rise to Joule heating and thus decreasing the thermally activated resistivity of insulating VO2. The values of these activation energies are very similar to the ones recorded previously for VO2 thin films deposited on sapphire, germanium, or silicon substrates.3,12,33 The activation bias of the device L31 (Vth 2 V) is slightly superior to the median value for the large MOM devices (1.92 V, Figure 3(a)), but it makes it well suited for the study of the electrical conduction in the insulating phase of the VO2. Among the large-size devices, the L11 device has the lowest MIT-activation threshold (Vth 0.8 V), a low bias resistivity of 0.94 X m, and one of the highest resistivity ratios among the collection of investigated MOM devices. In Figure 5(a), we compared the I-V characteristics (measured by sweeping the applied voltage) of two large devices (9 9 lm2), namely L31 and L11. A sensibly different shape of the


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FIG. 5. (a) Comparison of current-voltage characteristics (measured by sweeping the voltage) for two representative large-type MOM devices (L11—red circles and L31—green triangles) with dissimilar threshold switching voltages and MIT transition magnitudes; linear regressions used for calculating the low bias resistivity (dashed lines) and high bias resistivity (dotted lines) are also displayed. (b) Quasi-static experimental DC currentvoltage plot (black dots) obtained by sweeping the injected current (from 0 to 1.5 mA) and recording the voltage across the L11 MOM device, displaying an S-shape with a distinct CC-NDR feature between points A and B. The super-imposed red curve is the simplified I-V characteristic used for the analytical model of the device (see text). The arrows indicate the values of the injected constant currents resulting in relaxation oscillations across the MOM device when inserted in a van der Pol oscillator circuit.

I-V curve is obtained when the injected current is imposed and ramped in the circuit between 0 and 1.5 mA while measuring the voltage across the devices. Such a typical quasi-DC current-voltage trace is shown in Figure 5(b) for the L11 MOM device (experimental records are represented as black dots). The curve exhibits a clear S-shape, characteristic of a CC-NDR between points A and B depicted on the curve, indicating the onset of an electrically triggered MIT for injected currents higher than 0.6 mA. As in the case of the voltage-swept I-V curves, the NDR region corresponds to the MIT transitive regime of the VO2 layer and, as observed on the current-swept I-V curve in Figure 5(b), it is confined between the high- and low-resistance states of the device. B. Dynamical characteristics of the MOM devices

The switching dynamics and the ability to generate current induced oscillations were investigated on the L11 device by integrating it into the electrical circuit similar to a Van der Pol35 or a Pearson-Anson36 relaxation oscillator, with the MOM device (device under test—DUT) acting as a CCNDR element.37 The equivalent circuit is shown schematically in Figure 6(a). It includes a controlled current source, a 50 X series resistance (RS), an external inductance (L), and a capacitance (CEXT) in parallel with the MOM device. In our case, these two last circuit elements are actually distributed parasitic capacitances and inductances related to the BNC cables of the experimental set-up but they can be also modified by externally introducing shunt discrete capacitors or inductances in the circuit. The voltage across the device under test (VDUT) during current excitations was monitored using a high bandwidth oscilloscope (Tektronix DPO7254). When injecting in the circuit a constant current I0 with values corresponding to the NDR region of the I-V characteristic shown in Figure 5(b), spontaneous voltage self-oscillations were recorded across the MOM device. Figure 6(b) shows the VDUT plotted against time measured on the L11 device for four

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FIG. 6. (a) Schematics of the equivalent electrical circuit used to perform dynamical measurements of self-oscillations when exciting the L11 VO2 DUT with constant currents. (b) Measurements of time traces of the voltage across the DUT (black lines) for the device L11 when excited with current biases ranging from 0.7 mA (top) to 1 mA (bottom); the oscillation frequencies range from 96 kHz (I0 ¼ 0.7 mA) to 294 kHz (I0 ¼ 1 mA). Red curves are simulations performed with the phenomenological model discussed in the paper. (c) Experimental values of the self-oscillations frequency for the device L11 (black squares) and simulated frequency (continuous red line) as a function of the constant current injected in the circuit (I0).

distinct injected currents of I0 ¼ 0.7 mA, 0.8 mA, 0.9 mA, and 1 mA, respectively. One may observe that the increase of the excitation constant current results in increasing the oscillation frequencies, between 96 kHz for I0 ¼ 0.7 mA up to 294 kHz for I0 ¼ 1 mA, which is also the upper limit of the excitation currents producing the oscillation effect. Despite the presence of the parasitic inductor in the circuit, the oscillation traces have a shape that is more typical of a Pearson-Anson oscillator, suggesting that the influence of the inductor element (L 37 lH) on the oscillating phenomena is minimal. The voltage oscillations developed across the MOM device are analogous to those observed in CC-NDR organic,38,39 inorganic materials,21,22 bulk VO226,28 and in VO2 needles and nano-beams.27,29 They are related to the switching between its HRS and LRS, both states being made unstable by the external capacitance CEXT (which is charged and discharged as the device evolves between HRS and LRS).22,39 Similar performance results were obtained on VO2-based MOM devices of different sizes. Overall, for the collection of investigated devices it was found that the oscillation frequencies vary between 50 kHz and 300 kHz (with no clear dependence on their dimensions). For given RS and CEXT values, the oscillation frequencies and amplitudes are function of the switch characteristics (resistances, MIT threshold), current excitation values, and ambient temperature. C. Implementation of an analytical model for simulating the oscillatory phenomena

Modelling the oscillation phenomena in VO2-based devices is still an issue of debate in the literature. At this stage of


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research, it would be highly speculative to propose a physical mechanism for the phase change and the origin of the MIT in the VO2 layer integrating the MOM devices (i.e., whether the MIT is thermally or purely electronically triggered). A simple heat-dissipation model assuming a constant temperature in the VO2 layer may be used to evaluate the insulator to metal transition speed as a function of the power delivered by the DC source when the E-MIT transition occurs (PT ¼ VthIth).7,12,13 The model, initially proposed by Stefanovich et al.7 and subsequently used by Leroy et al.12 and Ha et al.,13 allows to obtain the minimum electrically activated insulator-to-metal transition time as tI!M ¼ cqX(TMIT-T0)/PT, where c is the heat capacity of VO2 (690 J kg1 K1), q is its density (4340 kg m3), X is the volume of the material performing MIT, TMIT is the temperature of the transition, and T0 is the ambient temperature. In the case of the static characteristic of the device L11 presented in Figure 5(a), this formula provides a value of tI!M ¼ 2.6 ls, which is almost one order of magnitude higher than the experimental switching time recorded on the same device (in the order of 10–12 ns) by using a measurement protocol described in Ref. 12. This analysis reinforces the assumption that the Joule heating alone cannot explain the fast transition times during E-MIT.7,12,13 Moreover, the model cannot be used to describe the fast transient behavior of our devices as they are developing self-oscillations. Recently proposed physical models implying a temperature induced MIT with a non-homogeneous repartition at the microscopic scale21,22 are neither adapted to the behavior of our MOM devices and fails to adequately describe our data, in particular, the sharp aspect of the NDR region in the static current-swept I-V curves (see the supplementary material for details34). Additional reports on simulation of electrical oscillations in VO2 planar two-terminal devices show that a temperature-only mechanism for the MIT fails to reproduce the oscillation effects in these planar devices and support the evidence of an electrically triggered MIT through the percolative nature of the VO2 phase transition (co-existence of insulating and metallic grains), which initiates electrical avalanche-driven oscillations.20 However, the hypotheses and the analysis of the physical mechanisms described in this report are also difficult to be adapted for our out-of-plane MOM devices and failed to reproduce our data. The question of whether the origin of the threshold switching and of the current-induced oscillations in VO2-based devices is the result of a structural (temperaturedriven) or of a pure electric-field driven MIT is still an open research subject. In order to reveal the main parameters dictating the oscillation effects on our devices, a phenomenological model was derived. This was performed by first considering the work of Kim et al., who derived the oscillations frequencies by fitting the I-V curves during capacitor charging.17 In the aim to go further and to gain accuracy and generality (e.g., for cases where the discharging time is not negligible compared to the charging time), we modelled the oscillations in the VO2 device by employing analytical equations describing the equivalent electrical circuit shown in Figure 6(a). Thus, the current-swept experimental I-V curve

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of the MOM device (black dots in Figure 5(b)) was simplified and retraced as the red curve on Figure 5(b), defined by four points: the origin or the current-voltage axes and the A, B, and C points. Point A corresponds to the beginning of the MIT transition, point B corresponds to the end of the transition, and point C is taken at a high current bias, which ensures that the transition is complete. The model implies a purely linear conduction from the origin of the curve up to point A and between points B and C. In the particular case of the device L11, the following coordinates were used for the points A, B, and C: VA ¼ 0.81 V-IA ¼ 0.67 mA, VB ¼ 0.41 V-IB ¼ 1.04 mA, and VC ¼ 0.41 V-IC ¼ 1.5 mA. Once these points have been defined, the current flowing through the DUT is defined for each part of the static I-V as follows: iDUT ¼ rVDUT þ b;

(1)

where r is the conductance of VO2 device and is worth ri or rm depending on whether the VO2 is in insulating or metallic phase, respectively; b is the value of the current when the voltage is null (bi ¼ 0 in insulating phase but bm 6¼ 0 in metallic phase). Once ri and rm have been derived from experimental data, a simple model of charging/discharging of CEXT is carried out, using the circuit presented in Figure 3(a). The detail of the calculations is available in the supporting information part.34 Briefly, the model leads to the following differential equation: LCEXT

d2 Vc CEXT dVC I0 b þ VC ¼ ; þ dt2 r dt r

(2)

where vC is the voltage across the external capacitor and I0 is the value of the current injected by the current source. By solving this equation in the case of both charging of CEXT (from VB to VA, in the HRS of the device) and discharging of CEXT (from VA to VB, in the LRS of the device), it is possible to express the oscillation frequency as 0 0 1 ri VB 1 B B1 C I0 b i 1 1 B C logB þ1 f B B C ri VA @ 1 @2 2ri Ldi A 1 di I0 b i 2ri L 0 111 rm VB BI b 1CC 1 B CC m (3) þ arccosB 0 CC ; @ rm VA AA dm 1 I0 bm where di,m is a constant homogeneous to a frequency defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CEXT 2 74LCEXT 6 ri;m : (4) di;m ¼ 2LCEXT Note that the VO2 device can be described also as a variable resistance/variable capacitance element, but its intrinsic capacitance (in the order of hundreds of fF) is negligible towards the 3.25 nF for CEXT.


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D. Discussion

The capacitance value for CEXT is coherent with the estimated parasitic capacitance present in our experimental set-up and the value of L (37 lH) accounts well for the parasitic inductance of the unguarded cables and the connectors used in the circuit. Although the linear approximations taken for the modelled I-V curve are strong for the non-linear HRS part of the static I-V, our phenomenological model was found to simulate very well the global shape of the electrical oscillations, as shown on Figure 6(b) (red curves). We should note that, except for the oscillation traces obtained under the 0.8 mA bias, the model fits very well the first oscillation periods of the time traces but fails to perfectly match the experimental data after a few periods. The reason comes from possible phase noise in experimental data, whereas the simulation traces are rigorously periodic and, therefore, the long-term stability of the oscillation effects is a parameter that needs to be further investigated and optimised in the aim to implement these devices in practical applications. The plots of the oscillation frequencies versus the injected current I0 derived from Eq. (3) are displayed in Figure 6(c) (continuous red curve) and show a very good agreement with the experimental oscillation frequencies data obtained for the device L11 (black squares on the same figure). The model developed here enables to predict the maximum frequency at which this type of devices can operate (Eq. (3)) and points out that the main parameters affecting the oscillation phenomenon are the external capacitance of the circuit, CEXT, the magnitudes of the VO2 conductance in both insulating and metallic states, ri and rm as well as the magnitude and the threshold position of the MIT transition (i.e., position of the A and B points on the I-V trace of Figure 5(b)). Accordingly, for a specific device, the most obvious way to increase the oscillation frequency is to reduce the value of CEXT. In our case, a non-optimized electrical set-up with parasitic capacitance values in the range of several nF is limiting the oscillation frequencies to around 300 kHz. However, a moderate optimization of the electrical circuit may reduce CEXT towards tens of pF, enabling a two orders of magnitude increase in frequency until the tens of MHz range. This would be enough, for instance, for microcontrollers clocking applications. Further reduction of the parasitic capacitance at 1 pF levels (customary in well-optimized driving circuits) will result in oscillation frequencies in the GHz range and may authorize the implementation of such simple CC-NDR devices in circuit designs for high-frequency applications. Downscaling of the devices dimensions to the nanometer scale (easily attainable through electron-beam lithography) is not likely to alter the maximum reachable oscillation frequencies. However, the model predicts an increase of this device’s figure of merit by further lowering the VO2 layer thickness and/or their resistivity in both states (insulating and metallic, while keeping a reasonable magnitude of the MIT transition). This can be achieved by properly designing the VO2 layer properties, for instance, by doping the VO2 material with metallic atoms while taking care to keep the MIT at a temperature compatible with targeted applications.

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IV. CONCLUSIONS

MIT triggering by voltage and current is clearly demonstrated by the experimental data gathered here on more than 50 MOM micrometre-scale devices. Clear CC-NDR in their current-voltage characteristics is also shown and under appropriate excitation conditions, the onset of self-sustained, spontaneous current-controlled oscillations with frequencies up to 300 kHz is established across the VO2-based devices. A simple phenomenological model based on charging and discharging of a shunt capacitor was able to predict the dynamical performance of such MOM devices and to extract the parameters describing the oscillation effects (frequency and amplitude of the oscillations). The model can be further integrated in simulation packages for circuit designs in order to extrapolate the characteristics of similar nanometre-scale devices or other complex relaxation oscillators. These results are significant since the potential of scalability, high-density integration, and the current-controlled ability of these VO2-based MOM devices make them a viable alternative for high-density networks of oscillators able to operate until the range of radiofrequencies. Beside integration as inverters and oscillators in high-speed circuits, a prospective potential application may be the parallel production of periodic signals in large scale integrated circuits, analogous to the action potentials in neural architectures. Such out-of-plane devices may further contribute to the general understanding of the driving mechanism in metal-insulator devices, a prerequisite to promising applications like MIT-based field effect transistors or high-speed resistive random access memories. ACKNOWLEDGMENTS

This work was supported by the Labex Sigma-Lim (No. ANR-10-LABX-0074-01) and by the CNRS under an interdisciplinary INSIS—PEPS 2013 grant (DINAMO). 1

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