Role of joule heating effect and bulk-surface phases in voltage-driven metal-insulator transition in VO 2 crystal

We report the characteristics of a voltage-induced metal-insulator transition (MIT) in macro-sized VO2 crystals. The square of MIT onset voltage (VCMIT2) value shows a linear dependence with the ambient temperature, suggesting that the Joule heating effect is the likely cause to the voltage-induced MIT. The combination of optical microscope images and Laue microdiffraction patterns show the simultaneous presence of a metallic phase in the bulk of the crystal with partially insulating surface layers even after the MIT occurs. A large asymmetry in the heating power just before and after the MIT reflects the sudden exchange of Joule heat to its environment.

) value shows a linear dependence with the ambient temperature, suggesting that the Joule heating effect is the likely cause to the voltageinduced MIT.The combination of optical microscope images and Laue microdiffraction patterns show the simultaneous presence of a metallic phase in the bulk of the crystal with partially insulating surface layers even after the MIT occurs.A large asymmetry in the heating power just before and after the MIT reflects the sudden exchange of Joule heat to its environment.V C 2013 Author(s).All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.[http://dx.doi.org/10.1063/1.4817727]Strongly correlated materials (SCMs) exhibit many remarkable physical properties, such as metal-insulator transition (MIT), high temperature superconductivity, and colossal magnetoresistance.3][4][5][6][7][8][9] However, the coexistence of these interactions makes it difficult to identify the primary cause of the MIT.From the view of the practical application of the MIT characteristics of VO 2 in electrical/ optical devices, it is essential to understand the intrinsic driving force of the voltage-induced MIT.Kim et al. 10 have reported that the voltage-induced MIT in VO 2 films occurs without SPT, when the external field is large enough to induce the carrier density to be above a critical carrier density (n c ) of $3 Â 10 18 cm À3 , supporting a field-induced breakdown mechanism.On the other hand, numerous alternate reports do not support this model. 11,12In the report of Kim et al., the magnitudes of the critical electric field (E C ) at the MIT appeared to be less than 1 V/lm, a value much smaller than the theoretical estimated value of E C ¼ 50 V/ lm.This theoretical value of E C has been calculated from the electric field required for inducing the critical concentration of carriers ($3 Â 10 18 cm À3 ) in VO 2 by the field-induced Poole-Frenkel effect. 13In fact, there are large variations in experimental E C values reported in the literature, varying from $0.05 to $20 V/lm.
In this letter, we report on the characteristics of the voltage-induced MIT in macro-sized VO 2 single crystals.Various experimental tools, such as transport measurements, optical microscopy, and synchrotron-based x-ray microdiffraction, were applied to investigate the MIT properties.Our results suggest that the voltage-induced MIT in VO 2 crystals occurs via a Joule heating effect rather than a field-induced breakdown effect.Also, the voltage-induced metallic state of VO 2 crystals is composed of the metallic phase in the bulk of the crystal with partially insulating surface layers, indicating different MIT behaviors at the surface.
VO 2 single crystals were synthesized with a self-flux method, the details of which are reported elsewhere. 9The crystals have an average length of 1-3 mm and width of 0.05-0.10mm with a square cross section.No other chemical elements were found except for vanadium and oxygen from energy dispersive X-ray spectroscopy (EDS) measurements.Temperature vs resistance (T-R) and voltage vs current (V-I) measurements of VO 2 crystals were performed using a dc two-contact four-probe method.During V-I measurements, the crystals were connected in series with either a 10 kX or a 6.4 kX resistor (R EXT ) as shunt resistance to protect the crystal and instruments.Optical microscopy was employed to monitor the metallic and insulating phases of VO 2 during the temperature-driven and voltage-induced MIT measurements.To investigate the SPT during the voltage-induced MIT, synchrotron-based x-ray Laue microdiffraction (l-XRD) was carried out on Beamline 12.3.2at the Advanced Light Source at Lawrence Berkeley National Laboratory.Authors to whom correspondence should be addressed.Electronic addresses: bsmun@gist.ac.kr and tesl@yonsei.ac.krFig. 1(a) shows a series of V-I curves measured as the applied bias voltage is increased at different temperatures (T A ) in the range of 40 to 65 C. The inset picture illustrates the schematics of the circuit constructed for the V-I measurements with the VO 2 crystal sample, in which the current was measured as the voltage was increased.The resistance of external resistor was measured independently and applied for the observed values.When the external voltage was ramped up starting from zero, the current increased linearly with the initial slopes corresponding to resistances of (4.0 $ 10.0) Â 10 4 X for each temperature.When the voltage reached the MIT onset value (V MIT ), the current suddenly jumped to a value 5 to 6 times higher than the one before the MIT.Just before the MIT, the sample resistance is almost independent of the temperature with values in the range of (2.2-3.0)Â 10 4 X.Just before the MIT, the resistance (R CMITÀ ) of the crystal is a few times larger than R EXT .However, immediately after the MIT, the resistance of the crystal, estimated to be less than $10 X, drops to a value much smaller than R EXT (6.4 Â 10 3 X).Consequently, the entire load from the external voltage is applied to the external resistor after the MIT.Since the magnitude of the current after the MIT is determined by R EXT , the current jump ratio R EXT are the current just after and just before MIT, respectively.Thus, the ratio of R CMIT /R EXT determines the current jump ratio.As expected, V MIT monotonically decreases with increasing ambient temperature from 27.5 V at 40 C to 8.6 V at 65 C. Before the MIT, the applied external voltage is shared between the crystal and the resistor.In this case, the voltage (V CMIT ) across the crystal can be obtained as V MIT R CMITÀ R CMITÀ þR EXT , with values of 22.5, 16.7, 12.9, 10.7, and 6.8 V at 40, 50, 55, 60, and 65 C, respectively.The magnitude of the critical electric field (E CMIT ) at the MIT, defined as V CMIT =L (L: the crystal length) is linked to the origin of the voltage-induced MIT and our E C values vary from 3.0 Â 10 À2 V/lm at T A ¼ 65 C to 0.11 V/lm at T A ¼ 40 C. Interestingly, the magnitude of the critical field is less than 0.25% of the theoretical estimate of 50 V/lm, to generate a carrier concentration of $3 Â 10 18 cm À3 inside VO 2 in the field-induced breakdown model. 15It is possible that the presence of defects can lower the critical fields.However, the defect density in high quality VO 2 crystal is expected to be much smaller than the one in VO 2 thin films.Considering this significant difference in magnitude of the critical field, it appears to be very difficult to explain the origin of the voltage-induced MIT in the framework of the field-induced breakdown model.
As an alternative model to explain the voltage-induced MIT, we have tested the Joule heating model.First, we tested whether the temperature dependence of the critical voltage agrees with predictions from Joule heating.In this model, the MIT occurs when the voltage-induced Joule heating is sufficient to raise the crystal temperature to the MIT temperature ($67 C).Assuming the heat obtained in the VO 2 crystal is mainly due to the balance between resistive Joule heat and heat loss from the crystal to the environment via heat conduction, this relation can be expressed by the following simple heat equation: where Q, V C , k, and T C are the total net heat in the crystal, the voltage drop across the crystal, the effective thermal conductance, and the crystal temperature, respectively.Since the resistance between the contact and the VO 2 sample is low compared to the resistance of the crystal, when VO 2 is in the insulating state, the contact resistance is ignored in our treatment.When the generated heat due to Joule heating is equal to the heat loss via thermal conduction to the surroundings, a steady state condition ( dQ dt ¼ 0) is reached.At this steady state, the crystal temperature T C is equal to kR C and can be further increased as bias voltage increases.Finally, the crystal temperature of the critical MIT temperature, T CMIT , can be reached when sufficient bias voltage is applied.Thus, V CMIT can be expressed as In Fig. 1 Considering the fact that these metallic and insulating phases of VO 2 generate a significant contrast in optical reflectivity, monitoring the presence, and its motion of the phase boundary during the voltage induced MIT is possible by using optical microscopy. 8The dark and bright areas in the optical microscope pictures represent the metallic and insulating states of VO 2 , respectively.Figure 2 displays both the V-I curve (left hand side of Fig. 2) and optical microscopy images (right hand side of Fig. 2) recorded simultaneously as a function of increasing voltage at T A of 40.0 C. Optical microscope images in Fig. 2 show the formation of multiple phase boundaries as a function of time during the voltage-induced MIT (voltage ramp rate ¼ 0.2 V/s).The time interval covered is about 0.5 s and images are therefore $0.1 s apart.The sizes of the metallic and insulating phases are of macroscopic scale, in contrast to the metallic nano-puddles observed in thin films. 5The optical image A in Fig. 2 represents the insulating phases of VO 2 , corresponding to a small flow of current and only the insulating phase is visible on the surface.However, in images B $ D at the onset of the MIT, the surface shows the presence of both insulating (bright) and metallic (dark) phases.Interestingly, a combination of metallic and insulating phases remains at the surface even after V > V MIT .The optical image E of Fig. 2 taken at V > V MIT shows the metallic phase occupying an area of 39% and the insulating phase occupying an area of 61%.However, from the V-I curve for V > V MIT , the crystal resistance was measured to be less than 0.2% of R EXT , which clearly suggests that the entire crystal should be in its metallic state.Since the optical microscope images reflect the surface properties of the crystal, the likely explanation for this discrepancy is that the bulk of the crystal is in conducting state, while some portions of the surface remain in the insulating state.This possibility was tested by applying bulk sensitive x-ray microdiffraction experiments.The probing depth of Laue diffraction is much larger than the crystal thickness, 16 while the optical microscope images reflect the surface sensitive properties of the crystal.
Figure 3 shows both the V-I curve and the Laue diffraction patterns which were recorded simultaneously as a function of increasing voltage at T A ¼ 40 C, a temperature identical to the one used in the optical microscope measurement in Fig. 2. In the Laue diffraction experiment, a single line scan of Laue patterns was collected with a step size of 2 lm after the external voltage was set, while the V-I curve was measured in parallel.The time interval between different voltage sets is 180 s.For easy comparison, only 15 out of a total of 30 diffraction images are shown at the critical voltage set points.Literature values of the lattice parameters were used to index the Laue diffraction patterns 7 and its structures are marked on the Laue diffraction patterns in Fig. 3.The diffraction images of Fig. 3 show that our VO 2 sample is in a pure monoclinic insulating M2 phase at 0.0 V voltage (I).The M2 phase remained up to 11.0 V (III).However, this M2 phase suddenly changes to the M1 phase as the voltage is increased above 11.0V (III to IV).Simultaneously, the V-I curve shows a small kink near 11.0 V, which was also shown at $27.0 V in Fig. 2. It indicates that Joule heating at this voltage is sufficient enough to raise the crystal temperature for the M2-M1 insulating-insulating phase transition (IIT).This IIT was previously reported for VO 2 single crystals 8,9 and different IIT set voltages were found for different sample sizes, indicating a size effect.The different IIT voltage values of Figs. ), yet the V-I curve indicates the sample to be in the insulating state at this voltage.Finally, when the voltage reached V MIT , 24.0 V (VII), the metallic R phase starts to appear together with the M1 phase on the left hand side (#1 $ 9), while only the R phases remain on the right hand side of sample (#10 $ 15).At the voltage above V MIT (VIII), diffraction patterns remain identical to the one from 24.0 V.That is, the insulating M1 phase still exists together with metallic R phase even after the sample is in full metallic states.As mentioned above, there is a big difference in bulk sensitivity from Laue diffraction to optical microscope.Therefore, the coexistence of M1 and R phases on the left hand side of Fig. 3 at V > V MIT confirms the finding from optical microscopy (Fig. 2), i.e., that half of VO 2 crystals are composed of the metallic phase in the body of the crystal with a partially insulating surface skin layer.The conducting path for the electrons is dominated by the bulk.One thing to note is that there is a shift of the phase boundary from 23.5 V to 24.0 V, outlined with yellow in Fig. 3.In fact, this shift of the phase boundary during the MIT reveals evidence for local thermal fluctuations between surface skin layer and bulk layer, as discussed below.First, it is important to understand how this insulating surface skin layer is formed as this will provide critical insights on the origin of the voltage-induced MIT in VO 2 .Immediately after the MIT, the entire applied voltage goes into the external series resistor since the resistance in the VO 2 metallic phase is negligible compared to R EXT .The heating power (I 2 R C ) just before and just after the MIT is estimated to be I MITÀ 2 R CMITÀ $ 2.2 Â 10 À2 W and I MITþ 2 R CMITþ $ less than 3.8 Â 10 À4 W, respectively.As can be seen, the heating power just after the MIT is much reduced compared to just before MIT.(R CMITþ is the crystal resistance just after the MIT.)Therefore, immediately after the MIT (V > V MIT ) the temperature of the sample cannot be further increased because of the significant drop of heating power due to the low resistance in the sample.This large asymmetry in the heating power around the MIT can be viewed as an on-off heating power switch, i.e., the switch is on before the MIT and off after the MIT; this keeps the crystal at the MIT temperature.Our result is also consistent with a recent report made by Zimmers et al., in which the presence of the thermal heating effect on the voltage-induced MIT in VO 2 is observed by fluorescence spectroscopy. 17Also, it will be important to understand this insulating skin layer in the future applications of VO 2 in memory devices.
The sudden change of heating power at the MIT can be also applied to explain the shift of the observed phase boundary in Fig. 3.At the onset of MIT, 23.5 V (VI) in Fig. 3, the metallic R phase starts to propagate from the right to the left and more than half of the sample area is covered with the metallic phase (#7 $ 15 in VI).Once the sample reached the full conducting state at 24.0 V (VII), the heating power is lost cooling the sample from the surface and the insulating skin layer is formed (#7 $ 9 in VII), as shown in Fig. 3.The origin of these mixed states, R and M1 phases, is not clearly known at the moment.There could be local fluctuations of sample thickness which could generate different heat losses during the voltage-driven MIT.In turn, the sample can form localized insulating skin layer.Considering that the temperature-driven MIT does not show the mixed state in previous reports, 8,9 it is likely that the mechanism of the Joule heating effect in the voltage-driven MIT causes results of Figs. 2 and 3. When the substrate temperature is raised to 67 C, which is near to the critical temperature of the temperature-driven MIT, no mixed states are observed from optical microscope images.
Our results show that the voltage-induced MIT in a macroscopic VO 2 crystal occurs due to the Joule heating effect under the conditions of the present experiment.A self-switching effect, which is caused by the large asymmetry in heating power just before and after the MIT, allows to maintain the crystal temperature at MIT temperature.
Division of Applied Chemistry and Biotechnology, Hanbat National University, Daejon 305-719, South Korea and Advanced Nano Products, Chungwon, Chungbuk 363-942, South Korea (Received 10 April 2013; accepted 21 July 2013; published online 6 August 2013) We report the characteristics of a voltage-induced metal-insulator transition (MIT) in macro-sized VO 2 crystals.The square of MIT onset voltage (V CMIT 2

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a) FIG. 1.(a) V-I curves measured by increasing the applied bias voltage at varying temperatures (T A ) in the range between 40-65 C. The inset shows a schematic drawing of the sample geometry used to carry out the voltage induced transitions.(b) A plot of V CMIT 2 versus T A , where V CMIT is the voltage on the crystal just before MIT.

FIG. 2 .
FIG. 2. (Left) Voltage (V) versus current (I) curves and (Right) optical microscopy images as a function of increasing voltage at temperature (T A ) of 40.0 C.

2 and 3
are due to the different sample sizes.Above 11.5 V, only the pure monoclinic insulating M1 phase was observed, and this M1 phase remained stable up to V MIT .When the voltage reached 23.5 V (VI), individual diffraction images along the scan line show variably either the tetragonal metallic R (images #7 $ 15) or the insulating M1 phases (images #1 $ 6