Temperature-induced metal–insulator transition (MIT) in vanadium dioxide (VO2) has been under intense research interest for decades both theoretically and experimentally. Due to the complex nature of electron correlations, the underlying physics behind the MIT in VO2 has yet to be fully grasped. In this work, we utilize the fine resolution of the scattering-type scanning near-field optical microscope to investigate the MIT in an epitaxial VO2 thin film on the (100)R TiO2 substrate with mid-infrared light. Bidirectional tweed-like metal–insulator phase coexistence patterns are observed and understood under the Landau free energy paradigm. More interestingly, delayed metallic nucleation is observed near the surface cracks due to local strain relief. This research proposes ideas in investigating the temperature–pressure phase diagram and tuning the interplay between local strain and MIT in oxide thin films.

Among various types of solid–solid phase transitions, metal–insulator transitions (MITs) in strongly correlated materials have received extensive research interest due to their importance in fundamental science and potential in device applications.1,2 The representative transition metal oxide, vanadium dioxide (VO2), is known to exhibit a first-order phase transition from a low-temperature monoclinic insulating phase to a high-temperature rutile metal phase. The transition temperature, Tc, associated with the bulk single crystal VO2 is 340 K,3,4 only slightly above room temperature. The significant conductivity change during the MIT is a desirable trait in many applications.5–8 However, the precise physics that describes the MIT in VO2 is still under heated debate despite decades of research.9–11 Furthermore, the MIT behavior in strongly correlated materials can be effectively tuned through external parameters, such as electric field,12 magnetic field,13 and doping.14,15 Strain, as another external stimulus, not only enables fine-tuning of many intrinsic properties of materials but also sheds light on the mechanism behind many physical phenomena, such as the Mott transition. Numerous studies have demonstrated that Tc and phase separation pattern in transition metal oxides can be effectively tuned in a wide range with strain.16–20 Recent experimental evidence has also demonstrated that the appropriate strain environment leads to the decouple of electronic and structural transitions.21–23 

Although the spatially averaged features of the MIT can be experimentally determined by electric transport or optical spectroscopy, such as ellipsometry, the mesoscopic details related to the phase segregation can only be indirectly interpreted by the effective medium approach using these methods.24–26 The mid-infrared (IR) scattering-type scanning near-field optical microscope (s-SNOM), on the contrary, enables direct visualization of the phase coexistence at the nanoscale and has been systematically employed to investigate the MIT for strongly correlated materials, such as VO2 and V2O3.27–39 The nano-imaging experiment is schematically depicted in Fig. 1(a). A 75 nm VO2 film grown on the TiO2 (100) substrate is placed on a heating stage on top of an atomic force microscope (AFM) scanner. Coherent mid-IR radiation (∼11 μ m wavelength) generated from a CO2 laser is impinged on the AFM tip, generating a strong near-field tip-sample interaction. The AFM is operating in tapping mode with the tapping frequency of Ω250kHz and an amplitude of 50nm. Backward scattered light containing local sample dielectric information from the tip-sample system is collected by the detector using a homodyne detection scheme.40,41 To effectively eliminate the undesired far-field background signal coming from direct scattering off the sample or the tip while preserving the genuine near-field information, the detector signal is demodulated by a Lock-in amplifier at higher harmonics of Ω. The signal demodulated at the n th harmonic will be denoted by Sn. For mid-IR, n=2 or 3 is usually sufficient to eliminate the undesired background. A detailed description of the experimental technique can be found elsewhere.42,43 Although demodulation effectively gets rid of the background signal, the multiplicative far-field effect is still present.31 This effect can be eliminated by considering the ratio of different demodulated signals.44,45 Throughout this work, we present the ratio of the near-field signal demodulated at the third harmonic (S3) to the signal demodulated at the second harmonic (S2) and refer to this ratio (S3/S2) as the near-field signal.

FIG. 1.

(a) Schematic of the temperature-dependent IR nano-imaging experiment. (b) Temperature-dependent IR nano-imaging data of a 75 nm VO2 film on the (100) TiO2 substrate (an uncracked region). Clear phase coexistence with a bidirectional herringbone pattern is observed throughout the MIT. Scale bars: 1 μm. (c) Normalized near-field signal distribution histograms at different temperatures. (d) The ratio of the metallic regions as a function of temperature. Inset: electrical transport measurement of the sample film. (The inset y-axis is on a logarithmic scale.)

FIG. 1.

(a) Schematic of the temperature-dependent IR nano-imaging experiment. (b) Temperature-dependent IR nano-imaging data of a 75 nm VO2 film on the (100) TiO2 substrate (an uncracked region). Clear phase coexistence with a bidirectional herringbone pattern is observed throughout the MIT. Scale bars: 1 μm. (c) Normalized near-field signal distribution histograms at different temperatures. (d) The ratio of the metallic regions as a function of temperature. Inset: electrical transport measurement of the sample film. (The inset y-axis is on a logarithmic scale.)

Close modal

Temperature-dependent nano-imaging results are presented in Fig. 1(b). At room temperature, the sample surface exhibits uniform insulating behavior with low near-field signal intensity. At 313 K, metallic puddles initiate. The nucleation starts at a temperature much lower than the global phase transition temperature determined by the transport measurement [see the inset of Fig. 1(d)]. The bidirectional herringbone-tweed pattern emerges at about 320 K and presents until 358 K, above which the sample surface is uniformly metallic. The same herringbone pattern was reported in our previous work,27 but here we demonstrate the possibility of having a high-quality sample surface with no or very few cracks. This is important since it allows us to clearly distinguish the metallic and the insulating regions. We draw histograms of the near-field intensity distributions in Fig. 1(c), where S3/S2 can be qualitatively regarded as the signature of metallicity. With the increase in temperature, the distribution gradually shifts from low signal intensity (insulating behavior) to high signal intensity (metallic behavior). Figure 1(d) shows the ratio of the metallic region as a function of temperature. The metallic domains experience a compressive strain, despite the overall c-axis strain being tensile due to the larger lattice parameters of (100) TiO2. This is confirmed by our x-ray diffraction measurement (not shown) and our previous observation.27 

While the cracks along the rutile c-axis ([001]R) do present in our samples, they are well separated. This allows us to perform a controlled study. A temperature-dependent nano-imaging reveals that MIT is delayed near the cracks as demonstrated in Fig. 2(a). At 328 K for example, the bi-directional metallic strips formed away from the cracks while regions near the cracks still exhibit a uniform insulating behavior. Near-field signal intensity averaged parallel to the left side of the left crack at different distances to the crack is plotted in Fig. 2(b) as a function of temperature. It is clear that at all distances, the spatially averaged near-field signal increases with rising temperature. However, by comparing the film at 40 nm away from the crack to that at 1.25 μm, there is a roughly 8 K maximum delay in the insulator-to-metal transition. This delay in the evolution of optical contrast gradually diminished toward higher temperatures as the whole film enters a uniform metallic state.

FIG. 2.

(a) Temperature-dependent nano-imaging data reveal the delay of MIT close to the surface cracks. (b) Temperature-dependent average near-field signal as a function of distance to the left crack. (c) Schematics of the cracked VO2 thin film on the TiO2 substrate. The top image shows the near-field image taken at 328 K. White dashed lines indicate the boundaries of the strain-released region. Red dashed lines in the cross section schematically show the strain distribution around the crack. The strain released region forms a triangle with height t and width 2w.

FIG. 2.

(a) Temperature-dependent nano-imaging data reveal the delay of MIT close to the surface cracks. (b) Temperature-dependent average near-field signal as a function of distance to the left crack. (c) Schematics of the cracked VO2 thin film on the TiO2 substrate. The top image shows the near-field image taken at 328 K. White dashed lines indicate the boundaries of the strain-released region. Red dashed lines in the cross section schematically show the strain distribution around the crack. The strain released region forms a triangle with height t and width 2w.

Close modal

The crack leads to strain release in the VO2 film, forming an unloaded region, as schematically illustrated in Fig. 2(c). This narrow crack, to a good approximation, leaves a triangular unloaded region in the cross section with a height t (crack depth) and width 2w. Griffth derived the relation between w and t using an energy-balanced approach based on Inglis's previous linear elastic solution for the stress field of an elliptical crack.46–48 In essence, for a linear elastic material, the strain energy per unit volume is given by u=σdε=σ22E, where σ is the stress and E is the Young's modulus. Assuming that the crack is infinitely long, the strain energy released in the formation of the crack per unit length along the crack is

U=σ22Ewt.
(1)

Here,wt is the cross-sectional area of the unloaded region. According to Inglis' solution, the stress fields around an elliptical crack are given by Rαα, Rββ, and Sαβ in the elliptic coordinate with the displacements given by uα and uβ. Exact analytical forms are omitted here and can be found in the original paper.47 The strain energy per unit length in the elliptic coordinate is then calculated by the integral

U=1202πuαhRααdβ+1202πuβhSαβdβ,
(2)

where h=2c2(cosh2αcosh2β). The Cartesian coordinates (x,y) and elliptic coordinates (α,β) are related by x+iy=ccosh(α+iβ), where c is the distance from the origin to the focus in the elliptic coordinate. Equating results given by Eqs. (1) and (2) leads to the conclusion that w=πt (Ref. 48). That is, the width is roughly three times the crack depth. For our 75 nm crack, assuming that the crack extends through the whole film,19 the strain-released region width w would roughly be 236 nm. This indeed agrees with our experimental observation that the near-crack region without metallic nucleation is about 250 nm wide [e.g., at 328 K in Fig. 2(c)]. The depth-dependent strain relief in principle suggests an interesting scenario to control the mesoscale pattern of strained films, which can be more prominent in strongly correlated electron materials than in semiconductors.49 

In the end, we introduce an intuitive method to illustrate the strain and temperature-dependent mesoscopic metal–insulator domain formation: performing s-SNOM raster scans while cooling or heating the sample provides direct visualization of the domain evolution. In Fig. 3(a), the areal scan is initiated at 358 K while gradually cooling the sample down to 313 K at the end of the scan. With the decrease in temperature, the sample transitions from uniform metal (top) to metal–insulator coexistence (middle) and eventually a uniform insulator (bottom). Performing this procedure near the cracked region can be more beneficial: The strain and temperature-dependent pattern formation can be clearly visualized, as shown in Fig. 3(b). The white dotted lines mark the cracks, while the blue dashed lines mark the “phase” boundaries of the MIT across the sample due to changes in strain and temperature. Therefore, interestingly, this image can be interpreted as a real space pressure–temperature “phase diagram” for pattern formation, where the horizontal distance from the crack represents epitaxial strain and the vertical direction corresponds to temperature. Note that the image of Fig. 3(b) is temperature-drift-corrected so that the cracks are aligned to the vertical axis (rutile c axis).

FIG. 3.

(a) Raster s-SNOM scan of the uncracked VO2/(100)TiO2 film while cooling. The slow axis is vertical. (b) Raster s-SNOM scan of the VO2/(100)TiO2 film in the cracked region while changing the temperature (drift corrected). Cracks are indicated by dashed lines. The image contrast in (a) and (b) is S3/S2, and the scale bars are 1 μm.

FIG. 3.

(a) Raster s-SNOM scan of the uncracked VO2/(100)TiO2 film while cooling. The slow axis is vertical. (b) Raster s-SNOM scan of the VO2/(100)TiO2 film in the cracked region while changing the temperature (drift corrected). Cracks are indicated by dashed lines. The image contrast in (a) and (b) is S3/S2, and the scale bars are 1 μm.

Close modal

In conclusion, we have demonstrated that the MIT behavior is locally impacted by interfacial strain around the surface cracks on VO2/(100)TiO2 films. The nucleation of metallic domains is found to be delayed in the strain-released region, occurring at a temperature closer to the bulk Tc of 340 K. The lateral size of the region is roughly three times the depth of the crack, consistent with the prediction by a straightforward energy-balanced mechanical analysis. This result could inspire future engineering efforts to manipulate the local strain environment and achieve electronic properties in mesoscale on demand.

This work was supported by the RISE2 node of NASA's Solar System Exploration Research Virtual Institute under NASA Cooperative Agreement No. 80NSSC19MO2015. X.Z.C., M.K.L., and D.N.B. acknowledge support from the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under Contract No. DE-SC0012704. S.K. acknowledges support from the National Science, Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation (Grant No. B05F640051). T.V.S. and H.T.K. acknowledge support from the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) via Grant No. 2017-0-00830.

The authors have no conflicts to disclose.

Xinzhong Chen: Data curation (lead); Formal analysis (lead); Visualization (lead); Writing – original draft (lead); Writing – review and editing (lead). Salinporn Kittiwatanakul: Methodology (equal); Supervision (equal); Validation (equal); Writing – review and editing (equal). Yinke Cheng: Validation (equal); Visualization (equal); Writing – review and editing (equal). Tetiana Slusar: Resources (equal); Validation (equal); Writing – review and editing (equal). Alexander Swinton McLeod: Formal analysis (equal); Investigation (equal); Writing – review and editing (equal). Zhuoqi Li: Formal analysis (equal); Visualization (equal); Writing – review and editing (equal). Hyun-Tak Kim: Investigation (equal); Validation (equal); Writing – review and editing (equal). D. N. Basov: Funding acquisition (equal); Project administration (equal); Resources (equal); Writing – review and editing (equal). Mengkun Liu: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review and editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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