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Quantitative spatial mapping of distorted state phases during the metal-insulator phase transition for nanoscale VO2 engineering

ABSTRACT Vanadium dioxide (VO2) material, known for changing physical properties due to metal-insulator transition (MIT) near room temperature, has been reported to undergo a phase change depending on the strain. This fact can be a significant problem for nanoscale devices in VO2, where the strain field covers a large area fraction, spatially non-uniform, and the amount of strain can vary during the MIT process. Direct measurement of the strain field distribution during MIT is expected to establish a methodology for material phase identification. We have demonstrated the effectiveness of geometric phase analysis (GPA), high-resolution transmission electron microscopy techniques, and transmission electron diffraction (TED). The GPA images show that the nanoregions of interest are under tensile strain conditions of less than 0.4% as well as a compressive strain of about 0.7% (Rutile phase VO2[100] direction), indicating that the origin of the newly emerged TED spots in MIT contains a triclinic phase. This study provides a substantial understanding of the strain-temperature phase diagram and strain engineering strategies for effective phase management of nanoscale VO2.


Introduction
Vanadium dioxide (VO 2 ) exhibits a metal-insulator transition (MIT) due to external fields such as heat [1,2], light [3,4], electric fields [5,6], and magnetic fields [7], which are accompanied by structural phase transition. In addition, strain [2,8,9], and doping [10][11][12][13][14][15] change the MIT conditions and properties. Since the electrical and optical properties of VO 2 change significantly with the phase transition, applications in photonics and electronics are particularly promising [16][17][18][19][20][21]. Some optical switches have been developed combining VO 2 exhibiting the MIT with a silicon waveguide for miniaturizing optical switches [7]. The low-temperature VO 2 phases include not only the well-known M1 phase (monoclinic) but also two metastable structures, the insulating M2 phase (monoclinic) and T phase (triclinic), due to stoichiometric defects and strain effects, which can pose challenges for nanoscale devices [22,23]. Due to their metastable structures and spatial phase inhomogeneities in the film/bulk samples, these structural phases can exhibit different phase transition behaviors and properties. In recent years, a wide range of device applications involving miniaturization using nanostructures and nanofilms of oxides have been expanding [24][25][26]. Precise control of domain structures and phase transitions at the single domain level is also expected for VO 2 materials, and the development of a method to precisely characterize the phase structure of VO 2 at the nanoscale is a major challenge [27].
According to Wang et al. [28] and Kim et al. [29], the M2 and T phases are stabilized by doping, external strain, and oxygen nonstoichiometry. Effective strain control strategies are necessary to create VO 2 crystals with stabilized multiphase because doping and stoichiometry can cause large structural distortions in the VO 2 lattice, changing its intrinsic properties and applications. Strained VO 2 fields are not a problem in conventional macroscopic devices but are critical in nanoscale devices; the area covered by the strained field is large and spatially non-uniform, and the amount of strain can change during the phase transition process. However, the challenge is that there is no way to quantitatively measure the strain state of those VO 2 in actual nanomaterials.
In this study, using geometric phase analysis (GPA), an analysis of high-resolution electron microscopy (HRTEM), we have exhibited crystallographic evidence from transmission electron diffraction (TED) that there is indeed an intermediate phase of the MIT while quantitatively evaluating the strain in thin films of VO 2 grown on sapphire. In order to precisely control VO 2 and even the properties of the phase transition process in the future, we need a recipe to quantitatively measure the strain of the desired nanostructure. We will demonstrate that GPA and TED can be used to quantitatively evaluate the strain of phase transitions in the single domain, which was not readily apparent due to the sub-resolution displacement of HRTEM.

Experimental details
A c-cut sapphire substrate (10 × 10 mm 2 ) was ultrasonically cleaned with acetone, ethanol, and an ultrapure water bath for 5 min each. After removing the surface moisture with a nitrogen gun, the washed sample was introduced into a load lock chamber. Then, the sample was transferred to a deposition chamber equipped with a pulse laser deposition system (Lambda Physics) [25]. A V 2 O 5 target was used for the growth of VO 2 film. The deposition chamber was evacuated to a 2 × 10 −5 Pa prior to deposition. The thickness of the VO 2 thin film of 100 nm was formed on the substrate by pulsed ArF laser deposition (wavelength 248 nm, energy 50 mJ, frequency 10 Hz, substrate temperature 723 K, O 2 pressure 1.0 Pa). The temperature dependence of the electrical conductivity of the VO 2 film was measured between 300 and 400 K by the van der Pauw method (self-made) to confirm the phase transition temperature (Supporting information Figure S1 (a)). The crystallinity of the fabricated VO 2 film was evaluated by X-ray diffraction (XRD) measurements (Rigaku, Ultima IV) with 2θ-ω scan (Supporting information Figure S1(b)).
Focused ion beam processing (Thermo Fisher Scientific, Scios 2) was performed to thin the VO 2 film so that it could be observed from [010] M1 (Rutile phase VO 2 [0 � 10] R ) orientation. The TED pattern and cross-sectional HRTEM were taken at 200 keV (HITACHI, HF-2000). The temperature was repeatedly lowered and raised 323-373 K (323 K, 353 K, 373 K) in the TEM with a temperature variable holder (Gatan, 628). The temperature was held for about 15 minutes until each temperature became constant, and then HRTEM and TED observations were performed. There was no significant change in the diffraction pattern at the same temperature when the temperature was raised and lowered. Geometric Phase Analysis (GPA) was used to visualize the strain changes in the VO 2 film using Grillo's algorithm STEM_cell [30]. The diffracted spots of VO 2 (002) M1 and (20 � 2) M1 were used as reference points for the GPA. The output GPA images are 16 bits.

Results and discussion
The TED pattern shown in Figure 1 [11 � 20]) direction, which allows us for detailed measurements of the atomic arrangement changes in M1, M2, T, and R phases. The R phase is known as metallic. The pattern was obtained at 353 K from a 5 μm VO 2 thin film region together with the sapphire substrate as a reference for d-spacing. As shown in the crosssectional TEM image (Figure 1(b)) of a VO 2 film formed on the substrate, VO 2 domains grow perpendicular to the interface. Although it is difficult to see in the wide-area TEM image in Figure 1(b), the VO 2 domain is 10-20 nm size in parallel to the interface and is long in the surface direction. Figure 1(c-f) are enlarged images of the area enclosed by the square at 353 K and 373 K. These spots are indexed as 200 VO2_R and � 200 VO2_R . When the sample temperature is further lowered to 353 K form 373 K, the intensity of the newly emerging spots, which could hardly be visualized at 373 K, becomes more intense. The spots appeared along the line parallel to the [100] R direction; it was observed as a strong intensity at 353 K and as a small intensity at 323 K. Streaky diffraction spots were observed parallel to the VO 2 [001] R direction ( Figure 1(g,h)). The streak spots correspond to the presence of a VO 2 single domain with a width of 10-20 nm. The domain size was also confirmed by atomic force microscopy images of the surface (Supporting information Figure S2).
There are two possible explanations for the newly emerging spots. One explanation is that the VO 2 domain has a T phase with the M1 and R phases due to a strain. The relationship between temperature and strain proposed by Raman spectroscopy has suggested that VO 2 becomes T phase at 0.5-1% relative strain [31]. Another explanation is the generation of a new long-period strained structure, as discussed later. First, we consider the former in detail. Assuming that the newly emerged spots are the lattice spacing (d-spacing) of the new crystal phase, it corresponds to d = 0.24 ± 0.05 nm. According to the previous reports of XRD, the emerging spots correspond to 020 VO2_T on reciprocal space [11,12]. There is no evidence as to how strained the VO 2 domains are at 353 K, although it has been reported that the area near the interface with sapphire is under a strain state [32]. However, the difference in the arrangement of V atoms between M1, M2, and T phases is reported to be smaller than 0.02 nm, which is difficult to distinguish even with the help of HRTEM image simulations. In addition, the XRD of the T phase was measured by creating a strained state by doping with Al [23], which can be different from the phase caused by external pressure or force fields.
Moreover, the biggest question is why the spots that appeared at 353 K were not observed at 323 K.
Next, to check the strain state at 353 K, GPA was performed for the acquired HRTEM images. The lattice mismatch between the VO 2 (M1 and R phases) and Al 2 O 3 (0001) substrates is 4.50% and 4.92% parallel to the interface, respectively. [001] R direction is the y-axis. Strain components ε xx and ε yy visualize the strain state in the VO 2 domain. Especially in 353 K the distortion is concentrated in the central domain of the ε xx image, which is only under the compressive strain of below 0.7% but also under the tensile strain of 0.2% (Figure 3). Although the strain is almost zero on average in 353 K, the width of the peak is broader, i.e. the area containing the tensile strain is −0.7 to +0.4%. The ε yy images showed that the strains are concentrated near the interface. The compressive strain applied in the x-direction change significantly at each of the temperatures of 323 K and 373 K. This VO 2 thin film is formed so that nanorods are growing in the x-direction. As shown in Figure 4(a,b), The change from the M1 phase to the R phase (or vice versa) is accompanied by a volume change that changes the angle and the lattice constant. In the x-direction, there is a space in which the crystal volume change is possible. However, for the y-direction, a phase transition with a large volume change is difficult because another VO 2 domain exists right next to those. This can result in increased compressive strain with anisotropy at 373 K, as shown in Figure 5(b). As shown in Figure 3, both compressive and tensile strains are present at 323K in the nanoscale range, but they are offset in total. This situation may be the reason for the wide range in strains, although it is plotted where there are no strains in total at 323 K, as shown in Figure 5(b).
To interpret the results of all the above analyses, the atomic arrangement of the T phase was considered together with that of the M1 and R phases. A schematic diagram of V atoms shifts in the M1-R phase transition is illustrated in Figure 4(a). As is well known, the V atoms aligned in the c-axis direction of the rutile-type structure form a zigzag chain at low temperatures, with the V atoms alternately shifting by 0.02 nm. This structural change reduces the symmetry and changes the structure from Tetragonal to Monoclinic. The lattice spacing of d(002) M1 and d(200) R is almost equal, 0.227 nm. In contrast, the structural models of the M1 phase (blue) and T phase (orange) focusing on the shift of V atoms are illustrated in Figure 4(b), although the slight difference in angle is not shown. Compared to the M1 phase, the T phase has a zigzag sequence of V atoms every other row. The lattice spacing of d(020) T is 0.243 nm, corresponding to 4.1 nm −1 in reciprocal space. The peaks of XRD between 2θ = 36 and 44 degrees in previous works of VO 2 (M2) [22], VO 2 (T) [12], and VO 2 (R) [33] are shown in Figure 5(a) (Full range XRD data are shown in Supporting Information,   Figure S5). The black lines in Figure 5(a) stand for Bragg peaks that can be appeared in the TED spots of Figure 1(c-f).
The zigzag chains of the T phase are aligned perpendicular to the [100] R direction every cycle, which can be considered as stacking defects generated during the phase transition from R to M1. The T phase can be mixed with the M1 as a metastable structure. While the angle β of the unit cell in the M1 phase is 122.6 degrees, the corresponding angle in the T phase is angle α, which is 65.0 degrees (supporting information  Table S1). Since the obtuse angle of the parallelogram of the unit cell of the M1 phase is wider in the T, this structural change in the T compared to the M1 means that the volume change in the x-axis direction, that is, the direction parallel to the [100] R direction, is more prominent. This difference in the angle of the structural phase is consistent with the fact that the VO 2 domains at 353 and 373 K are more strained in both parallel and perpendicular directions in the [100] R direction than those in the M1 phase, especially compressive strain at higher temperatures.
The major difference between the characteristics of phase transitions on the nanoscale and those on the microscale is that the amount and type of strain can change during the phase transition process. The  [22], VO 2 (T) [12], and VO 2 (R) [33]. The black lines in stand for Bragg peaks that can be appeared in the spots of Figure 1 Figure 5(b) [34]. Since their results were obtained by Raman spectroscopy at the microscale under external stress, the metastable T phase can be observed at the nanoscale even under low strain states. The diamond marks stand for the strain peaks in Figure 3. The bar is in the range of 2000 counts or more in the histogram obtained from our GPA (Figure 3). The dotted line means an estimated change in average strain during the phase transition process. If a region of M2 phase existed in our samples, a diffraction spot of VO 2 (400) M2 should appear at 373 K as shown in Figure 5(a). However, the spot did not appear in the actual TED pattern. This suggests a single rutile phase at 373 K. Our measurements suggest that the degree of strain depends on the external field in the structural phase transition process of VO 2 , implying that the control of the single domain or nanostructure is crucial.
Finally, we discuss the possibility of generating a new strain long-period structure as described in the previous paragraph. The strained component appears to have a superstructure with a period of 0.24 nm, corresponding to 4 nm −1 in reciprocal space (shown in supporting information, Figure S4). This period is close to the value of Δq shown in Figure 1(i). However, if a long-period structure occurred, a peak should also appear near the 000-transparent spot, but no clear peak was observed. Assuming that a long-period strain exists in the x-direction (VO 2 [100] R ), its half-period is 4 ± 0.5 nm, as shown in Figure S4. In reciprocal space, this value corresponds to 0.222-0.285 nm −1 . Even if spots due to long-period strain appear, they should be broad, not the sharply peaked spots observed here. Indeed, the corresponding peaks were not identified in the line profiles obtained from the fast Fourier transform (FFT) for the HRTEM image ( Figure S3 (e)). Therefore, the possibility of a long-period structure of strain was ruled out.
The GPA in this study directly shows that an obstacle in the direction of the volume change associated with the phase transition causes strains in the VO 2 nanocrystal, which in turn affects the phase transition phase. Due to the strain caused by the lattice mismatch between the sapphire substrate interface and VO 2 , it has been reported that strains are internalized at the interface. The strains act to lower the phase transition temperature of MIT [2]. These reports refer to the structural phase change within only 10 nm from the interface; however, there is no direct indication that strains can occur in the structural phase transition process of the entire domain shown in this study. There was a large difference in the change rate of electrical conductivity near the high-temperature phase and near the low-temperature phase of VO 2 (Supporting information Figure S1(a)). The mixture of the two phases in the low-temperature phase may cause this difference. Stable and precise control of the phase structure of VO 2 is essential to fabricate the desired nanostructure. We believe that this study is of great significance as it demonstrates the possibility of controlling the intermediate phase of VO 2 in the future. Recently, VO 2 materials have been considered promising candidates for optical switches, which undergo ultrafast light-induced structural phase transitions on the order of 100 femtoseconds [3,4,[35][36][37][38]. However, little analysis has been done taking strain into account. Our study also suggests that it is meaningful to evaluate the implied strain when tracing the structural changes in VO 2 induced by ultrafast pulsed light irradiation.

Conclusion
In conclusion, we have provided crystallographic evidence by electron diffraction that the MIT intermediate phase exists while quantitatively characterizing the strain in VO 2 thin film grown on sapphire using GPA. The new diffraction spots at 353 K suggested the presence of a phase with the d-spacing of 0.243 nm (4.1 nm −1 ) in the [100] R orientation. The GPA shows the tensile strain of −0.7 to +0.4% (Rutile phase VO 2 [100] direction) in the single domain at 353 K and 373 K compared to that at 323 K, which may cause the T phase to hybridize with the M1 phase. Those methods used in this study could be helpful for precise control of the nanostructure of VO 2 , monitoring the variable strain field during the phase transition process in a nanoscale domain.

Disclosure statement
No potential conflict of interest was reported by the authors.