In Situ Atom Scale Visualization of Domain Wall Dynamics in VO2 Insulator-Metal Phase Transition

A domain wall, as a device, can bring about a revolution in developing manipulation of semiconductor heterostructures devices at the atom scale. However, it is a challenge for these new devices to control domain wall motion through insulator-metal transition of correlated-electron materials. To fully understand and harness this motion, it requires visualization of domain wall dynamics in real space. Here, domain wall dynamics in VO2 insulator-metal phase transition was observed directly by in situ TEM at atom scale. Experimental results depict atom scale evolution of domain morphologies and domain wall exact positions in (202) and (040) planes referring to rutile structure at 50°C. In addition, microscopic mechanism of domain wall dynamics and accurate lattice basis vector relationship of two domains were investigated with the assistance of X-ray diffraction, ab initio calculations and image simulations. This work offers a route to atom scale tunable heterostructure device application.

I n semiconductor heterostructures, the interface is the device 1,2 As development in semiconductor technology is propelling dimensions of devices down to atom scale, this description is becoming increasingly truthful [3][4][5] . Today semiconductor heterostructures rely on interfaces not only between different materials but also between different domains in the same material 6,7 . A domain wall is used as a device which can demonstrate many amazing varieties of electronic and optical properties, given device sizes can be smaller and domain wall location be controlled 8,9 . It is possible to bring about a revolution for tunable optoelectronic and microelectronic atom scale device application, based on efficient manipulation of domain walls through insulator-metal transition with correlated-electron materials [10][11][12][13][14] . However, the development of these new devices has been probably hampered by the lack of understanding of atom scale domain walls motion during insulator-metal transition process [15][16][17][18] .
In this paper, we laid emphasis on a typical correlated-electron material VO 2 19 , with key feature of a first-order insulator-metal phase transition from the low-temperature monoclinic (M) phase to the high-temperature rutile (R) phase (Fig. 1a) at around room temperature. Despite it has characteristics of early discovery, convenient transition temperature and comparatively simple structures, the dynamic phase transition process still is not observed directly at atom scale [19][20][21][22][23] . Previous works only focused on characteristics of initial and final static states in phase transition process 10,11,14,[19][20][21][22][23] . Here, we use an aberration-corrected transmission electron microscopy, which is extended to the limit of atomic scale, to directly observe domain wall dynamics. The experiments with high resolution images make unprecedented forms of information regarding atomic scale structural features accessible during dynamic phase transition process. In addition, temperature-dependent X-ray diffraction (XRD) is used to characterize and analyze domain wall dynamics. Empirical examinations with high resolution images and more quantitative analyses of integrated peak position profiles, when developed in conjunction with theory-supported modeling, provide deep insights into atomic level features of domain wall dynamics in VO 2 phase transition.
In situ HRTEM images were obtained on FEI Titan 80-300, which operates with the nanocrystalline VO 2 fabricated by a thermal oxidation method (see Supplementary Information). VO 2 were mounted on a designed heating stage and were heated to the desired temperature (Methods). VO 2 were mounted on a designed heating stage and were heated to the desired temperature (Methods). Fig. 1b shows a series of VO 2 HRTEM images during  the heating process. At room temperature (25uC), we observed, as expected, a HRTEM image with a corresponding fast Fourier transform (FFT) for ,001. zone axis in monoclinic VO 2 phase. As temperature increase to 50uC, the domain of monoclinic VO 2 phase gradually decreases and that of rutile VO 2 phase starts to emerge. The coexistence of monoclinic and rutile VO 2 phases is clearly seen, which exhibits a first-order insulator-metal phase transition. Corresponding selected area FFT images can be used to identify domain phase categories. Thus, the changes of corresponding FFT images observed in Fig. 1b (image1, 2, 3, 4 and 5 labeled by the white lines) clearly presents domain wall motion process. Fig. 1c illustrates the schematic diagrams of VO 2 band structure of monoclinic (insulator) and rutile (metal) phases before they form domain walls 18,24,25 . Fig. 1d shows energy band change diagram for tunable heterostructures, accompanied by domain wall motion. To understand detailed structural characterization of domain wall dynamic process, we analysis three representative in situ HRTEM images (image 1, 2 and 5 in Fig. 1b) before VO 2 phase transition (Fig. 2a), the HRTEM image of two-phase coexistence during VO 2 phase transition( (Fig. 2b), and that after VO 2 phase transition (Fig. 2c). The simulated electron diffraction patterns (Methods) show that these patterns are for ,001. zone axis of monoclinic structure (indicated by ii in Fig. 2a) and ,101. zone axis of rutile structure (indicated by ii in Fig. 2c), which match well with that of FFT images obtained at temperature of 25uC (indicated by i in Fig. 2a) and 70uC (indicated by i in Fig. 2c), separately. In Fig. 2b, the selected area FFT images show two sets of diffraction spot, which are assigned to monoclinic and rutile phase, respectively. The domain walls are marked by a white dotted line in Fig. 2b. Symmetrical lattice fringes with interplanar distance of 4.86 and 4.60 Å can be observed in Fig. 2a, which can be indexed as (100) plane and (010) plane of monoclinic VO 2 . In Fig. 2c, the interplanar distance of 4.61 and 2.14 Å can be indexed as (010) plane and (111) plane of rutile VO 2 , respectively. Geometrical phase analysis (GPA) of Fig. 2b is also used to calculate the strain map around the domain wall 26 . GPA obtains the corresponding strain field relative to some presumably unstrained area of the HREM image. The results of the strain components e xx and e yy are shown in Fig. 2d, respectively. The variation of rutile phase domain indicates the strain field change, which can be noticed that there are several convergence regions of strain. Conversely, the monoclinic phase presents a homogeneous strain distribution.
In order to categorically identify phase interface and atom structure changes, atom structure models were applied in HRTEM analysis. Fig. 3a shows a magnified view of Fig. 2b, which is smoothed for reducing noise (not affecting interpretation of atomic position) 27 . To distinguish phase structure changes, we used simulated HRTEM  images to compare predicted contrast variations. By adjusting image defocus and resolution (see Methods), HRTEM image simulations can characterize domain walls in VO 2 phase transition. In Fig. 2b, region I and II represent simulated rutile and monoclinic phase HRTEM images, separately 28 . These simulated HRTEM images match well with our experimental HRTEM images. The simulated HRTEM images indicate that rutile phase owns bright continuous dots, which are marked in Fig. 2b region I. However, monoclinic phase has bright interrupted dots (in region II of Fig. 2b). This directly shows differences between VO 2 rutile and monoclinic phases. By enlarging coexisted rutile and monoclinic phase region, the positions of domain walls (white solid line) are clearly localized in Fig. 3a. The rutile phase structure is on the left, whereas monoclinic phase structure is on the right. The domain walls are in (202) and (040) planes of rutile structure, which is consistent with earlier results 29,30 . Taking into account that the upper surface is a (001) plane of the monoclinic phase, the angles between domain walls and the direction of monoclinic VO 2 phase b M axis are 0uand 90u. The ,010. axis of monoclinic VO 2 phase corresponds to a ,010. direction of rutile VO 2 phase. The color inserts in Fig. 3a correspond to atomic structure model images. The red and black spheres represent O and V atoms, respectively. In inserts, the atomic arrangements of two phases have obvious differences, which are shown in green dotted and solid rectangles, respectively. In Fig. 3a, a V atom and another V atom, which we call V-V pair, are found to have relative motion, but there is no relative motion between O atoms during VO 2 phase transition. In Fig. 3a, experimental lattice parameters of interrelationship between rutile and monoclinic domains were obtained from corresponding domain FFT images (Fig. S3). The interplanar distance indexed as (100) plane of monoclinic domain was 4.862 Å , the same as corresponding distance in rutile domain. Monoclinic (010) plane with inter-plane spacing of 4.604 Å was equivalent to corresponding distance of rutile phase (010) plane. These results indicate that there was no expansion perpendicular to c M axis, where M refers to monoclinic phase.
In situ HRTEM images show no expansion perpendicular to c M axis, to confirm the expansion along c M axis, temperature-dependent XRD measurements were performed using a Siemens-Brucker D8DISCOVER diffractometer with the X-ray cathode source of CuKa (l 5 1.5406 Å ). Fig. 4a shows monoclinic VO 2 (002) M peaks shifting to (200) R peaks of rutile phase during heating process, which is consistent with atomic structure models in Fig. 4b. The lattice parameters in heating process can be estimated by means of Bragg's law, which is expressed as where l is wavelength of X-ray, h is scattering angle, n is an integer representing order of XRD peak. The lattice parameters (Fig. 4c) can be calculated on the basis of structural characteristic and similarities between monoclinic and rutile phases shown in Fig. 4b. The calculated values are obtained from data in Fig. 4a (marked as i and ii ) and b is 122.6u (Table S1 in Supplementary Information). The results show a tiny expansion between two domains. The crystal fine-structure in VO 2 phase transition is discussed further. Dynamic experiments show direct accurate relationship of lattice basis vectors at initial (monoclinic phase), coexisting (monoclinic/rutile phase) and final (rutile phase) states. These are the basis of theoretical and experimental explorations in VO 2 phase transition [31][32][33] . For example, Cs-corrected scanning transmission electron microscopy (STEM) is recently performed to investigate microstructures of the epitaxial polycrystalline VO 2 thin films 34 . The atomic resolved STEM experiments are done at room temperature. However, corresponding high temperature rutile structure experiment has not been done and its structure is only deduced from the relationship of two phase lattice basis vectors. These works only researched static initial (monoclinic phase) and final (rutile phase) lattice basis vector relationship 31 . At static experiments, there are many matching results of monoclinic and rutile crystal orientations, which is very difficult to find accurate matching relationships. But in situ HRTEM atom scale dynamic experiments makes it possible for accurately and directly identifying crystal structure relationships of two phases. Corresponding with initial, coexisting and final HRTEM images in Fig. 2a to 2c, a schematic illustration of this crystal structure variation at atomic level is shown in Fig. 3b and 4c. To explain detailed structure changes, a unit VO 2 structure diagram is shown in Fig. 5a. The figure clearly shows V-V pair positions of two stable structures. A V atom and another V atom can be bound together to form V-V pair through chemical bonding with two O atoms. During phase transition, motion of V atoms is from the initial gray V 1 and V 2 positions to the final green V 1 9 and V 2 9 positions, respectively. V-V pair undergoes not only elongation from 2d 1 (distance of two gray V atoms) to 2d 2 (distance of two green V atoms) but also a twist h angle in X-Z plane. Fig. 5b shows a three dimensional schematic view of inter-relationship between rutile and monoclinic structures. In Fig. 5c, three-view depictions show accurate lattice basis vectors relationships of monoclinic and rutile phases. Viewed from rutile ,010. zone axis direction, monoclinic (010) M plane is turned into rutile (010) R plane (marker i to i9 in Fig. 5c). Along rutile ,001. and ,100. zone axis direction, monoclinic (100) M and (001) M planes are turned into rutile (001) R and (100) R planes (from ii, iii to ii9, iii9 in Fig. 5c), respectively. Contrary to previous reports 30,34 , the corresponding structural relationship of rutile and monoclinic phases can be written as a R by our dynamic HRTEM experiments. This provides a direct evidence of these two phases spatial relationship during the insulator-metal phase transition, which is important in clarifying the mechanism of VO 2 phase transition.
To understand domain wall dynamical process, real-time observation of experimental phase transitions in structured variants with high spatial resolution is needed to be conducted. In fact, atom movement spatial scale, temporal resolution and domain wall positions are crucial to understand and harness VO 2 domain wall dynamics. In previous work, Peter Baum and colleagues have shown the temporal displacements of atoms in picoseconds, that the V-V bond dilation is the initial step of the insulator-metal transition and an long-range shear rearrangements follows the V-V movement 35,36 . In this study, we use the high-resolution TEM to directly elucidate the spatial VO 2 domain wall dynamical process at the atomic level. The atom scale exact domain wall positions have been also observed. On the other hand, we present the clear direct experimental evidence that V atomic motion in VO 2 phase transition from the initial to the final position forms the V-V pair movement, which is concordantly predicted by numerous theoretical treatments. In addition, microscopic mechanism of domain wall dynamics in VO 2 phase transition is also investigated. We propose a possible two-step process (Fig. 6a) of domain wall motion: first step is movement of V-V pairs and second step is expansion along c M axis. First, at room temperature primary rutile phase VO 2 nucleates on defect domain of monoclinic phase, as defect domain possess enough free electrons 37,38 . Then a  Schottky junction is formed at monoclinic/rutile domain walls shown in Fig. 6b. Previous reports have shown band bending on the domain wall can alter the spatial distribution of electron concentration and VO 2 phase transition behavior 24,39 . Electric field at the domain walls produces a force on electrons, which prevents electrons diffusion from rutile to monoclinic phase domains. Simultaneously, the further extend of rutile phase domain is suspended. When the sample is heated, thermal equilibrium of domain walls loses at two sides, some electrons of rutile phase domain are injected into monoclinic phase domain 20,22,40 . This may strengthen electron-phonon interactions and electron-electron interactions 41 , which drives the movement of V-V pairs (Fig. 5a). When the sample reaches its phase transition temperature, many electrons of rutile phase domain can cross over Schottky battier of domain walls to monoclinic phase domain. This process can be described by the Richardson equation, written as 42 where J RRM is thermionic emission electron current density, A 0 is Richardson constant which is equal to 120 A/(cm 2 ?K 2 ) for electrons, T is temperature, eW BO is Schottky barrier height, and k is Boltzmann constant. The thermionic emission electron current densities depending on temperature are calculated when Schottky barriers height is 0.11 eV shown Fig. 6c, and results show thermionic emission electrons current densities rapidly increasing at approximately 62uC. The Schottky barrier height of this model is consistent with earlier measurements 24 . A schematic illustration is shown in Fig. 6d. Second, when movement of V-V pairs is completed, the whole structure expands along c M axis to form final stable rutile phase state. The XRD results show that a tiny expansion of approximately 0.023 Å (Fig. 6e) occurs during phase transition. When movement of V-V pairs is finished, this structure will possess a higher lattice potential than final stable VO 2 rutile sructure 43,44 . As separation of two adjacent V-V pairs along c M axis can decrease lattice potential, the expansion along this direction occurs and form final stable VO 2 rutile phase structure, as shown in Fig. 6a.
In summary, we directly observed domain wall dynamics in VO 2 phase transition using in situ HRTEM at the atom scale. In contrast to no expansion perpendicular to c M axis between two domains, a tiny expansion of approximately 0.023 Å is found along c M axis. Domain wall positions are exactly located in (202) and (040) planes of rutile structure at the temperature of 50uC. Microscopic mechanism of domain wall dynamics is also analyzed. The structure analysis offers fine-structure views at initial (monoclinic phase), coexisting (monoclinic/rutile phase) and final (rutile phase) states. The corresponding structural relationship of rutile and monoclinic phases is written as a More efforts will still be required to clarify comprehensive theoretical description of VO 2 insulator-metal phase transition. Nonetheless, the fine-structure information and accurate relationship of lattice basis vectors presented here can supply a structural framework for theoretical and experimental further explorations in VO 2 phase transition 45,46 . The work can be used to design and engineer atom scale heterostructures devices. Crucially, this treatment method of domain wall used as a device can make us to dynamically modify domain walls even after the assembly into device architecture, and also plays an important role in overcoming device size limit when individual element dimensions in devices continue to shrink 47,48 .

Methods
The in situ HRTEM images were obtained with an image aberration-corrected microscope (FEI Titan 80-300 operating at 300 kV). A charge-coupled device camera (2 k 3 2 k, Gatan UltraScan 1000) was used for image recording with an exposure time of 1 s to 2 s. The third-order spherical aberration was set in the range of 10 mm to 20 mm, and the TEM images were recorded under slightly defocused condition.
The heating was conducted using a heating sample holder (Gatan 628). To ensure that the sample temperature was consistent with that of the measured temperature, we waited for at least 30 min to achieve thermal equilibrium before further imaging. The electron diffraction patterns were simulated by means of CRYSTALMAKER software packages with the value from the theoretical simulation (Supplementary Information). The atomic models of the monoclinic phase and rutile phase were created via Accelrys Discovery Studio Visualizer 27 and the corresponding simulation of the HRTEM images were performed by means of the multislice algorithm with parameters set in accordance to the approximations for the microscope 28 .