High quality vanadium dioxide films

Abstract

Layers of high quality VO.sub.2 and methods of fabricating the layers of VO.sub.2 are provided. The layers are composed of a plurality of connected crystalline VO.sub.2 domains having the same crystal structure and the same epitaxial orientation.

Claims

1. A layer of VO.sub.2 comprising a plurality of connected crystalline VO.sub.2 domains having the same crystal structure and the same epitaxial orientation, wherein the layer of VO.sub.2 is a continuous layer in which the crystalline VO.sub.2 domains in the plurality of connected crystalline VO.sub.2 domains are in direct contact with other crystalline VO.sub.2 domains in the plurality of crystalline VO.sub.2 domains.

2. The layer of VO.sub.2 of claim 1, wherein the layer is crack free.

3. The layer of VO.sub.2 of claim 1, wherein the layer is strain free.

4. The layer of VO.sub.2 of claim 1, having a layer thickness of at least 100 nm.

5. The layer of VO.sub.2 of claim 4, having a layer thickness in the range from 100 nm to 500 nm.

6. The layer of VO.sub.2 of claim 4, wherein any cracks present in the layer are confined to within 10 nm or fewer of one surface of the layer.

7. The layer of VO.sub.2 of claim 4, wherein any strain present in the layer is confined to within 10 nm or fewer of one surface of the layer.

8. The layer of VO.sub.2 of claim 4, wherein the crystalline VO.sub.2 domains have an average width of no greater than 500 nm and any cracks present in the layer are confined to within 5 nm or fewer of one surface of the layer.

9. The layer of VO.sub.2 of claim 1, wherein the crystalline VO.sub.2 domains have an average width of no greater than 500 nm.

10. The layer of VO.sub.2 of claim 1, wherein the crystalline VO.sub.2 domains have an average width of no greater than 300 nm.

11. The layer of VO.sub.2 of claim 1, wherein the VO.sub.2 has a metal-insulator phase transition critical temperature, below which the VO.sub.2 has a monoclinic crystal structure and above which the VO.sub.2 has a rutile crystal structure, the layer of VO.sub.2 being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO.sub.2 undergoes the phase transition from monoclinic to rutile with a transition sharpness of no greater than 2 K.

12. The layer of VO.sub.2 of claim 11, wherein the VO.sub.2 has a metal-insulator phase transition critical temperature, below which the VO.sub.2 has a monoclinic crystal structure and above which the VO.sub.2 has a rutile crystal structure, the layer of VO.sub.2 being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO.sub.2 undergoes a phase transition from monoclinic to rutile and the electrical resistance of the layer of VO.sub.2 decreases by at least four orders of magnitude.

13. The layer of VO.sub.2 of claim 1, wherein the VO.sub.2 has a metal-insulator phase transition critical temperature, below which the VO.sub.2 has a monoclinic crystal structure and above which the VO.sub.2 has a rutile crystal structure, the layer of VO.sub.2 being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO.sub.2 undergoes the phase transition from monoclinic to rutile with a transition sharpness of no greater than 1 K.

14. The layer of VO.sub.2 of claim 1, wherein the VO.sub.2 has a metal-insulator phase transition critical temperature, below which the VO.sub.2 has a monoclinic crystal structure and above which the VO.sub.2 has a rutile crystal structure, the layer of VO.sub.2 being characterized in that, when it is heated from a temperature below its metal-insulator phase transition critical temperature to a temperature above its metal-insulator phase transition critical temperature, the VO.sub.2 undergoes a phase transition from monoclinic to rutile and the electrical resistance of the layer of VO.sub.2 decreases by at least four orders of magnitude.

15. The layer of VO.sub.2 of claim 1, wherein the layer overlies a template layer with which the VO.sub.2 has a lattice mismatch.

16. The layer of VO.sub.2 of claim 1, wherein layer of VO.sub.2 overlies a layer of columnar, crystalline domains of rutile SnO.sub.2.

17. The layer of VO.sub.2 of claim 1, wherein the plurality of connected crystalline VO.sub.2 domains includes crystalline VO.sub.2 domains having different rotational orientations.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like numerals denote like elements.

(2) FIG. 1. Schematic diagram showing a multilayered structure comprising a VO.sub.2 overlayer below its critical phase transition temperature (right) and above its critical phase transition temperature (left). The rutile (left) and monoclinic (right) crystal structures of the VO.sub.2 are shows above the multilayered structures.

(3) FIG. 2. TEM of a multilayered structure comprising a VO.sub.2 overlayer below its critical phase transition temperature, with different rotational orientations of the VO.sub.2 domains indicated.

(4) FIG. 3. Schematic diagram of a two-terminal switch with a VO.sub.2 channel layer.

(5) FIG. 4. Schematic diagram of a three-terminal switch with a VO.sub.2 channel layer.

(6) FIG. 5A. Atomic structures of rutile, metallic VO.sub.2 (upper left); monoclinic, insulating VO.sub.2 (upper right); rutile TiO.sub.2 (lower left); and rutile SnO.sub.2 (lower right) (corresponding lattice parameters are also shown). FIG. 5B. Schematic diagram showing the expected lattice-strain profiles for epitaxial VO.sub.2 films on TiO.sub.2 without a SnO.sub.2 template. FIG. 5C. Schematic diagram showing the expected lattice-strain profiles for epitaxial VO.sub.2 films on TiO.sub.2 with a SnO.sub.2 template.

(7) FIG. 6A. Monoclinic-to-rutile structural-phase transition upon heating, modeled using in situ TEM measurements of a 300-nm-thick VO.sub.2 film on TiO.sub.2. The phase boundaries between monoclinic and rutile structures at each temperature are represented using solid lines. FIG. 6B. Spatial map of out-of-plane strain .sub.yy for VO.sub.2 films on TiO.sub.2. FIG. 6C. Spatial map of electrical potential for VO.sub.2 films on TiO.sub.2. FIG. 6D. Monoclinic-to-rutile structural-phase transition upon heating a 300-nm-thick VO.sub.2 film on an SnO.sub.2-templated TiO.sub.2. FIG. 6E. Monoclinic portion as a function of temperature T, as estimated based on the relative areas of the monoclinic regions in FIGS. 6A and 6D.

(8) FIG. 7A. Resistance R versus temperature T for the VO.sub.2 films of the Example. FIG. 7B. The derivative curves of R for a 300-nm-thick VO.sub.2 film on an SnO.sub.2-templated TiO.sub.2 (closed circles and squares indicate derivatives of the R logarithm, as measured during heating and cooling, respectively; experimental data are fitted using Gaussian curves [solid lines]). FIG. 7C. Refractive index n as function of temperature and for the 300-nm-thick VO.sub.2/SnO.sub.2/TiO.sub.2 film. FIG. 7D. Extinction coefficient k as function of temperature and , for the 300-nm-thick VO.sub.2/SnO.sub.2/TiO.sub.2 film. FIG. 7E. Refractive index n as function of temperature and , for the 300-nm-thick VO.sub.2/TiO.sub.2 film. FIG. 7F. Extinction coefficient k as function of temperature and , for the 300-nm-thick VO.sub.2/TiO.sub.2 film.

(9) FIG. 8A. Schematic drawing showing strain relaxation and cracking in VO.sub.2 films without SnO.sub.2 templates; in the VO.sub.2 film on an SnO.sub.2-templated TiO.sub.2, severe structural defects, such as strain relaxation and cracks, were well-confined to the interface, and this protects such films against degradation caused by repeated phase transitions. FIG. 8B. Resistance, measured at room temperature and 400 K, after repeated phase transitions of the VO.sub.2 films without SnO.sub.2 templates. FIG. 8C. Schematic drawing showing strain relaxation and cracking in VO.sub.2 films with SnO.sub.2 templates; in the VO.sub.2 film on an SnO.sub.2-templated TiO.sub.2, severe structural defects, such as strain relaxation and cracks, were well-confined to the interface, and this protects such films against degradation caused by repeated phase transitions. FIG. 8D. Resistance, measured at room temperature and 400 K, after repeated phase transitions of the VO.sub.2 films with SnO.sub.2 templates.

(10) FIG. 9A. Microscopic images of the VO.sub.2 films' surfaces for VO.sub.2 grown on TiO.sub.2 (left) and on SnO.sub.2/TiO.sub.2 (right); the image in the inset shows a film surface as observed with a scanning electron microscopy (SEM); prior to SEM imaging, the film surface was chemically etched to observe the resultant cracks more clearly. FIG. 9B. AFM images of the VO.sub.2 films' surfaces for VO.sub.2 grown on TiO.sub.2 (left) and SnO.sub.2/TiO.sub.2 (right).

DETAILED DESCRIPTION

(11) Layered oxide structures comprising an overlayer of high quality VO.sub.2 and methods of fabricating the layered oxide structures are provided. Also provided are high-speed switches comprising the layered structures and methods of operating the high-speed switches.

(12) The layered oxide structures comprise high quality VO.sub.2 epitaxial films grown on a symmetrically isostructural SnO.sub.2 template. The lattice mismatch between the VO.sub.2 and SnO.sub.2 produces small, well-connected domains of VO.sub.2 having the same crystal structure in the epitaxial film and confines severe structural defects (e.g., strain gradients and cracks) to the area near the SnO.sub.2/VO.sub.2 interface. This leads to homogeneous, bulk-like lattices in the VO.sub.2 film, without compromising the film's epitaxial nature. This structural homogeneity also enables homogeneous electronic and chemical states throughout the films, which is highly desirable for creating reliable, high performance devices, such as high-speed switches.

(13) The VO.sub.2 in the epitaxial films is characterized by a metal-insulator phase transition critical temperature. Below this critical temperature, the VO.sub.2 in the epitaxial crystalline domains has an electrically insulating monoclinic crystal structure. As the VO.sub.2 is heated to and above its critical temperature, the crystal structure transitions to a metallic conducting rutile crystal structure. In the VO.sub.2 films, the transition is very sharp and is accompanied by a large decrease in the films' electrical resistance. In addition, the small crystalline domains in the VO.sub.2 films help them to absorb the stresses and strains that accompany the phase transition, enabling the films to undergo many phase transition cycles without cracking. As a result, the VO.sub.2 films are well suited for switching applications. For example, the VO.sub.2 films can be used in electronic switches and optoelectronic switches in circuits, including integrated circuits, for memory devices (e.g., CMOS chips) and communication devices.

(14) One embodiment of a layered structure comprising a VO.sub.2 overlayer is shown schematically in FIG. 1. The right side the figure shows the structure at a first temperature that is below the phase transition critical temperature (T.sub.crit) and the left side of the figure shows the structure at a second temperature that is above the T.sub.crit. The structure comprises a single-crystalline, rutile TiO.sub.2 substrate 102 having an exposed TiO.sub.2 (001) growth surface. A template layer 106 comprising columnar crystalline domains of rutile SnO.sub.2 is disposed on TiO.sub.2 substrate 102. The columnar, crystalline domains of rutile SnO.sub.2 are grown epitaxially and, therefore, have an epitaxially relationship with the underlying TiO.sub.2. Rutile SnO.sub.2 domains have an exposed (001) surface on which an overlayer 110 comprising a plurality of connected crystalline VO.sub.2 domains of is disposed. Epitaxial growth of the SnO.sub.2 and VO.sub.2 can be accomplished using, for example, pulsed laser deposition (PLD) as illustrated in the Example.

(15) The lattice mismatch between the TiO.sub.2 substrate and the SnO.sub.2 results in the epitaxial, nanoscale, crystalline columnar domains in the SnO.sub.2 growing upward from the TiO.sub.2 growth surface. These domains, which have the same crystal structure (rutile) and orientation nucleate separately on the growth surface and grow together to a growth template that is isostructural with the subsequently grown VO.sub.2 at growth temperatures above T.sub.crit. As such, the SnO.sub.2 films are not polycrystalline films in which a plurality of crystal domains are oriented randomly within the film. As used herein, the term nanoscale columnar domains refers to columnar domains having average cross-sectional diameters that are no greater than 200 nm. This includes columnar domains having average cross-sectional diameters that are no greater than 100 nm; no greater than 50 nm; and no greater than 20 nm. For example, in some embodiments of the SnO.sub.2 films, the columnar domains have average cross-sectional diameters in the range from about 5 nm to about 10 nm. The thickness of the SnO.sub.2 layer is typically in the range from about 100 nm to about 300 nm, but thicknesses outside of this range can be used.

(16) The lattice mismatch between the SnO.sub.2 and the VO.sub.2 limits the size of the epitaxially grown VO.sub.2 domains and concentrates and/or confines any cracks in the VO.sub.2 film to a small volume near the SnO.sub.2/VO.sub.2 interface, while the remainder of the VO.sub.2 may be crack- and strain-free. This is advantageous because it allows the VO.sub.2 layers to be grown to commercially practical thicknesses without any significant cracking beyond the lowermost portion of the layer. By way of illustration only, in some embodiments of the layered structures, the VO.sub.2 layer has a thickness of at least 100 nm. This includes layered structures having a VO.sub.2 layer thicknesses of at least 200 nm and further includes layered structures having a VO.sub.2 layer thicknesses of at least 300 nm. For example, in some embodiments, the VO.sub.2 layer thickness is in the range from about 100 nm to about 500 nm. This includes embodiments in which the VO.sub.2 layer thickness is in the range from about 200 nm to about 400 nm. In each of these embodiments, the cracks and/or strains (if present at all) may be confined to within a few nanometers (for example, 10 nm or fewer, including 5 nm or fewer) of the SnO.sub.2NO.sub.2 interface.

(17) The small size of the VO.sub.2 domains helps the VO.sub.2 film to absorb the stresses and strains of the MIT, which reduces cracking during phase change cycling and improves and sustains device performance. As used here, the size of the domains refers to the largest cross-sectional width of the domains, where the width dimension is perpendicular to the thickness dimension. In some embodiments of the layered structures, the average width of the VO.sub.2 domains is no greater than about 500 nm. This includes embodiments in which the average width of the VO.sub.2 domains is no greater than about 400 nm and further includes embodiments in which the average width of the VO.sub.2 domains is no greater than about 300 nm. The VO.sub.2 domains are well-connected, have a common crystal structure and an epitaxial relationship with the underlying SnO.sub.2. At temperatures below T.sub.crit, the VO.sub.2 has a monoclinic crystal structure and is electrically insulating. The monoclinic VO.sub.2 domains can have four different rotational orientations that are rotated by 90 from each other in the plane of the film. The different rotational domains are represented by areas of different shading in overlayer 110 on the right side of FIG. 1. The four different rotational domain variants of the monoclinic VO.sub.2 are shown in the upper right side of FIG. 1. At temperatures above T.sub.crit, the VO.sub.2 has a tetragonal rutile crystal structure and acts as an electrical conductor. The rutile crystal structure is shown in the upper left side of FIG. 1.

(18) The T.sub.crit for the VO.sub.2 in the overlayer is greater than room temperature (i.e., greater than 300 K). Typically, the T.sub.crit is greater than 340 and in the range from about 338 to about 345 K (e.g., about 340 to 343 K, including about 341 K). (Unless otherwise indicated, the phase transition critical temperatures referred to in this disclosure refer to the critical temperature in the absence of an applied external field or strain.)

(19) The high quality VO.sub.2 films grown on SnO.sub.2 template layers can be characterized by their sharp metal-insulator phase transitions, where the sharpness of a transition is characterized by the full width at half maximum (FWHM) of the derivative curve of a heating curve, as illustrated in the Example. Some embodiments of the VO.sub.2 films have a phase transition sharpness of 2 K or less. This includes VO.sub.2 films having a phase transition sharpness of 1.5 K or less and further includes VO.sub.2 films having a phase transition sharpness of 1 K or less. These sharp transition can be achieved even in films with thicknesses above 100 nm, above 200 nm, and above 300 nm.

(20) The monoclinic to rutile (insulating to conducting) phase transition is accompanied by a large drop in the vanadium dioxide's magnitude of electrical resistance (R), which can be measured as described in the Example. Some embodiments of the VO.sub.2 films have a R of at least 2 orders of magnitude. This includes VO.sub.2 films having a R of at least 3 orders of magnitude and further includes VO.sub.2 films having a R of at least 4 orders of magnitude.

(21) The layered structure can be used as a switch by heating the VO.sub.2 above its T.sub.crit to trigger the phase transition. Devices configured to induce or monitor this heating-induced switching can be used as thermal switches and thermal sensors. Alternatively, an external stimulus, such as an electric field, an optical field, a mechanical strain, or a combination thereof, can be applied to the VO.sub.2 to induce the phase transition. These external stimuli shift the critical temperature for the MIT and induce the reversible phase transition, which changes the resistance (and, therefore, conductance) of the VO.sub.2, thereby modulating current flow through the material. Devices configured for field-induced switching can be used as high-speed switches for a variety of electronic, optical, and optoelectronic applications. A basic embodiment of a two-terminal switch comprising the layered structure is shown in the schematic diagram of FIG. 3. This switch is designed to undergo an electric field-induced crystalline phase transition. The switch comprises a channel layer comprising the crystalline domains of VO.sub.2 302, a first electrically conducting contact 304 in electrical communication with layer 302, and a second electrically conducting contact 306 in electrical communication with layer 302. The switch embodiment shown here also includes a dielectric substrate 307 comprising the SnO.sub.2 308 and TiO.sub.2 309 layers of the layered structure. The crystalline phase change in the VO.sub.2 channel layer can be triggered by the application of an external electric field. This is typically accomplished by applying an external voltage from an external voltage source to first electrically conducting contact 304. If the magnitude of the applied voltage is meets a certain voltage threshold, it will induce the phase change and trigger the switch.

(22) FIG. 4 is a schematic diagram of the three-terminal field effect switch that incorporates a VO.sub.2 layer as a channel. The switch comprises a source 412, a drain 414, and a channel layer comprising the crystalline domains of VO.sub.2 402 disposed between source 412 and drain 414. A gate stack comprising a gate dielectric 416 and a gate contact 418 is disposed on channel layer 402. The field effect switch also includes a dielectric substrate 407 comprising the SnO.sub.2 408 and TiO.sub.2 409 layers of the layered structure. The crystalline phase change in the VO.sub.2 channel layer can be triggered by the application of a gate voltage, such as a negative gate voltage, to gate contact 418. If the applied gate voltage is greater than the threshold voltage, it will induce the phase change and trigger the switch.

(23) Although the switches shown in FIGS. 3 and 4 include the SnO.sub.2 template layer and TiO.sub.2 substrate upon which the VO.sub.2 layer is grown, it is also possible to remove one or both of these layers after VO.sub.2 layer growth and then transfer the VO.sub.2 layer onto another support substrate, which may be an electrically conducting (metallic), semiconducting, or electrically insulating substrate.

Example

(24) In this example, VO.sub.2 films were grown on an SnO.sub.2-templated TiO.sub.2 (001) substrate. SnO.sub.2 is insulating and has a rutile symmetry isostructural with VO.sub.2 at its growth temperature, making it relevant as a template for epitaxial VO.sub.2 growth (FIG. 5A). A large lattice mismatch (4.2%) between VO.sub.2 and SnO.sub.2 results in an abrupt strain relaxation at the interface region within a few nanometers. As a result, severe structural defects, including strain gradient, were confined only near the interface between the VO.sub.2 and SnO.sub.2, leading to homogeneous, bulk-like lattices in the VO.sub.2 film (FIG. 5C) and a sharp MIT above room temperature. Additionally, the low solid solubility between VO.sub.2 and SnO.sub.2 significantly enhanced the materials' chemical sharpness at the interface by reducing interfacial intermixing. Thus, thin-film epitaxy using an SnO.sub.2 template is a suitable process for producing homogeneous, crystalline, crack-free VO.sub.2 films.

(25) Materials and Methods

(26) Crystalline VO.sub.2 epitaxial thin films were grown on (001) TiO.sub.2 substrates using the pulsed laser deposition (PLD) method. Before deposition, low miscut (<0.1) TiO.sub.2 substrates were cleaned by sonicating with acetone and then rinsing with isopropanol. An SnO.sub.2 epitaxial layer with a thickness of 100 nm was deposited as a bottom template on the TiO.sub.2 substrate. A KrF excimer laser (=248 nm) beam was focused on SnO.sub.2 and V.sub.2O.sub.5 ceramic targets to an energy density of 2.0 J/cm.sup.2 and pulsed at 5 Hz (for SnO.sub.2 layer) or 10 Hz (for VO.sub.2 layer). SnO.sub.2 layers were grown at a substrate temperature of 400 C. and oxygen partial pressure of 50 mTorr. After growth of the SnO.sub.2 layer, the VO.sub.2 layer was grown at the temperature of 400 C. and oxygen partial pressure of 18 mTorr. After growth, the VO.sub.2/SnO.sub.2 films were cooled down to room temperature at an oxygen partial pressure of 18 mTorr.

(27) The structural qualities of the films were examined using high-resolution X-ray diffraction (XRD). The XRD pattern of the VO.sub.2/SnO.sub.2/TiO.sub.2 film showed a clear film peak at 2=64.8 along with (002) diffraction peaks from the underlying rutile SnO.sub.2 and TiO.sub.2 substrate. This film peak comes from the (402) reflection of monoclinic VO.sub.2, and these correspond with the (002) reflection of VO.sub.2's high-temperature rutile phase. No other peaks were observed using XRD analysis, proving that the VO.sub.2 film was highly oriented and had a pure phase. The peak position (i.e., 2=64.7) was almost identical to that of the (402) reflection for bulk, monoclinic VO.sub.2, suggesting that the film was fully relaxed and had bulk-like lattices. Importantly, the VO.sub.2/SnO.sub.2/TiO.sub.2 film exhibited a symmetric diffraction peak, well fitted with a single peak, implying that the misfit strain was abruptly relaxed without gradual strain relaxation. In contrast, the VO.sub.2/TiO.sub.2 film exhibited an asymmetrical diffraction peak, implying the presence of a gradual strain relaxation in the film, consistent with this study's initial predictions.

(28) To obtain further information on lattice strains, X-ray reciprocal-space mappings (RSMs) were used. In the case of the VO.sub.2/TiO.sub.2 film, the film's RSM peak position (denoted by a closed, circle) was far from that of the VO.sub.2's bulk (denoted by a closed, star), indicating that the VO.sub.2 film was still partially strained. Furthermore, the film's RSM peak featured a shoulder directed toward the bulk peak position, confirming gradual strain relaxation in the film. As for the VO.sub.2/SnO.sub.2/TiO.sub.2 film, the peak position of the film was identical to that of the bulk VO.sub.2. This indicates that the use of an SnO.sub.2 template leads to homogeneous lattices, as well as to complete relaxation for the misfit strain in the VO.sub.2 film.

(29) Results

(30) Based on initial predictions, structural inhomogeneity determined the MIT behavior of the VO.sub.2 films. To visualize the role of local inhomogeneities on MIT, in situ transmission electron microscopy (TEM) was used. The monoclinic-to-rutile structural phase transition was monitored by heating the VO.sub.2 films. Abrupt changes to lattice parameters (FIG. 5A), as well as to symmetry, during the phase transition caused noticeable contrast between the monoclinic and rutile regions, allowing clear visualization of the structural phase transition. For VO.sub.2 films on bare TiO.sub.2, the rutile phase started to nucleate from the interface at 315 K, which is much lower than the nucleation point for bulk T.sub.MIT (i.e., 341 K), and the phase transition was complete near the surface and cracks. The local profile of the films' respective strains and electric potentials were measured using inline holography (FIGS. 6B, 6C), and there was a close relationship between local strain and T.sub.MIT. However, whereas regions near the surface and cracks experienced negligible strain in the bulk-like T.sub.MIT, the interfacial regions with relatively more strain preferred the rutile structure and had much lower T.sub.MIT, resulting in a broad MIT (FIG. 6E).

(31) In contrast, the VO.sub.2 film on SnO.sub.2-templated TiO.sub.2 exhibited a much sharper, bulk-like phase transition and did not exhibit any structural or electronic inhomogeneities distinct from those of the VO.sub.2 film on bare TiO.sub.2. As a result, the VO.sub.2 film on SnO.sub.2/TiO.sub.2 had a much sharper transition, and most of its structural-phase transition was complete between 341 and 343 K (FIGS. 6D, 6E). Interestingly, for the VO.sub.2 film on SnO.sub.2/TiO.sub.2, the structural phase transition began at the surface and ended at the interface, which is the opposite of how the transition progresses in VO.sub.2 films on bare TiO.sub.2 (FIG. 6A). These phase-field simulations reveal that homogeneous VO.sub.2 single crystals have a monoclinic-to-rutile phase transition that begins at the surface. Thus, the present study's in situ TEM and simulation results demonstrate that placing a VO.sub.2 epitaxial film on an SnO.sub.2-templated TiO.sub.2 offers a more reliable, enhanced MIT, whose sharpness and magnitude are as good as those of intrinsic VO.sub.2 single crystals.

(32) To characterize the MIT and its sharpness, electrical resistance was measured as a function of temperature in VO.sub.2 films with or without an SnO.sub.2 template (FIG. 7A). The resistance of the 300-nm-thick VO.sub.2 film on the SnO.sub.2/TiO.sub.2 substrate caused a change of four orders of magnitude (i.e., 310.sup.6%) during MIT, while the resistance change was drastically reduced in VO.sub.2 films on bare TiO.sub.2, possibly due to the presence of a strain gradient and cracks (FIGS. 9A and 9B). The transition temperature for the VO.sub.2/SnO.sub.2/TiO.sub.2 film was 341 K, the same as for the bulk VO.sub.2. As FIG. 7A also clearly shows, the VO.sub.2/SnO.sub.2/TiO.sub.2 film exhibited a much sharper MIT compared with films of the same thickness on bare TiO.sub.2. The sharpness of the VO.sub.2/SnO.sub.2/TiO.sub.2 film's MIT was quantitatively estimated to be <1 K using the width of its derivative curves (FIG. 7B). This MIT sharpness (i.e., 0.5 K) is comparable to that of fully coherent, 10-nm-thick VO.sub.2 films on bare TiO.sub.2. Thus, this study's electrical-transport measurements indicate that homogeneity engineering using an SnO.sub.2 template allows for a sharp, pronounced resistance change across MIT, while maintaining a bulk-like transition temperature.

(33) Thus far, electrical-transport measurements have been used to determine the sharpness of the MIT. However, electrical conduction can be dominated by low-resistive local regions and associated short-circuit currents so that the transport measurements might not effectively reflect MIT sharpness for the overall film region. Because of this, optical measurements were adopted in addition to electrical measurements. Using spectroscopic ellipsometry, refractive index n and extinction coefficient k were measured as a function of temperature. It is known that the complex dielectric function and associated n and k exhibit a noticeable change during MIT. (See, J. B. Kana Kana et al., Opt. Commun. 284, 807 (2011).) Furthermore, in contrast to electrical measurements, measurements of n and k are governed by the averaged optical response for the whole film region, rather than for local regions alone. Thus, optical measurements of n and k effectively reveal genuine MIT features, such as sharpness, in VO.sub.2 films.

(34) FIGS. 7C-F show the values for n and k measured during heating as functions of temperature, as well as wavelength of incidental light for 300-nm-thick VO.sub.2 films. For the VO.sub.2/SnO.sub.2/TiO.sub.2 film (FIGS. 3C, 3D), n and k exhibited abrupt changes for every across MIT with a T.sub.MIT of 341 K, and this was the same as with the bulk sample. This sharp transition in n and k is attributable to the film's homogeneous nature (FIG. 5C). And yet, for the VO.sub.2/TiO.sub.2 film (FIGS. 7E, 7F), n and k exhibited gradual changes across MIT with an average T.sub.MIT of 320 K, and this is attributable to the film's local inhomogeneities (FIG. 5B). Furthermore, the lower average T.sub.MIT value compared with the bulk value is attributable to the film's average tensile strain. Thus, these optical measurements confirm that the VO.sub.2/SnO.sub.2/TiO.sub.2 film had a sharp MIT, and they underscore the importance of homogeneity engineering in producing high-quality epitaxial VO.sub.2 films.

(35) Last, SnO.sub.2 template's contributions were examined to prevent the VO.sub.2 from cracking. VO.sub.2 bulk crystals tend to crack under large amounts of stress during MIT, and they degrade upon repeat cycling. Strain relaxation in VO.sub.2 epitaxial films can also cause such cracks (FIG. 8A). In this study, an increasing number of such cracks were formed after repeated thermal cycles, and they severely affected the MIT features of the VO.sub.2 film on bare TiO.sub.2. A more significant, increased resistance to cracks occurred during the nominally metallic phase, and as a result, the magnitude of resistance change across the MIT was far less, down to 10.sup.5%. On the other hand, the VO.sub.2 films on SnO.sub.2/TiO.sub.2 had robust MITs, and the magnitude of their resistance change remained at 10.sup.6%, even after 1,000 cycles. This indicates that, once confined to the interface, structural defects like cracks don't spread into the films after repeated cycles with VO.sub.2/SnO.sub.2/TiO.sub.2 films.

(36) This example demonstrates thin-film epitaxy of structurally homogeneous, crack-free VO.sub.2 with a sharp, reliable MIT grown using an SnO.sub.2 template layer. Furthermore, correlated electron materials have exhibited various other novel phenomena in addition to the MIT, including superconductivity and colossal magnetoresistanceboth of which are desirable for emerging electronics applications. These properties are, generally, strongly dependent on lattice strain due to a combination of charge, spin, orbitals, and degrees of lattice freedom. Thus, this study provides a general framework for predictively designing homogenous, heteroepitaxial materials with reliable electronic functions that include, but are not limited to, material MIT.

(37) The word illustrative is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as illustrative is not necessarily to be construed as preferred or advantageous over other aspects or designs. Further, for the purposes of this disclosure and unless otherwise specified, a or an means one or more.

(38) The foregoing description of illustrative embodiments of the invention has been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention. The embodiments were chosen and described in order to explain the principles of the invention and as practical applications of the invention to enable one skilled in the art to utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents.