Self‐Assembly of Nanocrystalline Structures from Freestanding Oxide Membranes

The exploration of crystalline nanostructures enhances the understanding of quantum phenomena occurring in spatially confined quantum matter and may lead to functional materials with unforeseen applications. A novel route to fabricating nanocrystalline oxide structures of exceptional quality is presented. This is achieved by utilizing a self‐assembly process of ultrathin membranes composed of the desired oxide. The thermally induced self‐assembly of nanocrystalline structures is driven by dewetting the oxide membranes once they are lifted off and transferred onto sapphire surfaces. In three successive steps, the process provides nanovoids, nanowires, and nanocrystals. Regardless of substrate orientation, the nanostructures are highly anisotropic in shape due to material retraction favoring low‐index crystalline lattice directions of the membranes. The orientation of the nanostructures is provided precisely by the crystal lattice of the transferred membrane. The microstructure of the nanocrystals exhibits exceptional quality, characterized by a pristine crystal structure and uniform stoichiometry, both maintained all the way down to the well‐developed crystalline facets. The demonstrated self‐assembly process holds the potential to improve the understanding of surface diffusion phenomena at the interface of materials, which is important for advancing epitaxial growth technology and paves the way to fabricating crystalline nanostructures by the transfer and self‐assembly of membranes.


Introduction
Nanocrystalline materials have been in use since the Bronze Age in ancient Egypt, [1] primarily for producing vivid colors and rich hues in pigments and glass. Nanomaterials provide an excellent example of nanoscience that has long been applied historically based on empirical knowledge, albeit without a the driving microscopic processes. [14,[36][37][38][40][41][42][43] It is interesting to note that, despite the long history of dewetting elemental films, the fabrication of complex oxide nanostructures based on self-assembly has remained largely unexplored. [32,44,45] We attribute this lack of studies to the generally high temperatures required to induce material agglomeration by oxide films due to the high bonding energies involved. We will describe how highquality, freestanding oxide membranes [46] enable the growth of nanocrystalline functional oxides by such a self-assembly process. Using such membranes, we reveal how dewetting initiates the growth of nanocrystallites of excellent quality by self-assembly of transferred membranes. While we use complex oxides for the possible usefulness of the nanostructures, we suggest that our process could be applied to additional complex functional materials such as carbides or nitrides.

Materials and Methods
Complex oxides are a fascinating class of materials. For example, they feature a variety of functionalities and physical states, including superconductivity, ferroelectricity, magnetism, and multiferroicity. Recently, new prospects for using complex oxides have been created by technological advances that allow the fabrication of freestanding membranes consisting of epitaxially grown perovskite films. These membranes can be transferred to any platform, and therefore are no longer bound to the substrate, upon which the films were originally grown. [46,47] For instance, this technique has enabled oxide membranes to be strained up to 8% with different strain symmetries, while the ground state is changed by the applied strain. [48,49] Freestanding oxide membranes have been shown to have exceptional nanomechanical properties [50] and can withstand extremely high strains. In a variety of materials, achievable strains exceed the bulk values by two orders of magnitude. [51][52][53] However, these complex oxide thin films, in both epitaxial and freestanding forms, still pose challenges to fabricating nanostructures. The standard patterning techniques for oxides are wet etching, focused ion beam patterning, or ion milling, which cause damage near the etched part of the material. [54][55][56][57] These methods are limited to the resolution of the lithographical process employed. Furthermore, it can prove difficult to align the patterned nanostructures precisely to the crystallographic axes of the crystal. To overcome these challenges, we exploit a dewetting-driven self-assembly of freestanding oxide membranes transferred onto a new substrate. This approach eliminates the strong bonding between the substrate and the film that is present after epitaxial growth. For appropriate substrates, this process indeed allows dewetting of the membrane. In this study, we chose sapphire as the substrate material because, like metallic films, sapphire has been used extensively to study dewetting processes.
Our process calls for preparing sapphire surfaces with the recently developed technology of heating substrates to various temperatures by in situ infrared radiation with a CO 2 laser beam of 10 µm wavelength. [58] This produces extremely high-quality sapphire surfaces, which are ideal for accommodating transferred freestanding membranes. Later in the process, equivalent laser heating is used to perform the dewetting by uniformly heating the substrates that carry the transferred membranes. To fabricate suitable membranes, thin films of oxides are first grown via pulsed laser deposition on a water-soluble aluminate buffer layer grown epitaxially on a SrTiO 3 (001) substrate, with in situ monitoring using reflection high-energy electron diffraction (RHEED) ( Figure S1, Supporting Information). Subsequently, the membranes are transferred via water-assisted liftoff at room temperature [46] onto the sapphire substrate ([0001] out-of-plane) for subsequent processing (Figure 2).

Orientation Dependence of Nanocrystallite Formation
For single-crystal films, we found that the dewetting morphology is determined by the initial film orientation, the lattice symmetry, the temperature T, and the initial thickness t of the membrane, in agreement with the previously explored behavior of Si and Ni. [18,36,37,59] Our studies, in which single-crystalline oxide films are transferred onto single-crystalline oxide substrates, provide an opportunity to study the orientation dependence of the dewetting process explicitly. Indeed, these studies revealed that the relative orientation of the membrane with Adv. Mater. 2023, 35, 2210989 Figure 1. Atomic transport processes that occur upon heating a thin film on a substrate. Surface diffusion along the surfaces of the film surface or substrate is a relevant process. A diffusing particle may encounter diffusion barriers along the substrate surface; it may bond to a site and nucleate a new crystalline island. Interdiffusion yields material exchange between the film and the substrate. Particles can also evaporate and condense on the film surface. Capillary-force-induced edge retraction may lead to dewetting of the substrate surface.
respect to the substrate is a key parameter in controlling nanocrystal self-assembly, as we will discuss below. To explore whether the relative orientations of the membrane and the substrate affect the dewetting morphology, we diced four pieces from a 5 mm × 5 mm sample consisting of 24 nm thick Sr 3 Al 2 O 6 and 5.9 nm thick SrTiO 3 layers grown on SrTiO 3 (001). We lifted the relieved SrTiO 3 membranes and transferred them onto a sapphire substrate, rotating the SrTiO 3 (001) axis to equal ≈0°, 30°, 50°, and 90° with respect to the sapphire [1120] axis (Figure 3 and Figure S2 (Supporting Information)). With this procedure, we ensured that the same membrane was employed for measuring the orientation dependence, thus ruling out sample-to-sample variations. These SrTiO 3 -sapphire stacks were systematically heated to 800-1200 °C at an oxygen ambient pressure of 0.075 mbar. Reaching such temperatures (and higher) with uniform heating across the substrate is achieved by laser heating equivalent to the one used for the substrate preparation. The voids that first form in this process are, with distinct exceptions, all strikingly rectangular in shape with the edges of the rectangle pointing exactly in the orientation of the transferred membrane. The boundaries of the transferred membrane match the <100> directions. Thus, the most prominent dewetting fronts are also oriented in <100> directions. Furthermore, we observe retraction facets at 45° from the dominant rectangular void edges, revealing that the <110> direction presents a second stable agglomeration front for the SrTiO 3 membrane. Figure S2 (Supporting Information) presents the full temperature-dependent evolution of dewetting for membranes as a function of the alignment angle with respect to sapphire [1120]. These results provide evidence that the surface energy of the SrTiO 3 facets commands the dewetting process. Remarkably, the interfacial adhesion energy between the membrane and the sapphire interface is less important in controlling facet formation. Indeed, in all cases we have found the dewetting membranes of other orientations and materials to be consistent with the transferred orientation.

Dependence of Nanocrystalline Structures on Membrane Thickness and Process Temperatures
We now proceed to our studies of the influence of membrane thickness and processing temperature on the formation of nanocrystalline structures. Both parameters have proved critical in affecting the dewetting of metal films. [14,16] We studied the effects of these two parameters by growing SrTiO 3 membranes of four different thicknesses and LaAlO 3 membranes of three different thicknesses. These membranes were transferred onto prepared sapphire substrates and processed via a temperature series, while the evolution of the resulting dewetting  The grown heterostructure of an aluminate buffer layer and oxide films is coated with a polymer support and put in water to dissolve the buffer layer. The polymer-supported film is then transferred to the sapphire substrate, where the polymer is dissolved. b) AFM image of the surface of an as-prepared sapphire substrate. c) AFM image of a 6.6 nm thick SrTiO 3 membrane transferred onto a sapphire substrate, where the boundary between the bare substrate and the membrane is clearly visible. The inset shows an optical microscopy image of the transferred membrane. The outline of the transferred SrTiO 3 membrane is marked. Note that the color scales and scan sizes in (b) and (c) differ. morphology was studied (Figure 4). For LaAlO 3 , we used 24 nm thick Sr 2 CaAl 2 O 6 films as the buffer layer. Their thickness was empirically optimized to obtain intact freestanding membranes with a practical liftoff duration. In all cases, we find that, independent of membrane thickness, the samples self-assemble in the same three stages, albeit for given heating times at different temperatures ( Figure S3, Supporting Information). The first stage of the agglomeration process is always the appearance of voids or holes in the membranes. According to the literature, this void formation requires local defects or preexisting holes to seed thinning and retraction of material. [14] Such defects are point defects, dislocations in the membrane, or irregularities on the substrate surface. The defects reduce the nucleation energy of new surfaces and voids. In the second stage, the boundaries of the voids retreat, allowing the voids to grow. The voids, which are enclosed most frequently by welldefined facets, continue growing until the percolation threshold is reached and highly faceted lines or strands form on an ≈500 nm length scale connecting the separating nanocrystals. As crystalline faceting stabilizes the nanocrystallites against a Rayleigh-Plateau instability, [16,60] these strands can be large with aspect ratios far exceeding 1. Upon further processing at higher temperatures, the connectivity of the nanostructures is lost completely. At this third stage, well-facetted 3D nanocrystals oriented vertically in growth direction develop with welldefined lateral facets. These three agglomeration stages occur consistently for all membrane thicknesses, with the temperature required for each stage generally shifting with increasing membrane thickness to higher values. The step edges of the substrate, in general, do not affect the process of void formation and depercolation, but serve as diffusion barriers for adatoms. Indeed, numerous particles can be seen touching the step edges but rarely is a particle observed to drape over one ( Figure S3, Supporting Information). The coverage of the sapphire surface by the membrane decreases monotonically with processing temperature, with the coverage-temperature curve shifting to higher temperatures as the thickness is increased (Figure 5a,b). For the sake of clarity, we will henceforth establish the dewetting temperature (T dw ) of the membranes as the temperature at which voids became observable. T dw increases  monotonically as a function of membrane thickness for both SrTiO 3 and LaAlO 3 ( Figure 5c). Furthermore, we observe that the T dw of LaAlO 3 membranes is consistently higher than that of SrTiO 3 membranes of similar thicknesses. A possible reason for this behavior is the higher stability of the LaAlO 3sapphire compared to the SrTiO 3 -sapphire interface. This increase of T dw agrees with the dewetting behavior of other materials such as gold, silver, and copper reported in the literature. [61,62] In addition to T dw , the mean height of the nanocrystals is another key parameter characterizing the self-assembly process. Indeed, we find that the thickness of nanocrystallites increases as a function of the initial film thickness (Figure 5d). This finding is consistent with straightforward expectations, as thicker films provide more material to agglomerate.

Transmission Electron Microscopy of SrTiO 3 Membrane Dewetting
To gain further insight into the formation of nanocrystals and their properties, we analyzed the membranes microscopically. The crystalline quality, chemical homogeneity, and facets of dewetted SrTiO 3 nanocrystallites were studied by scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy at two stages of dewetting of an initially 6.6 nm thick SrTiO 3 membrane, annealed at 1000 and 1100 °C for 200 s. Consistent with atomic force microscopy (AFM) results, the STEM analysis of cross-sectional sample cuts shows that the density of dewetted nanocrystallites decreases with higher process temperatures, together with a reduction and enhancement of the lateral size and thickness of the nanostructures, respectively ( Figure S4, Supporting Information). Furthermore, the dewetted SrTiO 3 nanocrystallites possess exceptional crystalline quality and show low-indexed facets. High-resolution high-angle annular dark field-scanning (HAADF)-STEM images present the atomic lattice devoid of visible defects anywhere on the SrTiO 3 nanocrystalline crosssection (Figure 6a,b and Figure S5 (Supporting Information)). The uniformity of the contrast in the HAADF image demonstrates the excellent structural homogeneity of these dewetted structures. The retraction edge maintains high crystallinity with well-defined crystalline facets comprehensively to the boundary (Figure 6a,b). Furthermore, we find that the overall curvature of the edge increases at higher process temperatures, which, after annealing at 1100 °C, is accommodated by the introduction of higher indexed crystalline facets. These findings clearly reveal that the surface energy of the lattice planes stabilizes the faceted geometry. We observed no droplet formation, which would provide the lowest surface area and would be obtained if purely cohesive capillary forces were active. Nevertheless, the increase in curvature at higher annealing temperatures reveals that the surface energies of a faceted structure and a smoothly curved surface are comparable. Throughout the heating process, the crystals were found to maintain their out-of-plane orientation in the [001] direction. Note that during sample fabrication, the Al 2 O 3 substrates and membranes are not perfectly aligned, thus, the high symmetry directions of the substrate and the membrane differ.
The distribution of the constituent elements in a single SrTiO 3 nanocrystallite was analyzed by electron energy-loss spectroscopy (EELS). As illustrated by the elemental EELS maps (Figure 6c), the constituent elements of the SrTiO 3 nanocrystallites are distributed uniformly across the agglomerated geometry. The interface between the SrTiO 3 membrane and the sapphire substrate is sharp without visible interdiffusion. The elements are identified using the O-K, Sr-L 2,3 , Ti-L 2,3 , and Al-K edges ( Figure S6, Supporting Information). Atomically resolved STEM-EELS maps resolve an atomically sharp interface between the transferred membrane and the substrate. At the interface, the intensity of the Sr and Ti signals drops to their baseline value within 1 unit cell across the boundary (Figure 6d). These results provide evidence of highquality crystallinity and composition that the self-assembly process can achieve. To our knowledge, nanocrystalline structures of such high quality extending to the crystal surface have not been reported for nanostructures prepared by electron beam lithography or other top-down techniques based on material removal such as ion milling.

Nanocrystalline Self-Assembly through Material Agglomeration
Having reported our findings on the experimental control of the self-assembly and microscopic properties of nanostructures, we will now analyze the self-assembly process and its potential for nanofabrication and device applications. Throughout all stages of nanocrystalline restructuring, we observe selfassembly and the formation of pristine crystalline nanostructures. Starting at low temperatures, voids enclosed by facets are formed. With increasing T, oriented nanowires self-assemble. The membranes eventually depercolate and form individual nanocrystals. Destabilization effects seen in single-crystal metal and semiconductor dewetting are largely absent. [40,43] The oxide crystal facets define the recrystallization of the material during agglomeration.
For all SrTiO 3 and LaAlO 3 membrane thicknesses we have tested, processing at 1300 and 1400 °C, respectively, resulted consistently and repeatably in the formation of well-defined, singly oriented nanocrystals. For nanocrystalline particles formed by complete depercolation, we noted two key characteristics. First, the top surface of the particle is atomically flat and its surface being a plane consistent with the orientation of the original membrane. Second, we observe that the top and Figure 5. a,b) Measurements of substrate coverage as a function of process T. The stages of dewetting depict a decrease in overall coverage with increasing temperature. The membrane coverage decreases monotonically as a function of temperature, with the temperature at which films start dewetting shifting to higher temperatures with increasing thickness. c) The dewetting temperature (T dw ) where we initially observe voids plotted as a function of initial membrane thickness. T dw increases monotonically with increasing thickness, but remains significantly lower than the melting temperature of SrTiO 3 and LaAlO 3 . Asymmetric error bars represent the size of subsequent temperature steps during thermal processing (50 °C). d) The mean height of nanocrystals plotted as a function of the initial thickness of membranes. The mean heights increase monotonically, which is expected because a larger amount of material is available for nanocrystal formation. Error bars give the standard deviations of the height distributions.
the bottom surfaces of the particle are connected primarily by a low-index plane. For example, along the <100> direction of a (001)-oriented SrTiO 3 nanocrystal (Figure 7), the plane that connects the top and bottom surfaces is a {101} plane. Similarly, in <110> direction, {111} is the connecting plane. Faceting planes are also equivalently identified for the (111)-oriented SrTiO 3 nanocrystal (Figure 6b). Finally, we note that the facets are not clearly visible in the AFM scans of LaAlO 3 nanocrystals (Figure 6c), which is likely because the vertical face is located at the edges of the crystal.
Potential applications of thermal dewetting of membranes are not restricted to the growth of nanocrystals. During stage 2 of the processing step, void growth occurs by retracting fronts of the holes retreating in the low-index directions of the transferred membrane. This is illustrated by the measured ≈90° angle between the retraction fronts ( Figure 7a). Faceting at this stage of retraction is well-defined and crystalline, as evident from the STEM images of SrTiO 3 ( Figure 6).
As discussed above, the crystalline nature of retraction fronts can stabilize the high-aspect-ratio nanowires, because the edges of the nanowire do not undergo a Rayleigh-Plateaulike instability. For example, we show high-quality SrTiO 3 and LaAlO 3 nanowires self-assembled and oriented along the <100> direction (Figure 7b). The largest aspect ratio nanowire that we found to be formed by this process was ≈30 for SrTiO 3 ( Figure S7, Supporting Information).
To elucidate the energies relevant to the self-assembly process, we apply a straightforward model to the dewetting of SrTiO 3 . This model follows the dewetting model of ref. [32] and provides an estimation of whether a hypothetical hole initially present in a membrane may dewet to reduce coverage due to void growth. We compare the energy after dewetting E dw to the intact membrane energy E 0 for a square film with an initial thickness of h and size a, with a square hole of size x with {101} facets (Figure 8). Using this geometry, we obtain the ratio of the energy of the dewetted structure to the energy of the initial structure Adv. Mater. 2023, 35, 2210989   Figure 6. a) STEM and EELS observations of nanocrystalline structures obtained by self-assembly. After processing at 1000 °C, a SrTiO 3 membrane reveals material agglomeration and recrystallization by dewetting. The thickness of this region is nearly 3 times the initial membrane thickness. There is a transition region between the top and bottom surfaces, where these surfaces are connected via crystalline facets, as marked in the image. b) Upon annealing the membrane at 1100 °C, the edges retreat further, resulting in thicker regions after dewetting. The boundaries show more curvature for this thicker structure, but this is accommodated by the introduction of additional crystalline facets between the top and bottom faces of the crystallite. The crystal structure is still maintained completely to the boundary; the uniform contrast indicates a minimal defect density in such a structure. c) Annular dark-field (ADF) image, elemental EELS maps for Sr, Ti, Al, and O, and color-coded overlay of the elemental maps for Sr, Ti, and Al throughout the entire dewetted geometry showing the exceptional uniform elemental distribution and a sharp interface between the membrane and the substrate. d) High-resolution ADF image, elemental EELS maps for Sr, Ti, Al, and O, color-coded overlay of the elemental maps for Sr, Ti, and Al, and horizontally integrated intensity profiles for the elements Sr (red), Ti (green), and Al (blue) across the interface demonstrating the uniform distribution of Sr and Ti in the membrane and the atomically sharp interface between the membrane and the substrate.
where d = x/a and r = h/a, γ s is the surface energy density of the substrate, γ i the interfacial surface energy density and γ 001 and γ 011 are the energy densities of the {001} and {011} planes, respectively. As we are dealing with oxides on both the substrate and membrane sides, we take γ s /γ 001 = 1 to simplify the understanding of the energy landscape. By plotting the energy ratio for different interfacial energy densities and r, we infer that, for a fixed aspect ratio, the propensity to dewet increases with increasing interfacial energy (Figure 8a). Note that the ratio E dw /E 0 = 1 is the threshold for dewetting, i.e., if E dw /E 0 < 1, then the film self-assembles into a new structure. This model also shows that, for a fixed ratio of interface energy to the {001} face energy (E r = γ i /γ 001 ), thinner films more easily dewet (Figure 8b). Furthermore, a maximum thickness is Adv. Mater. 2023, 35,   found for which the film will dewet for a given E r . In addition, an energy barrier is identified for the film to start dewetting and the voids to increase. As shown, the voids are found to acquire a critical size before they spontaneously increase. This energy barrier increases with thickness together with an increase in critical void size ( Figure S8, Supporting Information). The energy landscape of agglomeration is illustrated by the maps of E r and r versus d, shown in Figure 8c-f. By tracing the contour of 1, a critical E r is defined for every r. Dewetting is only possible for E r > r crit E (Figure 8c,d). Furthermore, dewetting does not occur for fixed E r above a well-defined value of r (Figure 8e,f). The critical size increases monotonically with decreasing E r and increasing r, as shown by the local maximum marked as the barrier in Figure 8c-f. This simple model consistently explains the thicknessdependent behavior of SrTiO 3 membranes. It further provides a tool to derive the interface energy between the membrane and the substrate from the measured nanostructures. To do so, we take the largest mean r ≈ 0.1 found for the self-assembled SrTiO 3 nanocrystals because these are the largest nanostructures formed without a void in the middle. In Figure 8c,d, the agglomeration energy maps use the interface energy as a continuously varying parameter and thus we can explore this parameter at the boundary of wetting-dewetting for a given r.
Taking this threshold value for r = 0.1, as in Figure 8c, we derive E r ≈ 2.4. With γ 001 for TiO 2 -terminated SrTiO 3 (001) plane, [63] we obtain γ i = 3.11 J m −2 for SrTiO 3 on sapphire. This value is comparable to the surface energies of binary oxides with rock salt structure. [64] It is ≈50% higher than the surface energies of pure metals, [64] a factor of ≈3 higher than common semiconductors [65] and exceeds the one of the SrTiO 3 (001) plane by a factor ≈2.4. We therefore expect the membrane-substrate interfaces to be thermodynamically less stable than the material-vacuum interfaces, and therefore conducive to dewetting.

Conclusion and Outlook
A way to produce crystalline nanostructures of complex oxides has been found using self-assembly of membranes by dewetting. Dewetting is already well understood for a variety of materials from metals to semiconductors but has barely been utilized to fabricate complex oxide nanostructures. By applying recent developments in oxide film growth, we transferred complex oxide membranes of LaAlO 3 and SrTiO 3 onto sapphire substrates. Upon annealing at temperatures below the melting point of the membranes, we achieved crystalline selfassembly of the membrane into a variety of nanostructures.
Adv. Mater. 2023, 35, 2210989 Figure 8. Results of the model calculations of the self-assembly process. The panels compare the energies of a dewetted geometry versus a structure with complete coverage under volume-conserving dewetting. a) The energy ratio of the dewetted structure versus a fully intact membrane transferred onto a substrate, where the initial aspect ratio is kept constant and the ratio of the interface energy to the energy of the (001) plane (E r ) is varied, plotted as a function of d, the ratio of void size to the lateral size of the initial membrane. The propensity to dewet increases with increasing interface energy, with larger void sizes and higher energy differential between the dewetted and the initial geometry. b) Energy ratio for different initial r = h/a, with the same interface energy. Stability of the dewetted structure increases with decreasing r, meaning thinner membranes are easier to agglomerate. Close to full coverage an energy barrier is observed which provides a critical size to be reached before membranes dewet spontaneously ( Figure S8, Supporting Information). c,d) Energy landscapes for a given r as a function of different values of E r , where the dashed white curve marks the contour of E dw /E 0 = 1, demarcating the region where the dewetted membrane is thermodynamically more stable than the initial membrane. The phase space available for dewetting at different values of r can be clearly seen between (c) and (d). The red curve marks the critical size of dewetting, tracing the maximum of the energy barrier. The black curve traces the minimum of E dw /E 0 . e,f) Similar maps as in (c) and (d), but for given E r as a function of different r values. This process is governed by the crystallographic orientation of the transferred film and shows that agglomeration fronts prefer crystalline directions for retraction during agglomeration. Formation of nanocrystals with sizes down to 100 nm laterally and nanowires with aspect ratios exceeding 10 have been obtained. Transmission electron microscopy confirms the high quality of crystallinity extending to the crystal facets as well as a uniform elemental distribution. No intermixing with the substrate was observed.
We have presented a straightforward analytical model from which the interface energy between the membrane and the substrate is derived. This self-assembly of a variety of nanostructures, their high quality, and the temperature and thickness dependencies of the self-assembly process opens new possibilities for crystalline nanostructuring of oxide materials without damage induced by ion-beam radiation or wet chemical etching. At the current stage, we have control over facet orientation, size, and percolative character of these nanostructures, but not over the location of nanocrystals and voids, nor the location and orientation of strands. Control of the latter parameters may be achievable by templating the membranes or substrates. [15,20,22,29] Aside from the possible applications, self-assembly provides an opportunity to explore membranesurface interaction for transferred membranes as well as the role of interfacial energy.
These findings illustrate the nanofabrication opportunities created by dewetting complex oxides. The high-quality crystallinity and self-orienting nature of dewetting along crystalline axes is unprecedented, and their alignment exceeds the capabilities of lithography and ion-milling techniques. These nanostructures are suggested for use in optics, catalysis, and nanoelectronics. Furthermore, they are expected to shed new light on finite size and interface effects as well as on spacecharge layers in nanocrystals. [66,67] We expect that the dewetting of membranes will enhance our understanding of adatom diffusion on substrate interfaces and nanocrystal facets, and thus be useful to the vast field of epitaxial thin film growth. [68] Owing to the universality of membranes being inherently unstable, we expect this work to be generalizable to other oxides, as well as to carbides, nitrides, and other functional materials.

Experimental Section
Epitaxial Film Growth: Before growth, the SrTiO 3 (001) and (111) substrates were preannealed in an ultra-high vaccuum (UHV) chamber at 1105 °C for 200 s under oxygen partial pressure P O2 of 7.5 × 10 −2 mbar using a CO 2 laser to achieve atomically flat single-terminated surfaces. For pulsed laser deposition, an excimer laser with a wavelength of 248 nm was used. The buffer layer of Sr 3 Al 2 O 6 was grown on the annealed SrTiO 3 (001) substrate at a substrate temperature of 900 °C and P O2 = 1 × 10 −5 mbar, 1.6 J cm −2 laser fluence, and a repetition rate of 1 Hz. For Sr 2 CaAl 2 O 6 , a growth temperature of 850 °C and P O2 = 1 × 10 −5 mbar were used with a laser fluence of 1.6 J cm −2 . All targets were commercial targets (Kurt J. Lesker). The SrTiO 3 films were grown at a substrate temperature of 900 °C and P O2 = 1 × 10 −5 mbar, using 0.8 J cm −2 laser fluence. LaAlO 3 films were grown at substrate temperature of 630 °C and P O2 = 1 × 10 −3 mbar, using 1.2 J cm −2 laser fluence. The films were grown in the layer-by-layer mode, and the thickness of the films were monitored by RHEED oscillations (Figure S1, Supporting Information). The crystallographic figures used in Figure 2 were obtained using the VESTA [69] program.
Transfer of Freestanding Membranes: The Al 2 O 3 substrates were annealed at 1615 °C for 200 s in vacuum to achieve a smooth, welldefined step-and-terrace surface. A poly(methyl methacrylate) (PMMA) layer was spin-coated onto the thin film grown on the SrTiO 3 substrate. The structure was immersed into room-temperature deionized water to dissolve the Sr 3 Al 2 O 6 buffer layer. After liftoff with the PMMA support, the freestanding membranes were attached to the annealed Al 2 O 3 substrate by heating them on a hot plate to 110 °C. The membrane remained on the substrates after the PMMA layer was dissolved with acetone.
Dewetting and Characterization: For the dewetting process, the samples were annealed at the desired specified temperatures for 200 s under oxygen partial pressure P O2 of 7.5-10 × 10 −2 mbar. The AFM images (Figure 2) used for the orientation-dependence study were taken in tapping mode with a Bruker Dimension ICON AFM. The other AFM images were taken with an Asylum Cypher AFM in tapping mode. The X-ray diffraction data were acquired with a monochromated Cu-K α1 source.
STEM Studies: STEM specimens were prepared by mechanical wedge polishing followed by Ar ion-beam milling at liquid-N 2 temperature. [70] Prior to STEM sample preparation, the transparent SrTiO 3 region was determined with an optical microscope using polarized light. The sample was cut into slabs of 0.5 mm width and 1.5 mm length with a wire saw (Well, Model 3242). A thin layer of glass was mounted to the surface of the slab with glue (Epoxy bond 110) to protect the surface structure from contamination and damage during further processing. Then, the samples were attached to a Pyrex specimen holder using Crystal Bond thermoplastic wax for mechanical polishing. An Allied MultiPrep System was used for automated tripod polishing of the samples in cross-sectional geometry, making the thin part of the wedge down to about 10 µm. Afterward, a Gatan Precision Ion Polishing System (PIPS II, Model 695) was used for Ar + ion milling of the samples at liquid-N 2 temperature. To thin the sample and to reduce the ionbeam-induced damage, the acceleration voltage during Ar + ion milling was progressively lowered from 3.4 to 2.7 to 2.0 to 1.0 and 0.3 kV. The central region of the thin part of the wedge was milled using the ion beam at an angle of 8°, forming a curved region, where the material was thin enough for final STEM observations. Dewetted SrTiO 3 nanocrystallines were studied using a sphericalaberration-corrected STEM (JEM-ARM200F, JEOL Co. Ltd.) equipped with a cold field-emission gun and a DCOR probe Cs corrector (CEOS GmbH) operated at 200 kV. The STEM images were obtained by a JEOL ADF detector with a probe size of 0.8 Å (corresponding to the spot size 8C in the experimental setting), a convergent semiangle of 20.4 mrad, and a camera length of 6 cm. The resulting collection semiangles for HAADF imaging were 70-300 mrad. EELS acquisition was performed by a Gatan GIF Quantum ERS imaging filter equipped with a Gatan K2 Summit camera with a convergent semiangle of 20.4 mrad and a collection semiangle of 111 mrad. STEM-EELS spectrum imaging was performed with a dispersion of 0.5 eV per channel and 456 eV drift tube energy with a 4000 pixel wide detector for the simultaneous acquisition of signals of Ti-L 2,3 , O-K, Al-K, and Sr-L 2,3 edges. STEM-EELS elemental maps and atomic-resolution maps were acquired with scan steps of 3 and 0.57 Å, respectively.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.