Oxides present a wide range of remarkable properties (from metal-insulator transitions to multiferroïcity) that lead to various competing devices such as sensitive sensors, non-volatile memories, low consumption transistors, energy harvesters, and transducers, etc. [1]. Functional oxide nanostructures can even exhibit enhanced or novel physical properties compared to their bulk counterparts, and are thus of great interest for future devices in various application fields. The ability to generate and control different nanostructures (even more complex) would lead to a larger range of physical properties, with a fine understanding of the correlations between the structures at the atomic and nanometer scale and their properties being a key point. Since applications mainly require integration of single-crystalline materials in thin film form, the progress in the elaboration and characterization techniques of epitaxial thin films and supported nanostructures, has been done and has allowed designing materials with an atomic-scale control. Although nanostructures can be designed by top-down approaches (e.g., [2–4]), its high cost and size limitations (~100 nm) have made the low-cost bottom-up approaches involving self-organization processes attractive. This approach is still investigated, as confirmed by the numerous recent papers and the recent issue of MRS Bulletin dedicated to the fabrication of ordered patterns and nanostructures via self-organization [5]. However, the realization of oxide nanostructures is still much less advanced than metal and semiconductor nanostructures, certainly because of the structural and chemical complexity of functional oxides. This complexity of oxides may be an advantage, leading to a larger range of structural/chemical/electronic flexibility and accessible properties, with respect to metals and semiconductors. Indeed, the rich variety of iono-covalent complex oxide structures allows various surface and nanostructure self-assembling properties. The range of available mismatched oxide epitaxial heterostructures is wider than metals and semiconductors and that can therefore lead to many nanostructures through the modulation of interface structure and energy. The nanostructures formation through interface energy modulation is governed by many parameters in dissimilar structures such as the structural mismatch with the most favorable coincident site lattices (CSL), the epitaxial elastic strain, the plastic relaxation created by misfit-accommodation dislocations, with domain matching epitaxy (DME) reducing the global mismatch when the accommodation dislocations are periodic [6–8]. The 3D island growth relieved by epitaxial strain is scarcely observed in oxides in comparison to metals or semiconductors, such as the archetype case of Si_1−xGe_x growth on Si (001) surface [9, 10], probably because of the larger elastic constants in oxides compared to Si and III-V semiconductors (at least by a factor of two). The strain-relieved formation of 3D oxide epitaxial islands has been observed only very low-nanoscale islands (lower than ~100 nm in diameter and a few nanometers in height) [7, 11, 12]. The formation of other nanostructures should be explained by more complex mechanisms taking into account all the above mentioned parameters, the structural anisotropy (driving diffusion anisotropy), the chemical ordering and stoechiometry, surface polarity, and the balance between thermodynamics and kinetic driven by diffusion to flux ratio (D/F) during growth [13–15]. For instance, crystallization annealing of lattice mismatched oxides deposited by chemical solution (CSD) can lead to the formation of epitaxial nanoislands by solid state dewetting where the size, shape, and spatial ordering can be controlled through self-patterning [7, 12, 16–18]. It is also worth noting that some oxide nanocomposites of different structures can be formed by self-assembly through spinodal decomposition mechanisms, as the artificial multiferroic nanocomposites composed of a ferromagnetic spinel and ferroelectric perovskite [19–23]. Stencil masks or nanoporous polymeric layers can also be used as templates for the realization of periodic arrays of functional oxide nanodots or nanowires [3, 24–26]. Another example is the fabrication of oxide-semiconductor core-shell nanowires that can be elaborated by molecular beam epitaxy (MBE) [27]. In addition to these mechanisms, the chemical termination of single-crystalline perovskite oxide substrates has played a major role in the conducted epitaxial growth of high quality oxide films and nanostructures. The progress made to control the chemical termination by chemical and thermal treatments of the most used oxide single-crystal substrates, SrTiO₃(001) in particular [28, 29], has opened doors toward the control, enhancement and emergence of original physical properties [30–32], with the most famous example of the formation of a high-mobility two-dimension electron gas (2DEG) at the LaAlO₃/SrTiO₃ interface appearing only on the TiO₂ termination of the SrTiO₃ (001) surface [30]. In addition, we will see that self-assembly of the chemical terminations of (001)-oriented perovskite single-crystals can also be used to generate different nanostructures. Here, it will be briefly reviewed how the structural and chemical surface properties of oxide single-crystalline substrates can be used to tailor oxide nanostructures involving some of these self-assembly processes. In particular, it will be enlightened that the atomic structural anisotropy, surface step ordering, self-assembled chemical terminations, and more generally interface energies, are key parameters for the design of nanostructures by preferential atomic diffusion, nucleation and crystallographic orientation. Some examples of nanostructures will be given such as self-organized nanodots, nanowires or nanostripes, with different functional oxides of different structures.

By nature, single-crystalline surfaces are structurally anisotropic due to the specific atomic ordering (see Figure 1A). Atomic rows corresponding to crystallographic directions of low Miller indexes are the most compact and thus with the strongest cohesion energy. This anisotropic atomic ordering of the surface leads to anisotropic atomic surface diffusion, governed by Ehrlich-Schwoebel (ES) barriers [33]. Values of anisotropic diffusion are still unknown, probably because of the structural complexity of oxides. However, the anisotropic diffusion is revealed by epitaxial growth or by annealing single-crystals where faceted edges can be discerned along the crystallographic directions of low Miller indexes at the surface. Similarly to the 90° atomic step-edges of the well-known Si(001) surface [33], faceted atomic step-edges of hundreds of nanometers can be observed on oxide single-crystal surfaces, such as perovskite SrTiO₃(001) [29] and SrTiO₃(110) [34], and spinel MgAl₂O₄(001) [35]. Similarly to surface facets of low energy (low Miller indexes) driven by thermodynamic processes (large D/F), elastic interactions and surface polarity reasons [36, 37], epitaxial nanoislands or nanopits can also exhibit faceted edges from tens to hundreds of nanometers along the low-index crystallographic directions [17, 38]. The shape of the nanoislands (pyramidal, hut, or hexagonal) depends on the crystallographic orientation, symmetry, epitaxial strain, surface energy, polarity, etc. The atomic surface reconstructions, that may depend on the oxygen vacancy ratio (e.g., [36, 39, 40]), can be another key parameter to control, favorizing different nanostructures. These anisotropic surface properties have also be used to favor a lateral growth by preferential coarsening along the low index directions, that can lead to horizontal 1D nanowires assisted by epitaxial strain, as in the case of (011)-oriented fluorite Ce_1−xGd_xO_2−y lateral nanowires grown by CSD on LaAlO₃ (001) surface, having dimensions of ~20 nm in width and height and more than 1 μm in length [41]. It is worth noting particular oxide materials with high energy anisotropy for which the growth along one direction is favored, naturally leading to 1D nanostructures, as the case of ZnO [42] and WO₃ [43] for instance. The mean surfaces of single-crystals present atomic steps due to inevitable (polar and azimuthal) miscut angles because of the accuracy limitations of sample positioning during its cutting and polishing processes (see Figures 1B,C). The standard single-crystalline substrates have polar miscut angles lower than 0.3°, which corresponds to a unit-cell (uc) step every 75 nm at the SrTiO₃(001) surface for instance. Because of available specific substrates with different miscut angles that can be provided (from low 0.1 to 10°), the terrace width can be tuned from ~250 to 2.5 nm. Surface steps are preferential nucleation sites (lowering the local free energy) and are anisotropic barriers for atomic surface diffusion [33]. As the step edges preferentially follow the low-index directions, the stepped surface morphology can be determined by the azimuthal miscut angle. Straight step edges will preferentially form on substrates with an azimuthal miscut angle along a low-index direction whereas “zigzag” steps will form when the azimuthal angle is off-low-index directions [34]. Since surface steps give rise to ES barriers for atomic diffusion, preferential alignment along the steps of epitaxial nanodots of ~50 nm in diameter and less than 10 nm in height has been grown by preferential diffusion along the steps [44]. Also, as the surface atomic steps have an energetic cost (lower coordination sites), they will preferentially assemble together when the atomic surface diffusion will be larger than the mean terrace width, to form well-defined stable higher steps and wider terraces of lower energy (like surface facets of low Miller indexes). Almost-nominal atomically-flat surfaces can then be obtained by annealing on perovskite single-crystals like SrTiO₃(001) [29, 45, 46], NdGaO₃(001) [47], on sapphire [48], and on spinel MgAl₂O₄(001) single-crystals [35] for instance. Similarly to semiconducting and metallic single-crystal surfaces, step bunching at oxide single-crystal surfaces can thus occur when increasing the polar miscut angle and/or annealing temperatures, leading to “hill and valley” surface nanostructures with periodicity of ~80 nm and total height difference of ~10 nm [7, 9]. In such a way, well-defined 1D surface nanostructures from faceted 10°-off vicinal α-Al₂O₃(0001) surfaces have been used for the realization of 1D well-ordered arrays of oxide nanodots of ~35 nm in diameter and ~8 nm in height through preferential 1D atomic surface diffusion in the valleys [7]. In the case of high miscut angles (high density of surface steps) and dissimilar heterostructures, the out-of-plane lattice mismatch existing between the film and a step of the substrate surface can lead to a crystallographic tilt, that can be written as follows: δω = m_p.arctan (h_f − h_s/h_s), where m_p is the polar miscut angle, h_f and h_s are the height of the steps of the film and the substrate, respectively [49]. Consequently, the morphology of the nanostructures and in particular the tilt of the crystal and its facets can be controlled by the density of surface steps via the polar miscut angle, as tilted YSZ (002) islands on highly vicinal sapphire surfaces [7, 50].

In addition to structural anisotropy, single-crystal surfaces may have different chemical terminations, as it is the case with the (001)-oriented perovskite surfaces. Because of the inevitable miscut angle and the perovskite ABO₃ structure, that can be seen as a periodic stack of AO and BO₂ layers in the (001) direction, the epi-polished (001) surfaces of ABO₃ single-crystals present both AO and BO₂ terminations (see Figure 1D), that have motivated numerous studies from the 90's starting on the SrTiO₃ (001) surface with the objective of controlling them for high-quality epitaxial oxide growth and realization of abrupt oxide heterointerfaces [28, 29, 45, 46]. This quest for the control of chemical termination in (001) single-crystal perovskite surfaces has followed with LaAlO₃ [47], NdGaO₃ [47], LSAT [51], and DyScO₃ [52], and on layered SrLaAlO₄ substrates [53, 54]. Due to polishing effects, the as-received perovskite substrates have not well-defined step-and-terrace surfaces and contain both chemical terminations, which are mixed at the atomic scale and are difficultly distinguishable by atomic force microscopy (AFM) techniques [55]. Atomic surface diffusion reveals both chemical terminations by self-assembly with well-defined terraces separated by half-uc high steps and terraces of ~150 nm wide depending of the miscut angle and the termination ratio in as-received substrates. This has been observed on SrTiO₃ [56], on LaAlO₃ [57], on DyScO₃ [52], and on LSAT [11]. Surface potential differences between both terminations in SrTiO₃ have been predicted to be around 2.3 eV but measured with lower value [32]. These chemically-patterned surfaces have then been used to elaborate different nanostructures by selective growth (see Figure 2). Taking advantage of the termination-dependent chemical or energy properties (hydrophilic SrO termination in SrTiO₃ for instance), a selective growth and adsorption of different materials such as SrRuO₃, water, and organic tioles has been shown [29, 56, 58]. Ordered 1D nanostructures such as arrays of conducting SrRuO₃ nanostripes (of the single-terminated terrace width) or nanodots (~70 nm wide and ~4 nm high) have then been realized in such a way on LaAlO₃ [59], SrTiO₃ [53, 60], on DyScO₃ [52, 61], and on LSAT [11]. In the case of low energy interface, 2D epitaxial growth can occur without preferential nucleation with the chemical terminations replicating themselves at the film surface (see Figure 2A). In addition to the possible modulation of the properties in the out-of-plane direction with layered heterostructures elaborated by advanced deposition techniques, self-assembled chemical terminations have allowed to laterally modulate the interface and surface properties of heterostrucutres [32], generating for instance a 2DEG only at the specific (LaO/TiO₂) laterally-confined regions on the single-terminated terrace width of the LaAlO₃/SrTiO₃ interface [62], as predicted [63]. More generally, that has allowed to study both chemical terminations of various functional perovskite oxides, such as ferromagnetic (La,Sr)MnO₃ and ferroelectric BaTiO₃, which are difficulty accessible even with advanced and widely used oxide deposition techniques such as pulsed laser deposition (PLD) [32]. The chemical terminations can also have a dramatic effect on the crystallographic orientation and the morphology of thin films, as YSZ on SrTiO₃(001) surface where it has been shown that 2D growth of YSZ film only occurs on the SrO termination with (001)-orientation whereas dome-shaped tilted (111)-oriented YSZ islands of a few tens of nanometers in diameter and a few nanometers in height epitaxially grow on the TiO₂ termination [64]. This observation has been explained by the differences in terms of chemical bonding and interfacial energies. However, specific energy values for these complex interfaces are tricky to determine and are still unknown.

In addition to surface structure and chemistry, interface structure and energy play a particularly important role in the control of the shape of the epitaxial nanoobjects. Lattice mismatch (defined as f = (a_s − a_f)/a_f, where a_s and a_f are the in-plane lattice parameter of the substrate and the film, respectively) can generate elastic strain in heteroepitaxial nanostructures. Dissimilar epitaxial structures can thus have different possible structural matching at the interface, with different coincidence site lattices (CSL), and thus different interfacial energies. Epitaxial heterostructures with high interface energy will have tendency to minimize the interface whereas those with low interface energy will have tendency to maximize it [12]. For instance, in the case of dissimilar fluorite (YSZ) on sapphire (0001) surface, two epitaxial orientations can occur: (111) with low interface matching and (001) with domain interface matching reducing the lattice mismatch to 0.9%. It has been observed that for YSZ epitaxial nanoislands grown by CSD, which is a thermodynamically driven growth (very large equivalent D/F), (111)-oriented nanoislands are dome-shaped with minimized interface area and (001)-faceted surfaces, whereas (001)-oriented nanoislands are top-flat with larger interface area, in agreement with their structural matching and expected interface energy [7, 65]. Indeed, it has been shown that the ratio of (111)-oriented dome-shaped nanoislands can be increased by artificially increasing the substrate surface energy, through a soft deterioration of the epi-polished substrate surface done by gentle scratching and further soft annealing leading to an enhancement of the density of surface steps [65]. Another example is the case of the epitaxial growth of SrRuO₃ on chemically self-assembled LSAT (001) surface, where a selective growth on only one termination is also observed, similarly to deposition on chemically self-assembled SrTiO₃ (001) surface, but forming in that case 1D arrays of nanodots by 3D growth instead of nanostripes by 2D growth (see Figures 2B,C). This difference can be explained by the lattice mismatch that is larger on LSAT (−1.5%) than on SrTiO₃ (−0.6%), although the epitaxial strain is in-plane compressive in both cases. The in-plane compressive strain can favor nanoislands formation, whereas in-plane tensile strain can favor nanopits formation, as shown in some epitaxial (La,Sr)MnO₃ films grown on SrTiO₃ (001) surface by sputtering [66]. Epitaxial growth of films with high surface energy may lead to 3D growth of nanostructures with surface facets of lower energy. That is the case with (001)-oriented spinel films, as ferromagnetic CoFe₂O₄, that tends to form nanopyramids with more stable (111) facets of lower surface energy at least by a factor of 5 [67, 68]. That is also the case with (110)-oriented perovskite films, such as (La,Sr)MnO₃ that tend to form nanohuts with more stable (001) facets [65]. This thermodynamically driven tendency can be kinetically limited by decreasing the D/F ratio, or enhanced by increasing it, tuning the size of the nanoobjects [13, 15, 69].

In summary, oxide single-crystal surfaces can be well-exploited for the control of various nanostructures grown by self-assembly processes. We briefly reviewed that the size, shape, and spatial ordering of nanoobjects can be tailored by diverse properties and parameters of oxide single-crystal surfaces such as the structural symmetry, anisotropy and reconstructions, density and morphology of atomic steps tunable by polar and azimuthal miscut angles, chemical terminations that can self-order at the nanoscale, in-plane and out-of-plane lattice mismatches, epitaxial strain, interface energy. Furthermore, the diversity is vast regarding the panoply of elaboration techniques that can be used to drive the growth processes (balanced between thermodynamic and kinetic), leading then to different nanostructures. Novel strategies combining different materials and elaboration techniques can lead to biomimetic hybrid nanostructures with enhanced properties for microfluidic management, sensing, energy conversion, electronic, photonic, biomedical applications [42, 70–73].

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