Layer matching epitaxy of NiO thin films on atomically stepped sapphire (0001) substrates

Thin-film epitaxy is critical for investigating the original properties of materials. To obtain epitaxial films, careful consideration of the external conditions, i.e. single-crystal substrate, temperature, deposition pressure and fabrication method, is significantly important. In particular, selection of the single-crystal substrate is the first step towards fabrication of a high-quality film. Sapphire (single-crystalline α-Al2O3) is commonly used in industry as a thin-film crystal-growth substrate, and functional thin-film materials deposited on sapphire substrates have found industrial applications. However, while sapphire is a single crystal, two types of atomic planes exist in accordance with step height. Here we discuss the need to consider the lattice mismatch for each of the sapphire atomic layers. Furthermore, through cross-sectional transmission electron microscopy analysis, we demonstrate the uniepitaxial growth of cubic crystalline thin films on bistepped sapphire (0001) substrates.

Scientific RepoRts | 5:14385 | DOi: 10.1038/srep14385 suggests that atoms on the sapphire surface migrate to minimise the surface energy at less than a half of the sapphire melting point (2326 K).
Substrate surface structures can affect crystallinity and morphology of thin-films [14][15][16] . Previously, we observed the formation of periodic nanogroove arrays on room-temperature pulsed-laser-deposited NiO (111) epitaxial thin films grown on atomically stepped sapphire (0001) substrates via post-thermal annealing in air, but the mechanism remained under discussion 17 . The structures were definitely related to the atomic steps of the sapphire (0001) substrates because the nanogroove periodicity corresponded well with the sapphire (0001) substrate terrace width 17 . The post-thermal annealing may have caused reconstruction to the most stable structure, i.e. periodic nanogroove arrays. It is needed to reveal the driving force for formation of the periodic nanogroove array without the coalescence of adjacent film terraces.
Here, the mechanism for NiO periodic straight nanogroove array formation is explained using a new concept 'layer matching epitaxy (LME) model' in which the lattice mismatch between the thin film and the substrate is postulated by the in-plane atomic geometry for each topmost surface layer. The LME model was substantiated by transmission electron microscopy (TEM) results and led to the fabrication of bistepped sapphire (0001) substrates. Figure 1(a) presents an atomic force microscopy (AFM) surface image of an NiO thin film on a 0.22-nm-high stepped sapphire (0001) substrate after rapid thermal annealing (RTA) at 1373 K for 60 s. A periodic straight nanogroove array was formed over the RTA-treated NiO thin-film surface. The cross-sectional scanning transmission electron microscopy bright field (STEM-BF) image shown in Fig. 1(b) revealed that V-shaped and terraced-rice-field-shaped grooves alternately existed on the NiO thin-film surface. In the magnified STEM images presented in Fig. 1(c,d), periodic linear defects stretching over the deepest part of a nanogroove towards the substrate interface can be more clearly observed. The STEM-energy dispersive X-ray spectrometry (EDX) results shown in Fig. 1(e) further revealed that atomic diffusion at the interface was virtually negligible, even though the sample was annealed at 1373 K for 60 s. Furthermore, the cross-sectional transmission electron microscopy and selected-area electron diffraction (TEM-SAED) results shown in Fig. 1(f) indicated that the NiO diffraction patterns were mirror-symmetrical between the next NiO crystal domains, with the linear defect as the mirror plane. Finally, the high-resolution transmission electron microscopy (HRTEM) images presented in Fig. 1(g,h) revealed that the sapphire substrate under the deepest part of the nanogroove was dented, and after RTA, the substrate did not exhibit the 0.22-nm-high atomic steps observed at the interface between the NiO (111) epitaxial thin film and sapphire (0001) substrate prior to RTA. Considering the SAED patterns shown in Fig. 1(f), it can be concluded that the V-shaped groove comprised NiO (002) facets and the terraced-rice-field-shaped grooves comprised (111) and (111) facets. Therefore, the linear defects were planar defects that occurred at the NiO twin domain boundaries near the atomic steps, and these NiO twin boundaries were the driving force for the formation of the periodic nanogroove array without coalescence of the adjacent film terraces.
These results suggest that the NiO crystal grains were uniepitaxially grown on each terrace of the 0.22-nm-high stepped sapphire (0001) substrate. In fact, after RTA at 973 K for 60 s, two types of 180°-rotated triangular crystalline domains were alternately grown on each film terrace divided by the nanogrooves, and the two types of triangular crystals were not mixed on one film terrace 17 18,19 . Consequently, NiO thin-film epitaxy on sapphire has been conventionally explained using the domain matching epitaxy (DME) theory in which matching between the film and substrate is estimated using the integral multiple of the lattice planes [18][19][20][21] . For instance, the lattice mismatch between NiO (ICDD card No. 47-1049) and sapphire (ICDD card No. 46-1212) can be calculated as follows: where d denotes lattice plane determined by three or four Miller indices (hkl) or (hkil). However, the mirror-symmetrical SAED patterns observed in Fig. 1(f) cannot be interpreted using the DME concept, because there is no difference in the mismatches before and after rotating the NiO (111) plane by 180°. There must be a reason why the two different types of 180°-rotated triangular crystalline domains were alternately grown on each film terrace divided by the nanogrooves. Therefore, the mismatch between the NiO film and the sapphire substrate was considered using a new concept based on a layer matching epitaxy (LME) model in which the misfit between the thin film and the substrate is estimated on the basis of the difference in the in-plane atomic geometry for each topmost surface layer. In the stepped sapphire (0001) plane, the oxygen layer comprises equilateral triangles, each with a side length of 0.2525 nm, surrounded by six equilateral triangles, each with 0.2867-nm-long sides that are tilted by 3.87°, as shown in Fig. 2(a). Furthermore, the oxygen sublattices are mirror-symmetrical between the adjacent terraces, with a 1/6 th height of the c-axis in the sapphire unit cell. On the other hand, the NiO (111) atomic layer comprises regular rhombuses with 0.2954-nm-long sides in which the Ni layer and the O layer are alternately stacked [ Fig. 2(b)]. Therefore, NiO is epitaxially grown on the 0.22-nm-high stepped sapphire (0001) plane to match the mirror-symmetrical oxygen layer between the adjacent substrate terraces. In short, although sapphire is a single crystal, two types of terraces exist in accordance with the step height. For example, six-fold biepitaxy is observed rather than three-fold epitaxy for NiO deposited on a 0.22-nm-high stepped sapphire (0001) plane due to the presence of the two types of mirror-symmetrical oxygen sublattice in the sapphire (0001) plane. Therefore, the lattice mismatch for all of the sapphire atomic layers should be considered. Formation of grooved nanostructures was then achieved on the surfaces of Li x Ni 1−x O thin films (x < 0.5) deposited on atomically stepped sapphire (0001) substrates after RTA at 1373 K for 60 s. The depth of the nanogroove array was five times greater than that on the annealed nondoped NiO film [ Fig. 3(a)]. This deeper nanogroove formation may be due to the low boiling point of Li. The planar defects near the atomic steps of the sapphire (0001) substrate diffused because of thermal annealing with  simultaneous Li migration in all directions, resulting in restructuring and deeper nanogroove formation. The magnified TEM image shown in Fig. 3(b) revealed that the lattice spacing near the thin-film surface was 0.24 nm and corresponded to the interplanar spacing of NiO (111), while that near the interface was 0.47 nm. In the STEM-EDX images presented in Fig. 3(c), an interface reaction layer different from that observed in the annealed pure NiO thin film [compare Fig. 3(c) with Fig. 1(e)] can be seen. Then, the STEM-electron energy loss spectroscopy (EELS) spectra [ Fig. 3(d)] indicated that this interface reaction layer comprised Al, Ni, O and diffused Li. Thus, while sapphire has high thermal durability, it was affected by diffused Li at 1373 K in just 60 s. It should also be noted that (i) the dark areas in the NiO thin film in the STEM-HAADF image shown in Fig. 3(c) represent the lower-density areas and (ii) the Li completely disappeared from the NiO thin film. Therefore, mirror-symmetrical NiO crystal domains were formed in the RTA-treated LiNiO thin film, and the Li reacted with the sapphire (0001) substrate to generate a lithium nickel aluminate phase. Wide area surface observation via scanning electron microscopy (SEM) revealed a uniform array of straight nanogrooves over a large area [ Fig. 3(e)], leading to a rainbow-coloured interference pattern on the surface of the film [ Fig. 3(f)]. Although the reflectivity was less than 20% [ Fig. 3(g,h)] 22 , the reflective angular profiles of these rainbow-coloured films corresponded well with the grating equation sin α− sin β = λ/d, where α, β, λ and d are incident and diffraction angles, wavelength of incident light and groove pitch, respectively. Furthermore, manifestation of structural colour suggested that the NiO thin film was grown in accordance with the LME model uniformly over the entire substrate, despite heavy Li doping.
According to the mechanism for nanogroove formation based on the LME model, NiO thin films should be uniepitaxially grown on bistepped sapphire (0001) substrates. However, to the best of our   shown in (a). The relationship between the annealing time and the sapphire bistep ratio for a sapphire off-angle of 0.13° is displayed in (b). A surface image and cross-sectional height profile of the bistepped sapphire (0001) substrate are presented in (c), and the step heights corresponded well to 1/3 rd the height (0.433 nm) of the c-axis in the sapphire unit cell. An NiO thin film grown on the substrate shown in (c) reflected the step-and-terrace structure, as can be seen in (d), suggesting the layer-by-layer growth of NiO on the sapphire (0001) plane. After RTA at 1373 K for 60 s, the step-and-terrace structure seen in (d) changed to that shown in (e). The XRD φ-scan results that can be seen in (f) were obtained by tilting the specimen shown in (d) in order to detect the NiO{002} and sapphire {0336} peaks.
Scientific RepoRts | 5:14385 | DOi: 10.1038/srep14385 knowledge, the fabrication of sapphire (0001) substrates that are bistepped over the entire surface has not been previously reported. Thus, step formation was examined by systematically varying the annealing temperature at a heating rate of 10 K/min (Fig. 4). It was found that step formation in the sapphire (0001) substrate occurred at 973 K, and the step linearity was improved at 1273 K. After annealing at temperatures above 1473 K for 3 h, the atomic steps of the sapphire (0001) planes bunched up with random heights, and the bunched step array was not straight. Furthermore, the step heights were not always equal to an integral multiple of the sapphire (0006) planes, i.e. 0.55-nm-high steps were found. Therefore, the sapphire (0001) surface after annealing for 3 h at temperatures between 1473 K and 1573 K was mixed with the Al and O layers. Furthermore, the step array of the sapphire (0001) surface was nearly straight after annealing at 1673 K for 3 h, but the step heights were not uniform in the measurement area [compare Fig. 4(j) with (k)], and the terrace widths were irregular over 5 × 5 μ m 2 area. Notably, a bistepped sapphire (0001) surface was only partially obtained when the annealing was performed at 1473 K for 3 h with the heating rate decreased from an initial rate of 10 K/min to 1 K/min at 1373 K [ Fig. 5(a)]. The bistep ratio r b increased as the annealing time increased [ Fig. 5(b)] and was estimated using the following equation: In equation (2), n b and n m represent the number of bisteps and monosteps, respectively. The step morphology and the cross-sectional height profile are shown in Fig. 5(c). It should be noted that bistep formation occurred only for off-angles greater than 0.13°. After deposition of NiO, the thin-film surface definitely reflected the step-and-terrace structure [ Fig. 5 In summary, we have discovered that NiO thin films are uniepitaxially grown on bistepped sapphire (0001) substrates in accordance with a new concept LME model which is modelled from the results that the driving force for the formation of the periodic nanogroove array without coalescence of the adjacent film is NiO twin boundaries resulting from the crystal growth behaviour that NiO is uniepitaxially grown on one terrace of 0.22-nm-high stepped sapphire (0001) plane to match the mirror-symmetrical oxygen sublattice layer between the adjacent substrate terraces, despite heavy Li doping. In future, various cubic functional thin-film materials will be grown on the bistepped sapphire (0001) substrate, and the twin boundary will decrease leading to fabrication of high-quality cubic thin films on sapphire (0001) substrate.

Methods
NiO epitaxial thin films were grown on atomically stepped sapphire (0001) substrates at room temperature in 1.3 mPa O 2 via pulsed laser deposition using a sintered ceramic target and a pulsed KrF excimer laser (wavelength: 248 nm, pulse duration: 20 ns, frequency: 5 Hz). The target was rotated for uniform ablation and to preclude droplet formation. During the deposition of each film, the distance between the target and the substrate was 5 cm. The film growth rate was between 0.02 and 0.03 nm/s. The surface morphologies of the films were observed using atomic force microscopy. The crystal structure and epitaxial growth of the films were examined via X-ray diffraction analysis. After deposition, the obtained NiO (111) epitaxial thin films were annealed via rapid thermal annealing (RTA) at a heating rate of 20 K/s at 1373 K for 60 s and subsequently quenched to room temperature. During RTA, the samples were annealed using a near-infrared ray collimated using a parabolic reflector to uniformly heat the samples. The microscale morphology of the RTA-treated LiNiO thin film was confirmed by scanning electron microscopy (SEM). The interface between the thin film and sapphire (0001) substrate was observed via scanning transmission electron microscopy combined with energy dispersive X-ray spectroscopy (STEM-EDX) and electron energy loss spectroscopy (STEM-EELS). The local crystal domains of the films were examined via transmission electron microscopy and selected area electron diffraction (TEM-SAED) analysis.