X-ray diffraction studies. Figure 1a shows a diffraction pattern of the ZnO/Au/Al2O3 sample in a wide angular range, the diffraction indices of reflections from the crystallographic planes of the ZnO film and the Al2O3 substrate are marked. The diffraction pattern shows the order of reflections for the family of (0001) planes of the film and substrate, as well as the reflections of the Au layer. The X-ray diffraction pattern of the ZnO/LaMgAl11O19 sample had a similar appearance. Synchrotron studies (Figs. 1b–1e) made it possible to reveal both the imperfection of their crystal structure and a number of its features in the ZnO film samples.

Experimental dependences of the intensity of the diffraction reflection of ZnO-film samples: (a) DRC of the ZnO/Au/Al2O3 sample in a wide angular range, (b, c) DRC 0004 of the ZnO/Au/Al2O3 and ZnO/LaMgAl11O19 samples, respectively, FWHM is the half width of the reflection curve, (d, e) dependences of the intensity of the reflections 0002 (triangle), 0004 (square), and 0006 (circle) of the ZnO/Au/Al2O3 and ZnO/LaMgAl11O19 samples, respectively, obtained in the ω-scanning mode.

Figures 1b and 1c show the DRC of 0004 ZnO of the studied ZnO/Au/Al2O3 and ZnO/LaMgAl11O19 samples obtained on the SR source, respectively. In the case of the ZnO/Au/Al2O3 sample, the maximum intensity corresponds to the Bragg angle θB = 17.154°, and in the case of ZnO/LaMgAl11O19 – θB = 17.275°, which is consistent with the data in [18]. Using the obtained values of the half width of the DRC at half maximum (FWHM) and angles θB, the average sizes of the CSR and microstresses in the film structure were determined according to formula (1), which were: L = 855 ± 129 nm, εexp = 0.020 ± 0.003% for the ZnO/Au/Al2O3 sample; L = 170 ± 12 nm, εexp = 0.054 ± 0.023% for the ZnO/LaMgAl11O19 sample (Table 1).

Figures 1d and 1e show the dependences of the intensity of reflections 0002, 0004, and 0006 of the studied ZnO film samples, obtained in the ω scanning mode. It can be seen that for each of the samples the half widths of the reflection curves of the indicated reflections practically coincide. In order of magnitude, the broadening of these curves indicates the presence of a mosaic structure and a significant scatter in the inclination angles of crystallites in the ZnO films (Table 1). Since the width of the peaks (Figs. 1d and 1e) does not change depending on the order of reflection, it is not possible to estimate the lateral size of the CSR in accordance with [19].

In addition, based on the experimental synchrotron data, the scatter in the inclination angles of the crystallites δ in the structure of the studied ZnO films was determined (Table 1). The value of δ corresponds to the half width of the reflection curve obtained in the ω scanning mode (Figs. 1d, 1e).

The lateral misorientation of the ZnO-film crystal lattice relative to the substrate lattice was experimentally determined. In the [\(11\bar 0\)] direction, the crystallographic unit cells of the ZnO film of the ZnO/Au/Al2O3 and ZnO/LaMgAl11O19 samples are misoriented relative to the substrate by 30° (Figs. 2b and 2d), but the structure of the film of the ZnO/Au/Al2O3 sample also contains crystallites, the orientation of which coincides with the orientation of the substrate (Fig. 2b).

Pole figures of the studied samples ZnO/Au/Al2O3 (a) and ZnO/LaMgAl11O19 (b) and their azimuthal sections (b, d), \(11\bar 2\) reflection; (b, d) the dotted line shows the reflections of the Al2O3 substrate, the solid line shows the reflections of the ZnO film. The results were obtained using a laboratory X-ray diffractometer.

Figure 2a shows the experimental PF of the ZnO/Au/Al2O3 sample; the diffraction reflections are indicated by arrows. The broadening of the reflection (\(11\bar 2\)) of ZnO along the azimuthal scanning angle confirms the conclusion about the presence of an amorphous component of the layer and a mosaic structure. On the PF of the ZnO/LaMgAl11O19 sample (Fig. 2c), the reflections (\(11\bar 2\)) are point-like, from which one can make the conclusion that the misorientation of crystallites in the plane of the layer is small (relative to the [\(11\bar 2\)] direction).

Research using methods of electron microscopy. To study the ZnO/Au/Al2O3 sample by SEM using FIB, indentations were made to observe the layered structure of the samples, and the face perpendicular to the surface of the sample was polished to reveal the thickness of the ZnO layer, as well as the Au layer. Figure 3a shows a microphotograph of such a section indicating the film thicknesses characteristic of the sample. The thickness of the measured ZnO layer was ~8.5 μm, and the Au layer ~45 nm. Next, the sample was prepared by the FIB method for TEM in order to reveal the fine structure of the ZnO film. Figure 3b shows a STEM image of the ZnO film. The average width of the ZnO crystallites, calculated from a section parallel to the surface of the sample, was 500 nm. In this case, due to the thickness of the thin section of the sample obtained for a TEM of ~70 nm, there is a possibility that only the edges of crystallites will fall into the visible region in the electron-microscopy image, since only a small area of the entire crystalline film is covered. Crystallites are columnar structures that grow from the surface and perpendicular to the Au film throughout the entire thickness of the ZnO layer. Micrographs of the interface between two ZnO crystallites have been obtained. Calculation of the interplanar distances of the structure from micrographs and the Fourier transform shows the correspondence of the crystallites to the ZnO structure. The ZnO crystallites are rotated relative to each other at different angles, as described earlier.

Results of studying samples using electron-microscopy methods: (a) SEM image of a section of the ZnO/Au/Al2O3 sample, (b) HRTEM image of the interface between ZnO crystallites of the ZnO/Au/Al2O3 sample, (c) TEM image of the layered structure of the LaMgAl11O19 substrate, ZnO film, and sputtered electronic (Pt-e) and ionic (Pt-i) protective layers of platinum in the ZnO/LaMgAl11O19 sample, (d) HRTEM image of the interface between the ZnO film and the LaMgAl11O19 substrate in the ZnO/LaMgAl11O19 sample.

A ZnO/LaMgAl11O19 sample was also prepared using FIB. The thickness of the ZnO crystalline film ranges from 250 to 300 nm. The film consists of crystallites (columnar structures) growing perpendicular to the surface of the LaMgAl11O19 crystal and often having uneven boundaries. The upper boundary of the film has a wave-like shape, which is apparently due to the different growth rates of individual crystallites. As shown in [20], the predominant orientation of the ZnO film relative to the cleavage of the LaMgAl11O19 crystal is in the (0001) direction, as well as (0001), as can be seen in TEM micrographs (Figs. 3c and 3d).

It is clear from the experimental data (Fig. 2) that the ZnO film of the ZnO/LaMgAl11O19 sample is formed by crystallites laterally rotated by 30° relative to the substrate lattice (crystallite type A). Moreover, the presence of relatively narrow (half width is 0.39° ± 0.01°) and bright reflection peaks on the PF indicates an insignificant scatter in the misorientation values of various crystallites of this type.

In the structure of a thicker ZnO/Au/Al2O3 film, a bidomain structure appears, where an additional type of crystallites (type B) is present, corresponding to the case of growth when their lateral orientation coincides with the orientation of the substrate. For the type-A crystallites, relatively narrow reflection peaks (1.03° ± 0.09°) are also observed on the PF, while for the type-B crystallites, the peaks are significantly broadened (19° ± 1°) and less intense, which indicates a fairly strong misorientation and imperfection of the crystal structure. Comparison of the integrated intensities of peaks on the PF corresponding to two types of crystallites shows that the volume fraction of the type-A crystallites is only ~10%.

Comparing these data with the results obtained in [10], it can be assumed that in the case of a thicker ZnO/Au/Al2O3 film, growth of the type-A ZnO crystallites also occurs at the initial stages. After reaching a critical thickness of ~200 nm of the ZnO film, type-B crystallites are formed in the structure. Thus, the structure of the ZnO/Au/Al2O3 film consists of two regions: a thin epitaxial ZnO layer on the substrate and a main, more imperfect film layer formed predominantly by columnar crystallites (grains).

Since it is possible that the thickness of the zinc-oxide film on the LaMgAl11O19 substrate is not critical for the formation of type-B crystallites, as described in [10], a direct comparison of the two samples is difficult to carry out correctly.