## 3 Results and Discussion
### X-ray Studies  
As results from XRR measurements show in Figure 2, our samples annealed at 1150 \({}^{\circ}\)C may be considered as still multilayered films with some point distortions. Indeed, pronounced Bragg peaks (at around 1.1 and 1.5 degree for SN1 and SN2 sample, respectively) indicate the presence of superlattices, whose periods are estimated as 3.9 nm (SN1) and 3.1 nm (SN2), which matches well those obtained by TEM measurements (4.25 and 3.35 nm, respectively). At the same time, relatively large width of Bragg peaks also points out at the multilayered structure imperfections, which are most likely coalescent nanocrystals. In turn, an increase of annealing temperature up to 1250 \({}^{\circ}\)C resulted in destruction of SL structure, as evident from Bragg peaks disappearing for both SN1 and SN2 samples (see Figure 2). Such a temperature-dependent SL structure breakdown was observed in our previous study of SiO\({}_{\mathrm{x}}\)/SiO\({}_{\mathrm{2}}\) and SiO\({}_{\mathrm{x}}\)N\({}_{\mathrm{y}}\)/SiO\({}_{\mathrm{2}}\) multilayered films with 1.5 nm thick Si-rich layers, and explained by the gain in the Gibbs free energy for a mixed system as compared with initial unmixed one [11]. At the same time, it is worth noting that similar SiN\({}_{\mathrm{x}}\)/Si\({}_{\mathrm{3}}\)N\({}_{\mathrm{4}}\) multilayered structures even with ultrathin (1 nm) Si\({}_{\mathrm{3}}\)N\({}_{\mathrm{4}}\) barriers remain stable after high temperature treatment as demonstrated recently [9; 10]. Hence, we can assume that the most probable reason for the effect of Si NC coalescence demonstrated in Figure 1 is the small enough thickness of SiN\({}_{\mathrm{x}}\) layers (1.6-2 nm), leading to an appearance of distinct intermixing regions. This trend is in full agreement with our previous observations of SL structure intermixing for SiO\({}_{\mathrm{x}}\) and SiN\({}_{\mathrm{x}}\)-based multilayers with ultrathin Si-rich layers [11; 22; 23]. Figure 1: (**a**) HRTEM image, (**b**) EFTEM image, and (**c**) size distribution of Si NCs for SiN\({}_{\mathrm{x}}\)/Si\({}_{\mathrm{3}}\)N\({}_{\mathrm{4}}\) (2/2.25 nm) SN1 sample; (**d**) HRTEM image, (**e**) EFTEM image, and (**f**) size distribution of Si NCs for SiN\({}_{\mathrm{x}}\)/Si\({}_{\mathrm{3}}\)N\({}_{\mathrm{4}}\) (1.6/1.75 nm) SN2 sample. Figure 2: XRR scans for (**a**) SN1 and (**b**) SN2 samples annealed at different temperatures. The formation of Si NC with an increase of annealing temperature was additionally studied by means of XRD and XPS techniques. XRD scans of SN2 sample are shown in Figure 3. As can be seen, 900 \({}^{\circ}\)C annealing temperature is obviously not enough to form nanocrystals, since XRD pattern constitute of a broad band around the position of Si (111) diffraction peak, which is a signature of amorphous silicon nanoclusters. In contrast, for higher annealing temperatures relatively narrow peak is observed, which is a typical XRD pattern for Si NCs [9]. Remarkably, the peak becomes narrower with the rise of annealing temperature from 1150 \({}^{\circ}\)C to 1250 \({}^{\circ}\)C, consequently the mean size of Si NCs increases by about 30% according to the estimation by means of Scherrer equation (the same trend is reproduced for SN1 sample). This fact is consistent with SL structure breakdown at 1250 \({}^{\circ}\)C demonstrated by XRR, hence the formation of Si NCs with a larger mean size can be expected, in a similar way as demonstrated previously in case of SiO\({}_{\text{x}}\)N\({}_{\text{y}}\)/SiO\({}_{2}\) SL annealed at the same temperature [24]. The mean size of Si NCs grows together with the thickness of SiN\({}_{\text{x}}\) layers: As results from comparative XRD measurements (see inset in Figure 3), on the average Si NCs in SN1 sample are about 14% larger than those in SN2 sample (\(4.1\pm 0.1\) nm vs. \(3.6\pm 0.1\) nm), according to calculations using Scherrer equation [9], which agrees well with the mean size estimations performed by analyzing HRTEM images.