## 3 Results and Discussion
### Photoluminescence Measurements  
PL spectra of SN1 and SN2 samples annealed at 1150 \({}^{\circ}\)C are shown in Figure 5a. An observed PL peak shift may be associated with the size-dependent quantum confinement effect for excitons in Si NCs. Spectra are characterized by maxima in the near IR range (885-940 nm), which is not typical for Si NCs in Si\({}_{3}\)N\({}_{4}\) matrix, as mentioned above. Nevertheless, luminescence in this spectral region was also observed recently from similar SiN\({}_{\text{x}}\)/Si\({}_{3}\)N\({}_{4}\) SLs with Si NCs, but produced by different methods [10; 23]. Moreover, bare theory of quantum confinement predicts the reduction of an energy gap (i.e., red shift) for Si nanocrystals with the decrease of confinement barriers, i.e., when nanocrystals are incorporated into Si\({}_{3}\)N\({}_{4}\) matrix instead of SiO\({}_{2}\)[4]. Thus, PL with lower peak energies from Si NCs in silicon nitride as compared with silicon oxide matrix (\(\sim\)1.7 eV at most) is indeed justified. At the same time, the majority of experimental data on Si NC luminescence in Si\({}_{3}\)N\({}_{4}\) reveals the PL maximum at relatively high photon energies (above 1.6-1.7 eV), which is blue-shifted as compared to a typical emission of Si NCs in SiO\({}_{2}\) characterized by a maximum at about 1.2-1.7 eV [2; 26]. From the theoretical point of view, this discrepancy is usually solved by empirical modification of the theoretical parameters to achieve a better fit with the experimental data [4]. On the other hand, in silicon rich nitrides there are numerous matrix-related radiative defects having strong emission lines, which makes it difficult to distinguish the contribution of Si NCs, especially when short-wavelength excitation is used [13; 15]. With respect to SL structures, matrix-related luminescence signal intensity may be reduced by decreasing the thickness of Si\({}_{3}\)N\({}_{4}\) barriers, as demonstrated recently by an example of SiO\({}_{x}\)N\({}_{y}\)/Si\({}_{3}\)N\({}_{4}\) hetero-SLs [6]. Indeed, in general, luminescence from Si NCs in SiN\({}_{\text{x}}\)/Si\({}_{3}\)N\({}_{4}\) SLs with the peak energy at about 1.7 eV or below is observed, when Si\({}_{3}\)N\({}_{4}\) barriers has the thickness under 2 nm [9; 10; 23]. On the opposite, in case of thicker barriers or SiN\({}_{\text{x}}\) monolayered films with Si NCs the position of PL peak is usually found in the spectral range above 1.7 eV [13; 16; 27]. Taking into account a number of radiative defects in SiN\({}_{\text{x}}\) which emit at such high photon energies, an attempt to attribute certain PL bands to Si NC emission in SiN\({}_{\text{x}}\) seems highly questionable in this case, as emphasized elsewhere [17].  
To confirm that exciton recombination in Si NCs is the origin of observed PL for our SL structures, time-resolved PL measurements were carried out. The results for SN1 sample are shown in Figure 5b for two different photon energies. Both curves are characterized by a stretched exponential decay:  
\[I=I_{0}\,\exp\,[-\,(t/\tau)^{\beta}] \tag{2}\]  
with the time constant \(\tau\) reducing from 1.84 to 0.35 \(\upmu\)s upon increase of photon energy. Such reduction as well as relatively long PL lifetime (in a microsecond range) and non-exponential parameter \(\beta\sim\) 0.5-0.6 are typical for quantum confined Si NCs-related PL [3; 28]. At the same time, characteristic time  
Figure 5: (**a**) PL spectra of fabricated samples annealed at 1150 \({}^{\circ}\)C; (**b**) PL decay curves for SN1 sample (points) and corresponding approximation using stretched exponential function (lines).  
constant seems to be several times smaller than that for SiO\({}_{\rm x}\)-embedded Si NCs [3]. The latter may be explained by a more defective nature of SiN\({}_{\rm x}\) matrix as compared to SiO\({}_{\rm x}\) one [6]. Defects like dangling bonds act as luminescence quenching centers, increasing the nonradiative recombination rate and, hence, reducing the measured PL lifetime.