Figure 1 shows a typical RBS spectrum of a SiN _x layer with the corresponding simulation curve obtained using the SIMNRA code with a composition of 49.8, 48.6, and 1.6 at.% of Si, N, and Ar, respectively. The presence of residual Ar attests that the film is as-deposited. Interestingly, no oxygen was detected in all RBS spectra whatever the synthesis method, suggesting that the films do not contain oxygen or less than the detection threshold (0.2 at.%).

Figure 2 shows the evolution of the dispersion curves of SiN _x films deposited on Si wafer by the co-sputtering and N₂-reactive methods with the synthesis parameters Si/Si₃N₄ and N₂/Ar, respectively. The dispersion curves progressively change from the one of stoichiometric amorphous Si nitride (a-Si₃N₄) to that of amorphous Si (a-Si) with increasing Si/Si₃N₄ or decreasing N₂/Ar. This evolution is due to the only increase of the Si incorporation during the growth, which is explained by the drop of the amount of reaction between N₂ and Si for the N₂-reactive method, and by the increase of the Si content into the plasma for the co-sputtering method. Indeed, one can notice that the dispersion curves change in the same way independently of the deposition method.

Figure 3 shows the evolution of the refractive index of SiN _x films (given at 1.95 eV) produced by the two methods as a function of the [N]/[Si] ratio x. The numerous results show that x progressively increases independently of the synthesis method with increasing either Ar/N₂ or Si/Si₃N₄. Bustarret et al. 24 proposed that the refractive index n could be represented as the bonding-density-weighted linear combination of reference refractive indexes taken at x = 0 and x = 4/3 using the empirical relation:

x = 4 / 3 n a − si − n / n + n a − Si − 2 n a − S i 3 N 4

Nevertheless, one can notice in Figure 3 that our experimental results progressively diverge from the models obtained by this group and also by Hasegawa et al. 25 while x is decreased. However, the two groups both studied hydrogenated SiN _x films (SiN _x :H) in contrast to our results. Besides, these latter authors have shown that the Si-H density increased while x was experimentally decreased. Consequently, the drop of n is explained by the H incorporation in their material as suggested elsewhere 26 . However, we could use this model to fit the experimental data but using the refractive index of a-Si (n _a-Si = 4.37, see Figure 2) instead of hydrogenated a-Si (n _a-Si:H = 3.3) used by Bustarret et al. 24 . This shows again the influence of H on the optical properties of the films. We obtained n a - S i 3 N 4 = 1.85, which is similar to many previous results 25 26 27 , but is lower than 2.03 that is commonly used for a-Si₃N₄ 28 . This difference could be explained by the incorporation of voids in the microstructure 27 as attested by the presence of residual Ar atoms detected by RBS in the as-deposited films. Besides, this explanation is confirmed by the density ρ _v of our SiN _x films which was calculated using the atomic areal density ρ _s , and the film thickness d, obtained by RBS and ellipsometry analyses, respectively, with the following relation: ρ _v = ρ _s / d. We found that the density varied from 2.4 to 2.8 g/cm³, which is again sensibly lower than that of a-Si₃N₄ of 3.1 g/cm³ reported in the literature 29 .

Considering the RBS and the ellipsometry spectra, we have produced thin SiN _x films with various compositions that do not depend on the synthesis method, but only on the Si content. As a consequence, n is a precise indicator of the composition that will be used in the following sections.

Figure 4 shows the typical FTIR spectra of a SiN _x film with a low refractive index of 2.1 (SiN_1.12) which were recorded with a normal incidence and with an incidence angle of 65°. One can observe only one absorption band centered at 833 cm⁻¹ in the spectrum measured with the normal incidence, whereas an additional shoulder at 1115 cm⁻¹ emerged while the incidence angle was changed to 65°. Moreover, it is essential to note that no other absorption bands were discernible in the 700 to 4000 cm⁻¹ spectral range whatever the deposition approach. No Si-O absorption bands (transverse optical (TO₄) at 1200 cm⁻¹, longitudinal optical (LO₄) at 1160 cm⁻¹, TO₃ at 1020 to 1,090 cm⁻¹, LO₃ at 1215 to 1260 cm⁻¹, TO₂ at 810 cm⁻¹, and LO₂ at 820 cm⁻¹) 30 31 were detected in all spectra. This demonstrates the absence of O contamination that has been also confirmed by RBS and the absence of any oxide layers at the interface between the Si-wafer and the SiN _x layers which has been confirmed by HRTEM observations. Besides, no absorption bands of Si-H stretching mode in the 2090 to 2200 cm⁻¹ spectral domain were detected because of our synthesis methods involving no hydrogen. Since the latter band is generally the most intense Si-H vibration mode observed in SiN _x :H, one can then conclude on the absence of the Si-H wagging (630 to 650 cm⁻¹) and asymmetric stretching (840 to 900 cm⁻¹) modes in the spectra 24 25 27 32 33 34 . In the same manner, no absorption bands of N-H stretching mode were detected in the 3320 to 2500 cm⁻¹ spectral region suggesting that the N-H bending (1140 to 1200 cm⁻¹) modes are also absent in our spectra 24 25 32 33 . As a consequence, the 833-cm⁻¹ band and the 1115-cm⁻¹ shoulder can be unambiguously assigned to the transverse (TO) and the longitudinal (LO) modes of the asymmetric Si-N stretching vibration, respectively 24 33 34 35 36 37 . The TO-LO splitting is due to the Berreman effect 38 according to which only the TO mode is IR active in normal incidence, and the shoulder observed with an incidence angle of 65° corresponds to the LO mode. Then, the analysis of the FTIR spectra in the 700 to 1200 spectral domain is particularly interesting since it definitely concerns the Si-N bonding alone, in contrast to many works on the FTIR study of SiN _x :H films 5 27 32 33 34 39 , Si nitride layers containing oxygen 19 20 , or SiN _x layers stacked between Si oxide layers 17 40 .

Figure 5 shows the evolution of the FTIR spectra of SiN _x thin films measured with the two incidence angles. The spectra are arranged with increasing order of n of SiN _x films deposited by both methods. One can notice that the evolution of the FTIR spectra is not influenced by the deposition method but only by the composition. The spectra in Figure 5a showing the TO band only change slightly with n, whereas the evolution of the spectra in Figure 5b is more pronounced because of the significant blueshift of the LO band and the concomitant increase of its intensity with decreasing n. The TO band shifts to higher wavenumbers as well but with a lesser extent.

Similar blueshifts of the TO band 5 25 27 32 33 34 and of the LO band 24 27 33 were also observed in SiN _x :H films. Lucovsky et al. 32 explained the TO band blueshift by the incorporation of H. They suggested that one of the near silicon atoms of the N(−Si)₃ bonding configuration where Si has only one N neighbor is replaced by a H atom. The H incorporation was also evoked to be responsible for the LO band blueshift in SiN _x :H 24 27 33 39 . However, our spectra in Figure 5 demonstrate that these two blueshifts are not necessarily linked to H. Besides, similar blueshifts of the TO band 15 35 and of the LO band 35 have also been reported in O- and H-free SiN _x thin films while the Si content was decreased. As a consequence, these two blueshifts are partly or completely due to some change of the [N]/[Si] ratio in the case of SiN _x :H or pure SiN _x , respectively. The change in the positions of the TO and the LO modes of Si-N absorption bands are due to some modifications intrinsic to the Si-N binding configuration. In their calculation, Hasegawa et al. 25 have predicted that the blueshift of the TO mode is linked to the decrease of the Si-N bond length which is caused by a compositional change of SiN _x 25 41 . In addition to this, some stress in the films induced by the Si incorporation may also contribute to such shifts 35 . Moreover, one can assume that the TO-LO coupling of the Si-N asymmetric stretching modes is induced by the disorder in the material in the same manner as that established in Si oxide 42 43 . Consequently, the increase of the LO band intensity is a signature of the ordering of the films while the Si content is decreased.

The inset of Figure 4 shows the TO and LO band positions as a function of the stoichiometry. Again, one can notice that the LO band position is more sensitive to the composition than that of the TO band. The LO mode position is obviously a better indicator of the composition of Si-rich SiN _x than that of the TO band, as mentioned elsewhere 35 . We found that the TO and the LO band positions increase linearly with increasing Si/N ratio x following the two relations:

ν TO x = 21.4 x − 4 / 3 + ν TO 4 / 3

ν LO x = 323.4 x − 4 / 3 + ν LO 4 / 3

where ν _TO(x) and ν _LO(x) are the TO and the LO band positions, respectively, and ν _TO(4/3) and ν _LO(4/3) are the TO and the LO band positions calculated for x = 4/3, which correspond to the stoichiometric condition, respectively. We found ν _TO(4/3) = 840 cm⁻¹ which is interestingly the value attributed to the Si-N stretching vibration of an isolated nitrogen in a N-Si₃ network 33 44 and ν _LO(4/3) = 1197 cm⁻¹. These relations can be used to estimate the composition of as-deposited Si-rich SiN _x films in the same way as the empirical one concerning Si-rich silicon oxide 30 .

In Figure 6a, the effect of the annealing on the FTIR spectra of a SiN _x film with n = 2.22 is shown. It is seen that the intensity of the TO mode increases with increasing annealing temperature which is manifestly due to the increase in the amount of Si-N bonds. It is also seen that the TO peak position slightly shifts to higher wavenumbers. Moreover, Figure 6b shows that the LO band evolves similarly, i.e., an increase of its intensity and a significant blueshift. All these observations indicate a rearrangement of the Si nitride network toward that of the stoichiometric structure with a lower structural disorder. This can be due to a phase separation between Si and Si nitride.

Figure 7 shows the evolution of the Raman spectra of SiN _x thin layers deposited on fused silica with various Si contents and with various annealing temperatures. Again, it is seen that the evolution of the Raman spectra does not depend on the deposition methods but only on the composition that is set by n. Upon annealing at 900°C, the two broad vibration bands of the transverse acoustic (TA) phonon and of the TO phonon of a-Si at 150 and 480 cm⁻¹, respectively, became clearly narrower and more pronounced (Figure 7). This evolution can be explained by the formation of small amorphous Si-np 45 . Unlike this deduction, the appearance of new sharp peaks slightly shifted towards lower wavenumbers compared to bulk crystalline Si (c-Si) at approximately 520 cm⁻¹ upon annealing at 1100°C as shown in Figure 7b, which unequivocally demonstrates the formation of small crystalline Si-np. Besides, the formation of a c-Si phase is also consistent with the appearance of a weak peak at 300 cm⁻¹ that is attributed to the second order of the transverse acoustic (2TA) phonon mode in the thin films containing a high Si content (n = 2.89 and 2.98). It is seen that the condensation of the excess of Si in small crystalline Si-np during the annealing at 1100°C occurs but only in thin films having a refractive index higher than 2.5 (Figure 7b) or maybe equal to 2.5 as indicated by the presence of a weak shoulder (see the arrow) in Figure 7a. Nevertheless, thin films with a low Si content (SiN _{x > 0.8}, see Figure 3) could also contain small Si-np upon annealing at 1100°C but having an amorphous structure.

Figure 8 shows the Raman spectra of the thin films with n > 2.5 (Figure 7b) after annealing at 1100°C. A low excitation energy density of 0.14 MW/cm² was used to record these spectra in order to avoid any heating and induced stress of the films that may affect the Raman spectra of crystalline Si-np 46 . One can observe that the c-Si peaks progressively shift to higher wavenumbers toward the peak position of bulk c-Si with increasing n. This progressive shift is related to a QCE on the optical phonon in confined crystalline Si-np 46 47 48 49 , as it is seen in the inset of Figure 8 where the Raman shift is plotted as a function of the diameter. The Raman shift was obtained by fitting the Raman signal with the asymmetric Lorentzian functions, and the particle size corresponded to the maximum of the lognormal distribution of crystalline Si-np sizes measured by HRTEM (see Figure 9). Then, we compared our experimental results with the Richter, Wang, and Ley (RWL) model 47 and the bond polarizability (BP) model 48 that account for the QCE on optical phonons in crystalline Si-np. In these two models, the Raman redshift can be presented as a function of the Si-np size using the analytical expression:

Δω = β a / d γ

where Δω is the frequency redshift; a, the Si lattice parameter (a = 0.543 nm); d, the crystalline Si-np diameter; and β and γ, the model parameters (β = 52.3 cm⁻¹ and γ = 1.586 for the RWL model, and β = 47.41 cm⁻¹ and γ = 1.44 for the BP model). Interestingly, one can notice that our experimental results are in good agreement with the previous works suggesting that the latter models can be applied to crystalline Si-np embedded in Si nitride as well.

In order to further investigate the microstructure of the 1100°C-annealed films, HRTEM observations have been performed on several thin films with various n > 2.5. Figure 9b shows the diffraction pattern of one film with n = 2.89. One can observe three quasi-continuous rings corresponding to various orientations of c-Si because of the presence of randomly oriented crystalline Si-np. These numerous crystalline Si-np can be easily distinguished from the host matrix (Figure 9a) because of the lattice fringes of c-Si. They are rather small with an average size of about 6.0 ± 0.5 nm (Figure 9c).

Figure 10 shows the effect of the annealing temperature on the XRD patterns of one SiN _x layer produced by the co-sputtering method with n = 2.89. One can observe that two new peaks of c-Si with the (111) and (220) orientations distinctly emerge in the XRD pattern upon annealing at 1100°C, which demonstrates the formation of a c-Si phase in the material.

In Figure 11, the evolution of the XRD pattern of the 1100°C-annealed films with n is shown. Again, we could not notice any dependence of the synthesis method on the structure since the spectra of the two films produced by the co-sputtering and the N₂-reactive methods which have a close refractive index of 2.72 and 2.74, respectively, are very similar. The XRD patterns depend only on the Si content given by n. One can notice that the thin films with n = 2.12 do not show any c-Si peak with the exception of the (311) c-Si peak emanating from the substrate. This is in contrast with the spectra of thin films with a higher refractive index (n > 2.5) that also show the (111) and (220) c-Si diffraction peaks attesting the presence of crystalline Si-np. Besides, the XRD results are in perfect agreement with the Raman spectra shown in Figure 7, since the c-Si Raman peaks were also detected but only when n was above 2.5 (SiN _x<0.8).

Figure 12 shows the PL and the absorption spectra of several SiN _x thin films with various n. In the right part of the figure, it is seen that the absorption rises with increasing n which is explained by the increase of the Si content. In the same time, we observed a progressive redshift of the PL bands with a concomitant increase of their widths as displayed in the inset. Moreover, one can notice that the PL intensity significantly increases while n increases from 2.01 to 2.12, which is partly explained by the rise of the absorption. Reminding that FTIR spectra showed that the disorder increased with increasing n, the increase of the non-radiative recombination rate would then explain the decrease of the PL intensity while n reaches 2.14. Besides, thin films with n > 2.4 (SiN _x<0.85) did not exhibit any PL even after annealing with various temperatures ranging up to 1100°C. The typical variation of the PL intensity of one luminescent film with the annealing temperature is shown in Figure 13. Interestingly, as-deposited films showed no PL, and it is seen that the highest integrated PL intensity was found at 900°C. The origin of the visible PL easily perceivable by the naked eye is investigated in the ‘Discussion’.

Figure 14 shows the Raman spectra of one luminescent film with n = 2.34 recorded with various excitation power densities. Although we did not detect by Raman spectroscopy (Figure 7a) any crystalline Si-np even after annealing at 1100°C, we could however form small Si nanocrystals by laser annealing. This formation has been evidenced by Raman measurements that are separated in two steps for clarity. During the first step (white arrows), the power density of the laser was increased from 0.14 to 0.70 MW/cm². It is seen that the Raman signal increased because of the rise of the number of both Raman-scattered photons and PL photons. When the excitation power density reached 1.4 MW/cm², a sharp new Raman peak slightly shifted from that of bulk c-Si appeared. During the second step (black arrows), the power density was decreased back. One can observe that the c-Si peak remained whatever the power density suggesting that the structure of the SiN _x thin layer was definitively modified. This is then explained by the formation of small crystalline Si-np in the spot of the focused laser as observed elsewhere 45 50 51 . Moreover, one can notice that, for the same excitation densities, all baselines levels significantly dropped after the local formation of small Si nanocrystals. This drop of the baseline level is explained by the PL quenching of the broad PL band centered at about 700 nm, corresponding to approximately 4000 cm⁻¹, since the baseline is actually located on the green tail of the broad PL band. This demonstrates that this PL band cannot emanate from crystalline Si-np. This PL could however be related to amorphous Si-np. Nevertheless, Volodin et al. 45 showed that the presence of amorphous Si-np is not required for the laser-induced formation of crystalline Si-np which is in agreement with our results showing that this formation occurred in films containing a low Si content (SiN_0.9) and in as-deposited films as well.

Figure 15 shows the effect of the irradiation time on the Raman spectra of the latter SiN _x films during the laser annealing which was performed while the power density was set to 1.4 MW/cm² (Figure 14). The formation of small crystalline Si-np is very fast since the c-Si peaks at 300 and 510 cm⁻¹ emerged almost immediately or at least in less than the acquisition time of approximately 0.5 s after the laser irradiation started. Moreover, one can observe that, after the laser-induced formation of crystalline Si-np, the Raman spectra changed while the thin SiN _x layer was continuously exposed to the intense radiation. Indeed, three modifications are clearly seen: (1) The baseline progressively dropped with increasing irradiation time which has been previously explained by the PL quenching of the material (see Figure 14). (2) The c-Si peak of 7.5 cm⁻¹ shifted towards the position of c-Si in bulk material, and its intensity dropped after 1 min. However, its position and its intensity remained fixed for longer irradiation times. This latter modification, which is actually also discernible in Figure 14, can be explained by the unceasing growth of the crystalline Si-np until they reached a maximal size and/or by the relaxation of stress 46 . Also, (3) the intensity of the 2TA phonon mode at 300 cm⁻¹ was quenched after 1 min of laser exposure which may result from disorder in the crystalline structure 52 . Besides, in the inset of Figure 15, a picture of the laser spot course while the thin layer was displaced perpendicularly to the laser beam is shown. This dark laser print reveals some local damages caused by the long exposition. However, since the main peak remains shifted to lower wavenumbers compared with bulk c-Si after a long illumination, one can assure that the film structure was definitively modified and that the films contained crystalline Si-np locally formed by laser annealing.

Optically active defect states within the bandgap of amorphous SiN _x could play a role in the radiative recombination of SiN _x as reported by several authors 18 53 . This interpretation is based on the wide PL spectra that contained distinct PL peaks with several energy levels that corresponded to the calculated values of various defect states found by Robertson 54 55 . Similar spectra were observed in the 1.75 to 3.1 eV spectral range by Ko et al. 56 who noticed a redshift of the PL with decreasing Si content. This evolution is in contrast to that of our PL spectra which, moreover, do not contain any distinct PL peaks attributable to distinct defect state levels. As a consequence, we believe that the origin of the PL of our SiN _x samples cannot be ascribed to defect states localized within the bandgap.

Let us consider the optical transition between photogenerated carriers localized in the band tail of the material in accordance with the static disorder model 57 . In this model, the carrier distribution in the exponential band tail density of states accounts for the PL band position and the PL shape of SiN _x :H 16 . An increase of the width of the localized states results in a blueshift and an increase of the width of the PL band. On one hand, many groups 13 16 explained that the increase of the structural disorder caused by the nitrogen alloying in Si-rich SiN _x :H with a very high Si content (SiN _x<0.6) accounts for the widening of the band tail states and then for the PL behavior. On the other hand, many groups 2 3 4 explained that the increase of the structural disorder induced by the incorporation of more nitrogen in N-rich SiN _x>1.33:H films accounts for the widening of the band tails and the PL properties. The increase of disorder in N-rich SiN _x>1.33 films with increasing N content is consistent with the FTIR spectra of Huang et al. 35 which show a drop of the LO band intensity.

Figure 5b showed that the situation is inversed in our Si-rich SiN _x films with a low Si excess content since the disorder manifestly increases with the Si incorporation. Therefore, the redshift of the PL band (Figure 12) cannot be explained by the tail-to-tail radiative recombination which would anyway be in contradiction with the widening of the PL band (inset of Figure 12). As a consequence, unlike Si-rich SiN _x :H films with a very high Si content (SiN _x<0.6) 13 16 , we believe that the static disorder model cannot account for the PL properties of H-free Si-rich SiN _x films containing a low Si content (SiN _x>0.85). Besides, it has been shown that the hydrogen concentration plays an important role in the PL properties (intensity and peak position) of hydrogenated films 13 .

Crystalline Si-np were detected by Raman, XRD, and HRTEM in numerous SiN _x films annealed at 1100°C that had a high n > 2.5 (SiN _x<0.8). Furthermore, we have demonstrated in Figure 8 that the progressive redshift of the crystalline Raman peak while n decreased is due to the decrease of the crystalline Si-np average size. The average sizes in the films with n ranging from 2.53 to 2.89 are between 2.5 and 6 nm, respectively. Theses sizes are theoretically small enough to show PL from excitons confined in crystalline Si-np according to the QCE model 58 . This model was proposed to explain the size dependence of the PL peak position that was noticed in oxide systems 1 59 . This size effect was evidenced in free crystalline Si-np surrounded by a thin Si oxide shell 60 , which however slightly differ from that generally observed while the crystalline Si-np are embedded in a Si oxide host medium 59 61 . In the case of Si nitride as embedding matrix, several authors suggested that the PL could emanate from confined states in crystalline Si-np, which were present in the materials as attested by HRTEM observations, mainly because of a perceivable size effect on the PL 10 11 12 13 14 . Although our measurements (Figure 12) also show that the PL peak shifted to lower energies with increasing Si content, which is consistent with the QCE model, crystalline Si-np cannot be responsible for the radiative emission for two reasons: (1) Although small (2.5 to 6 nm) Si nanocrystals could be formed in films with n > 2.5 during annealing at 1100°C, we could not detect any PL. PL was detected only for smaller refractive indexes (n < 2.4). Besides, we demonstrated in Figure 7b and Figure 10 that this temperature is necessary to crystallize the excess of Si. Furthermore, (2) the PL of luminescent SiN _x films (i.e., with n < 2.4) was quenched while we could form crystalline Si-np by another annealing method using an intense laser irradiation (Figure 14).

Although we have demonstrated that crystalline Si-np are not valid to explain the PL, let us consider Si-np with an amorphous phase as proposed by several authors 5 6 7 8 . The annealing temperature dependence of the FTIR spectra of one luminescent SiN _x film (n = 2.22) shown in Figure 6 suggests that a phase separation between Si-np and the Si nitride host media occurred during the annealing. The two Raman bands of a-Si at 150 and 485 cm⁻¹ shown in Figure 7 indicate that luminescent films (i.e., with n < 2.4) could contain amorphous Si-np. Besides, the Raman spectra would then show that the density of amorphous Si-np increased with increasing annealing temperature. This explains the absence of PL in the as-deposited samples and why the highest integrated PL intensity (Figure 13) was found at 900°C and not at 1100°C when crystalline Si-np could form. The redshift of the PL bands with increasing Si content (Figure 12) would then be due to a size effect. Also, the increase of the PL band width would then result from the widening of the size distribution as experimentally observed in Si oxide matrices 59 61 . Then, we have imaged a 1,000°C-annealed SiO _x /SiN _x multilayer by energy-filtered transmission electron microscopy enabling to distinguish small amorphous Si-np from the host media because of the high contrast of this technique. Because of PL interest, the refractive index of the SiN _x sublayer was set between 2.1 and 2.3. We could distinctly observe amorphous Si-np in the 3.5-nm-thick SiO _x sublayers, but no particles were perceivable in the 5-nm-thick SiN _x sublayers 40 . Si-np could be however very small, below the EFTEM detection threshold of about 1 to 2 nm, and then constituted less than 1000 of Si atoms. Besides, such an amorphous Si-np size seems possible compared to the average size of 2.5 nm of crystalline Si-np detected by Raman spectroscopy in SiN _x with n = 2.53. Consequently, the origin of the PL would be related to small amorphous Si-np, and the recombination would originate either from confined states in the Si-np and/or from defect states at the interface between the Si-np and the Si nitride medium 7 .