, (9)

(10)

. So, the

� <sup>3</sup>a<sup>2</sup> <sup>16</sup> � �<sup>2</sup>

DOI: http://dx.doi.org/10.5772/intechopen.86508

crystals with diamond-type lattice. The frequency is given by

the phonon dispersion for the three main directions in Si.

Raman spectrum becomes asymmetric.

13

þ 3 8 ∑ i ∑ 4 k,j<sup>&</sup>gt;<sup>k</sup>

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic…

ω<sup>Г</sup> ¼

TO and LO phonons at the Brillouin zone center is equal to 520.5 cm�<sup>1</sup>

<sup>E</sup> <sup>¼</sup> <sup>3</sup> <sup>16</sup> <sup>∑</sup> i ∑ j kl <sup>a</sup><sup>2</sup> <sup>r</sup> ! <sup>i</sup> � rj ! � �<sup>2</sup>

where n ω<sup>0</sup> ð Þ<sup>q</sup> � � <sup>þ</sup> <sup>1</sup> <sup>¼</sup> <sup>1</sup> <sup>e</sup>ℏω0ð Þ<sup>q</sup> <sup>=</sup>kT�<sup>1</sup> <sup>þ</sup> 1 is the Bose-Einstein factor, <sup>ω</sup><sup>0</sup> ð Þ q is phonon dispersion, and Γ is FWHM of the Raman peak of a single phonon [12–14]. We also have taken into account that the vibration modes (phonons) with lower frequencies have higher amplitudes of vibration. Energy of vibration ℏω<sup>0</sup> is proportional to u<sup>2</sup> � �k, where u<sup>2</sup> � � is standard deviation of an atom from equilibrium position k which is Hooke's coefficient for a bond, and <sup>k</sup> <sup>¼</sup> <sup>m</sup>ω0<sup>2</sup> (<sup>m</sup> is mass of an atom). So, one can derive <sup>u</sup><sup>2</sup> � � � <sup>ℏ</sup>=ω<sup>0</sup> (Eq. (2.26) in book [15]). This correction is substantial especially for phonons with large frequency dispersion, so we use the equation

$$I(\boldsymbol{\alpha}) \cong \int\_0^1 |\mathbf{C}(\mathbf{0}, \mathbf{q})|^2 \frac{n\left(\boldsymbol{\alpha}'(\mathbf{q})\right) + \mathbf{1}}{\boldsymbol{\alpha}'(\mathbf{q}) \cdot \left(\left(\boldsymbol{\alpha} - \boldsymbol{\alpha}'(\mathbf{q})\right)^2 + \left(\Gamma/2\right)^2\right)} d^3 \mathbf{q} \tag{6}$$

It was shown [14] that using a Gaussian curve as eigenfunction for a confined phonon leads to more adequate results than experimental spectra.

Usually, it can be assumed that NCs have a spherical shape with diameter L. Therefore, in spherical coordinate system, the phonon weighting function Wð Þ r; L depends only on radius coordinate r and does not depend on angles. Assuming that at the boundary of NC (r=L/2) the phonon amplitude is equal to 1/e (the phonon amplitude at center of NC is equal to 1), one can obtain.

$$\mathcal{W}(\mathbf{r},L) = \exp\left(-4r^2/L^2\right), \text{ so } \mathcal{C}(\mathbf{0},\mathbf{q}) \cong \exp\left(-\frac{|\mathbf{q}|^2L^2}{16}\right)|\mathcal{C}(\mathbf{0},q)|^2 \cong \exp\left(-\frac{q^2L^2}{8}\right) \tag{7}$$

Usually, only empirical expressions for phonon dispersion were used in PCM [12, 13]. But the empirical expressions are accurate enough only near the Brillouin zone center. Also, in earlier approaches, the differences between dispersions of longitudinal optic (LO) and transverse optic (TO) phonons were usually not taken into account. In general, for crystals with diamond-type lattice, there are six phonon branches with dispersions ω<sup>i</sup> 0 ð Þq , so the first-order Raman spectrum for phonon weighting function <sup>W</sup>ð Þ¼ <sup>r</sup>; <sup>L</sup> exp �4r<sup>2</sup>=L<sup>2</sup> � � is

$$I(\boldsymbol{\alpha}) \cong \sum\_{i=1}^{6} \int\_{0}^{q\max} \exp\left(-\frac{q^{2}L^{2}}{8}\right) \frac{n\left(\boldsymbol{\alpha}\_{i}^{\prime}(\boldsymbol{q})\right) + \mathbf{1}}{\boldsymbol{\alpha}\_{i}^{\prime}(\mathbf{q}) \cdot \left(\left(\boldsymbol{\alpha} - \boldsymbol{\alpha}\_{i}^{\prime}(\mathbf{q})\right)^{2} + \left(\Gamma/2\right)^{2}\right)} q^{2} d\boldsymbol{q}.\tag{8}$$

Wavenumbers are varied from 0 up to qmax (edge of the Brillouin zone). For directions with high symmetry (<100> and <111>), it should be noted that some phonon branches are degenerated. The density of states for phonons is proportional to q<sup>2</sup>dq.

In some approaches, the phonon frequencies are determined using "ab initio" quantum mechanical calculations [16], but this method requires large computational resources, while NCs with diameters >3 nm contain more than 1 thousand atoms. So, for calculation of phonon dispersion, the Keating model of

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic… DOI: http://dx.doi.org/10.5772/intechopen.86508

valence forces [17] was used. In this simple but adequate model, the elastic energy of the crystal depends on bond length and on deviation of bond angle from ideal tetrahedral angles. We consider atom-atom interaction only between the nearest neighbor. For a crystal with diamond-type lattice, the elastic energy of unit cell is

$$E = \frac{3}{16} \sum\_{i} \sum\_{j} \frac{k\_{l}}{a^2} \left( \left( \overrightarrow{r}\_{i} - \overrightarrow{r}\_{j}^{\cdot} \right)^2 - \frac{3a^2}{16} \right)^2 + \frac{3}{8} \sum\_{i} \sum\_{k\_2, j > k} \frac{k\_{\varphi}}{a^2} \left( \left( \overrightarrow{r}\_{i} - \overrightarrow{r}\_{j}^{\cdot} \right) \cdot \left( \overrightarrow{r}\_{i} - \overrightarrow{r}\_{k}^{\cdot} \right) + \frac{a^2}{16} \right)^2 \right], \tag{9}$$

where kl and k<sup>ϕ</sup> are elastic constants (Hooke's coefficients) and a is lattice constant. TO and LO phonons at the Brillouin zone center are degenerated for crystals with diamond-type lattice. The frequency is given by

$$
\alpha\_{\varGamma} = \sqrt{\frac{8\left(k\_l + 3k\_\wp\right)}{3m}}\tag{10}
$$

where m is the mass of Ge atoms. As it was mentioned above, Si frequency of TO and LO phonons at the Brillouin zone center is equal to 520.5 cm�<sup>1</sup> . So, the elastic constants k<sup>ϕ</sup> and kl are not independent [see Eq. (10)]. The elastic constant kl was determined from approximation of calculated dispersions in directions <100>, <110>, and <111>, obtained from neutron scattering data [18, 19]. It is important to consider phonons of different directions, because in experiment, Raman signal comes from a large amount of randomly oriented NCs, and all phonon modes are intermixed. The exact expressions for phonon dispersions in directions <100>, <110>, and <111> for Keating model are published in Ref. [14] and are very cumbersome. To calculate the first-order Raman spectrum, one should use these dispersions in the Eq. (8). Dispersion in different directions should be used with its corresponding weight. There are 6 physically equivalent <100> directions, so the weight of this dispersion is 6. Similarly the weight of dispersion along <111> and <110> directions are, respectively, equal to 8 and 12. Thus, all calculations were performed with the phonon dispersion in the Keating model, taking into account the phonon dispersion for the three main directions in Si.

Figure 1 shows the results of calculations of the Raman spectra of Si NCs of different diameters using improved PCM. It is seen that for Si NC with diameter of 10 nm, the effect of phonon confinement is significant. The peak shifted and broadened relative to the peak from the bulk Si. For sizes below 10 nm, the NCs' Raman spectrum becomes asymmetric.

Figures 2 and 3 summarize the results of calculations compared with experimental results. Figure 2 shows the difference between the position of Raman peaks of Si NCs and bulk Si. The average sizes of the Si NCs were determined from HRTEM data. As can be seen, the results of calculations in improved PCM agree well with experimental data but have some differences from the simulation results presented in earlier works [12, 13, 16]. It should be noted that results of calculations in the improved PCM are adequate for a broad range of Si NCs'sizes (from 3 to 10 nm). Note, however, that if during measurements, the heating of the sample under laser spot takes place, the Raman peak will shift (due to anharmonicity of phonons). If the system contains mechanical stress, it will also cause a shift of the Raman peak [14]. Figure 3 shows the dependence of the Raman peak width with the size of the NCs, for calculation with improved PCM and for experimental data. Some differences between the experimental data and calculations are visible. In particular, large width of the experimental spectra, compared with the calculated spectra, may be due to the dispersion of the size of the Si NCs. Thus, if anharmonicity effect due to heating or mechanical stress is not relevant, the present

The wavenumber of scattered photon is in our case about three orders of magnitude lower than the wavenumber of a phonon at the Brillouin zone boundary,

<sup>2</sup> n ω<sup>0</sup>

dispersion, and Γ is FWHM of the Raman peak of a single phonon [12–14]. We also have taken into account that the vibration modes (phonons) with lower frequencies

u<sup>2</sup> � �k, where u<sup>2</sup> � � is standard deviation of an atom from equilibrium position k which is Hooke's coefficient for a bond, and <sup>k</sup> <sup>¼</sup> <sup>m</sup>ω0<sup>2</sup> (<sup>m</sup> is mass of an atom). So,

especially for phonons with large frequency dispersion, so we use the equation

<sup>2</sup> n ω<sup>0</sup>

ω0

phonon leads to more adequate results than experimental spectra.

ω � ω<sup>0</sup> ð Þ ð Þ q

<sup>e</sup>ℏω0ð Þ<sup>q</sup> <sup>=</sup>kT�<sup>1</sup> <sup>þ</sup> 1 is the Bose-Einstein factor, <sup>ω</sup><sup>0</sup>

ð Þ <sup>q</sup> � � <sup>þ</sup> <sup>1</sup>

<sup>2</sup> <sup>þ</sup> ð Þ <sup>Γ</sup>=<sup>2</sup> <sup>2</sup> <sup>d</sup><sup>3</sup>

(Eq. (2.26) in book [15]). This correction is substantial

<sup>2</sup> <sup>þ</sup> ð Þ <sup>Γ</sup>=<sup>2</sup> <sup>2</sup> � � <sup>d</sup><sup>3</sup>

ð Þ <sup>q</sup> � � <sup>þ</sup> <sup>1</sup>

L2 16 !

> 0 ð Þ<sup>q</sup> � � <sup>þ</sup> <sup>1</sup>

<sup>0</sup> ð Þ ð Þ q

ð Þ� q ω � ω<sup>i</sup>

Wavenumbers are varied from 0 up to qmax (edge of the Brillouin zone). For directions with high symmetry (<100> and <111>), it should be noted that some phonon branches are degenerated. The density of states for phonons is proportional

In some approaches, the phonon frequencies are determined using "ab initio"

computational resources, while NCs with diameters >3 nm contain more than 1 thousand atoms. So, for calculation of phonon dispersion, the Keating model of

j j <sup>C</sup>ð Þ <sup>0</sup>; <sup>q</sup> <sup>2</sup> ffi exp � <sup>q</sup><sup>2</sup>L<sup>2</sup>

ð Þq , so the first-order Raman spectrum for

<sup>2</sup> <sup>þ</sup> ð Þ <sup>Γ</sup>=<sup>2</sup> <sup>2</sup> � � <sup>q</sup><sup>2</sup>

ð Þ� q ω � ω<sup>0</sup> ð Þ ð Þ q

It was shown [14] that using a Gaussian curve as eigenfunction for a confined

Usually, it can be assumed that NCs have a spherical shape with diameter L. Therefore, in spherical coordinate system, the phonon weighting function Wð Þ r; L depends only on radius coordinate r and does not depend on angles. Assuming that at the boundary of NC (r=L/2) the phonon amplitude is equal to 1/e (the phonon

Usually, only empirical expressions for phonon dispersion were used in PCM [12, 13]. But the empirical expressions are accurate enough only near the Brillouin zone center. Also, in earlier approaches, the differences between dispersions of longitudinal optic (LO) and transverse optic (TO) phonons were usually not taken into account. In general, for crystals with diamond-type lattice, there are six

0

� � n ω<sup>i</sup>

ωi 0

quantum mechanical calculations [16], but this method requires large

q (5)

is proportional to

ð Þ q is phonon

q (6)

8 � �

dq: (8)

(7)

so one can assume q0 ffi 0. So, the first-order Raman spectrum is

j j Cð Þ 0; q

have higher amplitudes of vibration. Energy of vibration ℏω<sup>0</sup>

Ið Þffi ω

ð Þ<sup>q</sup> � � <sup>þ</sup> <sup>1</sup> <sup>¼</sup> <sup>1</sup>

where n ω<sup>0</sup>

Nanocrystalline Materials

one can derive <sup>u</sup><sup>2</sup> � � � <sup>ℏ</sup>=ω<sup>0</sup>

Wð Þ¼ r; L exp �4r

Ið Þffi ω ∑ 6 i¼1

to q<sup>2</sup>dq.

12

Ið Þffi ω

ð 1

j j Cð Þ 0; q

amplitude at center of NC is equal to 1), one can obtain.

phonon weighting function <sup>W</sup>ð Þ¼ <sup>r</sup>; <sup>L</sup> exp �4r<sup>2</sup>=L<sup>2</sup> � � is

exp � <sup>q</sup><sup>2</sup>L<sup>2</sup> 8

<sup>=</sup>L<sup>2</sup> � �,so <sup>C</sup>ð Þffi <sup>0</sup>; <sup>q</sup> exp � j j <sup>q</sup> <sup>2</sup>

0

2

phonon branches with dispersions ω<sup>i</sup>

ð qmax

0

ð

Figure 1. Calculated Raman spectra of Si NCs of diameters from 10 to 3 nm.

#### Figure 2.

Shift of the position of the Raman peak for optical phonons confined in Si NCs of various sizes is shown relative to position of Raman peak for bulk Si. The solid curve represents the results obtained using improved PCM (dispersion is calculated in the Keating model taking into account the angular phonon dispersion); red crosses show the experimental data.

improved model allows us to determine the average size of the Si NCs from the analysis of the Raman spectra for a wide range of sizes.

Experimental data on Figures 2 and 3 were obtained for Si NCs in SiOx, SiNx, and amorphous Si matrix and also for free-standing Si nanopowders. This indicates that the PCM is adequate for various matrices; the main demand is that localized phonons in NCs strongly damp in matrix.

In Figure 4 the Raman spectra of PECVD-deposited SiOx:H films are shown. Deposition was made from the mixture of monosilane (SiH4) diluted by argon (Ar) and oxygen (O2) diluted by helium (He). The stoichiometry parameter "x" was changed by varying of oxygen concentration. The temperature of Si (100) monocrystalline substrate was 200°C. The thickness of SiOx:H films was about 200 nm. The value of stoichiometry parameter "x" was obtained from the analysis of X-ray photoelectron spectroscopy (XPS) data.

Raman spectra were registered at room temperature in back-scattering geometry. For excitation, the 514.5-nm line of an Ar<sup>+</sup> laser was used. No polarization analysis for scattered light was performed. A Horiba Jobin Yvon T64000 spectrometer was used for measuring Raman spectra with a spectral resolution better

Width of the Raman peak for optical phonons confined in Si NCs of various sizes. The solid curve represents the

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic…

results of calculation; red crosses show the experimental data.

DOI: http://dx.doi.org/10.5772/intechopen.86508

Figure 3.

Figure 4.

15

Raman spectra of SiOx:H films of different stoichiometry.

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic… DOI: http://dx.doi.org/10.5772/intechopen.86508

Figure 3.

Width of the Raman peak for optical phonons confined in Si NCs of various sizes. The solid curve represents the results of calculation; red crosses show the experimental data.

#### Figure 4.

improved model allows us to determine the average size of the Si NCs from the

Experimental data on Figures 2 and 3 were obtained for Si NCs in SiOx, SiNx, and amorphous Si matrix and also for free-standing Si nanopowders. This indicates that the PCM is adequate for various matrices; the main demand is that localized

Shift of the position of the Raman peak for optical phonons confined in Si NCs of various sizes is shown relative to position of Raman peak for bulk Si. The solid curve represents the results obtained using improved PCM (dispersion is calculated in the Keating model taking into account the angular phonon dispersion); red crosses

In Figure 4 the Raman spectra of PECVD-deposited SiOx:H films are shown. Deposition was made from the mixture of monosilane (SiH4) diluted by argon (Ar) and oxygen (O2) diluted by helium (He). The stoichiometry parameter "x" was changed by varying of oxygen concentration. The temperature of Si (100) monocrystalline substrate was 200°C. The thickness of SiOx:H films was about 200 nm. The value of stoichiometry parameter "x" was obtained from the analysis of X-ray

analysis of the Raman spectra for a wide range of sizes.

Calculated Raman spectra of Si NCs of diameters from 10 to 3 nm.

phonons in NCs strongly damp in matrix.

Figure 2.

14

Figure 1.

Nanocrystalline Materials

show the experimental data.

photoelectron spectroscopy (XPS) data.

Raman spectra of SiOx:H films of different stoichiometry.

Raman spectra were registered at room temperature in back-scattering geometry. For excitation, the 514.5-nm line of an Ar<sup>+</sup> laser was used. No polarization analysis for scattered light was performed. A Horiba Jobin Yvon T64000 spectrometer was used for measuring Raman spectra with a spectral resolution better

than 2 cm<sup>1</sup> . A special facility for microscopic Raman studies was also employed. The laser-beam power reaching the sample was 2 mW. For minimization of the heating of the structures under the laser beam, the sample was placed somewhat below the focus in a situation in which the laser-spot size was equal to 10 μm.

One can see in Raman spectra of as-deposited SiNx:H films the amorphous Si

In Figure 5b the spectra of SiNx films after annealing at Ar atmosphere (1100°C, 2 hours) are presented. One can see that in spectrum of sample with low concentration of Si (x = 1.1), the annealing leads to growth of TO and TA peaks related to amorphous Si. It means that the annealing contributed to the gathering of excess silicon atoms into amorphous clusters and the structure of annealed film is close to RM model. Nevertheless, even such a high-temperature annealing did not lead to crystallization of amorphous nanoclusters. In spectrum of SiN0.75 film, there is

such shift is corresponding to Raman scattering by optical phonons localized in Si NCs with average size about 3 nm. It is worth to note that this size is closed to

The photoluminescence under excitation with ultraviolet laser HeCd laser (λ = 325 nm) was also studied in as-deposited and annealed SiNx:H films. Annealing leads to an increase in the intensity of the photoluminescence, apparently due to the annealing of non-radiative defects. The maximum of the photoluminescence signal shifted to the long-wavelength direction (redshift) with an increase in the content

4. IR absorption in SiOx and SiNx films: the evidence of deviation from

The SiOx:H and SiNx:H films were studied using Fourier transform infrared (FTIR) absorption spectroscopy; the spectrometer FT-801 having a spectral resolu-

The IR spectra of SiOx samples in Figure 6 show an absorption peak on the stretching vibrations of the Si▬O bonds (TO3 peak [20]). Pai et al. [21] found that the position of this peak (in inverse centimeters) in SiOx films almost linearly

From the data of Figure 6, it can be seen that the position of the TO3 peak for the

). It is worth also to note that the peaks

expected stoichiometry of silicon oxide SiOx should change only slightly. But, according to XPS data, the stoichiometry of the SiOx films varies widely (from 0.7 to 1.2). This suggests that the structure of our films does not correspond to the RB model (otherwise, the shift range of the TO3 peak position would be much wider). However, the structure of our films does not correspond to the RM model either (the position of the TO3 peak for all the films would correspond to the SiO2 matrix

corresponding to absorption by Si▬H and O▬H bonds were observed in the films,

Figure 7a shows the IR absorption spectra of as-deposited SiNx:H films as well as silicon substrate. Nonpolar Si▬Si bonds that are active in the Raman process are not active in the absorption process, but Si▬N, Si▬H, and N▬H bonds are active in it, which makes it possible to obtain information on the structure of a-SiNx:H films

. The shift compared with position of peak

. According to the data presented in Figure 2,

ν ¼ 925 þ 75x (11)

. So, according to Eq. (11), the

peaks (Figure 5a). It should be noted that the spectrum of Si substrate was subtracted from spectra of studied structures. One can see that the SiNx:H films with x < 1 contain noticeable amount of amorphous Si clusters. In the as-deposited

sample with x = 1.1, the signal from amorphous Si is present, but small.

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic…

narrower peak with position 514.5 cm�<sup>1</sup>

DOI: http://dx.doi.org/10.5772/intechopen.86508

critical size of stable crystalline nuclei of Si.

of excess silicon in silicon nitride films.

depends on the stoichiometry parameter x, like.

studied samples varies from 1040 to 1060 cm�<sup>1</sup>

so the as-deposited SiOx films are hydrogenated.

the RM model

tion of 4 cm�<sup>1</sup> was used.

and would be about 1075 cm�<sup>1</sup>

17

of monocrystalline Si is about 6 cm�<sup>1</sup>

So, registered Raman spectra of the SiOx:H films and the Raman spectrum of a monocrystalline silicon substrate are shown in Figure 4. Evidently, a very intense signal due to silicon substrate is observed; this is a line due to the 520.5 cm<sup>1</sup> longwave optical phonon. For clarity, the vertical scale is plotted logarithmic. Besides, features originating from two-phonon scattering phenomena, namely, those due to events involving two acoustic phonons (2TA 300 cm<sup>1</sup> , LA + TA 425 cm<sup>1</sup> ), were observed in the spectrum of single-crystal silicon. SiOx:H films are semitransparent ones in the visible light, and their spectrum also exhibits a signal due to the substrate. The narrow peaks with wavenumbers lower than 160 cm<sup>1</sup> resulted from the inelastic scattering of light by atmospheric molecules. As it was mentioned, in Raman spectrum of amorphous Si clusters, there are TO (480 cm<sup>1</sup> )- and TA (150 cm<sup>1</sup> )-related broad peaks.

In Figure 4 one can see that the SiOx:H films with x < 1 contain noticeable amount of amorphous Si clusters. In the spectrum of film with x = 1.2, the TO and TA peaks are practically absent. If the structure of this film corresponded to the RM model, then a significant number of clusters of amorphous silicon would be present in it.

A similar picture is observed for PECVD-grown SiNx:H films (Figure 5a).

The studied SiNx:H films of different stoichiometric composition were grown using PECVD from a mixture of ammonia (NH3) and monosilane (SiH4) on Si substrates with orientation (001). It is known that the composition of SiNx films (0 < x < 4/3) depends on the NH3/SiH4 flow ratio. The temperature of the substrates during deposition was 150°C. The value of stoichiometry parameter "x" was defined using of XPS data.

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic… DOI: http://dx.doi.org/10.5772/intechopen.86508

One can see in Raman spectra of as-deposited SiNx:H films the amorphous Si peaks (Figure 5a). It should be noted that the spectrum of Si substrate was subtracted from spectra of studied structures. One can see that the SiNx:H films with x < 1 contain noticeable amount of amorphous Si clusters. In the as-deposited sample with x = 1.1, the signal from amorphous Si is present, but small.

In Figure 5b the spectra of SiNx films after annealing at Ar atmosphere (1100°C, 2 hours) are presented. One can see that in spectrum of sample with low concentration of Si (x = 1.1), the annealing leads to growth of TO and TA peaks related to amorphous Si. It means that the annealing contributed to the gathering of excess silicon atoms into amorphous clusters and the structure of annealed film is close to RM model. Nevertheless, even such a high-temperature annealing did not lead to crystallization of amorphous nanoclusters. In spectrum of SiN0.75 film, there is narrower peak with position 514.5 cm�<sup>1</sup> . The shift compared with position of peak of monocrystalline Si is about 6 cm�<sup>1</sup> . According to the data presented in Figure 2, such shift is corresponding to Raman scattering by optical phonons localized in Si NCs with average size about 3 nm. It is worth to note that this size is closed to critical size of stable crystalline nuclei of Si.

The photoluminescence under excitation with ultraviolet laser HeCd laser (λ = 325 nm) was also studied in as-deposited and annealed SiNx:H films. Annealing leads to an increase in the intensity of the photoluminescence, apparently due to the annealing of non-radiative defects. The maximum of the photoluminescence signal shifted to the long-wavelength direction (redshift) with an increase in the content of excess silicon in silicon nitride films.

#### 4. IR absorption in SiOx and SiNx films: the evidence of deviation from the RM model

The SiOx:H and SiNx:H films were studied using Fourier transform infrared (FTIR) absorption spectroscopy; the spectrometer FT-801 having a spectral resolution of 4 cm�<sup>1</sup> was used.

The IR spectra of SiOx samples in Figure 6 show an absorption peak on the stretching vibrations of the Si▬O bonds (TO3 peak [20]). Pai et al. [21] found that the position of this peak (in inverse centimeters) in SiOx films almost linearly depends on the stoichiometry parameter x, like.

$$\mathbf{v} = \mathbf{925} + \mathbf{75x} \tag{11}$$

From the data of Figure 6, it can be seen that the position of the TO3 peak for the studied samples varies from 1040 to 1060 cm�<sup>1</sup> . So, according to Eq. (11), the expected stoichiometry of silicon oxide SiOx should change only slightly. But, according to XPS data, the stoichiometry of the SiOx films varies widely (from 0.7 to 1.2). This suggests that the structure of our films does not correspond to the RB model (otherwise, the shift range of the TO3 peak position would be much wider). However, the structure of our films does not correspond to the RM model either (the position of the TO3 peak for all the films would correspond to the SiO2 matrix and would be about 1075 cm�<sup>1</sup> ). It is worth also to note that the peaks corresponding to absorption by Si▬H and O▬H bonds were observed in the films, so the as-deposited SiOx films are hydrogenated.

Figure 7a shows the IR absorption spectra of as-deposited SiNx:H films as well as silicon substrate. Nonpolar Si▬Si bonds that are active in the Raman process are not active in the absorption process, but Si▬N, Si▬H, and N▬H bonds are active in it, which makes it possible to obtain information on the structure of a-SiNx:H films

than 2 cm<sup>1</sup>

Nanocrystalline Materials

(150 cm<sup>1</sup>

be present in it.

Figure 5.

16

was defined using of XPS data.

. A special facility for microscopic Raman studies was also employed.

, LA + TA 425 cm<sup>1</sup>

)- and TA

),

The laser-beam power reaching the sample was 2 mW. For minimization of the heating of the structures under the laser beam, the sample was placed somewhat below the focus in a situation in which the laser-spot size was equal to 10 μm.

events involving two acoustic phonons (2TA 300 cm<sup>1</sup>

)-related broad peaks.

Raman spectrum of amorphous Si clusters, there are TO (480 cm<sup>1</sup>

So, registered Raman spectra of the SiOx:H films and the Raman spectrum of a monocrystalline silicon substrate are shown in Figure 4. Evidently, a very intense signal due to silicon substrate is observed; this is a line due to the 520.5 cm<sup>1</sup> longwave optical phonon. For clarity, the vertical scale is plotted logarithmic. Besides, features originating from two-phonon scattering phenomena, namely, those due to

were observed in the spectrum of single-crystal silicon. SiOx:H films are semitransparent ones in the visible light, and their spectrum also exhibits a signal due to the substrate. The narrow peaks with wavenumbers lower than 160 cm<sup>1</sup> resulted from the inelastic scattering of light by atmospheric molecules. As it was mentioned, in

In Figure 4 one can see that the SiOx:H films with x < 1 contain noticeable amount of amorphous Si clusters. In the spectrum of film with x = 1.2, the TO and TA peaks are practically absent. If the structure of this film corresponded to the RM model, then a significant number of clusters of amorphous silicon would

A similar picture is observed for PECVD-grown SiNx:H films (Figure 5a). The studied SiNx:H films of different stoichiometric composition were grown using PECVD from a mixture of ammonia (NH3) and monosilane (SiH4) on Si substrates with orientation (001). It is known that the composition of SiNx films (0 < x < 4/3) depends on the NH3/SiH4 flow ratio. The temperature of the substrates during deposition was 150°C. The value of stoichiometry parameter "x"

Raman spectra of SiNx:H films of different stoichiometry: (a) as-deposited films and (b) as-annealed films.

Figure 6. IR-absorbance spectra of SiOx:H films of different stoichiometry.

using the IR absorption method. Optical density A (natural logarithm of 1/T, where T is transmission) is plotted on the vertical axis. In the spectra of the films grown at high ratio of ammonia to monosilane fluxes (x = 1.3), absorption peaks at 3340 cm<sup>1</sup> are visible. This is the absorption on the stretching vibrations of the nitrogen-hydrogen bonds [22]. In the spectra of the films grown at a ratio of ammonia to monosilane fluxes of 1 and 0.5 (x = 1.1 and 0.75 accordingly), the intensity of this peak is very low, which means that the concentration of hydrogen bound to nitrogen decreases with increasing concentration of excess silicon. It is also seen from Figure 7 that the spectra of samples containing excess silicon contain a peak with a position of 2150 cm<sup>1</sup> . This is the peak from absorption on the stretching vibrations of the silicon-hydrogen bonds [22]. The intensity of this peak depends on the ammonia/monosilane ratio; the intensity is very low in Si3N4 film, but it grows with increasing concentration of excess silicon. The peak at 1100 cm<sup>1</sup> observed in all spectra corresponds to the absorption of stretching vibrations of silicon-oxygen bonds in the silicon substrate. These bonds also give peaks from 400 to 800 cm<sup>1</sup> of twisting, wagging, rocking, and scissor modes. In addition, the spectrum of monocrystalline silicon contains peaks from multiphonon lattice absorption in silicon itself (features in the region of 607–614 cm<sup>1</sup> ). In some spectra, there is also a "parasitic" peak with a position of 2350–2400 cm<sup>1</sup> associated with absorption on carbon dioxide gas (in the process of measuring its concentration slightly changed, as a result it was not completely

removed when dividing the spectrum from the samples by the reference spectrum

IR-absorbance spectra of SiNx:H films of different stoichiometry: (a) as-deposited films and (b) as-annealed

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic…

DOI: http://dx.doi.org/10.5772/intechopen.86508

Let us turn to the absorption peak due to vibrations of the Si▬N bonds in Figure 7. In the spectra of all the films, there are peaks from the stretching vibrations of these bonds. The spectra were approximated by Gaussian curves, and peak positions were determined. The position of the absorption peaks on the stretching vibrations of the Si▬N bonds is shifted, depending on the stoichiometry,

references therein). The general dependence is that the oscillation frequency decreases with decreasing stoichiometric parameter x in a-SiNx film. This is observed in our experiment and again confirms that the structure of the films cannot be considered only within the framework of the RM model (in which the stoichiometry of the matrix surrounding the silicon inclusions is unchanged—

2 hours) SiNx:H films. One can see that annealing leads to evaporation of

Figure 7b shows the IR absorption spectra of annealed (Ar atmosphere, 1100°C,

hydrogen, except nearly stoichiometry (x = 1.3) film. In that film the Si▬H peak becomes even more intensive after annealing. So, hydrogen has been removed from N▬H bonds to Si▬H bonds. This effect has already been observed in the work [24]. In the work [24], it was shown that in order to remove hydrogen from Si▬H bonds, it is necessary to apply high-temperature annealing at very high pressure. It should be noted that in annealed films the position of the absorption peaks on the stretching vibrations of the Si▬N bonds is also shifted, depending on the stoichiometry. The lesser parameter x, the higher is frequency of stretching vibrations of

. This effect was previously known (see work [23] and

of the air).

Figure 7.

films.

from 880 to 860 cm<sup>1</sup>

the Si▬N bonds.

19

the matrix parameter x is 4/3).

Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic… DOI: http://dx.doi.org/10.5772/intechopen.86508

Figure 7.

using the IR absorption method. Optical density A (natural logarithm of 1/T, where T is transmission) is plotted on the vertical axis. In the spectra of the films grown at

stretching vibrations of the silicon-hydrogen bonds [22]. The intensity of this peak depends on the ammonia/monosilane ratio; the intensity is very low in Si3N4 film,

2350–2400 cm<sup>1</sup> associated with absorption on carbon dioxide gas (in the process of measuring its concentration slightly changed, as a result it was not completely

). In some spectra, there is also a "parasitic" peak with a position of

. This is the peak from absorption on the

high ratio of ammonia to monosilane fluxes (x = 1.3), absorption peaks at 3340 cm<sup>1</sup> are visible. This is the absorption on the stretching vibrations of the nitrogen-hydrogen bonds [22]. In the spectra of the films grown at a ratio of ammonia to monosilane fluxes of 1 and 0.5 (x = 1.1 and 0.75 accordingly), the intensity of this peak is very low, which means that the concentration of hydrogen bound to nitrogen decreases with increasing concentration of excess silicon. It is also seen from Figure 7 that the spectra of samples containing excess silicon contain

but it grows with increasing concentration of excess silicon. The peak at 1100 cm<sup>1</sup> observed in all spectra corresponds to the absorption of stretching vibrations of silicon-oxygen bonds in the silicon substrate. These bonds also give peaks from 400 to 800 cm<sup>1</sup> of twisting, wagging, rocking, and scissor modes. In addition, the spectrum of monocrystalline silicon contains peaks from multiphonon lattice absorption in silicon itself (features in the region of

a peak with a position of 2150 cm<sup>1</sup>

IR-absorbance spectra of SiOx:H films of different stoichiometry.

607–614 cm<sup>1</sup>

18

Figure 6.

Nanocrystalline Materials

IR-absorbance spectra of SiNx:H films of different stoichiometry: (a) as-deposited films and (b) as-annealed films.

removed when dividing the spectrum from the samples by the reference spectrum of the air).

Let us turn to the absorption peak due to vibrations of the Si▬N bonds in Figure 7. In the spectra of all the films, there are peaks from the stretching vibrations of these bonds. The spectra were approximated by Gaussian curves, and peak positions were determined. The position of the absorption peaks on the stretching vibrations of the Si▬N bonds is shifted, depending on the stoichiometry, from 880 to 860 cm<sup>1</sup> . This effect was previously known (see work [23] and references therein). The general dependence is that the oscillation frequency decreases with decreasing stoichiometric parameter x in a-SiNx film. This is observed in our experiment and again confirms that the structure of the films cannot be considered only within the framework of the RM model (in which the stoichiometry of the matrix surrounding the silicon inclusions is unchanged the matrix parameter x is 4/3).

Figure 7b shows the IR absorption spectra of annealed (Ar atmosphere, 1100°C, 2 hours) SiNx:H films. One can see that annealing leads to evaporation of hydrogen, except nearly stoichiometry (x = 1.3) film. In that film the Si▬H peak becomes even more intensive after annealing. So, hydrogen has been removed from N▬H bonds to Si▬H bonds. This effect has already been observed in the work [24]. In the work [24], it was shown that in order to remove hydrogen from Si▬H bonds, it is necessary to apply high-temperature annealing at very high pressure. It should be noted that in annealed films the position of the absorption peaks on the stretching vibrations of the Si▬N bonds is also shifted, depending on the stoichiometry. The lesser parameter x, the higher is frequency of stretching vibrations of the Si▬N bonds.

So, the analysis of IR absorption data is an evidence of deviation of structure of real SiOx and SiNx films from the RM model.
