5. New structural model explaining nanofluctuations of potential in SiOx and SiNx

Nonstoichiometric silicon oxide SiOx and nitride SiNx are tetrahedral compounds whose structure is defined by the Mott octahedral rule [7, 25]. SiOx and SiNx are synthesized under thermodynamically nonequilibrium conditions. Therefore, the structure of nonstoichiometric SiOx and SiNx layers depends on synthesis conditions, i.e., temperatures, gas pressure, and annealing.

The RB and RM models [7] are two extreme cases of the SiOx and SiNx structure description. As a rule, at low synthesis temperatures (<300°C), its structure is described by the RB model; higher synthesis temperatures promote phase separation in SiOx layers, i.e., such layers should be better described by the RM model.

According to the RB model [26], the probability of finding the SiOvSi(4–v) tetrahedron (the fraction of given v-type tetrahedra), where v = 0, 1, 2, 3, 4 in SiOx for composition x, is given by.

$$\mathcal{W}\_{\nu}^{RB}(\infty) = \frac{4!}{\nu!(4-\nu)!} \left(\frac{\infty}{2}\right)^{\nu} \left(1 - \frac{\infty}{2}\right)^{4-\nu} \tag{12}$$

According to the RM model [7], the calculated spectrum consists of two tetrahedron types, SiO4 and SiSi4. The fraction of SiO4 and SiSi4 tetrahedra in the calculation of Si 2p spectra is (1 � x/2) and x/2, respectively. To simulate the photoelectron spectrum I(E), the Wv peaks obtained using the RB and RM models were broadened by the Gaussian using the formula:

$$I(E) = \sum\_{\nu} \mathcal{W}\_{\nu} e^{-(E - E\_{\nu})^2 / 2\sigma\_{\nu}^2} \tag{13}$$

of the Si 2p level. The RB model underestimates the role of SiSi4 and SiO4 tetrahedra in calculating the intermediate SiOx composition (x = 0.7, 0.98, 1.47). Thus, there are five SiOvSi(4–v) tetrahedron types in SiOx; however, the probability of their

(a) (left) Experimental photoelectron spectra of the Si 2p level in SiOx (bold curve) and simulation results for determining the film composition (dashed curve). Symbols Si4+, Si3+, Si2+, Si, and Si indicate intensities of the Si 2p level for SiO4, SiSiO3, SiSi2O2, SiSi3O, and SiSi4 tetrahedra, respectively. (b) (right) Experimental photoelectron spectra of the Si 2p level in SiOx (bold curve) and the results of simulation using the RB model (dashed curve). Symbols Si4+, Si3+, Si2+, Si+, and Si indicate intensities of the Si 2p level for SiO4, SiSiO3,

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

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

We note that it is impossible to describe experimental spectra by summing the RB and RM spectra in corresponding proportions. This is easily seen in the case of the composition x = 0.7 for which both RB and RM models predict a significantly

Figure 9b shows the photoelectron spectra of the valence band of SiOx of variable composition, measured at an excitation energy of 1486.6 eV. At such an excitation energy, silicon states make the main contribution to the valence band

The calculation of experimental spectra using the RM model is shown in Figure 9a. According to the RM model, the calculation predicts the existence of two peaks corresponding to SiO4 and SiSi4 tetrahedra. The calculated energies of the Si 2p level peaks correlate with those of experimental spectra. The calculated spectra underestimate the contribution of SiSiO3, SiSi2O2, and SiSi3O tetrahedra which exist in experimental spectra. For example, for SiO0.98, the calculation predicts the presence of the SiO2 phase which is not observed in experimental spectra. Thus, the RM

model also does not describe the experimental photoelectron spectra.

smaller content of the SiO2 phase than it is observed in the experiment.

detection is not quantitatively described by the RB model.

SiSi2O2, SiSi3O, and SiSi4 tetrahedra, respectively.

Figure 8.

21

where Ev and σ<sup>v</sup> are the peak energy and "half-width" for a given tetrahedron type. The SiOx film composition was calculated assuming that the calculated spectrum is a superposition of five peaks corresponding to five SiOvSi(4–v) tetrahedra, v = 0, 1, 2, 3, 4. The fraction of tetrahedral was selected from the best fit of the spectrum I(E) calculated by Formula (12).

Figure 8a shows five experimental photoelectron spectra of the Si 2p level in SiOx. We can see that the energy and half-width of the Si4+ peak belonging to the a-SiO2 phase and the Si peak belonging to the a-Si phase are E0 = 103.5 eV and σ<sup>0</sup> = 1.2 eV and E4 = 99.5 eV and σ<sup>4</sup> = 0.6 eV, respectively. The position and halfwidth for Si3+, Si2+, and Si+ peaks (SiSiO3, SiSi2O2, and SiSi3O tetrahedra) were determined using linear interpolation of E0, E4, σ0, and σ<sup>4</sup> using the number of oxygen atoms as a parameter. Dashed curves in Figure 8a show the spectra calculated from the best fit with experimental spectra. The calculation for the SiOx film composition predicts the following values, x = 0, 0.7, 0.98, 1.47, and 2.0.

Figure 8b shows the experimental photoelectron spectra of the Si 2p level in SiOx and the results of RB model simulation. The RB model predicts a single peak being a superposition of five peaks corresponding to five SiOvSi(4–v) tetrahedra (v = 0, 1, 2, 3, 4). The calculated peak shifts to lower binding energies with decreasing oxygen concentrations. The position and half-width of the calculated SiOx peak for x = 0.7, 0.98, 1.47 is not in agreement with the experimental spectrum Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic… DOI: http://dx.doi.org/10.5772/intechopen.86508

#### Figure 8.

So, the analysis of IR absorption data is an evidence of deviation of structure of

5. New structural model explaining nanofluctuations of potential in

Nonstoichiometric silicon oxide SiOx and nitride SiNx are tetrahedral

SiNx are synthesized under thermodynamically nonequilibrium conditions. Therefore, the structure of nonstoichiometric SiOx and SiNx layers depends on

description. As a rule, at low synthesis temperatures (<300°C), its structure is described by the RB model; higher synthesis temperatures promote phase separation in SiOx layers, i.e., such layers should be better described by the RM model. According to the RB model [26], the probability of finding the SiOvSi(4–v) tetrahedron (the fraction of given v-type tetrahedra), where v = 0, 1, 2, 3, 4 in SiOx

> 4! ν!ð Þ 4 � ν !

hedron types, SiO4 and SiSi4. The fraction of SiO4 and SiSi4 tetrahedra in the calculation of Si 2p spectra is (1 � x/2) and x/2, respectively. To simulate the photoelectron spectrum I(E), the Wv peaks obtained using the RB and RM models

> I Eð Þ¼ ∑ ν Wνe

According to the RM model [7], the calculated spectrum consists of two tetra-

where Ev and σ<sup>v</sup> are the peak energy and "half-width" for a given tetrahedron type. The SiOx film composition was calculated assuming that the calculated spectrum is a superposition of five peaks corresponding to five SiOvSi(4–v) tetrahedra, v = 0, 1, 2, 3, 4. The fraction of tetrahedral was selected from the best fit of the

Figure 8a shows five experimental photoelectron spectra of the Si 2p level in SiOx. We can see that the energy and half-width of the Si4+ peak belonging to the a-SiO2 phase and the Si peak belonging to the a-Si phase are E0 = 103.5 eV and σ<sup>0</sup> = 1.2 eV and E4 = 99.5 eV and σ<sup>4</sup> = 0.6 eV, respectively. The position and halfwidth for Si3+, Si2+, and Si+ peaks (SiSiO3, SiSi2O2, and SiSi3O tetrahedra) were determined using linear interpolation of E0, E4, σ0, and σ<sup>4</sup> using the number of oxygen atoms as a parameter. Dashed curves in Figure 8a show the spectra calculated from the best fit with experimental spectra. The calculation for the SiOx film

Figure 8b shows the experimental photoelectron spectra of the Si 2p level in SiOx and the results of RB model simulation. The RB model predicts a single peak being a superposition of five peaks corresponding to five SiOvSi(4–v) tetrahedra (v = 0, 1, 2, 3, 4). The calculated peak shifts to lower binding energies with decreasing oxygen concentrations. The position and half-width of the calculated SiOx peak for x = 0.7, 0.98, 1.47 is not in agreement with the experimental spectrum

composition predicts the following values, x = 0, 0.7, 0.98, 1.47, and 2.0.

synthesis conditions, i.e., temperatures, gas pressure, and annealing.

compounds whose structure is defined by the Mott octahedral rule [7, 25]. SiOx and

The RB and RM models [7] are two extreme cases of the SiOx and SiNx structure

x 2 <sup>ν</sup>

�ð Þ <sup>E</sup>�E<sup>ν</sup> <sup>2</sup>

=2σ<sup>2</sup>

<sup>ν</sup> (13)

<sup>1</sup> � <sup>x</sup> 2 <sup>4</sup>�<sup>ν</sup>

(12)

real SiOx and SiNx films from the RM model.

SiOx and SiNx

Nanocrystalline Materials

for composition x, is given by.

WRB <sup>ν</sup> ð Þ¼ x

were broadened by the Gaussian using the formula:

spectrum I(E) calculated by Formula (12).

20

(a) (left) Experimental photoelectron spectra of the Si 2p level in SiOx (bold curve) and simulation results for determining the film composition (dashed curve). Symbols Si4+, Si3+, Si2+, Si, and Si indicate intensities of the Si 2p level for SiO4, SiSiO3, SiSi2O2, SiSi3O, and SiSi4 tetrahedra, respectively. (b) (right) Experimental photoelectron spectra of the Si 2p level in SiOx (bold curve) and the results of simulation using the RB model (dashed curve). Symbols Si4+, Si3+, Si2+, Si+, and Si indicate intensities of the Si 2p level for SiO4, SiSiO3, SiSi2O2, SiSi3O, and SiSi4 tetrahedra, respectively.

of the Si 2p level. The RB model underestimates the role of SiSi4 and SiO4 tetrahedra in calculating the intermediate SiOx composition (x = 0.7, 0.98, 1.47). Thus, there are five SiOvSi(4–v) tetrahedron types in SiOx; however, the probability of their detection is not quantitatively described by the RB model.

The calculation of experimental spectra using the RM model is shown in Figure 9a. According to the RM model, the calculation predicts the existence of two peaks corresponding to SiO4 and SiSi4 tetrahedra. The calculated energies of the Si 2p level peaks correlate with those of experimental spectra. The calculated spectra underestimate the contribution of SiSiO3, SiSi2O2, and SiSi3O tetrahedra which exist in experimental spectra. For example, for SiO0.98, the calculation predicts the presence of the SiO2 phase which is not observed in experimental spectra. Thus, the RM model also does not describe the experimental photoelectron spectra.

We note that it is impossible to describe experimental spectra by summing the RB and RM spectra in corresponding proportions. This is easily seen in the case of the composition x = 0.7 for which both RB and RM models predict a significantly smaller content of the SiO2 phase than it is observed in the experiment.

Figure 9b shows the photoelectron spectra of the valence band of SiOx of variable composition, measured at an excitation energy of 1486.6 eV. At such an excitation energy, silicon states make the main contribution to the valence band

Figure 9.

(a) (left) Experimental photoelectron spectra of the Si 2p level in SiOx (bold curve) and the results of simulation using the RM model (dashed curve). Symbols Si4+ and Si indicate intensities of the Si 2p level for SiO4 and SiSi4 tetrahedra, respectively. (b) (right) Experimental XPS data of the valence band of SiO2, SiOx, and Si. The top of the silicon valence band is taken as the reference point.

energy-level diagram boundary is sharp. Numeral 3 indicates the silicon cluster surrounded by silicon suboxide. In this case, the Si/SiO2 interface in the energylevel diagram is shown by a smooth curve. Hereafter, it is assumed that the intermediate region (silicon suboxide) size significantly exceeds the Si▬O and Si▬Si bond length. Numeral 4 indicated the suboxide silicon cluster in SiO2. Numeral 5 indicates the silicon cluster in silicon suboxide. Numeral 6 indicates the suboxide

(a) IM model: the schematic two-dimensional pattern of the SiOx structure and the SiOx energy-level diagram for section A–A. White, black, and gray colors correspond to SiO2, a-Si, and silicon suboxides, respectively. Φ<sup>e</sup> and Φ<sup>h</sup> barriers for electrons and holes at the interface a-Si/SiO2, respectively. (b) Model of potential fluctuation (Shklovskii-Efros model) in a heavily doped compensated semiconductor; μ is the Fermi level.

The model of large-scale potential fluctuations (Shklovskii-Efros model) in a heavily doped compensated semiconductor was developed earlier (Figure 10b) [28]. In this model, the bandgap is constant, and potential fluctuations occur due to the nonuniform spatial distribution of the charged ionized donors and acceptors. An electron-hole pair excitation results in spatial separation of electrons and holes, which does not facilitate their recombination. The principal difference between the proposed model of nanoscale potential fluctuations in SiOx and the Shklovskii-Efros model is as follows. Large-scale potential fluctuations in compensated

semiconductors are of electrostatic nature associated with spatial fluctuations of the charge density of donors and acceptors. The bandgap is constant (Figure 10b), and the electric field caused by spatial potential fluctuations promotes electron and hole separation. In SiOx, potential fluctuations are caused by local fluctuations of

In the IM model, in contrast to the Shklovskii-Efros model, the space charge is absent. According to the IM model, local fluctuations in the SiOx chemical composition result in spatial potential fluctuations which, in turn, lead to changes in local electric fields for electrons and holes. These fields at the same point of the SiOx sample are different in magnitude and direction (Figure 10a). When an

cluster in silicon, and numeral 7 indicates the SiO2 cluster in silicon.

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

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

the chemical composition.

23

Figure 10.

spectrum. Oxygen states (O 2p) at such excitation energies make a small contribution due to a low photoionization cross section. The SiOx (x > 0) photoelectron spectrum contains three distinct peaks. As the silicon contents in SiOx increase above the top of the silicon valence band (Ev Si), states caused by silicon appear (Figure 9b). The low-energy peak at 0–4 eV is caused by Si 3p orbitals in amorphous silicon. The peaks at energies above 4 eV are caused by Si 3s and 3p orbitals. These results independently point to the fact that SiOx contains SiO2 and Si.

To describe the SiOx structure, it was proposed to use the intermediate model (IM). The IM model assumes local fluctuations of the SiOx chemical composition, which result in bandgap fluctuations. For example, in [27], it was shown that the chemical composition of silicon oxide films can be identical, SiO1.94, while the bandgap can vary in the range of 5.0–7.5 eV. Figure 10a shows the SiOx energylevel diagram for section A–A. The horizontal line (E = 0) is electron energy reference point (the energy of vacuum). Symbols Ec and E<sup>v</sup> denote the bottom of the conduction band and the top of the valence band in SiOx. The SiO2 bandgap is 8 eV [7]. Bandgap narrowing indicates a local increase in the silicon concentration in SiOx. The least bandgap (Eg = 1.5 eV) corresponds to the silicon phase. Thus, the maximum scale of potential fluctuations for electrons and holes is 2.6 and 3.8 eV, respectively. Figure 10a shows all possible versions of the SiOx spatial structure. White, black, and gray colors correspond to SiO2, a-Si, and silicon suboxides, respectively. If the silicon cluster size L is small, size quantization effects can be observed in it. Such a cluster is indicated in the figure by numeral 1. Numeral 2 indicates the macroscopic silicon cluster in silicon oxide. In this case, the intermediate layer of silicon suboxides is absent, and the Si/SiO2 interface in the

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

Figure 10.

spectrum. Oxygen states (O 2p) at such excitation energies make a small contribution due to a low photoionization cross section. The SiOx (x > 0) photoelectron spectrum contains three distinct peaks. As the silicon contents in SiOx increase above the top of the silicon valence band (Ev Si), states caused by silicon appear (Figure 9b). The low-energy peak at 0–4 eV is caused by Si 3p orbitals in amorphous silicon. The peaks at energies above 4 eV are caused by Si 3s and 3p orbitals. These results independently point to the fact that SiOx contains

(a) (left) Experimental photoelectron spectra of the Si 2p level in SiOx (bold curve) and the results of simulation using the RM model (dashed curve). Symbols Si4+ and Si indicate intensities of the Si 2p level for SiO4 and SiSi4 tetrahedra, respectively. (b) (right) Experimental XPS data of the valence band of SiO2, SiOx,

and Si. The top of the silicon valence band is taken as the reference point.

To describe the SiOx structure, it was proposed to use the intermediate model (IM). The IM model assumes local fluctuations of the SiOx chemical composition, which result in bandgap fluctuations. For example, in [27], it was shown that the chemical composition of silicon oxide films can be identical, SiO1.94, while the bandgap can vary in the range of 5.0–7.5 eV. Figure 10a shows the SiOx energylevel diagram for section A–A. The horizontal line (E = 0) is electron energy reference point (the energy of vacuum). Symbols Ec and E<sup>v</sup> denote the bottom of the conduction band and the top of the valence band in SiOx. The SiO2 bandgap is 8 eV [7]. Bandgap narrowing indicates a local increase in the silicon concentration in SiOx. The least bandgap (Eg = 1.5 eV) corresponds to the silicon phase. Thus, the maximum scale of potential fluctuations for electrons and holes is 2.6 and 3.8 eV, respectively. Figure 10a shows all possible versions of the SiOx spatial structure. White, black, and gray colors correspond to SiO2, a-Si, and silicon suboxides, respectively. If the silicon cluster size L is small, size quantization effects can be observed in it. Such a cluster is indicated in the figure by numeral 1. Numeral 2 indicates the macroscopic silicon cluster in silicon oxide. In this case, the

intermediate layer of silicon suboxides is absent, and the Si/SiO2 interface in the

SiO2 and Si.

22

Figure 9.

Nanocrystalline Materials

(a) IM model: the schematic two-dimensional pattern of the SiOx structure and the SiOx energy-level diagram for section A–A. White, black, and gray colors correspond to SiO2, a-Si, and silicon suboxides, respectively. Φ<sup>e</sup> and Φ<sup>h</sup> barriers for electrons and holes at the interface a-Si/SiO2, respectively. (b) Model of potential fluctuation (Shklovskii-Efros model) in a heavily doped compensated semiconductor; μ is the Fermi level.

energy-level diagram boundary is sharp. Numeral 3 indicates the silicon cluster surrounded by silicon suboxide. In this case, the Si/SiO2 interface in the energylevel diagram is shown by a smooth curve. Hereafter, it is assumed that the intermediate region (silicon suboxide) size significantly exceeds the Si▬O and Si▬Si bond length. Numeral 4 indicated the suboxide silicon cluster in SiO2. Numeral 5 indicates the silicon cluster in silicon suboxide. Numeral 6 indicates the suboxide cluster in silicon, and numeral 7 indicates the SiO2 cluster in silicon.

The model of large-scale potential fluctuations (Shklovskii-Efros model) in a heavily doped compensated semiconductor was developed earlier (Figure 10b) [28]. In this model, the bandgap is constant, and potential fluctuations occur due to the nonuniform spatial distribution of the charged ionized donors and acceptors. An electron-hole pair excitation results in spatial separation of electrons and holes, which does not facilitate their recombination. The principal difference between the proposed model of nanoscale potential fluctuations in SiOx and the Shklovskii-Efros model is as follows. Large-scale potential fluctuations in compensated semiconductors are of electrostatic nature associated with spatial fluctuations of the charge density of donors and acceptors. The bandgap is constant (Figure 10b), and the electric field caused by spatial potential fluctuations promotes electron and hole separation. In SiOx, potential fluctuations are caused by local fluctuations of the chemical composition.

In the IM model, in contrast to the Shklovskii-Efros model, the space charge is absent. According to the IM model, local fluctuations in the SiOx chemical composition result in spatial potential fluctuations which, in turn, lead to changes in local electric fields for electrons and holes. These fields at the same point of the SiOx sample are different in magnitude and direction (Figure 10a). When an

electron-hole pair is excited in SiOx, the electric field for electron and hole promotes (see in Figure 10a) their recombination. In the case of the radiative recombination mechanism, SiOx is an efficient emitting medium. Nanoscale potential fluctuations in SiO2 promote electron and hole localization in potential wells (silicon clusters) [7]. This effect is used for developing the high-speed nonvolatile memory based on

In the case of SiNx films, the approach for determining the stoichiometric parameter x from XPS data analysis is similar, but unlike Eq. (12), the probability of finding the SiNvSi(4–v) tetrahedron (the fraction of given v-type tetrahedra), where

> 4! v!ð Þ 4 � v !

Experimental XPS spectra are also not described by pure RB or RM models. However, good agreement between the experimental and calculated spectra is

The nanoscale fluctuations of potential in SiNx films (Figure 12) are also similar to nanoscale fluctuations of potential in SiOx. In the case of SiNx films, the IM is more adequate to describe the real structure and fluctuation of potential. In

schematic picture in the bottom of Figure 12, one can see the possible appearance of

Resistive random-access memory (RRAM) [29, 30] is the highly promising candidate for the next-generation nonvolatile memory (NVM), because conventional charge-based memories, namely, dynamic random-access memory and flash memory, have too low capacitance after continuously downscaling into 1X-nm regimes. In addition, an RRAM array can be fabricated in the back end of the line of a complementary metal-oxide-semiconductor circuit, which makes such device an excellent candidate for embedded NVM (e-NVM) application. The typical write speed of RRAM device ranges from 100 ns to 1 μs, which is three to four orders of magnitude faster than flash memory. Such high-speed and process-compatible e-NVM can enable hardware technologies such as artificial intelligence and

The conduction mechanism of RRAM, however, is not fully understood, and it is generally attributed to metallic filament conduction because of its metal-insulatormetal (MIM) structure, where the insulator is usually formed by metal oxide-based dielectric. The first RRAM that does not contain any metal in both the electrodes and dielectric insulator (nonmetal RRAM) is demonstrated here. To obtain RRAM

junction electrode. The value x in SiOx was determined to be 0.62. Because no metal or metallic ions were present in the whole RRAM device, metallic filaments were

RRAM device. During the forming step, the device was first subjected to a 6 V and 100 μA compliance current stress to attain the LRS. The same device was reset into

such structures—Si core surrounded by SiNx shell and Si3N4 matrix. So, the

3x 4 <sup>v</sup>

<sup>1</sup> � <sup>3</sup><sup>x</sup> 4 <sup>4</sup>�<sup>v</sup>

(14)





charge localization in SiOx and can be used in memristors.

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

v = 0, 1, 2, 3, 4 in SiNx for composition x, is given by

<sup>v</sup> ð Þ¼ v; x

proposed IM also can be called as core-shell-matrix model.

device, a 15-nm-thick SiOx was deposited directly on a p+

Figure 13(a) depicts the measured I-V characteristics of an n<sup>+</sup>

sputtering. Then, a 15-nm-thick amorphous n<sup>+</sup>

WRB

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

observed for IM model (Figure 11).

6. Memristor effects in SiOx films

neuromorphic computing.

not formed.

25

Figure 11.

Experimental XPS spectra of the Si 2p level in SiNx (solid black lines) and the results of theoretical modeling using the IM model (dashed red lines). Green line is peak from Si▬Si4 tetrahedron, and magenta line is peak from Si▬N4 tetrahedron.

#### Figure 12.

Schematic diagrams illustrating the proposed intermediate model of SiNx: (a) a two-dimensional diagram of SiNx structure showing (bottom) the regions of a silicon phase, stoichiometric silicon nitride, and subnitrides and (top) the energy band profile of SiNx in the A–A section (Ec is the conduction band bottom; Ev is the valence band top; Φ<sup>e</sup> and Φ<sup>h</sup> are the energy barriers for electrons and holes at the a-Si–Si3N4 interfaces, respectively; Eg is the bandgap width). (b) The potential fluctuations in Shklovskii–Efros model.

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

electron-hole pair is excited in SiOx, the electric field for electron and hole promotes (see in Figure 10a) their recombination. In the case of the radiative recombination mechanism, SiOx is an efficient emitting medium. Nanoscale potential fluctuations in SiO2 promote electron and hole localization in potential wells (silicon clusters) [7]. This effect is used for developing the high-speed nonvolatile memory based on charge localization in SiOx and can be used in memristors.

In the case of SiNx films, the approach for determining the stoichiometric parameter x from XPS data analysis is similar, but unlike Eq. (12), the probability of finding the SiNvSi(4–v) tetrahedron (the fraction of given v-type tetrahedra), where v = 0, 1, 2, 3, 4 in SiNx for composition x, is given by

$$\mathcal{W}\_v^{\rm RB}(v,\infty) = \frac{4!}{v!(4-v)!} \left(\frac{3\varkappa}{4}\right)^v \left(1 - \frac{3\varkappa}{4}\right)^{4-v} \tag{14}$$

Experimental XPS spectra are also not described by pure RB or RM models. However, good agreement between the experimental and calculated spectra is observed for IM model (Figure 11).

The nanoscale fluctuations of potential in SiNx films (Figure 12) are also similar to nanoscale fluctuations of potential in SiOx. In the case of SiNx films, the IM is more adequate to describe the real structure and fluctuation of potential. In schematic picture in the bottom of Figure 12, one can see the possible appearance of such structures—Si core surrounded by SiNx shell and Si3N4 matrix. So, the proposed IM also can be called as core-shell-matrix model.
