Abstract

Semiconductor nanocrystals in dielectric films are interesting from fundamental aspect, because quantum-size effects in them appear even at room temperature, so such objects can be called as "quantum dots". Silicon nanocrystals and amorphous silicon nanoclusters in substoichiometric SiOx and SiNx films are traps for electrons and holes that apply in nonvolatile memory devices. In this chapter the formation of silicon nanocrystals and silicon amorphous nanoclusters in SiOx and SiNx films was studied using structural and optical methods. The phonon confinement model was refined to obtain sizes of silicon nanocrystals from analysis of Raman scattering data. Structural models that lead to nanoscale potential fluctuation in amorphous SiOx and SiNx are considered. A new structural model which is intermediate between random mixture and random bonding models is proposed. Memristor effects in SiOx films are discussed.

Keywords: silicon suboxides, silicon subnitrides, nanocrystals, amorphous nanoclusters, phonon confinement model, nanoscale potential fluctuations, memristor

### 1. Introduction

Nanometer-sized semiconductor crystals, the so-called nanocrystals (NCs) and amorphous nanoclusters, embedded in wide-gap insulating matrices, have shown significant promises for application in nanoelectronics (nonvolatile memory) and optoelectronics (light-emitting diodes (LEDs)) [1]. Quantum effects in such heterosystems are manifested even at room temperature. For example, a bright photoluminescence (PL) was observed in dodecyl-passivated colloidal Si NCs with external quantum efficiency (QE) up to 60% [2]. Since in some experiments single NCs originated delta-function-like energy photoluminescence spectra [3], they can be called as quantum dots. In metal-dielectric-semiconductor structures based on SiNx films with Si nanoclusters, an effective electroluminescence with red, green, and blue light-emitting diodes was demonstrated [4]. Since NCs in a dielectric matrices act also as traps for charge carriers, the NCs' based structures have also

perspectives to yield nonvolatile memory devices [5]. Last time the perspectives of application of nonstoichiometric SiOx and SiNx films with Si NCs and amorphous nanoclusters in memristors have arisen [6]. This chapter is devoted to formation, structural and optical studies of such films, and the development of new structural models which would explain the presence of nanoscale potential fluctuations in such nonstoichiometric films.

and amorphous nanoclusters are nondestructive and express. Among the optical methods, the most informative is inelastic light scattering—Raman scattering.

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

tains two broad peaks at approximately 480 and 150 cm�<sup>1</sup>

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

full width on half maximum (FWHM) usually is about 5 cm�<sup>1</sup>

parameter y on the size of nano- and micro silicon crystals [11].

(PCM) for the analysis of average size of Si NCs from Raman data.

quasi-momentum ℏq0 in an infinite crystal is

where <sup>Ψ</sup><sup>0</sup> q0; <sup>r</sup> � � is equal to <sup>W</sup>ð Þ <sup>r</sup>; <sup>L</sup> <sup>e</sup><sup>i</sup> q0 <sup>r</sup>

the wave packet is proportional to <sup>C</sup> q0; <sup>q</sup> � � � � �

<sup>Ψ</sup><sup>0</sup> q0; <sup>r</sup> � � <sup>¼</sup>

<sup>Ψ</sup><sup>0</sup> q0; <sup>r</sup> � � in a Fourier presentation:

phonon.

11

Raman scattering measurements are usually carry out to check the presence of a crystalline or amorphous Si phase in as-deposited and annealed SiOx and SiNx films. Due to the absence of long-range order and breaking of translation symmetry, the Raman spectrum of amorphous Si is an image of effective density of vibrational states for transversal optical (TO) and transversal acoustical (TA) modes and con-

According to the quasi-momentum selection rules, in monocrystalline silicon, only phonons from the center of the Brillouin zone are active in Raman scattering; therefore the frequency of the Raman peak in this case is 520.5 cm�<sup>1</sup> [9], and the

than the width of amorphous peak. The intensity of the crystalline peak depends on the contents of the crystalline phase, and, using the analysis of experimentally measured integrated Raman scattering intensities I<sup>c</sup> and I<sup>a</sup> for c-Si and a-Si phases, one can obtain the volume part of crystalline phase in a two-phase film. The critical parameter of this method is the ratio of the integrated Raman cross section for c-Si

ρ<sup>c</sup> ¼ Ic= I<sup>c</sup> þ yI<sup>a</sup>

Recently, we have clarified the Bustarret data [10] on the dependence of the

The position and the width of the peak strongly depend on the size and structure of the NCs [12, 13]. We have developed an improved phonon confinement model

PCM allows us to calculate the Raman spectra for NCs of various sizes [12–14]. The physical entity of the model is the following. The eigenfunction of phonon with

i q0 r

<sup>Ψ</sup> q0; <sup>r</sup> � � <sup>¼</sup> <sup>W</sup>ð Þ <sup>r</sup>; <sup>L</sup> <sup>Φ</sup> q0; <sup>r</sup> � � <sup>¼</sup> <sup>Ψ</sup><sup>0</sup> q0; <sup>r</sup> � �uð Þ<sup>r</sup> , (3)

<sup>i</sup> q r d<sup>3</sup>

. The confined phonon can be

<sup>Φ</sup> q0; <sup>r</sup> � � <sup>¼</sup> <sup>u</sup>ð Þ<sup>r</sup> <sup>e</sup>

where uð Þr has the periodicity of the lattice and q0 is the wavenumber of

The eigenfunction <sup>Ψ</sup> q0; <sup>r</sup> � � for a phonon confined in NCs is a function <sup>Φ</sup> q0; <sup>r</sup> � � multiplied by the phonon weighting function Wð Þ r; L ("envelope" function for displacement of atoms in NCs); the weighting function depends on NC size L:

described by a wave packet. To calculate the Raman spectrum, one should expand

The main task is the determination of Fourier coefficients <sup>C</sup> q0; <sup>q</sup> � � from an adequate physical model. The "weight" of the phonon with quasi-momentum ℏq in

<sup>C</sup> q0; <sup>q</sup> � � <sup>e</sup>

� 2 .

ð

Due to softening of the conservation law of quasi-momentum in NCs, the short-wave phonons can take part in Raman scattering in this case. The confined in NCs phonons are characterized by a narrow peak at a position of 500–520 cm�<sup>1</sup>

to a-Si, y = Σc/Σa. Knowing this parameter, one can use the next equation:

, correspondingly [8].

� � (1)

, (2)

q: (4)

; it is much narrower

.

#### 2. Forming of Si NCs and amorphous nanoclusters in dielectric films

There are several technological approaches for the fabrication of Si NCs and amorphous Si nanoclusters in various dielectric films: Si<sup>+</sup> ion implantation with consequent thermal annealing; co-sputtering of Si and SiO2 targets on cool substrates; chemical vapor deposition (CVD) and plasma-enhanced chemical vapor deposition (PECVD) methods; evaporation of Si, SiO, or SiO2 under high vacuum and their deposition onto cool substrates; evaporation of Si target in atmosphere with definite partial pressure of oxygen; and deposition on cool substrates. Each method has advantages and peculiarities.

The main advantage of ion implantation is a very precise control of the dose of the embedded silicon atoms—control of the projected range of silicon ions (it depends on the energy of ions). The disadvantage is the need for high-temperature annealing for the formation of silicon nanoclusters and even more hightemperature annealing (up to 1150°C) for their crystallization. So, this process cannot be "back-end-of-line" process in device production.

The benefits of different approaches that use co-sputtering are simplicity, the possibility to control stoichiometry using various intensity of evaporation of the targets, and the opportunity to use different substrates. The CVD and PECVD methods allow using large-scale substrates; the control of stoichiometry is possible using different ratios of reagent gases. The main advantage of PECVD is low temperature of the deposition process, but because almost all reagent gases contain hydrogen, the deposited SiOx and SiNx films are hydrogenated; in this case they should be marked as SiOx:H and SiNx:H films. Sometimes the hydrogen content is undesirable because it leads to instability of the characteristics of the films.

It should be noted that applying of various deposition methods leads to variation of the structural model of nonstoichiometric films. The structure of nonstoichiometric SiOx or SiNx films can be described in the framework of the random mixture (RM) or random bonding (RB) models [7]. In the RM model, SiOx is treated as a mixture of two phases: the stoichiometric phase SiO2 and the Si. In the RB model, SiOx is assumed to consist of Si▬O(ν)/Si(4 ν) structural units, ν = 0, 1, 2, 3, or 4, in which Si atoms statistically substitute O atoms in each Si▬O(4) structural unit. The structure of films formed by ion implantation and co-sputtering with ion beam evaporation of targets is closer to RB model; the structure of PECVD films can be closer to RM model. But structure of real films is always not pure RB or pure RM, and real structure of the films (which is the cause of nanoscale potential fluctuations in nonstoichiometric films) will be discussed below.

#### 3. Raman scattering in SiOx and SiNx films: phonon confinement in Si NCs

Direct methods for studying the structure of nonstoichiometric films (such as high-resolution transmission electron microscopy (HRTEM)) are usually very time-consuming and destructive. Optical methods for studying the structure of NCs Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic… DOI: http://dx.doi.org/10.5772/intechopen.86508

and amorphous nanoclusters are nondestructive and express. Among the optical methods, the most informative is inelastic light scattering—Raman scattering.

Raman scattering measurements are usually carry out to check the presence of a crystalline or amorphous Si phase in as-deposited and annealed SiOx and SiNx films. Due to the absence of long-range order and breaking of translation symmetry, the Raman spectrum of amorphous Si is an image of effective density of vibrational states for transversal optical (TO) and transversal acoustical (TA) modes and contains two broad peaks at approximately 480 and 150 cm�<sup>1</sup> , correspondingly [8]. According to the quasi-momentum selection rules, in monocrystalline silicon, only phonons from the center of the Brillouin zone are active in Raman scattering; therefore the frequency of the Raman peak in this case is 520.5 cm�<sup>1</sup> [9], and the full width on half maximum (FWHM) usually is about 5 cm�<sup>1</sup> ; it is much narrower than the width of amorphous peak. The intensity of the crystalline peak depends on the contents of the crystalline phase, and, using the analysis of experimentally measured integrated Raman scattering intensities I<sup>c</sup> and I<sup>a</sup> for c-Si and a-Si phases, one can obtain the volume part of crystalline phase in a two-phase film. The critical parameter of this method is the ratio of the integrated Raman cross section for c-Si to a-Si, y = Σc/Σa. Knowing this parameter, one can use the next equation:

$$\rho\_{\mathbf{c}} = I\_{\mathbf{c}} / \left( I\_{\mathbf{c}} + \mathcal{y} I\_{\mathbf{a}} \right) \tag{1}$$

Recently, we have clarified the Bustarret data [10] on the dependence of the parameter y on the size of nano- and micro silicon crystals [11].

Due to softening of the conservation law of quasi-momentum in NCs, the short-wave phonons can take part in Raman scattering in this case. The confined in NCs phonons are characterized by a narrow peak at a position of 500–520 cm�<sup>1</sup> . The position and the width of the peak strongly depend on the size and structure of the NCs [12, 13]. We have developed an improved phonon confinement model (PCM) for the analysis of average size of Si NCs from Raman data.

PCM allows us to calculate the Raman spectra for NCs of various sizes [12–14]. The physical entity of the model is the following. The eigenfunction of phonon with quasi-momentum ℏq0 in an infinite crystal is

$$\Phi(\mathbf{q}\_0, \mathbf{r}) = u(\mathbf{r}) \ e^{i \mathbf{q}\_0 \mathbf{r}},\tag{2}$$

where uð Þr has the periodicity of the lattice and q0 is the wavenumber of phonon.

The eigenfunction <sup>Ψ</sup> q0; <sup>r</sup> � � for a phonon confined in NCs is a function <sup>Φ</sup> q0; <sup>r</sup> � � multiplied by the phonon weighting function Wð Þ r; L ("envelope" function for displacement of atoms in NCs); the weighting function depends on NC size L:

$$
\Psi(\mathbf{q\_0}, \mathbf{r}) = \mathcal{W}(\mathbf{r}, L)\Phi(\mathbf{q\_0}, \mathbf{r}) = \Psi'(\mathbf{q\_0}, \mathbf{r})u(\mathbf{r}), \tag{3}
$$

where <sup>Ψ</sup><sup>0</sup> q0; <sup>r</sup> � � is equal to <sup>W</sup>ð Þ <sup>r</sup>; <sup>L</sup> <sup>e</sup><sup>i</sup> q0 <sup>r</sup> . The confined phonon can be described by a wave packet. To calculate the Raman spectrum, one should expand <sup>Ψ</sup><sup>0</sup> q0; <sup>r</sup> � � in a Fourier presentation:

$$
\Psi^{\nu}(\mathbf{q}\_{\mathbf{0}}, \mathbf{r}) = \int C(\mathbf{q}\_{\mathbf{0}}, \mathbf{q}) \, \, e^{i\mathbf{q} \cdot \mathbf{r}} \, \, d^{\beta} \mathbf{q}. \tag{4}
$$

The main task is the determination of Fourier coefficients <sup>C</sup> q0; <sup>q</sup> � � from an adequate physical model. The "weight" of the phonon with quasi-momentum ℏq in the wave packet is proportional to <sup>C</sup> q0; <sup>q</sup> � � � � � � 2 .

perspectives to yield nonvolatile memory devices [5]. Last time the perspectives of application of nonstoichiometric SiOx and SiNx films with Si NCs and amorphous nanoclusters in memristors have arisen [6]. This chapter is devoted to formation, structural and optical studies of such films, and the development of new structural models which would explain the presence of nanoscale potential fluctuations in

2. Forming of Si NCs and amorphous nanoclusters in dielectric films

There are several technological approaches for the fabrication of Si NCs and amorphous Si nanoclusters in various dielectric films: Si<sup>+</sup> ion implantation with consequent thermal annealing; co-sputtering of Si and SiO2 targets on cool substrates; chemical vapor deposition (CVD) and plasma-enhanced chemical vapor deposition (PECVD) methods; evaporation of Si, SiO, or SiO2 under high vacuum and their deposition onto cool substrates; evaporation of Si target in atmosphere with definite partial pressure of oxygen; and deposition on cool substrates. Each

The main advantage of ion implantation is a very precise control of the dose of

The benefits of different approaches that use co-sputtering are simplicity, the possibility to control stoichiometry using various intensity of evaporation of the targets, and the opportunity to use different substrates. The CVD and PECVD methods allow using large-scale substrates; the control of stoichiometry is possible using different ratios of reagent gases. The main advantage of PECVD is low temperature of the deposition process, but because almost all reagent gases contain hydrogen, the deposited SiOx and SiNx films are hydrogenated; in this case they should be marked as SiOx:H and SiNx:H films. Sometimes the hydrogen content is undesirable because it leads to instability of the characteristics of the films.

It should be noted that applying of various deposition methods leads to variation

nonstoichiometric SiOx or SiNx films can be described in the framework of the random mixture (RM) or random bonding (RB) models [7]. In the RM model, SiOx is treated as a mixture of two phases: the stoichiometric phase SiO2 and the Si. In the RB model, SiOx is assumed to consist of Si▬O(ν)/Si(4 ν) structural units, ν = 0, 1, 2, 3, or 4, in which Si atoms statistically substitute O atoms in each Si▬O(4) structural unit. The structure of films formed by ion implantation and co-sputtering with ion beam evaporation of targets is closer to RB model; the structure of PECVD films can be closer to RM model. But structure of real films is always not pure RB or pure RM, and real structure of the films (which is the cause of nanoscale potential

the embedded silicon atoms—control of the projected range of silicon ions (it depends on the energy of ions). The disadvantage is the need for high-temperature

annealing for the formation of silicon nanoclusters and even more hightemperature annealing (up to 1150°C) for their crystallization. So, this process

of the structural model of nonstoichiometric films. The structure of

fluctuations in nonstoichiometric films) will be discussed below.

in Si NCs

10

3. Raman scattering in SiOx and SiNx films: phonon confinement

Direct methods for studying the structure of nonstoichiometric films (such as high-resolution transmission electron microscopy (HRTEM)) are usually very time-consuming and destructive. Optical methods for studying the structure of NCs

cannot be "back-end-of-line" process in device production.

such nonstoichiometric films.

Nanocrystalline Materials

method has advantages and peculiarities.

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

$$I(\boldsymbol{\alpha}) \cong \int \left| \mathbf{C}(\mathbf{0}, \ \mathbf{q}) \right|^2 \frac{n \left( \boldsymbol{\alpha}'(\mathbf{q}) \right) + \mathbf{1}}{\left( \boldsymbol{\alpha} - \boldsymbol{\alpha}'(\mathbf{q}) \right)^2 + \left( \Gamma/2 \right)^2} d^3 \mathbf{q} \tag{5}$$

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

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

s

where m is the mass of Ge atoms. As it was mentioned above, Si frequency of

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

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'

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

kφ <sup>a</sup><sup>2</sup> <sup>r</sup> ! <sup>i</sup> � rj ! � � � <sup>r</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 kl þ 3k<sup>φ</sup> � � 3m

! <sup>i</sup> � rk ! � � <sup>þ</sup> <sup>a</sup><sup>2</sup> <sup>16</sup> � �<sup>2</sup>
