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## **Meet the editor**

Dr. V. I. Talanin was born in 1977 into a Russian noble family in Zaporozhye, USSR. He completed his MSc degree (2000) in Physics and Technology of Materials and Components in Electronic Technique, MSc degree (2006) in Software Engineering, and PhD degree (2002) in Physics of Semiconductors and Dielectrics. His PhD dissertation was on the mechanisms of grown-in microdefect for-

mation in dislocation-free silicon single crystals. Dr. Talanin was an assistant professor (2002–2003) and an associate professor (2003–2006) and is a full professor (since 2006). Since 2012, he has been working as the full professor and vice chief of Computer Science and Software Engineering Department at the Zaporozhye Institute of Economics and Information Technologies. Dr. Talanin was awarded a scholarship at the Ukraine Ministry Cabinet (2002– 2003) and President Grant for Scientific Researches (2007, 2008). He was awarded the title Doctor of Science, honoris causa (2012), and Full Professor (2013) at the Russian Academy of Natural History. Dr. Talanin has published extensively in material science and semiconductor physics and also in Russian history and genealogy (as hobbies). He has written 10 monographs and ca. 200 scientific papers. Dr. Talanin is a member of editorial board of the *Journal of Crystallization Process and Technology* (2011–present) and *Journal of Science and Technology* (2011–present). Dr. Talanin was a member of a program committee at the I (2013), II (2014), III (2015), and IV (2016) and is a member of a program committee at the V (2017) World Conference on Information Systems and Technologies. Dr. Talanin was a member of a Program Committee at the I (2015) and II (2016) International Conference on Semiconductor Physics and Devices.

## Contents

### **Preface XI**

## Preface

Chapter 8 **Silicon‐Germanium (SiGe) Nanostructures for Thermoelectric**

Chapter 9 **Silicon Growth Technologies for PV Applications 207**

**Type Silicon Photonic Crystal 227**

**Internal Photoemission Effect 245**

Chapter 12 **Advanced SiC/Oxide Interface Passivation 267**

Chapter 10 **Guiding On-Chip Optical Beams Without Diffraction in a Rod-**

Chapter 11 **Recent Advances in Silicon Photodetectors Based on the**

Wei Li, Hao Li, Ming Li, Haiyang Huang and Fuwan Gan

**Thermoelectric Efficiency 183**

Martín‐González

Maurizio Casalino

Yogesh Kumar Sharma

Pó

**VI** Contents

**Devices: Recent Advances and New Approaches to High**

Jaime Andrés Pérez‐Taborda, Olga Caballero‐Calero and Marisol

Guilherme Manuel Morais Gaspar, Antoine Autruffe and José Mário

As well known, silicon has a large impact on the modern world economy. Most free silicon is used in the steel refining, aluminum casting, and fine chemical industries. Silicon is the basis of the widely used synthetic polymers called silicones. The pure silicon such as hydro‐ genated amorphous silicon and upgraded metallurgical-grade silicon are used in the pro‐ duction of such applications as liquid crystal displays and thin-film solar cells. The very highly purified monocrystalline silicon is used to produce silicon wafers used in the semi‐ conductor industry, in electronics, and in photovoltaic applications. In silicon photonics, sili‐ con can be used as a continuous wave Raman laser medium to produce coherent light. Silicon has become the most popular material for both high-power semiconductors and inte‐ grated circuits because it can withstand the high temperatures and greatest electrical activi‐ ty. Monocrystalline silicon is expensive to produce and is usually used in the production of integrated circuits. In common integrated circuits, a wafer of monocrystalline silicon serves as a mechanical support for the circuits, which are created by doping and insulated from each other by thin layers of silicon oxide. In such systems, the tiny crystal imperfections (de‐ fects) can interfere with circuit paths. The quality of very highly purified silicon, which is used in semiconductor electronics, depends on such crystal imperfections (defects). There‐ fore, the modern technology—most computers, cell phones, and others—depends on it.

During the last 60 years, many aspects of silicon, especially the monocrystalline silicon, were seriously studied. However, some questions, such as structural perfection and some new applications of silicon, need further investigation and clarification. Such wide range of as‐ pects, from fundamental problems to technical and technological applications, conditioned the theme of this book. The overall purpose of this book is to provide timely information on selected topics in silicon technology. The articles for this book have been contributed by the much respected researchers in this area and cover the most recent developments and appli‐ cations of silicon technology and some fundamental questions. I hope that the scientists and all readers will find this book useful.

I thank all contributors for this book and give my special thanks of Ms. Mirena Čalmić for her assistance during the write-up of this book and its final preparation.

My greatest acknowledement goes to my family who have helped me all my life, to my Dad Prof. Dr. Igor Evgenievich Talanin and to my Mom Lubov' Ivanovna Talania for their pa‐ tience and support.

> **Prof. Dr. Vitalyi Igorevich Talanin** Department of Computer Science & Software Engineering Institute of Economics and Information Technologies Zaporozhye, Ukraine

## **Introductory Chapter: Description of the Real Monocrystalline Structure on the Basis of the Vlasov Model for Solids**

Vitalyi Igorevich Talanin, Igor Evgenievich Talanin and Vladislav Igorevich Lashko

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68684

### 1. Introduction

As well known, all characteristics of initial materials for following applications depend on the crystal structural perfection. In the last few decades, our knowledge of the nature of the solid state has sharply increased. At the same time, the areas of application of crystalline solids in various fields of technology are increased. The needs of technology stimulate the rapid development of a relatively young area of modern natural science—solid state chemistry. The main tasks of solid state chemistry are (i) the synthesis of solids, (ii) the research of their physicochemical properties and reactions with their participation, and ultimately (iii) the creation of materials with predetermined properties.

All real solids contain structural defects. Structural defects are violations of the periodicity of the spatial arrangement of atoms. The impact of defects on the physical properties of crystals is extremely diverse. The introduction or change in the concentration of defects in a solid can change the physical properties of the matter. Such operations lead to the creation of new optical, electronic, mechanical, and other characteristics of the solids. Creating a fairly complete picture of the nature and behavior of various defects is a prerequisite for a scientific approach to control structurally sensitive properties and processes in solids. Therefore, in the research of solids, the most informative is the way of a joint examination of their structure, formation, and properties.

Of all the variety of solids, semiconductor silicon occupies a completely unique position. Semiconductor (or electronic) silicon is the basis of the electronic industry at present and in the foreseeable future. On the basis of silicon, discrete device and integrated circuits are manufactured. For the requirements of microelectronics, it is necessary to grow single crystals (i) in which there are no dislocations completely, (ii) with a uniform distribution of doping and

background impurities, and (iii) with a controlled and limited content of intrinsic point defects. Stringent requirements stimulate intensive research into the nature of defect formation and improvement of methods for obtaining modern dislocation-free single crystals of silicon.

Requirements for the quality of modern microelectronic devices have led to the fact that silicon is the most pure material in the world. To obtain single crystals of silicon, the Czochralski method and the floating zone method are used. Both methods ensure the production of the initial silicon with the total content of residual impurities 1011 to 1012 cm�3 . Semiconductor silicon (a highly pure material with the perfect structure) can be considered as the initial model for the construction of theoretical models of defect formation in other semiconductor materials and metals. The obtained mathematical models and methods proposed for their solution in silicon make it possible to formulate and solve many problems on the kinetics of diffusion processes in solids.

The growth of dislocation-free silicon single crystals by the Czochralski method and floating zone melting is accompanied by the formation of structural imperfections known as grown-in microdefects. The formation of grown-in microdefects is caused by complex processes of interactions between intrinsic point defects (vacancies and interstitial silicon atoms) and impurity atoms of oxygen and carbon in cooling silicon ingots. Depending on the thermal conditions of crystal growth, grown-in microdefects are precipitates of impurities, microvoids, or interstitial dislocation loops [1]. The presence of grown-in microdefects in dislocation-free silicon single crystals significantly affects their mechanical, electrical, optical, and other properties. The problem of controlling the nature, content, size, and nature of the distribution of defects present in the dislocation-free silicon single crystal is primarily related to the development of effective methods for influencing the state of the ensemble of interacting point defects in the grown ingot. Advances in the control of the condition of the ensemble of point defects determine, ultimately, the success of the quality management of electronic devices. The problem of the formation of grown-in microdefects has both the technological aspect (control of the defect structure of the crystal during the growth for the purpose to increase its quality) and the fundamental scientific importance because its solution makes it possible to describe the physics of defect formation in ultra-pure dislocation-free silicon single crystals. The construction of a theoretical model of the formation of grown-in microdefects in dislocation-free silicon single crystals is an important scientific and practical problem from the viewpoint of the development of physical principles of the purposeful creation of new materials with a desired set of physical properties.

In 2010, we created a model of high-temperature precipitation of impurities [2]. In this model, the inclusion of thermal growth conditions of silicon single crystals in the form of the dependence TðtÞ (where T is temperature, t is time) allows us to theoretically describe the conditions for nucleation, growth, and coalescence of the precipitates in the range from the crystallization temperature to room temperature. The model of high-temperature precipitation is not only adequate to the experimental results of the investigation of grown-in microdefects but also does not contradict the classical theory of nucleation of second-phase particles. This model extends the field of application of the mathematical apparatus of the classical nucleation theory to the formation of nuclei in a solid during its cooling after the growth. The introduction and consideration of thermal conditions of crystal growth in the initial equations of the classical nucleation theory make it possible to demonstrate that the formation of critical nuclei of small sizes, with a higher probability, occurs in the vicinity of the crystallization front. Cooling of the crystal is accompanied by the growth and coalescence of precipitates. The interaction of impurities with intrinsic point defects has a fundamental character and determines the defect structure of the crystal from the onset of the crystallization to the fabrication of the finished device [3].

background impurities, and (iii) with a controlled and limited content of intrinsic point defects. Stringent requirements stimulate intensive research into the nature of defect formation and improvement of methods for obtaining modern dislocation-free single crystals of silicon.

Requirements for the quality of modern microelectronic devices have led to the fact that silicon is the most pure material in the world. To obtain single crystals of silicon, the Czochralski method and the floating zone method are used. Both methods ensure the production of the

silicon (a highly pure material with the perfect structure) can be considered as the initial model for the construction of theoretical models of defect formation in other semiconductor materials and metals. The obtained mathematical models and methods proposed for their solution in silicon make it possible to formulate and solve many problems on the kinetics of diffusion

The growth of dislocation-free silicon single crystals by the Czochralski method and floating zone melting is accompanied by the formation of structural imperfections known as grown-in microdefects. The formation of grown-in microdefects is caused by complex processes of interactions between intrinsic point defects (vacancies and interstitial silicon atoms) and impurity atoms of oxygen and carbon in cooling silicon ingots. Depending on the thermal conditions of crystal growth, grown-in microdefects are precipitates of impurities, microvoids, or interstitial dislocation loops [1]. The presence of grown-in microdefects in dislocation-free silicon single crystals significantly affects their mechanical, electrical, optical, and other properties. The problem of controlling the nature, content, size, and nature of the distribution of defects present in the dislocation-free silicon single crystal is primarily related to the development of effective methods for influencing the state of the ensemble of interacting point defects in the grown ingot. Advances in the control of the condition of the ensemble of point defects determine, ultimately, the success of the quality management of electronic devices. The problem of the formation of grown-in microdefects has both the technological aspect (control of the defect structure of the crystal during the growth for the purpose to increase its quality) and the fundamental scientific importance because its solution makes it possible to describe the physics of defect formation in ultra-pure dislocation-free silicon single crystals. The construction of a theoretical model of the formation of grown-in microdefects in dislocation-free silicon single crystals is an important scientific and practical problem from the viewpoint of the development of physical principles of

. Semiconductor

initial silicon with the total content of residual impurities 1011 to 1012 cm�3

the purposeful creation of new materials with a desired set of physical properties.

In 2010, we created a model of high-temperature precipitation of impurities [2]. In this model, the inclusion of thermal growth conditions of silicon single crystals in the form of the dependence TðtÞ (where T is temperature, t is time) allows us to theoretically describe the conditions for nucleation, growth, and coalescence of the precipitates in the range from the crystallization temperature to room temperature. The model of high-temperature precipitation is not only adequate to the experimental results of the investigation of grown-in microdefects but also does not contradict the classical theory of nucleation of second-phase particles. This model extends the field of application of the mathematical apparatus of the classical nucleation theory to the formation of nuclei in a solid during its cooling after the growth. The introduction and consideration of thermal conditions of crystal growth in the initial equations of the classical nucleation theory make it possible to demonstrate that the formation of critical nuclei of small

processes in solids.

2 New Research on Silicon - Structure, Properties, Technology

In general, in the last century to describe the physical properties of solids with a point of view of their atomic structure, two approaches were suggested. The classical approach posits the notion of the crystal lattice [4]. The classic approach assumes (i) the location of each atom in the vicinity of the fixed lattice site, (ii) the consistency of introducing the concept of probability and of the mechanical description of the behavior of particles, and (iii) the premise that the totality of atoms in a crystal is an integer. Statistical and quantum mechanical methods are used in the classical theory of the crystal. This theory has resulted in important results. In particular, one of such results is the creation of the classical theory of nucleation and growth of second-phase particles in solids [5]. With the help of this theory, we can describe the formation and development (transformation) of the defect structure of a solid, both in the process of its growth and as a result of various technological impacts [3].

In the second approach, a periodic structure of the crystal is not a consequence restriction on the freedom of movement of the atoms in the crystal. Periodic structure is caused by the specificity of statistical laws of motion of particles, where a periodic structure agrees with the freedom of movement of atoms. As a result, the probability of finding an atom in interstitials of the crystal lattice is always different from zero [6, 7]. The second approach is based on the solution of the Vlasov kinetic equation. Vlasov equation represents a system of equations that describe the evolution of the particle continuum with potential of the pair interaction [8]. Vlasov created the physical and mathematical apparatus of system of many particles. He has developed and entered into the reference the concept of collective variables. Vlasov assumed that the method used by him to solve the problem of the plasma has a universal character. This method can be applied to the description of plasma, gas, liquids, and solids. The interaction in those systems can be a short range or long range, weak or strong [9, 10].

For the first time, a solution for solid state was conducted by Vlasov. Vlasov showed that the spatial periodic distribution is one of the particular conditions of particle motion [6, 7]. Vlasov in particular investigated using the linearized Vlasov equation and found the criteria for the origin of the periodic structure in terms of the temperature, density, and microscopic interaction of particles of the medium.

It is noted that in his 1946 paper [11], Lev Landau wrote a very sharp remark: "these equations were used by A.A. Vlasov for investigation of the vibrations of plasma. However most of his results are incorrect." In Ginzburg et al. [12], which is not published in the English version, Lev Landau, Vitalyi Ginzburg, and others were even tougher: "Recently (in 1944-1945) in print appeared a number of works by AA Vlasov, dedicated to generalization of the concept of the electron plasma and solid state theory. In these works, the author concludes that in the self-consistent field method accounting of the interaction forces at large distances reveals new dynamic properties of polyatomic systems and leads to a change in our perceptions of gas, liquid, solid in the direction of combining them with the concept of plasma etc. Consideration of these works Vlasov led us, however, to the conclusion about their complete failure and about the absence of the results of scientific value."

In the field of plasma physics, history has judged critics and Vlasov [13]. However, in his 2000 paper [14] Vitalyi Ginzburg wrote: "I do not know about any Vlasov achievements in solid state theory and the general theory of many particles (outside of plasma physics)." Indeed, the Vlasov model for a solid was used only for ideal crystals. Hitherto, this model for solid state for the description of the real structure of the crystal has not been used.

Only in 2016 in the journal "Physics of the Solid State," we have considered the complex formation in the semiconductor silicon in accordance with the Vlasov model for solid state [15]. It was demonstrated that the Vlasov model for solid state can be applied not only for the research of the hypothetical ideal crystals but also for the description of the formation of structure of real crystal. In this article, the formation of silicon-carbon and silicon-oxygen complexes during cooling after the growth of dislocation-free silicon single crystals has been calculated using the Vlasov model of crystal formation. It has been confirmed that the complex formation begins in the vicinity of the crystallization front. The characteristic numbers of complexes (silicon-oxygen and silicon-carbon) were determined.

### 2. Mathematical model

Vlasov created a physical and mathematical apparatus of many-particle system, developed and introduced the concept of collective variables into circulation. The primary concept of Vlasov physics is the distribution function. The particle is characterized by spectrum of geometric and kinematic properties. Thus, the category of motion is included on the same level with the primacy of categories of space and time. Therefore, in Vlasov model for solid state, the periodic distribution of probability density of the particles is the state (motion) of the particles of the system, not the design.

The Vlasov model for solid state is based on the following fundamental physical positions [6, 10]: (1) rejection of the principle of spatial and speed localization of the particles (in terms of classical mechanics), which takes place regardless of the force interactions; (2) introduction of force interactions in analogy with classical mechanics, but taking into account the new principle of non-localization of particles; (3) the behavior of each particle of the system is described by means of an extended phase space f-function. In this approach, the ideas of continuity and of corpuscular are combined. The method of describing the motion of particle associated with the extended function, and the particle in the form of a point occurs only in the particular case [6].

In general, the equation of Vlasov describes the evolution of the function of distribution f x, ð Þ ν, t of the continuum of interacting particles in Euclidean space for speed ν and for coordinate x at time point t. The equation has the form

$$\frac{\partial f}{\partial t} + \left(\frac{\partial f}{\partial \mathbf{x}}, \nu\right) + \left(\frac{\partial f}{\partial \nu}, F\right) = 0$$

$$F = -\frac{\partial}{\partial \mathbf{x}} \left\{ K(\mathbf{x}, y) f(y, \nu, t) d\mathbf{v} dy \right.$$

where K is the pair interaction potential, which is in real problem depends on the distance jx � yj; F is the total force, with which all the particles act on one of them, which is located at time t at point x [8]. In order for distinguishing between the types of interactions, the systems of equations of Vlasov (equations of the Vlasov-Poisson, Vlasov-Maxwell, Vlasov-Einstein, and Vlasov-Yang-Mills [16]) are usually discussed about.

In the field of plasma physics, history has judged critics and Vlasov [13]. However, in his 2000 paper [14] Vitalyi Ginzburg wrote: "I do not know about any Vlasov achievements in solid state theory and the general theory of many particles (outside of plasma physics)." Indeed, the Vlasov model for a solid was used only for ideal crystals. Hitherto, this model for solid state for the

Only in 2016 in the journal "Physics of the Solid State," we have considered the complex formation in the semiconductor silicon in accordance with the Vlasov model for solid state [15]. It was demonstrated that the Vlasov model for solid state can be applied not only for the research of the hypothetical ideal crystals but also for the description of the formation of structure of real crystal. In this article, the formation of silicon-carbon and silicon-oxygen complexes during cooling after the growth of dislocation-free silicon single crystals has been calculated using the Vlasov model of crystal formation. It has been confirmed that the complex formation begins in the vicinity of the crystallization front. The characteristic numbers of

Vlasov created a physical and mathematical apparatus of many-particle system, developed and introduced the concept of collective variables into circulation. The primary concept of Vlasov physics is the distribution function. The particle is characterized by spectrum of geometric and kinematic properties. Thus, the category of motion is included on the same level with the primacy of categories of space and time. Therefore, in Vlasov model for solid state, the periodic distribution of probability density of the particles is the state (motion) of the particles

The Vlasov model for solid state is based on the following fundamental physical positions [6, 10]: (1) rejection of the principle of spatial and speed localization of the particles (in terms of classical mechanics), which takes place regardless of the force interactions; (2) introduction of force interactions in analogy with classical mechanics, but taking into account the new principle of non-localization of particles; (3) the behavior of each particle of the system is described by means of an extended phase space f-function. In this approach, the ideas of continuity and of corpuscular are combined. The method of describing the motion of particle associated with the extended function, and the particle in the form of a point occurs only in the particular case [6]. In general, the equation of Vlasov describes the evolution of the function of distribution f x, ð Þ ν, t of the continuum of interacting particles in Euclidean space for speed ν and for

> þ ∂f ∂ν , F � �

K x, y ð Þf y, ð Þ ν, t dνdy

¼ 0 ð1Þ

description of the real structure of the crystal has not been used.

4 New Research on Silicon - Structure, Properties, Technology

complexes (silicon-oxygen and silicon-carbon) were determined.

coordinate x at time point t. The equation has the form

∂f ∂t þ ∂f ∂x , ν � �

F ¼ � ∂ ∂x ð

2. Mathematical model

of the system, not the design.

For a description of stationary properties of the crystal, the concept of distribution density of particles ρð Þ¼ r ð f r, v ð Þdv is used. The molecular field is determined only by the probable locations of atoms that are described by the potential function. The potential function contains the density of probability of the particles considering the temperature distribution of the particles [6]. The choice of potential of the pair interaction depends on the problem under consideration. Nonlocal model of a crystal is described by nonlinear equations. These equations make it possible to calculate the molecular potential and density of location of particles in the conditions of temperature equilibrium [6]:

$$V(r) = \lambda kT \int\_{-\infty}^{\infty} K\_{1,2}(r) \exp\left(-\frac{K\_{1,2}(r)}{kT}\right) dr\tag{2}$$

$$\rho(r) = \lambda kT \exp\left(-\frac{K\_{1,2}(r)}{kT}\right)$$

where k is the Boltzmann constant, K1,2 is the potential of the pair interaction, λ is some characteristic number, and T is the temperature. The initial equations are equations for the two particles in a stationary condition ∂ ∂t ¼ 0 � � [6]. Under the characteristic number where the values of a parameter λ are to be understood, Eq. (2) has solutions different from the trivial [6]. If the position of one of the particles is taken as the origin of coordinates, it is possible to determine ρð Þ¼ 0 λkT [6]. The important task of Vlasov model for the solid state is the determination of characteristic numbers.

The characteristic number λ is determined from the basic criterion of the existence of the crystal state. The conditions of crystallization can be written as follows:

$$\frac{4\pi N}{kT\_m} \int\_0^\infty K\_{1,2}^\*(\rho) \rho^2 d\rho = 1\tag{3}$$

where N is the number of particles, Tm is the temperature of melting (crystallization) of crystal, K� 1,2 ¼ �K1, 2 [6].

Eq. (2) is written for the conditions of thermal equilibrium of system. The minima of interatomic potential correspond to the stable equilibrium position of atoms in the complexes (silicon-oxygen and silicon-carbon). Then, we can determine the density of the distribution of complexes as a function of the cooling temperature of the crystal

$$
\rho(T) = \lambda kT \exp\left(-\frac{V\_{1\text{min},2\text{min}}}{kT}\right) \tag{4}
$$

The formation of new phase nuclei takes place near the crystallization front of the crystal [2]. In article [2], the model of high-temperature precipitation of impurities is described. At the second stage of the precipitation process, clusters grow without a change in their number. Assuming that the precipitates have a spherical shape, it is possible to calculate the average radius of the precipitate at the growth stage:

$$R(t) = \sqrt[3]{\frac{3bi(t)}{4\pi}}\tag{5}$$

where b is the quantity of order of the distance between the particles in the cluster; i tðÞ¼½Nð Þ� 0 N tð Þ�=Nc is the average number of particles at the nucleation centers; Nð Þ0 is the monomer concentration at the initial instant of time; N tð Þ is the changes in the concentration of monomers over time; Nc is the concentration of nucleation centers; and t is the time [17].

At the third stage, when the new phase particles are large and supersaturation is low, new particles are not formed and the main role is played by coalescence, which is accompanied by the dissolution of small-sized particles and the growth of large-sized particles. Under condition R tð Þ=Rcrð Þt ≈ 1 (where Rcrð Þt is the critical radius of the precipitate), the precipitate is in equilibrium with the solution ð Þ dR=dt ¼ 0 . The precipitate grows at R tð Þ > Rcrð Þt and dissolves at R tð Þ < Rcrð Þt [17, 18].

It is possible to determine the critical size of the precipitates in accordance with [19]

$$\begin{aligned} R\_{cr}^{O}(t) &= \frac{2\sigma u V\_p}{kT(t) \ln(S\_0 S\_i^{-\gamma\_i} S\_{v^\gamma}^{\gamma\_v}) - 6\mu \delta \varepsilon u V\_p} \\ R\_{cr}^{\mathbb{C}}(t) &= \frac{2\sigma u V\_p}{kT(t) \ln(S\_c S\_i^{\gamma\_i} S\_v^{-\gamma\_v}) - 6\mu \delta \varepsilon u V\_p} \end{aligned} \tag{6}$$

where So ¼ Co Ceg o , Sc ¼ Cc Ceg c , Si ¼ Ci Ceg i , Sv ¼ Cv Ceg v are the supersaturations of the oxygen atoms, carbon atoms, intrinsic interstitial silicon atoms, and vacancies, respectively; σ is the density of the surface energy of the interface between the precipitate and the matrix; μ is the shear modulus of silicon; δ and ε are the linear and volume misfit strains of the precipitate and the matrix, respectively; γi and γv are the fractions of intrinsic interstitial silicon atoms and vacancies per impurity atom attached to the precipitate, respectively; Vp is the molecular volume of the precipitate; and u ¼ ð1 þ γi x þ γvxÞ �1 � ð1þε 1þδÞ 3 .

The average size of precipitates at the stage of the coalescence is proportional to the cube root of time [17]:

Introductory Chapter: Description of the Real Monocrystalline Structure on the Basis of the Vlasov Model for Solids http://dx.doi.org/10.5772/intechopen.68684 7

$$R\_{av}(t) = \sqrt[3]{R\_{cr}^3(t\_0) + \frac{4D\beta t}{9}}\tag{7}$$

where D is the diffusion coefficient of impurity atoms; β ¼ σΩ kT � �Nð Þ0 ; Rcrðt0Þ is the initial critical radius; σ is the surface tension at the precipitate-solid solution interface; and Ω is the atomic volume.

As is known, the formation and development of the structure of grown-in microdefects in silicon are determined by thermal conditions of growth and cooling of the crystal [1, 3]. The temperature distribution along the length of the ingot during its cooling varies depending on the thermal parameters of the growth according to the expression 1=T ¼ 1=Tm þ Gz=T2 m, where z is the distance from the crystallization front; G is the axial temperature gradient at the crystallization front; and Tm is the crystallization temperature [3]. It should be noted that, in the general case, it is necessary to take into account the radial inhomogeneity of the temperature field. We introduce the crystal growth rate (V) into this formula and obtain

$$T(t) = \frac{T\_m^2}{T\_m + VGt} \tag{8}$$

### 3. Results and discussion

(silicon-oxygen and silicon-carbon). Then, we can determine the density of the distribution of

ρð Þ¼ T λkTexp � V1min, 2min

The formation of new phase nuclei takes place near the crystallization front of the crystal [2]. In article [2], the model of high-temperature precipitation of impurities is described. At the second stage of the precipitation process, clusters grow without a change in their number. Assuming that the precipitates have a spherical shape, it is possible to calculate the average

> ffiffiffiffiffiffiffiffiffiffiffi 3bi tð Þ 4π

2σuVp

2σuVp

v Þ � 6μδεuVp

are the supersaturations of the oxygen atoms, carbon

i S�γv v Þ � 6μδεuVp

�γi i Sγv

γi

atoms, intrinsic interstitial silicon atoms, and vacancies, respectively; σ is the density of the surface energy of the interface between the precipitate and the matrix; μ is the shear modulus of silicon; δ and ε are the linear and volume misfit strains of the precipitate and the matrix, respectively; γi and γv are the fractions of intrinsic interstitial silicon atoms and vacancies per impurity atom attached to the precipitate, respectively; Vp is the molecular volume of the

The average size of precipitates at the stage of the coalescence is proportional to the cube root

3 r

where b is the quantity of order of the distance between the particles in the cluster; i tðÞ¼½Nð Þ� 0 N tð Þ�=Nc is the average number of particles at the nucleation centers; Nð Þ0 is the monomer concentration at the initial instant of time; N tð Þ is the changes in the concentration of monomers over time; Nc is the concentration of nucleation centers; and t is the time [17]. At the third stage, when the new phase particles are large and supersaturation is low, new particles are not formed and the main role is played by coalescence, which is accompanied by the dissolution of small-sized particles and the growth of large-sized particles. Under condition R tð Þ=Rcrð Þt ≈ 1 (where Rcrð Þt is the critical radius of the precipitate), the precipitate is in equilibrium with the solution ð Þ dR=dt ¼ 0 . The precipitate grows at R tð Þ > Rcrð Þt and dissolves

R tðÞ¼

It is possible to determine the critical size of the precipitates in accordance with [19]

kT tð ÞlnðS0S

kT tð ÞlnðSсS

RO crðÞ¼ t

RC crðÞ¼ t

> , Sv ¼ Cv Ceg v

x þ γvxÞ

�1 � ð1þε 1þδÞ 3 .

, Si ¼ Ci Ceg i

kT � �

ð4Þ

ð5Þ

ð6Þ

complexes as a function of the cooling temperature of the crystal

radius of the precipitate at the growth stage:

6 New Research on Silicon - Structure, Properties, Technology

at R tð Þ < Rcrð Þt [17, 18].

where So ¼ Co

of time [17]:

Ceg o

precipitate; and u ¼ ð1 þ γi

, Sc ¼ Cc Ceg c

In the paper [15], the interactions between the atoms of the substances and, consequently, their properties are determined on the basis of information about the potential of interatomic interaction. The exact form of the interaction potential of two atoms is determined from the quantum-mechanical calculations. The obtained potentials are usually described by the functions with a large number of parameters, which complicates their analytical treatment. Therefore, it is usual practice to operate model potentials that contain a small number of parameters.

An unambiguous determination of the interatomic potential for silicon crystals is complicated. Therefore, theoretical predictions within their formalism have used different fitting parameters whose behavior under various temperature conditions is difficult to predict or justify [15]. In the paper [15], characteristic numbers were determined from the basic criterion of the crystalline state (3) with the help of a model potential Mee-Lennard-Jones.

In this paper, the calculations were performed using the following parameters: U1min ¼ 2.84 eV (SiO2), U2min ¼ 2.71 eV (SiC), λ1 ¼ 4:482 � 108 eV�1 (SiO2), λ2 ¼ 1:099 � 109 eV�1 (SiC); а также Vp ¼ 4.302�10-2 nm3 (SiO2), Vp¼ 2.04�10-2 nm3 (SiС), σ ¼ 310 erg/cm2 (SiO2), σ ¼ 1000 erg/cm2 (SiС), μ ¼ 6.41�1010 Pa, δ ¼ 0.3, ε ¼ 0.15, DO ¼ 0:17 exp ð�2:54eV=kTÞ, Dc ¼ 1:9 exp ð�3:1eV=kTÞ, b ¼ 0.25 nm, k ¼ 8:6153 � 10�5 eV=K, Nc ¼ 1012 cm-3.

We performed three separate groups of calculations that simulated the processes of precipitation during the growth of crystals of large and small diameters with the use of the Czochralski method (CZ-Si) and crucibleless floating zone melting (FZ-Si). Calculations of the first group (I) were performed using the following parameters: the crystal growth rate was V ¼ 0.6 mm/min, the axial temperature gradient was G ¼ 25 K/сm, the oxygen concentration was NðÞ¼ 0 1018 cm-3, and the carbon concentration was Nð Þ¼ 0 1018cm-3. The corresponding parameters used in calculations of the second group (II) were as follows: the crystal growth rate was V ¼ 0.3 mm/min, the axial temperature gradient was G ¼ 25 K/сm, the oxygen concentration was Nð Þ¼ 0 1018 cm-3, and the carbon concentration was Nð Þ¼ 0 1018cm-3. These conditions correspond to the growth of large-sized silicon single crystals with the use of the Czochralski method. For calculations of the third group (III), we used the following parameters: the crystal growth rate was V ¼ 6 mm/min, the axial temperature gradient was G ¼ 130 K/сm, the oxygen concentration was Nð Þ¼ 0 1018 cm-3, and the carbon concentration was Nð Þ¼ 0 1018cm-3. Group III corresponds to the conditions for the growth of small-sized silicon single crystals with the use of crucibleless floating zone melting.

In this, the computing experiment is assumed that the concentration of nucleation centers for complexes constitutes � 1012 cm-3. This value corresponds to the experimental data obtained by transmission electron microscopy [1]. The densities of the distribution of complexes of silicon-carbon for crystals I and II groups are shown in Figure 1. The densities of the distribution of complexes of silicon-carbon for crystals III are shown in Figure 2.

In accordance with the Vlasov model for solid state, the process of precipitation begins in the vicinity of the crystallization front due to the disappearance of excess intrinsic point defects on sinks whose role is played by oxygen and carbon impurities. The results of the calculations performed in groups I, II, and III allow us to compare the processes of precipitation in the CZ-Si and FZ-Si crystals and to analyze them for almost maximum contents of the oxygen and carbon impurities. Changing growth conditions of crystal (in particular, an increase in the growth rate and the axial temperature gradient) results in reduced time of the nucleation stage. Besides, the calculations in group III showed that the change in thermal conditions of the growth leads to a decrease in the average radius of precipitates in the FZ-Si crystals as compared to the CZ-Si crystals at the stage of the growth of precipitates, as well as to the corresponding decrease in the precipitate sizes at the stage of the coalescence.

Figure 1. Changing the density of distribution of complexes silicon-carbon for crystals I (1) and II (2) groups.

Introductory Chapter: Description of the Real Monocrystalline Structure on the Basis of the Vlasov Model for Solids http://dx.doi.org/10.5772/intechopen.68684 9

Figure 2. Changing the density of distribution of complexes silicon-carbon for crystals III group.

the axial temperature gradient was G ¼ 25 K/сm, the oxygen concentration was NðÞ¼ 0 1018 cm-3, and the carbon concentration was Nð Þ¼ 0 1018cm-3. The corresponding parameters used in calculations of the second group (II) were as follows: the crystal growth rate was V ¼ 0.3 mm/min, the axial temperature gradient was G ¼ 25 K/сm, the oxygen concentration was Nð Þ¼ 0 1018 cm-3, and the carbon concentration was Nð Þ¼ 0 1018cm-3. These conditions correspond to the growth of large-sized silicon single crystals with the use of the Czochralski method. For calculations of the third group (III), we used the following parameters: the crystal growth rate was V ¼ 6 mm/min, the axial temperature gradient was G ¼ 130 K/сm, the oxygen concentration was Nð Þ¼ 0 1018 cm-3, and the carbon concentration was Nð Þ¼ 0 1018cm-3. Group III corresponds to the conditions for the growth of small-sized silicon single crystals with the

In this, the computing experiment is assumed that the concentration of nucleation centers for complexes constitutes � 1012 cm-3. This value corresponds to the experimental data obtained by transmission electron microscopy [1]. The densities of the distribution of complexes of silicon-carbon for crystals I and II groups are shown in Figure 1. The densities of the distribu-

In accordance with the Vlasov model for solid state, the process of precipitation begins in the vicinity of the crystallization front due to the disappearance of excess intrinsic point defects on sinks whose role is played by oxygen and carbon impurities. The results of the calculations performed in groups I, II, and III allow us to compare the processes of precipitation in the CZ-Si and FZ-Si crystals and to analyze them for almost maximum contents of the oxygen and carbon impurities. Changing growth conditions of crystal (in particular, an increase in the growth rate and the axial temperature gradient) results in reduced time of the nucleation stage. Besides, the calculations in group III showed that the change in thermal conditions of the growth leads to a decrease in the average radius of precipitates in the FZ-Si crystals as compared to the CZ-Si crystals at the stage of the growth of precipitates, as well as to the

tion of complexes of silicon-carbon for crystals III are shown in Figure 2.

corresponding decrease in the precipitate sizes at the stage of the coalescence.

Figure 1. Changing the density of distribution of complexes silicon-carbon for crystals I (1) and II (2) groups.

use of crucibleless floating zone melting.

8 New Research on Silicon - Structure, Properties, Technology

The condition providing changeover to the stage of the coalescence is written in the form RðtÞ ≈RcrðtÞ, which is satisfied at the temperature T ≈ 1423K. The stage of the coalescence in large-sized silicon single crystals begins at temperatures close to the temperatures of the formation of clusters of intrinsic point defects [17]. Figure 3 shows the variation of the average size of oxygen and carbon precipitates at the stage of the coalescence in the temperature range of cooling from 1423 to 300 K.

Changing of growth conditions for small-sized FZ-Si single crystals (high growth rates and axial temperature gradients) gives what the stage of the coalescence begins far in advance (at T ≈ Tm � 20K).

In the classical theory of the formation of second-phase particles during heat treatments of single crystals, the formation of critical nuclei of small sizes occurs at low temperatures. In this case, an increase in the temperature leads to the growth and coalescence of precipitates. In real silicon single crystals, there are grown-in microdefects that, during heat treatments, serve as sinks for intrinsic point defects and impurity atoms. Therefore, the growth of precipitates formed during the growth of single crystals can occur simultaneously with the formation of new precipitates.

However, the application of the Vlasov model for solid state to the processes of formation complexes during heat treatment of silicon crystals gives different result (Figure 4).

In accordance with the Vlasov model for solid state, the formation of complexes at temperature T ≈ 723K is the unlikely. This temperature corresponds to the average temperature of the formation of thermal donors. The formation of complexes in silicon during heat treatment is possible only at high temperatures. Excess intrinsic point defects and impurity atoms disappear at sinks whose role in this process is played by initial structural defects. This process leads to the growth and transformation of the initial defect structure of crystal.

At the same time, it is known that the thermal treatments of silicon lead to the formation of electrically active centers. If the formation of complexes in the temperature range 300 K ≤ T ≤ 600 K

Figure 3. Variation of the average size R\_av of (1) oxygen precipitates at the stage of the coalescence during cooling of the CZ-Si crystals in the temperature range from 1423 to 300 K.

Figure 4. Dependence of the density of distribution for the silicon-oxygen complexes from the temperature during the annealing of the crystal.

is unlikely, then the processes of coalescence occur in crystals of any diameter. Then, in accordance with the Vlasov model for solid state, it can be assumed that the grown-in precipitates, which dissolve, lead to the formation of electrically active centers.

In conclusion, we note that two theories of nucleation second-phase particles, which are based on different gnoseological approaches (classical theory of nucleation and growth of secondphase particles in crystals and the Vlasov model for solid state), lead to identical results. Both approaches describe the processes of high-temperature precipitation of impurities. In turn, the high-temperature precipitation of impurities is the basis of the process of defect formation in crystals.

### 4. Conclusions

The main task of the solid body is a description of the physical properties of solids in terms of their atomic structure. Despite the successful development of the classical approach in the last 100 years, the theoretical description of the process of defect formation in crystals has not received a satisfactory solution.

Until now, the probabilistic approach (Vlasov model for the solid state) for real crystals has not been applied. At the same time, joint use of both approaches would allow for a fresh look at the already-known facts and discover new phenomena and laws in the study of real solids. This work represents the first attempts in the last 70 years to obtain the solution of Vlasov model for solid state. Questions of the application of the Vlasov model for solid state for the description of the nucleation of defect structure, taking into account the thermal conditions of the crystal growth, were discussed. There are the following main results:

### Author details

Vitalyi Igorevich Talanin\*, Igor Evgenievich Talanin and Vladislav Igorevich Lashko

\*Address all correspondence to<EMAIL_ADDRESS>
Department of Computer Science & Software Engineering, Institute of Economics & Information Technologies, Zaporozhye, Ukraine

### References

is unlikely, then the processes of coalescence occur in crystals of any diameter. Then, in accordance with the Vlasov model for solid state, it can be assumed that the grown-in precipitates, which

Figure 4. Dependence of the density of distribution for the silicon-oxygen complexes from the temperature during the

Figure 3. Variation of the average size R\_av of (1) oxygen precipitates at the stage of the coalescence during cooling of the

In conclusion, we note that two theories of nucleation second-phase particles, which are based on different gnoseological approaches (classical theory of nucleation and growth of secondphase particles in crystals and the Vlasov model for solid state), lead to identical results. Both approaches describe the processes of high-temperature precipitation of impurities. In turn, the high-temperature precipitation of impurities is the basis of the process of defect formation in

dissolve, lead to the formation of electrically active centers.

CZ-Si crystals in the temperature range from 1423 to 300 K.

10 New Research on Silicon - Structure, Properties, Technology

crystals.

annealing of the crystal.

[1] Talanin VI, Talanin IE. Formation of grown-in microdefects in dislocation-free silicon monocrystals. In: Elliot TB, editor. New Research on Semiconductors. New York, USA: Nova Science; 2006. pp. 31–67.

## **Theoretical and Experimental Characterization of Silicon Nanoclusters Embedded in Silicon-Rich Oxide Films**

Néstor David Espinosa Torres, José Álvaro David Hernández de la Luz and Javier Martínez Juárez

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67614

### **Abstract**

[2] Talanin VI, Talanin IE. Kinetics of high-temperature precipitation in dislocation-free

[3] Talanin VI, Talanin IE. Diffusion model of the formation of growth microdefects: A new approach to defect formation in crystals (review). Physics of the Solid State. 2016;58:427–437.

[4] BornM, Huang K. Dynamical Theory of Crystal Lattices. Oxford, UK: Clarendon Press; 1954. [5] Cristian JW. The Theory of Transformations in Metals and Alloys. Oxford, UK: Pergamon

[6] Vlasov AA. On the theory of the solid state. Journal of Physics. 1945;9:130–139 (in USSR) [7] Vlasov AA. Thread-like and plate-like structures in crystals and liquids. Theoretical and

[8] Kozlov VV. The generalized Vlasov kinetic equation. Russian Mathematics Surveys.

[9] Vlasov AA. Many-Particle Theory and its Application to Plasma. New York, USA: Gor-

[11] Landau LD. On the vibration of the electronic plasma. Journal of Physics-USSR.

[12] Ginzburg VL, Landau LD, Leontovich MA, Fok VA. About inconsistency of works by A. A.Vlasov on general theory of plasma and physics of solid body. Journal of Experimental

[13] Pegoraro F, Califano F, Manfredi G, Morrison PJ. Theory and applications of the Vlasov

[14] Ginzburg VL. About some grief-historians of physics. Questions of History of Science

[15] Talanin VI, Talanin IE. Complex formation in semiconductor silicon within the framework of the Vlasov model of a solid state. Physics of the Solid State. 2016;58:2050–2054.

[16] Vedenyapin VV. Boltzmann and Vlasov Kinetic Equations. Moscow, Russia: Fizmatlit;

[17] Talanin VI, Talanin IE. Kinetic model of growth and coalescence of oxygen and carbon precipitates during cooling of as-grown silicon crystals. Physics of the Solid State. 2011;53:

[18] Slezov VV, Sagalovich VV. Diffusive decomposition of solid solutions. Uspekhi

[19] Vanhellemont J. Diffusion limited oxygen precipitation in silicon: Precipitate growth kinetics and phase formation. Journal of Applied Physics. 1995;78:4297–4299.

[10] Vlasov AA. Nonlocal Statistical Mechanics. Moscow, Russia: Nauka; 1978.

silicon single crystals. Physics of the Solid State. 2010;52:2063–2069.

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12 New Research on Silicon - Structure, Properties, Technology

Theoretical Physics (Russia). 1946;16:246–252.

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equation. European Physics Journal D. 2015;69,68:1–3.

We present theoretical calculations using DFT method and the Global Reaction Model (GRM) for molecular structures and photoluminescence (PL) and Fourier Transform Infrared (FTIR) spectroscopy for silicon nanoclusters (Si-NCs) embedded in silicon rich oxide (SRO) films. Correlations between theoretical predictions and experimental results are made taking as reference experimental results obtained from measurements performed on SRO thin films obtained by the Hot Filament Chemical Vapor Deposition (HFCVD) technique. Our theoretical predictions are general since they do not depend on the particular technique used to obtain such films but rather the suggested SinOn structures. A good correlation exists for Eg values for films grown at 1300°C corresponding to Si8 O8 and Si16O16 molecular structures suggested and for films grown at 1150°C with Si9 O9 . Regards PL correlation, a film grown at 900°C gives a spectrum peaked at 440nm and 548nm while theoretical one shows peaks at 471nm and 549.8 nm for a structure Si16O16. Such sample with a further annealing displays peaks at 405nm, 749nm and 820nm with theoretical predictions at 415nm using Si6 O6 . As for FTIR, theoretical calculations predict vibrational mode frequencies of bonds Si-O and Si-H whose values are well located in the experimental frequency range corresponding to the structure Si16O16.

**Keywords:** silicon-rich oxide, luminescence, DFT, GRM

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **1. Introduction**

It is well known that the crystalline silicon has no photoluminescence due to multiple phenomena of non-radiative recombination between electrons and holes, and that the SiO2 presents photoluminescence both by its amorphous nature and by their large gap. The latter has been taken as a starting point to consider silicon-confined systems of great interest because they offer the possibility of light emission from silicon-based materials. Following the initial report of the light emission from porous silicon, announced by Canham, this has been a novel subject of intense scientific activity currently along with other confined systems. Particularly, from the latter, it results in emphasizing the importance of the silicon rich oxides thin films. The physical microscopic structure of SiO*x* is still a subject of discussion nowadays, where its structural arrangement is a key knowledge to get a deep understanding of radiative emission mechanisms in this kind of nanostructured materials.

The silicon rich oxide (SRO) is a silicon oxide with silicon excess or at amount of oxygen less than that of a silicon dioxide (SiO2 ), so that the best appropriate notation would be SiO*x* , with *x* = 0,…,2. This material, after heat treatment, has a phase separation being composed of silicon nanocrystals (Si-NCs) surrounded by silicon oxide (Si-NCs/(SiO*x* ), regardless of the technique employed to obtain them (for instance, LPCVD, PECVD, etc.) [1]. The density and size of the Si-NCs have a strong dependence on the annealing temperature, the concentration of silicon, the characteristics of the silicon substrate, the partial pressure ratios between the reactant gases, the used production technique and the surrounding atmosphere during the annealing. It is remarkable to point out that the presence of phase separation (Si-NCs/ (SiO*x* ), with a fixed value of *x*, can produce Si-NCs embedded in SiOx with different values of *x* respect to SiO2 and, consequently, multiple defects appeared at the borders of the Si-NCs and also within them and probably porous silicon may be present there. The defects generated during the production of the material disappear with the annealing process, particularly, at temperatures greater than 1000°C. It has been reported that for annealing temperatures less than 1100°C, the generation of amorphous silicon clusters is favoured [2], while for higher temperatures, the number of interfacial states is increased between Si-NCs and SiO*x* , therefore the number of defects is also increased. A great field of active investigation has been opened in order to understand the underlying physical mechanisms of the SRO, which give rise to its crystalline structure and optical properties because it is a material, which promises important applications mostly in optoelectronic devices.

In the study of the SRO, one branch of research is focused on investigating the main mechanisms, which generate the luminescence phenomena in this material. In the case of structures such as SRO thin films, we found in the literature different approaches. So, it has been proposed several mechanisms involved in the luminescent emission observed, these include among others: quantum confinement of excitons, luminescence due to chemical species (such as siloxanes, silicon oxides and sub-oxides), interfacial states, defects and strain-related luminescence. Although there is a growing consensus that the quantum confinement effects (QCE) may explain some of the features of the two luminescence spectra [3], it is clear that in some cases, at least, other mechanisms are present. Up to now, there are no models that include several of these emission mechanisms.

In the proposal of quantum confinement as the dominant mechanism in luminescent effect, Qin and Li [4] proposed a limit on the size of the Si-NCs, considered as a critical size, above which dominates the quantum confinement effect while below it the effect of interfacial states prevails above all. With respect to photoluminescence in SRO including Si-NCs, it has been reported that it is dominated by strong quantum confinement above from a critical size of Si-NCs which may be about 1.1 nm in diameter, it corresponds to 10 times the Bohr radius of silicon, below this critical size, the photoluminescence may be dominated by the weak quantum well confinement as the interfacial defects.

Moreover, luminescent phenomenon in SRO structures can be excited by different forms, so we find that experimentally, luminescence spectra are generated by photoluminescence (PL), electroluminescence (EL) and cathode luminescence (CL) mechanisms. The fundamental physical mechanisms, which explain correctly the origin of luminescent phenomena in each one of these different forms of excitation, are still an active field of research.

Today, a few models are frequently used to describe a SRO network, namely the Mixture Model (MM) by Bell and Ley [5], the Random Bonding Model (RBM) by Philipp [6], and the Intermediate Model (IM) introduced in 2011 by Novikov and Gritsenko [7]. In 2012, Davor et al. [8], in an extensive review, considered that the actual structure seems to be greatly determined by the deposition procedure. In some works, the SiO*X* structures films obtained by radiofrequency sputtering and physical evaporation were claimed to correspond to RBM, whereas the SiO*x* films obtained by magneto-sputtering, Plasma-Enhanced Chemical Vapor Deposition (PECVD), have been assigned to MM. IM was used to describe SiO*x* layers prepared by low pressure chemical vapour deposition (LPCVD) technique using SiH4 and N2 O as a reactant precursors at 750°C. Finally, we find a new model, the Global Reaction Model (GRM) suggested lately by Espinosa-Torres et al. [9]. This model describes, first, the global and partial reaction(s) compulsory to produce the oxide matrices (SiO2 , Si2 O3 , SiO and Si2 O), second, the annealing reactions for elucidating the compositional changes after and before the thermal treatment, and subsequently, the variations in the intensity of luminescence spectra, and also it describes a set of secondary reactions of the oxide matrices with the hydrogen produced in the reaction chamber to obtain the charged species that could be associated to the emission in SRO thin films with explicit defects. This work is focused on studying the theoretical predictions about PL luminescence of SRO thin films based on DFT method and the GRM and make correlations with experimental PL results provided by measurements from SRO thin films obtained experimentally by the hot filament chemical vapour deposition (HFCVD) technique.

### **2. Relevant characteristics of silicon‐rich oxide (SRO)**

### **2.1. Some techniques of production of SRO**

**1. Introduction**

(SiO*x*

*x* respect to SiO2

The physical microscopic structure of SiO*x*

14 New Research on Silicon - Structure, Properties, Technology

less than that of a silicon dioxide (SiO2

applications mostly in optoelectronic devices.

several of these emission mechanisms.

mechanisms in this kind of nanostructured materials.

It is well known that the crystalline silicon has no photoluminescence due to multiple phenomena of non-radiative recombination between electrons and holes, and that the SiO2 presents photoluminescence both by its amorphous nature and by their large gap. The latter has been taken as a starting point to consider silicon-confined systems of great interest because they offer the possibility of light emission from silicon-based materials. Following the initial report of the light emission from porous silicon, announced by Canham, this has been a novel subject of intense scientific activity currently along with other confined systems. Particularly, from the latter, it results in emphasizing the importance of the silicon rich oxides thin films.

structural arrangement is a key knowledge to get a deep understanding of radiative emission

The silicon rich oxide (SRO) is a silicon oxide with silicon excess or at amount of oxygen

with *x* = 0,…,2. This material, after heat treatment, has a phase separation being composed

technique employed to obtain them (for instance, LPCVD, PECVD, etc.) [1]. The density and size of the Si-NCs have a strong dependence on the annealing temperature, the concentration of silicon, the characteristics of the silicon substrate, the partial pressure ratios between the reactant gases, the used production technique and the surrounding atmosphere during the annealing. It is remarkable to point out that the presence of phase separation (Si-NCs/

and also within them and probably porous silicon may be present there. The defects generated during the production of the material disappear with the annealing process, particularly, at temperatures greater than 1000°C. It has been reported that for annealing temperatures less than 1100°C, the generation of amorphous silicon clusters is favoured [2], while for higher

the number of defects is also increased. A great field of active investigation has been opened in order to understand the underlying physical mechanisms of the SRO, which give rise to its crystalline structure and optical properties because it is a material, which promises important

In the study of the SRO, one branch of research is focused on investigating the main mechanisms, which generate the luminescence phenomena in this material. In the case of structures such as SRO thin films, we found in the literature different approaches. So, it has been proposed several mechanisms involved in the luminescent emission observed, these include among others: quantum confinement of excitons, luminescence due to chemical species (such as siloxanes, silicon oxides and sub-oxides), interfacial states, defects and strain-related luminescence. Although there is a growing consensus that the quantum confinement effects (QCE) may explain some of the features of the two luminescence spectra [3], it is clear that in some cases, at least, other mechanisms are present. Up to now, there are no models that include

temperatures, the number of interfacial states is increased between Si-NCs and SiO*x*

and, consequently, multiple defects appeared at the borders of the Si-NCs

of silicon nanocrystals (Si-NCs) surrounded by silicon oxide (Si-NCs/(SiO*x*

), with a fixed value of *x*, can produce Si-NCs embedded in SiOx

is still a subject of discussion nowadays, where its

), so that the best appropriate notation would be SiO*x*

,

), regardless of the

with different values of

, therefore

Among the different techniques used for depositing thin films, we can mention those which are commonly employed to grow SRO as a nanostructured material. One such technique is called hot filament chemical vapour deposition (HFCVD). This technique is known by different names like initiated-CVD (I-CVD), catalytic-CVD (Cat-CVD) and hot wire-CVD (HWCVD). Amorphous and micro-crystalline silicon could also be obtained with this method [10]. The HFCVD technique gives some important advantages, it does not need a sophisticate temperature control and vacuum system, in addition, the deposition is free of plasma and we can obtain the precursors by a solid source or mixtures of gases. HFCVD system utilizes quartz-like solid source and makes use of the collision theory in order to describe the SRO deposition process [11]. The solid source to obtain SRO is made of Quartz, and it is etched by H0 .

Another technique is that known as low pressure chemical vapour deposition (LPCVD), it allows us to get silicon-rich oxide layers using oxide species like nitrous oxide (N2 O) and silicon compounds (silane, SiH4 ) as reactants gasses. Silicon excess is easily controlled by changing the partial pressure ratio *R*o between N2 O and SiH4 defined by *R*o = *P*(N2 O)/*P*(SiH4 ) or simply *R*o = N2 O/SiH4 .

When we make a SRO layer, first, the partial pressures must be calculated by choosing a suitable *R*o and *P*T value. The suitable pressure for each reactant gas is calculated by means of relations,

$$P\_{\text{SHH}\_i} = \frac{P\_{\text{\tiny T}}}{\frac{R\_o}{20} + 1}; \; P\_{\text{N}\_i\text{O}} = \frac{R\_o P\_{\text{SHH}\_i}}{20} \tag{1}$$

where *P*SiH4 is the partial pressure of diluted silane at 5% (by this reason, term 20 appears) in nitrogen, *P*N2 O is the nitrous oxide partial pressure and *P* is the total pressure. Si excess in the deposited films is controlled by the partial pressure ratio *R*o of the reactants gases.

The optical characteristics of SRO, obtained by this technique, can be varied with the excess silicon in the films, making SRO attractive to fabricate optoelectronic devices. Therefore, Si-NCs embedded in a SiO2 matrix are currently attracting much interest to be a good candidate for building efficient light-emitter devices [12–14]. Such devices are highly desirable for the integration of optical signal and electronic data processing circuits on the same chip. Furthermore, its fabrication process is compatible with the present large-scale integration technologies [15, 16]. The native band gap of Si-NCs is enlarged with respect to one of the bulk material; this fact brings the possibility to observe an intense visible PL spectrum at room temperature. The PL spectrum consists generally of intense emission peaks in the near- infrared (NIR) and visible (VIS) regions. It was established that blue and green PLs are caused by various emitting centres in the silicon oxide, while the nature of the intense PL in orange-red region is still discussed [17–19].

Experimentalists have reported in the literature that emission spectra of the SRO films vary in the interval of wavelengths from 400 to 850 nm for layers deposited by LPCVD. It has not been observed experimental emission outside of this range for samples obtained by this technique. Nevertheless, by preliminary theoretical studies, using the density functional theory (DFT), it has been found as isolated molecules, presumably found in SRO thin films that could emit in UV region.

In addition, for SRO thin films deposited by LPCVD, PL is only observed in annealed samples. In fact, only thin films annealed at 1100°C produce high emission, and the highest photoemission is obtained for SRO films with *R*o = 30, which corresponds to a silicon excess about 3%, and *R*o = 10 corresponds with a silicon excess about 12%. The PL is only obtained from the visible (VIS) to NIR range, and its intensity reduces as *R*o decreases. In contrast, we find that powders and thin films SRO deposited by other technique such as HFCVD technique, display a reduction in photoluminescence intensity in most cases after being annealed, and only in very particular conditions (deposited parameters) the PL is increased.

(HWCVD). Amorphous and micro-crystalline silicon could also be obtained with this method [10]. The HFCVD technique gives some important advantages, it does not need a sophisticate temperature control and vacuum system, in addition, the deposition is free of plasma and we can obtain the precursors by a solid source or mixtures of gases. HFCVD system utilizes quartz-like solid source and makes use of the collision theory in order to describe the SRO deposition process [11]. The solid source to obtain SRO is made of Quartz, and it is etched

Another technique is that known as low pressure chemical vapour deposition (LPCVD), it

When we make a SRO layer, first, the partial pressures must be calculated by choosing a

; *P*N2

The optical characteristics of SRO, obtained by this technique, can be varied with the excess silicon in the films, making SRO attractive to fabricate optoelectronic devices.

good candidate for building efficient light-emitter devices [12–14]. Such devices are highly desirable for the integration of optical signal and electronic data processing circuits on the same chip. Furthermore, its fabrication process is compatible with the present large-scale integration technologies [15, 16]. The native band gap of Si-NCs is enlarged with respect to one of the bulk material; this fact brings the possibility to observe an intense visible PL spectrum at room temperature. The PL spectrum consists generally of intense emission peaks in the near- infrared (NIR) and visible (VIS) regions. It was established that blue and green PLs are caused by various emitting centres in the silicon oxide, while the nature of the intense PL in

Experimentalists have reported in the literature that emission spectra of the SRO films vary in the interval of wavelengths from 400 to 850 nm for layers deposited by LPCVD. It has not been observed experimental emission outside of this range for samples obtained by this technique. Nevertheless, by preliminary theoretical studies, using the density functional theory (DFT), it has been found as isolated molecules, presumably found in SRO thin films that could emit

In addition, for SRO thin films deposited by LPCVD, PL is only observed in annealed samples. In fact, only thin films annealed at 1100°C produce high emission, and the highest photoemis-

O and SiH4

and *P*T value. The suitable pressure for each reactant gas is calculated by means

is the partial pressure of diluted silane at 5% (by this reason, term 20 appears) in

O is the nitrous oxide partial pressure and *P* is the total pressure. Si excess in the

O = *Ro P* \_\_\_\_\_\_ SiH4

) as reactants gasses. Silicon excess is easily controlled by chang-

defined by *R*o

= *P*(N2

20 (1)

of the reactants gases.

matrix are currently attracting much interest to be a

= 30, which corresponds to a silicon excess about 3%,

O) and sili-

) or

O)/*P*(SiH4

allows us to get silicon-rich oxide layers using oxide species like nitrous oxide (N2

= *P* \_\_\_\_*T R*\_\_*o* 20 + 1

deposited films is controlled by the partial pressure ratio *R*o

between N2

by H0 .

simply *R*o

suitable *R*o

of relations,

where *P*SiH4

nitrogen, *P*N2

in UV region.

con compounds (silane, SiH4

= N2

ing the partial pressure ratio *R*o

O/SiH4 .

16 New Research on Silicon - Structure, Properties, Technology

*P*SiH4

Therefore, Si-NCs embedded in a SiO2

orange-red region is still discussed [17–19].

sion is obtained for SRO films with *R*o

By using the LPCVD technique, the SRO refractive index can be changed, it has been reported that the index varies from 1.45 to 1.94 when the silicon excess is changed. It is observed that the refractive index of the SRO on silicon substrate increases with the increment of Si excess, it means that as *R*o augments, the index tends towards the refractive one of SiO2 , contrarily, it tends towards that of Si. Then, by measuring the refractive index, the inclusion of Si in these SRO films is easy to detect. For example, it has been found that for *R*o = 10, after thermal annealing, the refractive index reaches values greater than 2. In contrast, when the reactant ratios are *R*o = 20, 30 and 40, the refractive indexes diminish with a clear tendency to reach values less than 1.5 [20].

Relating to transmittance of SRO obtained by LPCVD (an important optical parameter measured in experiments), we find that the transmittance spectra for *R*o = 10, 20, 30 films deposited on sapphire substrates are reported in Ref. [2]. According to this reference, the observed transmittance of these films deposited on sapphire is high (>80%) and vanishes to zero when wavelength reduces. The annealing time parameter does not produce a clear variation on transmittance; however, when *R*o parameter undergoes increments it causes a clear shift of the curves towards lower wavelength. The absorption coefficients are determined from transmission spectra, and it can be observed that the position of the absorption edge moves towards higher energy when *R*o increases.

Other important technique is the sputtering one, where sputtering means an ionic bombardment process in vapour phase at room temperature. By this technique, plasma is formed by the ionized process gas, usually Argon, due to the presence of a strong electric field. The high voltage between cathode and anode causes that ions of the process gas hit the target with enough energy to pull out atoms from the surface of the target (cathode) by a momentum transfer process. The multiple collisions enable some atoms of the material acquire enough energy to leave the surface, then reach the substrate and stick to it. Sputtering technique can be divided into reactive and non-reactive. It is denominated no reactive sputtering to one in which the process gas does not react with the deposited material. Typically, Argon is used as inert gas due to the high yield obtained and its minor cost. When sputtering is made in the presence of a reactive gas as oxygen, the sputtering is called reactive. In this case, the presence of ionized oxygen causes oxidation of the material, thus obtaining films whose properties depend on the concentration of reactive gas in the chamber during the process.

In the sputtering technique, the growth model of SRO films is based in the work proposed by Nyberg and Berg [21], where they describe the reactive sputtering processing behaviour in many different ways to carry out. This model has been specially adapted to the growth of SiO*x* films where the growth kinetics is dependent on the flux of oxygen onto the substrate surface relative to the flux of Si incorporated into the film.

As to the optical properties of the Si/SO*x* , they differ due to the synthesis technique, indicating structural differences of the Si-NCs (as silicon nanocrystals, amorphous silicon and defects) and their environment [22]. Raman scattering measurements are frequently used to prove the presence of Si-NCs. With this fast and non-destructive method, it is possible to determine whether silicon particles are amorphous or crystalline. Moreover, information about mean size (MS) and sizes distribution (SD) of nanocrystallites can be obtained from the peak position and shape of the Raman band. For samples using Si wafers as substrates, Raman measurements must be undertaken with care because the strong Raman peak from the crystalline Si (c-Si) substrate masks the signal of the Si-NCs. To avoid this problem, sapphire substrates should be used. Then, the obtained Raman data can clearly be related to the deposited thin film, not to the substrate.

### **2.2. Morphological aspects of SRO films**

**Figure 1(a)** shows SEM micrograph of SRO film deposited by HFCVD at 409°C. The characteristics of the films depend on the deposition conditions such as substrate temperature, deposition time, solid sources and kind of substrate. So there are several factors that can change the morphology of the films. In this figure, we can see agglomerate structures, which form isomers Si7 with sphere shape; this geometric shape is a consequence of the elevated temperature. Also, we can appreciate that there are interspaces among agglomerates, so it leads to the formation of a porous film.

On the other hand, silicon-rich oxide powders (SROP) agglomerates and frost can be seen more clearly in SEM Micrographs shown in **Figure 1(b)** and **(c)**, where we can see that the big silicon rich oxide powders (SROPs) are formed by the agglomeration of small nanoparticles. The excess of precursors in gas phase is called supersaturation, and it is present in all SROP samples. In HFCVD technique, the filament-source distance controls the supersaturation. Therefore, the morphology is controlled by the saturation and growth temperature. This process can be described in the following manner: the precursor reacts in gas phase, and it creates clusters in the environment. Some clusters could be composed by silicon, silicon-hydrogen, silicon monoxide and silica as powder. The temperature between filament and source is very high, but it decreases between source and substrate due to a temperature gradient within the filament. When the distance of source-substrate increases, the growth temperature decreases, and with this conditions, the environment is supersaturated and it is partially condensed.

Relevant differences in SEM images shown in **Figure 1(a)**–**(c)**, are originated owing to the deposition temperatures, which were 409, 368 and 320°C, respectively. Grains formed at the highest temperature are bigger due to the matrix SiO2 that embedded silicon agglomerates or nanocrystals. Presence of silicon agglomerates was corroborated using micro Raman. Images of **Figure 1(a)** and **(b)** were taken with the secondary electron detector for high-resolution images. This detector uses a lower voltage, which favours the superficial resolution of images. In **Figure 1(b)** is observed a porous surface, probably formed by smaller isomers than those formed at 409°C, where their size is considerably greater than 8 µm.

Finally, **Figure 2** displays results of band gap values obtained by applying the Kubelka-Munk method to SiO*x* powders deposited by HFCVD at the temperatures of 300, 320 and 539°C and filament-source distances of 2, 9 and 10 mm whose values are 3.42, 3.63 and 3.72 eV, respectively [23].

Theoretical and Experimental Characterization of Silicon Nanoclusters Embedded in Silicon-Rich Oxide Films http://dx.doi.org/10.5772/67614 19

**Figure 1.** SEM micrograph of a SRO film deposited by HFCVD (a) at 409°C, (b) at 368°C and (c) at 320°C.

**Figure 2.** Band Gap values of SRO films measured by Kubelka–Munk's method.

### **3. Correlation between experimental results and theoretical predictions of the Global Reaction Model (GRM)**

### **3.1. Global Reaction Model**

As to the optical properties of the Si/SO*x*

18 New Research on Silicon - Structure, Properties, Technology

**2.2. Morphological aspects of SRO films**

leads to the formation of a porous film.

highest temperature are bigger due to the matrix SiO2

formed at 409°C, where their size is considerably greater than 8 µm.

form isomers Si7

method to SiO*x*

, they differ due to the synthesis technique, indicating

structural differences of the Si-NCs (as silicon nanocrystals, amorphous silicon and defects) and their environment [22]. Raman scattering measurements are frequently used to prove the presence of Si-NCs. With this fast and non-destructive method, it is possible to determine whether silicon particles are amorphous or crystalline. Moreover, information about mean size (MS) and sizes distribution (SD) of nanocrystallites can be obtained from the peak position and shape of the Raman band. For samples using Si wafers as substrates, Raman measurements must be undertaken with care because the strong Raman peak from the crystalline Si (c-Si) substrate masks the signal of the Si-NCs. To avoid this problem, sapphire substrates should be used. Then, the obtained Raman data can clearly be related to the deposited thin film, not to the substrate.

**Figure 1(a)** shows SEM micrograph of SRO film deposited by HFCVD at 409°C. The characteristics of the films depend on the deposition conditions such as substrate temperature, deposition time, solid sources and kind of substrate. So there are several factors that can change the morphology of the films. In this figure, we can see agglomerate structures, which

temperature. Also, we can appreciate that there are interspaces among agglomerates, so it

On the other hand, silicon-rich oxide powders (SROP) agglomerates and frost can be seen more clearly in SEM Micrographs shown in **Figure 1(b)** and **(c)**, where we can see that the big silicon rich oxide powders (SROPs) are formed by the agglomeration of small nanoparticles. The excess of precursors in gas phase is called supersaturation, and it is present in all SROP samples. In HFCVD technique, the filament-source distance controls the supersaturation. Therefore, the morphology is controlled by the saturation and growth temperature. This process can be described in the following manner: the precursor reacts in gas phase, and it creates clusters in the environment. Some clusters could be composed by silicon, silicon-hydrogen, silicon monoxide and silica as powder. The temperature between filament and source is very high, but it decreases between source and substrate due to a temperature gradient within the filament. When the distance of source-substrate increases, the growth temperature decreases, and with this conditions, the environment is supersaturated and it is partially condensed.

Relevant differences in SEM images shown in **Figure 1(a)**–**(c)**, are originated owing to the deposition temperatures, which were 409, 368 and 320°C, respectively. Grains formed at the

nanocrystals. Presence of silicon agglomerates was corroborated using micro Raman. Images of **Figure 1(a)** and **(b)** were taken with the secondary electron detector for high-resolution images. This detector uses a lower voltage, which favours the superficial resolution of images. In **Figure 1(b)** is observed a porous surface, probably formed by smaller isomers than those

Finally, **Figure 2** displays results of band gap values obtained by applying the Kubelka-Munk

ment-source distances of 2, 9 and 10 mm whose values are 3.42, 3.63 and 3.72 eV, respectively [23].

powders deposited by HFCVD at the temperatures of 300, 320 and 539°C and fila-

that embedded silicon agglomerates or

with sphere shape; this geometric shape is a consequence of the elevated

In this section, we present for first time a new model, which considers the global and partial reaction(s) necessary to generate the oxide matrices (SiO2 , Si2 O3 , SiO and Si2 O), the annealing reactions for explaining the compositional changes after and before the thermal treatment and consequently the changes in luminescence spectra intensity and a set of secondary reactions of the oxide matrices with the hydrogen produced to obtain the ions that could be associated to the emission in SRO thin films with specific defects. When SRO is prepared by LPCVD, a gas mixture of N2 O and silane is habitually used [24, 25] and the excess Si content can be modified by the gas flow ratio *Ro* = [ \_ *N*2 *O Si H*4 ]. The silicon excess can be as high as 17% for *R*o = 3; and experimentally stoichiometric SiO2 (a non-free silicon film) can be obtained for *R*o ≥ 50 [26]. Theoretically, *R*o = 40 corresponds to the stoichiometric silica, when a mixture silane-nitrogen at 5% is used. Experimentally, there is enough evidence that SRO thin films are constituted by a silicon oxides mixture and not only by one of them, independently of the value of *R*o . We can establish the global reactions of the chemical combination of N2 O, N2 and SiH4 , which generates the theoretical composition of SRO given by

$$\text{SiO}\_2 = \frac{(1-x)}{(4+z+v)} \; ; \; \text{Si}\_2\text{O}\_3 = \frac{(1-v)}{4+z+v} \; ; \; \text{SiO} = \frac{(1-y)}{(4+z+v)} \tag{2}$$

$$\text{Si}\_2\text{O} = \frac{(1-z)}{(4+z+\upsilon)} \; ; \; \text{Si} = \frac{\left(x+y+2z+2\upsilon\right)}{(4+z+\upsilon)}\tag{3}$$

where the parameters *x*, *y*, *z*, *ν* satisfy the conditions 0 ≤ *x*, *y*, *z*, *υ* ≤ 1.0 and 0 ≤ *x* + *y* + 2*x* + *υ* ≤ 1.0.

When SRO thin films are annealed, some oxides are degraded. The plausible 'annealing reactions' proposed are as follows:

$$\text{SiO}\_{2(\text{solid})} + \text{Heat} \rightleftharpoons \text{(1}-\text{\textquotedblleft} \text{SiO}\_{(\text{solid})} + \text{(0.5+0.5\text{\textquotedblright})}\text{O}\_{2(\text{gas})} + \text{\textquotedblleft Si}\_{\text{solid}}\tag{4}$$

$$\text{Si}\_2\text{O}\_{\text{3(solid)}} + \text{Heat} \rightleftharpoons \text{(1}-\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\textasciic{}}\text{\text{\textasci}}\text{\text{\textasciic{}}}\text{\text{\textasciic{}}}\text{\text{\textPi}}\text{\text{\textPi}}\text{\text{\textPi}}\text{\text{\textPi}}\text{\text{\textPi}}\text{\text{\textPi}}\text{\text{\text{\text$$

Double arrow stands for denoting equilibrium condition, *ξ and ξ*' are the progress of the annealing reactions. The extent of progress of reaction is defined as the ratio between the total change in the number of moles of a species and their stoichiometric coefficients.

As is known, a mole of any substance contains the number of atoms equal to the Avogadro's number, *NA* = 6.023x 1023. In order to perform first-principles calculations, the problem must be modelled with a maximum of 100 atoms, consequently, the oxides must be rewritten in terms of the number of atoms, that is, Si*n* O2*n* , Si2*n* O3*n* , Si*n* O*n* and Si2*n* O*n* . The hydrogen gases can react accordingly as H2 = [H]+ + [H]− .

The hydrogen ion formed, in turn, reacts with the silicon oxides to form ions such as [Si*n* O2*n* H] + , [Si*n* O2*n* H] 2+ etc. During heat treatment the reactions produce a dehydration of these cations, resulting in the formation of new ones, for example, [Si*n* O2*n* H2] 2+ ⇔ [Si*n* O2*n*−1] 2+ + H2 O↑, and so on. Finally, the moieties obtained from these reactions result as follows:

$$\left[\text{Si}\_{\text{n}}\text{O}\_{\text{2n}-1}\right]^{2\star};\ \left[\text{Si}\_{\text{2u}}\text{O}\_{\text{3u}-1}\right]^{2\star};\ \left[\text{Si}\_{\text{n}}\text{O}\_{\text{n}-1}\right]^{2\star}\text{ and }\left[\text{Si}\_{\text{2u}}\text{O}\_{\text{n}-1}\right]^{2\star}.\tag{6}$$

These anions formed are different oxides matrices containing vacancies or defects of silicon which may or not be present in the films of SRO.

### **3.2. Comparison between experimental results and theoretical predictions of GRM.**

In this section, we will display and discuss the results employing DFT to evaluate theoretically structures type Si*n* O*n* , where 5 ≤ *n* ≤ 26 is the number of silicon atoms. The GRM already discussed is employed to explain the physical microscopic structure of SRO thin films regardless of the technique used to obtain the SRO structure since we are only interested in its molecular composition and atomic arrangement. Also, we will show the results of the evaluation of structural and optical properties for a wide set of moieties, seemingly found in SRO. DFT results predict emission in visible region for molecules with a number of atoms less than 14 silicon ones. Results obtained in this research predict luminescence in visible region for just about half calculated structures, especially for *n* ≤ 16 silicon atoms, while large structures with *n* ≥ 17 display luminescence in ultraviolet region.

#### **3.3. Measurements of band gap** *E***g for SiOx thin films**

associated to the emission in SRO thin films with specific defects. When SRO is prepared by

\_ *N*2 *O Si H*4

silane-nitrogen at 5% is used. Experimentally, there is enough evidence that SRO thin films are constituted by a silicon oxides mixture and not only by one of them, independently of the

. We can establish the global reactions of the chemical combination of N2

where the parameters *x*, *y*, *z*, *ν* satisfy the conditions 0 ≤ *x*, *y*, *z*, *υ* ≤ 1.0 and 0 ≤ *x* + *y* + 2*x* + *υ* ≤ 1.0.

When SRO thin films are annealed, some oxides are degraded. The plausible 'annealing reac-

SiO2(solid) + Heat ⇄ (1 − *ξ*)SiO(solid) + (0.5 + 0.5*ξ*)*O*2(gas) + *ξ* Sisolid (4)

annealing reactions. The extent of progress of reaction is defined as the ratio between the total

As is known, a mole of any substance contains the number of atoms equal to the Avogadro's number, *NA* = 6.023x 1023. In order to perform first-principles calculations, the problem must be modelled with a maximum of 100 atoms, consequently, the oxides must be rewritten in terms

The hydrogen ion formed, in turn, reacts with the silicon oxides to form ions such as

These anions formed are different oxides matrices containing vacancies or defects of silicon

In this section, we will display and discuss the results employing DFT to evaluate theoretically

cussed is employed to explain the physical microscopic structure of SRO thin films regardless

; [Si*n* O*n*−1]

2+

**3.2. Comparison between experimental results and theoretical predictions of GRM.**

)Si2 O(solid) + (2 + *ξ*'

and Si2*n*

etc. During heat treatment the reactions produce a dehydration of these cat-

2+

, where 5 ≤ *n* ≤ 26 is the number of silicon atoms. The GRM already dis-

O*n*

2+

and [Si2*n* O*n*−1]

⇔ [Si*n* O2*n*−1]

2+

(4 + *z* + *υ*) ; Si2 O3 = \_\_\_\_\_ (1 − *υ*)

O and silane is habitually used [24, 25] and the excess Si content

= 40 corresponds to the stoichiometric silica, when a mixture

4 + *z* + *υ* ; SiO = (1 − *y*) \_\_\_\_\_\_

(4 + *z* + *υ*) ; Si = (*x* + *y* + 2*z* + 2*υ*) \_\_\_\_\_\_\_\_\_\_ (4 + *z* + *υ*) (3)

)O2(gas) + 2 *ξ*'

]. The silicon excess can be as high as 17%

(a non-free silicon film) can be obtained for

O, N2

(4 + *z* + *υ*) (2)

Sisolid (5)

are the progress of the

. The hydrogen gases can react

2+

+ H2 O↑, and so

. (6)

and

LPCVD, a gas mixture of N2

≥ 50 [26]. Theoretically, *R*o

SiO2 = \_\_\_\_\_\_ (1 − *x*)

tions' proposed are as follows:

of the number of atoms, that is, Si*n*

2+

O*n*

accordingly as H2 = [H]+ + [H]−

, [Si*n* O2*n* H]

[Si*n* O2*n*−1]

[Si*n* O2*n* H]

+

structures type Si*n*

Si2 O = \_\_\_\_\_\_ (1 − *z*)

Si2 O3(solid) + Heat ⇄ (1 − *ξ*'

for *R*o

value of *R*o

*R*o

SiH4

can be modified by the gas flow ratio *Ro* = [

20 New Research on Silicon - Structure, Properties, Technology

= 3; and experimentally stoichiometric SiO2

, which generates the theoretical composition of SRO given by

Double arrow stands for denoting equilibrium condition, *ξ and ξ*'

O2*n* , Si2*n* O3*n* , Si*n* O*n*

ions, resulting in the formation of new ones, for example, [Si*n* O2*n* H2]

on. Finally, the moieties obtained from these reactions result as follows:

; [Si2*n* O3*n*−1]

.

2+

which may or not be present in the films of SRO.

change in the number of moles of a species and their stoichiometric coefficients.

We begin by taking SiO*x* films obtained by HFCVD technique from our experimental group (results not even published). From these samples, we take into account the band gap parameter as the first one to be analysed. The approximate experimental values of the energy band gap *E*g are obtained by the relationship known as Tauc plot [27] as shown in **Figure 3(a)**. The methodology for obtaining the *E*g has been described in a previous work [28]. It is found that *E*g decreases when the substrate temperature is raised. The band gap of the SiO*x* films lies in the range of 1.8–2.5 eV. When *x* decreases out from 2.0 in a —SiO*x* (amorphous oxide), the valence band edge moves up, as the increased Si—Si bond states are gradually overlapped with the oxygen non-bonding states (ONS), and finally spread out into the Si valence band. Simultaneously, the conduction band edge also moves down, giving rise to the band gap decreasing nonlinearly when the Si concentration is increased continually.

In **Figure 3(a)**, we observe that by making an extrapolation through the straight line according to Tauc procedure, we obtain the approximated bang gaps which have values of 1.95eV and 2.15 eV for **Figure 3(b)**. At first glance, the variations of *E*g are originated by the difference in temperatures then it is observed that *E*g reduces as temperature increases. These two experimental values of *E*g fit well with those obtained theoretically using DFT as shown in **Table 1** further below that are results for structures type Si*n* O*n* .

**Figure 3.** Determination of Eg for a SiO*x* film by making use of the relationship known as Tauc plot [α(*hν*)]1/3 versus energy (*hν*) for two temperatures (a) *T*g =1300°C and (b) *T*g =1150°C.

**Table 1.** Highest Occupied Molecular Orbital (HOMO), *Lowest Unoccupied Molecular Orbital* (LUMO) and HOMO–LUMO gap calculated using DFT for [Si*n* O*n* ] structures with 5 ≤ *n* ≤ 16.

We have seen that SiO*x* thin films, deposited at *T*g = 1300°C, resulted with a bang gap of 1.95 eV, calculated using Tauc technique.

Now, by observing **Table 1**, we can correlate two possible theoretical values either *E*g = 1.93 eV corresponding to Si8 O8 molecule or *E*g = 1.96 eV corresponding to Si16O16 one, existing the possibility of a mixture of them. On the other hand, SiO*X* film deposited at 1150°C corresponds to an approximated experimental band gap of 2.15 eV, which correlates well with a theoretical value of *E*g = 2.06 eV associated to Si9 O9 molecule in accordance with **Table 1**.

In regard to the origin of the PL emission in Si-NCs, it is still a subject of debate; however, we can find some proposals of models suggested explaining this phenomenon. One of this model relates the PL to quantum confinement effects (QCEs) [29, 30]. The other model relates the PL to defects in the oxide matrix or at the interface SiO2 /Si-NCs [28, 31].

Broadly, both common accepted proposals make use of approximated quantum methods in order to solve the Schrödinger equation associated with quantum confinement of the electron restricted to move in so small spatial dimensions, thence their predictions about luminescent phenomenon are limited. Considering this important fact, we hope that an analysis of this phenomenon made from the view point of composition and molecular structures can significantly contribute to a better knowledge of luminesce in SRO considered as an arrangement of Si-NCs embedded in oxide matrices.

#### **3.4. Thermal effects in PL of the SiO***x*  **thin films**

Now, we proceed to our analysis in relationship to PL phenomenon. Inspecting, in **Figure 4(a)**, the experimental PL spectrum measured from the SiO*x* film as grown at *T*g = 900°C, we locate two emission bands both covering a wide spectral range from 380 to 750 nm (from violet to red).

The left band peaked around 440 nm while the right one peaked around 548 nm as can be confirmed by de-convolution curves. After making a further annealing to the same SiO*x* film, the PL spectrum **Figure 5(a)** displays two main bands, one is the A band, which lies in the violet-blue range (380–495 nm) peaked at 405 nm with a relatively weak PL intensity. The other band is the B one, which lies in the orange-near infrared range (590–875 nm), this band shows a strong intensity and two main peaks, one located at 749 nm and other at 820 nm as confirmed again by de-convolution curves.

Looking at **Figures 4(a)** and **5(a)** and making comparisons between them, we infer that the PL intensity that decreases after thermal annealing [32] due to the PL intensity is lower after a further annealing. According to this result, we conclude that annealing process stimulates the formation of crystalline silicon (c-Si) as well as the formation of defects both contributing to the PL emission. For this reason the PL spectrum shifts to the red region.

With regard to the theoretical PL spectrum, **Figure 4(b)** exhibits this one, for the SiO*X* film as grown at *T*g = 900°C, that was calculated considering the arrangement of a Si16O16 molecule. With this molecular structure, we obtained the PL spectrum which has two remarkable peaks, one of them located at 471 nm with the highest intensity and the other has two located peaks closer at 549.8 and 556 nm. In addition, an excited state at 683 nm was also found, but its intensity was too negligible or non-detectable.

We have seen that SiO*x*

gap calculated using DFT for [Si*n*

corresponding to Si8

value of *E*g

to red).

calculated using Tauc technique.

**Number of silicon atoms HOMO**

22 New Research on Silicon - Structure, Properties, Technology

**eV**

 –6.19 –3.14 3.05 –6.01 –3.46 2.55 –5.51 –3.58 1.93 –5.34 –3.28 2.06 –5.93 –3.22 2.71 –5.97 –2.96 3.01 –5.61 –3.30 2.31 –6.04 –2.79 3.25 –6.11 –3.39 2.72 –6.16 –4.20 1.96

O8

= 2.06 eV associated to Si9

to defects in the oxide matrix or at the interface SiO2

the experimental PL spectrum measured from the SiO*x*

Si-NCs embedded in oxide matrices.

**3.4. Thermal effects in PL of the SiO***x*

thin films, deposited at *T*g

] structures with 5 ≤ *n* ≤ 16.

molecule or *E*g

possibility of a mixture of them. On the other hand, SiO*X*

O*n*

Now, by observing **Table 1**, we can correlate two possible theoretical values either *E*g

O9

to an approximated experimental band gap of 2.15 eV, which correlates well with a theoretical

**Table 1.** Highest Occupied Molecular Orbital (HOMO), *Lowest Unoccupied Molecular Orbital* (LUMO) and HOMO–LUMO

In regard to the origin of the PL emission in Si-NCs, it is still a subject of debate; however, we can find some proposals of models suggested explaining this phenomenon. One of this model relates the PL to quantum confinement effects (QCEs) [29, 30]. The other model relates the PL

Broadly, both common accepted proposals make use of approximated quantum methods in order to solve the Schrödinger equation associated with quantum confinement of the electron restricted to move in so small spatial dimensions, thence their predictions about luminescent phenomenon are limited. Considering this important fact, we hope that an analysis of this phenomenon made from the view point of composition and molecular structures can significantly contribute to a better knowledge of luminesce in SRO considered as an arrangement of

 **thin films**

Now, we proceed to our analysis in relationship to PL phenomenon. Inspecting, in **Figure 4(a)**,

two emission bands both covering a wide spectral range from 380 to 750 nm (from violet

= 1300°C, resulted with a bang gap of 1.95 eV,

film deposited at 1150°C corresponds

**GAP eV**

= 1.96 eV corresponding to Si16O16 one, existing the

molecule in accordance with **Table 1**.

**LUMO eV**

/Si-NCs [28, 31].

film as grown at *T*g

= 1.93 eV

= 900°C, we locate

**Figure 4.** (a) Experimental PL spectrum from a SiO*x* film grown at 900°C. (b) Theoretical PL spectrum calculated for Si16O16 structure.

To complement the study of the PL spectrum including annealing effects, in **Figure 5(b)** we display results for the theoretical PL spectrum calculated by considering a small molecule type Si6 O6 . With this molecular structure we predicted excited states emitting in the region from 393.78 to 415.59 nm in addition to a region peaked at 772.8 nm, which corresponds approximately to the left side of the wide shoulder observed in the experimental spectrum displayed in **Figure 8** where the de-convolution curve points out a peak at 749 nm. We emphasize that in this theoretical spectrum the presence of the peak at 820 nm found in the experimental PL spectrum is not clear.

In relation to the study of the configuration of the molecular structure, we present in **Figure 6(a)** the two structures corresponding to the case of the SiO*x* film as grown at *T*g = 900°C and after a further annealing **Figure 6(b)**, both structures correspond to

**Figure 5.** (a) Experimental PL spectrum from a SiOx film after a further annealing. (b) Theoretical PL spectrum correlated to the experimental one of (a), including the annealing effects. This spectrum is reproduced by means of considering the small molecule type Si6 O6 .

Si16O16 molecule. The structure at the top of the figure consists of 16 hydrogen atoms linked to eight silicon atoms with tetra valences forming the Si16O16:H16 arrangement. On the other hand, in the bottom we display the Si16O16 molecule after annealing. It could be described as a set of seven rings constituted of three member's mini rings each one with two bonds Si—O and a third link Si—Si. There are four mini rings with a semi-circular arrangement and the rest is in orthogonal position.

To complement the study of the PL spectrum including annealing effects, in **Figure 5(b)** we display results for the theoretical PL spectrum calculated by considering a small molecule type

*T*g = 900°C and after a further annealing **Figure 6(b)**, both structures correspond to

**Figure 6(a)** the two structures corresponding to the case of the SiO*x*

24 New Research on Silicon - Structure, Properties, Technology

**Figure 5.** (a) Experimental PL spectrum from a SiOx

O6 .

small molecule type Si6

. With this molecular structure we predicted excited states emitting in the region from 393.78 to 415.59 nm in addition to a region peaked at 772.8 nm, which corresponds approximately to the left side of the wide shoulder observed in the experimental spectrum displayed in **Figure 8** where the de-convolution curve points out a peak at 749 nm. We emphasize that in this theoretical spectrum the presence of the peak at 820 nm found in the experimental PL spectrum is not clear. In relation to the study of the configuration of the molecular structure, we present in

film as grown at

film after a further annealing. (b) Theoretical PL spectrum correlated

to the experimental one of (a), including the annealing effects. This spectrum is reproduced by means of considering the

Si6 O6

> Regarding the molecular structure proposed for molecule Si6 O6 :H8 (as grown), it is represented at the top of **Figure 6(c)**, whereas at **Figure 6(d)** we localize the corresponding molecule Si6 O6 after a further annealing. This molecule was proposed for modelling the SiO*x* film after being annealed at 900°C. The structure of this molecule consists only of three mini-rings, two of which are three member rings with two Si—O bonds and one Si—Si bond. The third ring has four silicon atoms with two Si—O bonds and a Si—Si—Si chain. Within the molecule as grown, that is Si6 O6 :H8 , the six silicon atoms have tetra valence.

> We now deal with the situation where the growth temperature of H8 SiO*x* film is increased. This implies that the molecular structure should be modified giving rise to another new one with different properties. In **Figure 7(a)**, we display the experimental PL spectrum measured from a SiO*x* film as grown at temperature of 1150°C.With the naked eye a wide band is identified at right hand and approximately half wide band at left side. Through de-convolution curves of this spectrum, we can locate the positions of maxima of both bands. The half wide band is peaked around 385 nm and the right band around 690 nm.

**Figure 6.** Molecular structure suggested for the SiO*x* film: (a) Si16O16:H16, as grown at Tg = 900°C (b) Si16O16 after a further annealing. Molecular structure proposed for modelling the SiO*x* film after being annealed at 900°C, (c) as grown is type Si6 O6 :H8 and (d) after annealed is type Si6 O6 .

Comparatively by **Figure 7(b)** we can observe the correlated theoretical PL spectrum calculated for Si11O11 molecule. With this molecular structure, we have predicted a PL spectrum having only two bands where the half left band possesses the highest intensity being peaked at 380 nm, and the other one with lower intensity and its maxima corresponds to an excited state of emission at 699 nm. In this case, we did not look for triplets for Si11 O11 molecule, taking for granted that if they exist they would have a negligible intensity.

Furthermore, the molecular structure suggested for Si11O11 molecule is represented in **Figure 8(a)** that corresponds to as grown molecule Si11O11:H12. In the arrangement of this structure we figure out that there are 12 hydrogen atoms joined to six silicon ones with tetra valence. The 'backbone of this molecule' is a silicon atom joined to four silicon atoms shaping a tetrahedral arrangement, with six mini rings constituted where five of them have four silicon atoms and two Si—O bonds each one and a Si—Si—Si chain. The sixth mini ring has only one Si—O bond and a large silicon chain Si—Si—Si—Si. **Figure 8(b)** represents the afterannealed condition for the molecular arrangement of Si11O11.

**Figure 7.** (a) Experimental PL spectrum of a SiOx film as grown at 1150°C. (b) Correlated theoretical PL spectrum of (a). In this case the SiOx film is modelled with a molecular structure of type Si11O11 molecule.

Theoretical and Experimental Characterization of Silicon Nanoclusters Embedded in Silicon-Rich Oxide Films http://dx.doi.org/10.5772/67614 27

**Figure 8.** Molecular structure suggested. (a) As grown it corresponds to Si11O11:H12 arrangement, (b) after annealed, the molecular arrangement is type Si11O11.

#### **3.5. FTIR spectra of the SiOx thin films**

Comparatively by **Figure 7(b)** we can observe the correlated theoretical PL spectrum calculated for Si11O11 molecule. With this molecular structure, we have predicted a PL spectrum having only two bands where the half left band possesses the highest intensity being peaked at 380 nm, and the other one with lower intensity and its maxima corresponds to an excited state of emission at 699 nm. In this case, we did not look for triplets for Si11 O11 molecule, tak-

Furthermore, the molecular structure suggested for Si11O11 molecule is represented in **Figure 8(a)** that corresponds to as grown molecule Si11O11:H12. In the arrangement of this structure we figure out that there are 12 hydrogen atoms joined to six silicon ones with tetra valence. The 'backbone of this molecule' is a silicon atom joined to four silicon atoms shaping a tetrahedral arrangement, with six mini rings constituted where five of them have four silicon atoms and two Si—O bonds each one and a Si—Si—Si chain. The sixth mini ring has only one Si—O bond and a large silicon chain Si—Si—Si—Si. **Figure 8(b)** represents the after-

film as grown at 1150°C. (b) Correlated theoretical PL spectrum of (a).

ing for granted that if they exist they would have a negligible intensity.

annealed condition for the molecular arrangement of Si11O11.

26 New Research on Silicon - Structure, Properties, Technology

**Figure 7.** (a) Experimental PL spectrum of a SiOx

film is modelled with a molecular structure of type Si11O11 molecule.

In this case the SiOx

In order to get a more complete evaluation of the optical and structural properties of SRO structures, we now proceed to make a theoretical analysis of Fourier Transform Infrared (FTIR) spectroscopy. In practice, FTIR is a technique used for structural characterization of materials with which it is possible to study atomic bonds between elements that are present in a given film. The various bonds are manifested as different absorption bands which lie in different wavelength ranges. The position and shape of these bands are related to the density, stoichiometry and the nature of the bond primarily. The infrared energy causes vibrational motion of atoms in a molecule identified as rocking, stretching, wagging and bending when they interact with such energy. A fraction of the incident radiation is absorbed at specific wavelengths. A molecule must vibrate so that there is a displacement from the electrical centre and absorbed radiation in the infrared region, that is, there must be a change in the dipole moment.

In **Figure 9(a)** we display the experimental FTIR spectrum of a SiO*x* film as grown at 900°C. According to Ay and Aydinly [33] they have associated these vibrational frequencies as indicated in **Table 2**. In such **Table 2**, we make comparisons between vibrational frequencies as found experimentally in **Figure 9(a)** and theoretical frequencies as obtained in this report when considering a Si16O16 molecule in addition to being identified with the different vibrational modes reported in literature. Particularly, the experimental frequencies at 654 and 875 cm-1, in **Figure 9(a)**, have been associated as reported in the literature to Si—H vibrational frequencies. Comparing these frequencies with those found by our theoretical calculations, we find discrepancies since we observed such frequencies at 652 and 885 cm−1 which are due to Si—Si and Si—O bonds.

Apart from discrepancies in their values between experimental and theoretical frequencies, we also find differences between their associated intensities as is evident from **Figure 9(a)**

when is compared with **Figure 9(b)**. Two very remarkable differences in their intensities are found in peaks located at 875 and 1051 cm−1 in the experimental FTIR spectrum and their correlated theoretical values located in **Figure 9(b)** approximately at 885 and 1058 cm−1, in fact, if we observe carefully theoretical and experimental intensities are inverted in magnitude.

On the other hand, we stress that plot in **Figure 9(b)** corresponds to a Gaussian curve fitted to FWHH = 40, whereas plot in **Figure 9(c)** corresponds to a Gaussian curve fitted to FWHH = 80. We can observe clearly that the difference in Full Width at Half Maximum (FWHH) values gives rise to the effect that the peak at 1058 cm−1 in **Figure 9(b)** is transformed into a shoulder of the peak at 885 cm−1 as is shown in **Figure 9(c)**. The effect of varying FWHH to higher values causes the FTIR spectrum to become more intense in **Figure 9(c)**, it means physically the SiO*x* film were thicker; in addition to this, FTIR spectrum resembles more to the experimental one of **Figure 9(a)** although discrepancies in wavenumbers continue to persist.

**Figure 9.** (a) Experimental FTIR spectrum from a SiOx film as grown at 900°C, (b) theoretical FTIR spectra calculated using DFT for a Si16O16 molecule with FWHH = 40. Vibrational frequencies found in this spectrum when are correlated to those of (a) show discrepancies. This plot corresponds to a Gaussian curved fitted to FWHH = 40 and (c) same as (b) but FWHH = 80.

Now, we consider important to study the influence of annealing process on FTIR spectra. For this, we focus on a SiO*x* thin film deposited at 900°C with a further annealing, normally carried out in the (1100–1150)°C range. **Figure 10** displays the experimental FTIR spectrum for this sample. It is worthwhile to mention that after the films have been heat-treated (annealed), the FTIR spectrum peaks corresponding or associated to Si**–**H vibrational frequencies disappear. Also, the uppermost peak which corresponds to Si**–**O stretching mode (1051 cm−1) is considerably shifted to higher frequencies (1082 cm−1) indicating a phase separation.

when is compared with **Figure 9(b)**. Two very remarkable differences in their intensities are found in peaks located at 875 and 1051 cm−1 in the experimental FTIR spectrum and their correlated theoretical values located in **Figure 9(b)** approximately at 885 and 1058 cm−1, in fact, if we observe carefully theoretical and experimental intensities are inverted in magnitude.

On the other hand, we stress that plot in **Figure 9(b)** corresponds to a Gaussian curve fitted to FWHH = 40, whereas plot in **Figure 9(c)** corresponds to a Gaussian curve fitted to FWHH = 80. We can observe clearly that the difference in Full Width at Half Maximum (FWHH) values gives rise to the effect that the peak at 1058 cm−1 in **Figure 9(b)** is transformed into a shoulder of the peak at 885 cm−1 as is shown in **Figure 9(c)**. The effect of varying FWHH to higher values causes the FTIR spectrum to become more intense in **Figure 9(c)**, it means physically the SiO*x* film were thicker; in addition to this, FTIR spectrum resembles more to the experimental one

film as grown at 900°C, (b) theoretical FTIR spectra calculated

using DFT for a Si16O16 molecule with FWHH = 40. Vibrational frequencies found in this spectrum when are correlated to those of (a) show discrepancies. This plot corresponds to a Gaussian curved fitted to FWHH = 40 and (c) same as (b)

of **Figure 9(a)** although discrepancies in wavenumbers continue to persist.

28 New Research on Silicon - Structure, Properties, Technology

**Figure 9.** (a) Experimental FTIR spectrum from a SiOx

but FWHH = 80.

It is possible then, for example, that a molecule like Si16 O16 can be transformed in a smaller molecule like Si11O11 or Si6 O6 (it depends mainly on time and annealing temperature). On the other hand, it has been reported that amorphous silicon (a-Si) as well as crystalline one (c-Si)

**Table 2.** Comparison of vibrational frequencies observed experimentally in a SiO*x* film as grown at 900°C versus calculated FTIR spectrum for a Si16O16 molecule.

**Figure 10.** Experimental FTIR spectrum from a SiOx thin film after further annealing.

could be identified by Raman spectroscopy [34]. A broadband around **∼**480 cm−1 is typically associated to a-Si, while bulk silicon has a sharp intensity peak around 521 cm−1. As to Si-NCs, it is found that intensity peaks are shifted to smaller wavenumbers where this change is a function of decreasing Si-NCs size, this event has been extensively attributed to quantum confinement effects.

For example, in **Figure 11** which corresponds to a theoretical Raman spectrum that we have calculated for a Si11O11 molecule suggested, we can clearly identify frequencies at 460 and 508 cm−1, respectively.

We have explained previously that the molecule Si11O11 has two chains, one is type Si—Si—Si and the other is a larger chain type Si—Si—Si—Si (tetragonal arrangement shape).

#### **3.6. PL spectra of porous silicon in SiOx thin films**

Keeping in mind that in SRO thin films the generation of porous silicon as a consequence of phase separation of Si-NCs/SiO*x* are present, as just mentioned in Section 1, its results are attractive as we apply our theoretical methods, used along the optical and structural analyses on SiOx structures, to get a major comprehension of the radiative mechanisms linked with the atomic arrangement of molecular structures which contribute to the PL in this type of films. So, hereafter we focus specifically on the study of porous silicon which was obtained by HFCVD technique by our experimental group (unpublished results). **Figure 12** shows photoluminescence spectra between 40 and 296 K. PL measurements were carried out in vacuum and the sample was excited with a 407 nm excitation light source and an incident power of about 60 mW/mm–2.

**Figure 11.** Theoretical Raman spectrum calculated for [Si11O11] configuration. We identify in the centre of figure the atomic structure and the left side inset displays the orbital energy in units of (eV).

**Figure 12.** Experimental porous silicon PL spectra at several temperatures.

could be identified by Raman spectroscopy [34]. A broadband around **∼**480 cm−1 is typically associated to a-Si, while bulk silicon has a sharp intensity peak around 521 cm−1. As to Si-NCs, it is found that intensity peaks are shifted to smaller wavenumbers where this change is a function of decreasing Si-NCs size, this event has been extensively attributed to quantum

For example, in **Figure 11** which corresponds to a theoretical Raman spectrum that we have calculated for a Si11O11 molecule suggested, we can clearly identify frequencies at 460 and 508 cm−1,

We have explained previously that the molecule Si11O11 has two chains, one is type Si—Si—Si

 **thin films**

Keeping in mind that in SRO thin films the generation of porous silicon as a consequence of

tive as we apply our theoretical methods, used along the optical and structural analyses on SiOx structures, to get a major comprehension of the radiative mechanisms linked with the atomic arrangement of molecular structures which contribute to the PL in this type of films. So, hereafter we focus specifically on the study of porous silicon which was obtained by HFCVD technique by our experimental group (unpublished results). **Figure 12** shows photoluminescence spectra between 40 and 296 K. PL measurements were carried out in vacuum and the sample was excited with a 407 nm excitation light source and an incident power of about 60 mW/mm–2.

**Figure 11.** Theoretical Raman spectrum calculated for [Si11O11] configuration. We identify in the centre of figure the

atomic structure and the left side inset displays the orbital energy in units of (eV).

are present, as just mentioned in Section 1, its results are attrac-

and the other is a larger chain type Si—Si—Si—Si (tetragonal arrangement shape).

confinement effects.

**3.6. PL spectra of porous silicon in SiOx**

30 New Research on Silicon - Structure, Properties, Technology

phase separation of Si-NCs/SiO*x*

respectively.

It is easily identified that the PL intensity increases as temperature decrease and at the same time the energy peak is shifted towards higher energies when decreasing the temperature of the sample. It can be seen that each peak is symmetric which means a good surface morphology and a material without defects. The shift towards higher energies is given at a rate of 5.85 E-4 eV/K. Because in our theoretical analysis neither the technique used to obtain the material nor the experimental process are relevant, since we make only use of atoms in a specific arrangement, more details about experimental conditions to grow the sample are not necessary.

In accordance with information given by PL spectra in **Figure 12**, we have that the energies of peaks of the spectra are contained approximately between 1.65 and 2.6 eV (475–750 nm). The highest intensity for each peak fit well with temperature by the following equation: *E*(eV ) = 2.16 36 − 0.000585 *T*(K ) for 40 K ≤ *T* ≤ 300 K. Likewise, we can calculate the wavelength of the peak, if its associated energy is known, by using the simple equation *λ*(nm) = 1240 eV. In order to make the correlation between experimental PL results and theoretical ones, we evaluated four isomers for Si18 agglomerates. These correspond to isomers identified as 18A, 18B, 18C and 18D from which isomer 18D did not achieve convergence, consequently, information about it is not available. **Table 3** contains information about isomer 18A, 18B and 18C. We can appreciate that isomer 18C is not the most stable because it has the highest energy. Contrary, the isomer Si18A (18A) possesses the lowest energy (a difference of 0.96 eV as indicated in third column) by this reason is the most stable of all. Other parameters of interest were calculated such as, the band gap, the dipole moment, the polarizability and the ovality.

**Table 3.** Parameters calculated for isomers Si18.

With regard to Si18 cluster, four low-lying isomers were considered. The elongated isomer 18A has the lowest-energy at the HF/6–31G\* level of theory. Moreover, the Isomer18A has its structure similar to the ground-state structure predicted by Rata et al. [35]. It contains a magic-number-cluster Si6 unit and a hexagonal chair unit. A slight structural perturbation to this C3V isomer followed by a geometry relaxation gives isomer 18B with CS symmetry. Both 18B and 18C with C2V symmetry contain tri-capped-trigonal-prism unit and are also very viable in stability compared to 18A because of the calculated difference in energy as 0.92 and 0.96 eV, respectively. Isomer 18D is a new isomer with high symmetry but relatively high energy. It is composed of two capped tetragonal anti-prisms, and we did not obtain convergence at HF/6-31G\* level of theory for this isomer. We also observe from **Table 3** the predicted wavelength of the highest emission intensity corresponding to each isomer under the following order: 552.447567 nm for 18A isomer, 692.813713 nm for isomer 18B and 1732.74488 nm for isomer 18C. With this latter information we will try to make the correlation with experimental results regards PL curves shown in **Figure 12** as far as possible.

Prior to making the correlation, firstly we find out the information given in **Figure 13**, there with the naked eye, we locate at the top of the figure the FTIR spectrum and at the bottom of the one the PL spectrum both correspond to silicon agglomerate Si18 calculated using DFT. In the PL spectrum the appearance of the uppermost intensity peak predicted at 679.9 nm is outstanding according to our theoretical approach. Taking into account this wavelength value and making use of the simple equation to get its corresponding energy value, as just mentioned above, we obtain 1.82379 eV. This energy value when located in the experimental PL spectrum in **Figure 12** has a position as indicated by the black vertical line. As can be seen this energy may be correlated in a good approximation to the lowest PL spectrum, which corresponds to a temperature of 296 K, since it is closer to its maximum.