**Abstract**

This chapter mainly introduces five basic stages of the film deposition process (vapor adsorption, surface diffusion, reaction between adsorbed species, reaction of film materials to form bonding surface, and nucleation and microstructure formation), analyzes the influence of deposition process parameters on the three basic growth modes of the film, focuses on the relationship between the control parameters of homoepitaxy and heteroepitaxy and the film structure, gives the dynamic characteristics of each growth stage, and examines the factors determining epitaxy film structure, topography, interfacial properties, and stress. It is shown that two-dimensional nucleation is a key to obtain high-quality epitaxial films.

**Keywords:** deposition, adsorption, diffusion, nucleation, epitaxy, dynamic characteristics

## **1. Introduction**

Epitaxial thin films and artificial multilayers are grown on solid single-crystal surfaces with atomic monolayer thickness control either by chemical vapor deposition (CVD) [1, 2] or by molecular beam epitaxy (MBE). In CVD, precursor molecules are thermally decomposed in a continuous flow oven in a background atmosphere of clean inert gas, whereas in MBE the surface is held in ultrahigh vacuum (UHV, 10<sup>8</sup> Pa). Controlling the growth morphology is a challenge in both fabrication techniques; it requires knowledge of both thermodynamics and of kinetics.

As with other thin films, epitaxial films can provide properties or structures that are difficult or impossible to obtain in bulk materials. Indeed, many materials are easier to grow epitaxially than to grow and shape in bulk form. Compared to polycrystalline films, epitaxial films have at least four advantages, which are elimination of grain boundaries, ability to monitor the growth by surface diffraction, control of crystallographic orientation, and the potential for atomically smooth growth.

Epitaxy is the special type of thin film deposition and is particularly demanding about all aspects of process control. Film quality is readily degraded by small amounts of contamination, nonstoichiometry, and lattice mismatch. On the other hand, when good control is achieved, complex multilayered structures with unique properties can be fabricated with atomic layer precision. Moreover, the precise structural and compositional nature of the epitaxial growth surface allows the use of growth monitoring techniques that give detailed information about film growth mechanisms on an atomic scale.

which later coalesce. SK growth is characterized as the formation of one or more layers upon which nucleation and growth dominate. FM growth or layer-by-layer growth is the growth mode that has our interest because of the well-ordered surfaces produced this way. To achieve layer-by-layer growth of atoms, instead of 3D growth, one must try to reduce the nucleation rate. This can be done by (1) reducing the pressure since it is believed that residual gases can create nucleation sites on the substrate surface, (2) increasing the substrate temperature which promotes the mobility of the atoms on the surface, or (3) reducing the deposition rate. RHEED can be used to verify the growth mode because oscillations of the intensity

Firstly, the heart of the thin film process sequence will be discussed. Deposition may be considered as six sequential substeps, and that will be examined one by one in the next section. The arriving atoms and molecules must first (1) adsorb on the surface, after which they often (2) diffuse some distance before becoming incorporated into the film. Incorporation involves (3) reaction of the adsorbed species with each other and the surface to form the bonds of the film material. The (4) initial aggregation of the film material is called nucleation. As the film grows thicker, it (5) develops a structure, or morphology, which includes both topography (roughness) and crystallography. A film's crystallography may range from amorphous to polycrystalline to single-crystal. The last is obtained by epitaxy—that is, by replicating the crystalline order of a single-crystal substrate. Epitaxy has special techniques and features which are also the focus of this chapter, and (6) diffusional interactions occur within the bulk of the film and with the substrate. These interactions are similar to those of post-deposition annealing, since they occur beneath the surface on which deposition is continuing to occur. Sometimes, after deposition, further heat treatment of a film is carried out to modify its properties. For example, composition can be modified by annealing in a vapor, and crystal growth can be achieved by long annealing or by briefly melting. These post-deposition techniques

The word "epitaxy" comes from the Greek word epi, which means "located on," while "taxis" means "arranged." Epitaxial growth refers to the registration or alignment of the crystal atoms in the single-crystal substrate into the single-crystal film. More precisely, if the atoms of the substrate material at the interface occupy the natural lattice position of the film material, the interface between the film and the substrate crystal is epitaxial, and vice versa. These two materials do not have to be the same crystal, but they are usually like this. When the film material is the same as the substrate material, the crystallographic registration between the film and the substrate is usually called uniform epitaxy. The epitaxial deposition of thin film

Epitaxial growth technology has important advantages in material manufacturing of microelectronic and optoelectronic applications. It can be used to prepare films with very good crystal quality. This also makes it possible to fabricate composite films with ideal electronic or optical properties that do not exist in nature. There are many factors that affect the selection of materials and processing methods for epitaxial growth. It includes the chemical compatibility of the film material and the substrate material; the magnitude of the energy band gap of the film material and its relationship with the energy band gap and the edge of the energy band of the substrate material; whether the minimum value of the conduction band energy and the maximum value of the valence band energy are in the same wave vector position is an important factor in optical applications; and the chemical compatibil-

In heteroepitaxial film growth, the substrate crystal structure provides a template for locating the atoms of the first arriving film material, and each atomic layer

materials different from substrate materials is called heteroepitaxy.

ity of the dopant applied to produce the required functional behavior.

indicate that layer-by-layer growth is occurring.

*Growth Kinetics of Thin Film Epitaxy*

*DOI: http://dx.doi.org/10.5772/intechopen.91224*

will not be discussed in this chapter.

**5**

The purpose of this chapter is to guide the new readers who have just entered this field. Based on the in-depth analysis of the main aspects of epitaxy technology by cross-referencing the relevant literature provided by experts, the research and development direction of epitaxy technology are evaluated. Epitaxy refers to the orderly growth of crystal materials on the substrate crystal and the establishment of a clear crystal relationship at the interface between the two crystal lattices. In homoepitaxy, the epitaxial layer and substrate are made of the same material, while in heteroepitaxy, they are made of different materials. If two materials have the same crystal structure, they are called similar, otherwise they are called different. In the epitaxial structure, the same lattice spacing between the epitaxial material and the substrate material in the same direction plane is called lattice matching, otherwise, lattice mismatch. At one growth site, the constituent atoms are bonded to the epitaxial film, in which the bonding leads to the unequal probability of the atoms' attachment and desorption in the equilibrium. Atoms bonded with energy higher than the growth site are considered to be part of the epitaxial film. All atoms bonded with less energy than the growth sites are called adatoms. In the region of relatively high temperature, the mobility of atoms is stronger, and they can aggregate into two-dimensional islands, thus forming a new surface step. The method of epitaxy can be divided into (1) solid phase epitaxy (SPE), (2) liquid phase epitaxy (LPE), and (3) vapor phase epitaxy (VPE). This chapter only discusses the growth kinetics of each stage, including gas adsorption, surface diffusion, interaction of adsorbed species, bonding of surface-forming film materials, and nucleation and microstructure formation of epitaxial growth, rather than specific epitaxial growth methods.

### **2. General description of epitaxial growth**

In the early study of thin films, it was found that the growth process of thin films is a complex process, including atom arrival, atom adsorption, diffusion/migration on the surface, nucleation, and coalescence. It was also found that four parameters influence the film growth: pressure, deposition rate, substrate temperature, and substrate structure. Also, the binding energy of the adsorbent to the substrate is of vital importance, but since this is not a controllable parameter, we will ignore it here. For metals adsorbed on insulator surfaces, we assume that every atom that impinges on the surface stays there. For other systems one may operate with a sticking coefficient, which is the probability of an atom sticking to the surface upon impingement. The adsorbed atoms can exhibit a complicated dynamical behavior at the surface: Atoms can move around on the corresponding surface, and they can diffuse into the substrate or even desorb from the substrate. When two atoms meet, they form metastable nuclei. This is referred to as nucleation. Nuclei can also split up, rotate, or migrate across the surface. At a certain critical size, the nuclei become stable, and this is where actual crystal growth begins. Initial film growth is categorized into three different types of behaviors. The three growth modes are called Volmer-Weber (VW), Stranski-Krastanov (SK), and Frank-van der Merwe (FM) [3]. **Figure 1** illustrates the different growth modes, which can be described as follows. For VW growth the growth is occurring as three-dimensional (3D) nuclei

#### **Figure 1.** *Illustration of the three different growth modes. Left: FM growth. Center: SK growth. Right: VW growth.*

#### *Growth Kinetics of Thin Film Epitaxy DOI: http://dx.doi.org/10.5772/intechopen.91224*

growth monitoring techniques that give detailed information about film growth

The purpose of this chapter is to guide the new readers who have just entered this field. Based on the in-depth analysis of the main aspects of epitaxy technology by cross-referencing the relevant literature provided by experts, the research and development direction of epitaxy technology are evaluated. Epitaxy refers to the orderly growth of crystal materials on the substrate crystal and the establishment of a clear crystal relationship at the interface between the two crystal lattices. In homoepitaxy, the epitaxial layer and substrate are made of the same material, while in heteroepitaxy, they are made of different materials. If two materials have the same crystal structure, they are called similar, otherwise they are called different. In the epitaxial structure, the same lattice spacing between the epitaxial material and the substrate material in the same direction plane is called lattice matching, otherwise, lattice mismatch. At one growth site, the constituent atoms are bonded to the epitaxial film, in which the bonding leads to the unequal probability of the atoms' attachment and desorption in the equilibrium. Atoms bonded with energy higher than the growth site are considered to be part of the epitaxial film. All atoms bonded with less energy than the growth sites are called adatoms. In the region of relatively high temperature, the mobility of atoms is stronger, and they can aggregate into two-dimensional islands, thus forming a new surface step. The method of epitaxy can be divided into (1) solid phase epitaxy (SPE), (2) liquid phase epitaxy (LPE), and (3) vapor phase epitaxy (VPE). This chapter only discusses the growth kinetics of each stage, including gas adsorption, surface diffusion, interaction of adsorbed species, bonding of surface-forming film materials, and nucleation and microstructure formation of epitaxial growth, rather than specific epitaxial growth methods.

In the early study of thin films, it was found that the growth process of thin films is a complex process, including atom arrival, atom adsorption, diffusion/migration on the surface, nucleation, and coalescence. It was also found that four parameters influence the film growth: pressure, deposition rate, substrate temperature, and substrate structure. Also, the binding energy of the adsorbent to the substrate is of vital importance, but since this is not a controllable parameter, we will ignore it here. For metals adsorbed on insulator surfaces, we assume that every atom that impinges on the surface stays there. For other systems one may operate with a sticking coefficient, which is the probability of an atom sticking to the surface upon impingement. The adsorbed atoms can exhibit a complicated dynamical behavior at the surface: Atoms can move around on the corresponding surface, and they can diffuse into the substrate or even desorb from the substrate. When two atoms meet, they form metastable nuclei. This is referred to as nucleation. Nuclei can also split up, rotate, or migrate across the surface. At a certain critical size, the nuclei become stable, and this is where actual crystal growth begins. Initial film growth is categorized into three different types of behaviors. The three growth modes are called Volmer-Weber (VW), Stranski-Krastanov (SK), and Frank-van der Merwe (FM) [3]. **Figure 1** illustrates the different growth modes, which can be described as follows. For VW growth the growth is occurring as three-dimensional (3D) nuclei

*Illustration of the three different growth modes. Left: FM growth. Center: SK growth. Right: VW growth.*

mechanisms on an atomic scale.

*21st Century Surface Science - a Handbook*

**2. General description of epitaxial growth**

**Figure 1.**

**4**

which later coalesce. SK growth is characterized as the formation of one or more layers upon which nucleation and growth dominate. FM growth or layer-by-layer growth is the growth mode that has our interest because of the well-ordered surfaces produced this way. To achieve layer-by-layer growth of atoms, instead of 3D growth, one must try to reduce the nucleation rate. This can be done by (1) reducing the pressure since it is believed that residual gases can create nucleation sites on the substrate surface, (2) increasing the substrate temperature which promotes the mobility of the atoms on the surface, or (3) reducing the deposition rate. RHEED can be used to verify the growth mode because oscillations of the intensity indicate that layer-by-layer growth is occurring.

Firstly, the heart of the thin film process sequence will be discussed. Deposition may be considered as six sequential substeps, and that will be examined one by one in the next section. The arriving atoms and molecules must first (1) adsorb on the surface, after which they often (2) diffuse some distance before becoming incorporated into the film. Incorporation involves (3) reaction of the adsorbed species with each other and the surface to form the bonds of the film material. The (4) initial aggregation of the film material is called nucleation. As the film grows thicker, it (5) develops a structure, or morphology, which includes both topography (roughness) and crystallography. A film's crystallography may range from amorphous to polycrystalline to single-crystal. The last is obtained by epitaxy—that is, by replicating the crystalline order of a single-crystal substrate. Epitaxy has special techniques and features which are also the focus of this chapter, and (6) diffusional interactions occur within the bulk of the film and with the substrate. These interactions are similar to those of post-deposition annealing, since they occur beneath the surface on which deposition is continuing to occur. Sometimes, after deposition, further heat treatment of a film is carried out to modify its properties. For example, composition can be modified by annealing in a vapor, and crystal growth can be achieved by long annealing or by briefly melting. These post-deposition techniques will not be discussed in this chapter.

The word "epitaxy" comes from the Greek word epi, which means "located on," while "taxis" means "arranged." Epitaxial growth refers to the registration or alignment of the crystal atoms in the single-crystal substrate into the single-crystal film. More precisely, if the atoms of the substrate material at the interface occupy the natural lattice position of the film material, the interface between the film and the substrate crystal is epitaxial, and vice versa. These two materials do not have to be the same crystal, but they are usually like this. When the film material is the same as the substrate material, the crystallographic registration between the film and the substrate is usually called uniform epitaxy. The epitaxial deposition of thin film materials different from substrate materials is called heteroepitaxy.

Epitaxial growth technology has important advantages in material manufacturing of microelectronic and optoelectronic applications. It can be used to prepare films with very good crystal quality. This also makes it possible to fabricate composite films with ideal electronic or optical properties that do not exist in nature. There are many factors that affect the selection of materials and processing methods for epitaxial growth. It includes the chemical compatibility of the film material and the substrate material; the magnitude of the energy band gap of the film material and its relationship with the energy band gap and the edge of the energy band of the substrate material; whether the minimum value of the conduction band energy and the maximum value of the valence band energy are in the same wave vector position is an important factor in optical applications; and the chemical compatibility of the dopant applied to produce the required functional behavior.

In heteroepitaxial film growth, the substrate crystal structure provides a template for locating the atoms of the first arriving film material, and each atomic layer of the film material provides the same function for the next layer formed by FM growth, as described in the previous section. If the substrate is a single crystal with good quality and the vapor supersaturation is moderate, the atoms have a high mobility on the growth surface; this is a common growth mode. If the lattice parameter mismatch is not too large, for example, it is less than 0.5%, the growth tends to plane. If the mismatch is large, the material tends to gather on the surface of the island, but remains epitaxial.

Plane growth is carried out by attaching atoms to the edge of the step, which causes the step to move on the growth surface. Generally speaking, the unstressed lattice size of the thin film material in the direction parallel to the interface, such as *af* , will be different from the lattice size of the substrate, such as *as*; this difference may be as high as a few percent. However, the atomic position of the thin film material is consistent with that of the substrate, and the atomic structure of the thin film material is maintained. The thin film material bears any necessary strain along the interface, which makes it possible. In terms of lattice parameters, this mismatch strain is:

$$\mathfrak{e}\_m = \frac{\mathfrak{a}\_s - \mathfrak{a}\_f}{\mathfrak{a}\_f} \tag{1}$$

cost of adding strain material is easily offset by the energy gain associated with the potential chemical bonding effect in the process. This can be proved by a simple

Take a simple comparison of different forms of energy. Both the elastic energy and the bonding energy can be compared with *kTs* (Boltzmann constant times the absolute temperature of the substrate). This quantity is an indicator of the average energy per adatom in the substrate. At a typical deposition temperature of 800 K, the value of *kTs* is about 0.07 eV. Interestingly, this value is one order of magnitude smaller than the bond energy estimate, but one order of magnitude larger than the elastic energy estimate. Although these are rough estimates, the calculation is

argument, which only depends on the familiar block parameter value.

**3. Dynamic characteristics of each stage of epitaxial growth**

In this section, the factors controlling the early growth of thin films on the substrate are described from the perspective of atomism. This process starts with a clean surface of the substrate, which at a temperature of *Ts* is exposed to the vapor of the chemically compatible film material, which is at a temperature of *Tv*. In order to form a single-crystal film, the film material atoms in the vapor must reach the substrate surface, adhere to it, and locate a possible equilibrium position before the structural defects remain in the growth front. On the other hand, in order to form amorphous films, it is necessary to prevent atoms from reaching the growth surface to obtain a stable equilibrium position. In both cases, this must occur in a more or less identical way over a very large area of the substrate surface for structural development. At first glance, the result seems unlikely, but such films are made as usual. The atoms in the vapor touch the surface of the substrate, where they form chemical bonds with the atoms in the substrate. The idea that the temperature of the substrate must be sufficiently low so that the vapor phase is in a sense supersaturated with respect to the substrate will make the following more specific. In the process of adhesion, energy is reduced due to the formation of bond. As shown in the diagram in **Figure 3**, if the energy generated due to thermal fluctuation is enough to overcome the adhesion energy occasionally, some parts of the adhesion atom (called the adsorption atom) can be returned to vapor by evaporation.

**3.1 The process from vapor to adatoms**

*Growth Kinetics of Thin Film Epitaxy*

*DOI: http://dx.doi.org/10.5772/intechopen.91224*

instructive.

**Figure 3.**

**7**

*Schematic showing the atomistics of film formation on substrates.*

The definition of mismatch strain in Eq. (1) is consistent with the standard definition of tensile elastic strain of material in the state of no stress. Sometimes we use the denominator of *as* instead of *af* to measure the lattice mismatch. In this case, the value of the mismatch strain is slightly different. The definition in Eq. (1) is consistent with the concept of tensile strain, i.e., the change of material element length relative to the initial length, which will be used in all cases here. The process of epitaxial film growth is shown schematically in **Figure 2**. Although this process will lead to the potential large elastic strain in the film, for very thin film, the energy

#### **Figure 2.**

*Schematic illustration of heteroepitaxial film growth with lattice mismatch. The substrate thickness is presumed to be large compared to film thickness, and the structure extends laterally very far compared to any thicknesses. Under these circumstances, the lattice mismatch is accommodated by elastic strain at the deposited film.*

#### *Growth Kinetics of Thin Film Epitaxy DOI: http://dx.doi.org/10.5772/intechopen.91224*

of the film material provides the same function for the next layer formed by FM growth, as described in the previous section. If the substrate is a single crystal with good quality and the vapor supersaturation is moderate, the atoms have a high mobility on the growth surface; this is a common growth mode. If the lattice parameter mismatch is not too large, for example, it is less than 0.5%, the growth tends to plane. If the mismatch is large, the material tends to gather on the surface

Plane growth is carried out by attaching atoms to the edge of the step, which causes the step to move on the growth surface. Generally speaking, the unstressed lattice size of the thin film material in the direction parallel to the interface, such as *af* , will be different from the lattice size of the substrate, such as *as*; this difference may be as high as a few percent. However, the atomic position of the thin film material is consistent with that of the substrate, and the atomic structure of the thin film material is maintained. The thin film material bears any necessary strain along the interface, which makes it possible. In terms of lattice parameters, this mismatch

> *<sup>ϵ</sup><sup>m</sup>* <sup>¼</sup> *as* � *af af*

The definition of mismatch strain in Eq. (1) is consistent with the standard definition of tensile elastic strain of material in the state of no stress. Sometimes we use the denominator of *as* instead of *af* to measure the lattice mismatch. In this case, the value of the mismatch strain is slightly different. The definition in Eq. (1) is consistent with the concept of tensile strain, i.e., the change of material element length relative to the initial length, which will be used in all cases here. The process of epitaxial film growth is shown schematically in **Figure 2**. Although this process will lead to the potential large elastic strain in the film, for very thin film, the energy

*Schematic illustration of heteroepitaxial film growth with lattice mismatch. The substrate thickness is presumed to be large compared to film thickness, and the structure extends laterally very far compared to any thicknesses. Under these circumstances, the lattice mismatch is accommodated by elastic strain at the deposited film.*

(1)

of the island, but remains epitaxial.

*21st Century Surface Science - a Handbook*

strain is:

**Figure 2.**

**6**

cost of adding strain material is easily offset by the energy gain associated with the potential chemical bonding effect in the process. This can be proved by a simple argument, which only depends on the familiar block parameter value.

Take a simple comparison of different forms of energy. Both the elastic energy and the bonding energy can be compared with *kTs* (Boltzmann constant times the absolute temperature of the substrate). This quantity is an indicator of the average energy per adatom in the substrate. At a typical deposition temperature of 800 K, the value of *kTs* is about 0.07 eV. Interestingly, this value is one order of magnitude smaller than the bond energy estimate, but one order of magnitude larger than the elastic energy estimate. Although these are rough estimates, the calculation is instructive.
