Section 1 Thin Films

#### **Chapter 1**

## Preparation and Characterization of Thin Films by Sol-Gel Method

*Ehsan Rahmani*

#### **Abstract**

The sol-gel method has been widely used to prepare several materials, such as glass fibers, catalysts, electrochemical devices, or thin films. Sol-gel is considered an economical and straightforward method compared to physical vapor deposition (PVD) or chemical vapor deposition (CVD), which are more complex and need more facilities. At the same time, almost the same quality has been evaluated for sol-gel thin films. Furthermore, chemical tailoring of raw materials to produce new functional compositions is more feasible than conventional methods such as PVD. Thin films utilizing solgel were prepared by dip coating, spin coating, electrochemical coating, and spray coating methods, where these methods can be used for various substrate types. Prepared thin films may be utilized in several areas of application, such as semiconductors, catalysts, or photocatalysts.

**Keywords:** thin film, sol-gel, electrodeposition, dip coating, spin coating, spray coating, characterization

#### **1. Introduction**

Sol-gel processing began by Ebelman and Graham, who studied silica gels as early as the mid-1800s. Hydrolysis of tetraethyl orthosilicate (TEOS), Si(OC2H5)4, under acidic conditions, yielded SiO2; these early investigators observed that it was in the form of a "glass-like material" [1].

Sol-gel method can be implemented in several fields of scientific and engineering fields, such as the ceramic industry, nuclear industry, and the electronic industry or the development of new materials for catalysis, membranes, chemical sensors, photochromic applications, fibers, optical gain media, and solid-state electrochemical devices [2–13]. Thin film and powder catalysts have been widely produced using the sol-gel method. Several variants and manipulations have been implemented into the process to synthesize pure thin films or powders in large homogeneous concentrations and under stoichiometry control [14–16]. Process simplicity, optical complex shapes, uniform oxide complexes, special shapes of fibers and aerogels, synthesis of amorphous minerals, synthesis of porous material with high content of organic and polymeric compounds, and synthesis of highly optical transparent or low initial investment are the most advantages of the sol-gel method [17–19].

The term sol is attributed to a stable suspension containing colloidal nanoparticles (with diameters of 1–100 nm). The sol may contain amorphous or crystalline particles with dense, porous, or polymeric substructures [20, 21].

A rigid network with pores of sub-micrometer dimensions and polymeric chains whose average length is greater than a micrometer has been considered a gel [22]. A diversity of combinations of substances embraced as the "gel" can be classified into four categories: (1) structures of well-ordered lamellar; (2) networks of covalent polymer that is completely disordered; (3) formation of predominantly disordered through physical aggregation of polymer networks, (4) disordered particular structures [23–25].

The gel is attributed to a porous three-dimensional continuous solid network surrounding and supporting a continuous liquid phase. Synthesis of oxide materials and gelation is because of covalent bond formation between the sol particles [26, 27]. Gel formation can be reversed due to the presence of van der Waals interactions or hydrogen bonds. The gel structure network is dependent on the size and shape of the sol particles to a large extent [28].

#### **2. Preparation of thin film by sol-gel method**

Sol-gel monoliths have been prepared by three approaches: method 1, colloidal powders solution; method 2, alkoxide or nitrate precursors hydrolysis and polycondensation followed by hypercritical drying of gels; method 3, aging and drying of alkoxide precursors under ambient atmospheres after hydrolysis and polycondensation [29, 30].

The hydrolysis and condensation reactions (sol-gel process) would be influenced by several parameters, such as the metal alkoxide activity, solution pH, ratio of the water/alkoxide, temperature, solvent nature, and additive used. The addition of catalysts controls the rate, hydrolysis extent, and condensation reactions. By varying processing parameters, materials with different microstructures and surface chemistry can be obtained [31]. The fabrication of ceramic materials in various forms would be available by further processing the "sol." By casting the sol into the mold, a wet gel will form. Dense ceramic or glass particles will form, followed by drying and heat treatment of the gel [32]. Meanwhile, highly porous and low-density aerogel material is synthesized utilizing supercritical conditions to remove the liquid in a wet gel. Many natural systems like opals, agates, and particles are evidence of silicate hydrolysis and condensation to form polysilicate gel. Ebelman prepared the first metal alkoxide from SiCl4 and alcohol and found the first "precursor" for glassy materials can be Si-(OC2H5)4 and gelled compound on exposure to the atmosphere [33].

Step 1: Hydrolysis : Si OR ð Þ<sup>4</sup> <sup>þ</sup> H2O \$ SiOH OR ð Þ<sup>3</sup> <sup>þ</sup> <sup>R</sup>�OH (1)

Step 2: ð Þ Water condensation : SiOH OR ð Þ<sup>3</sup> þ SiOH OR ð Þ<sup>3</sup> \$ ½ � Si 2O OR ð Þ<sup>6</sup> þ H2O ð Þ Alcohol condensation : SiOH OR ð Þ<sup>3</sup> <sup>þ</sup> Si OR ð Þ<sup>3</sup> \$ ½ � Si 2O OR ð Þ<sup>6</sup> <sup>þ</sup> <sup>R</sup>�OHÞ┤ (2)

#### **2.1 Electrochemical aided deposition (EAD)**

Dip coating, spin coating, and spraying methods are usually used to prepare sol-gel films. Only flat surfaces can be coated by dip coating and spin coating, while the rheology of the precursor and fine-tuning must be considered for the spray coating

#### *Preparation and Characterization of Thin Films by Sol-Gel Method DOI: http://dx.doi.org/10.5772/intechopen.113722*

method. Sol-gel thin film preparation implementing the electrochemical deposition technique has been considered in the last two decades. Woo et al. applied this technique for preparing silane films as binders [34]. Electrodeposition of silane-based films and proposed its mechanism later studied by Shacham et al. [35]. Preparation of coatings on conductive materials based on the sol-gel principle utilizing EAD is a recently developed method, and thicker and rougher sol-gel films can be prepared by this method. Application of negative potential and in-situ catalysis of sol-gel chemistry (hydrolysis and condensation reactions) are the basic principles of EAD. Reduction of oxygen or some specific ions supporting the electrolyte or hydrolysis, which leads to an increase in pH value near the electrode, would accelerate the immediate condensation of the solute on the electrode surface. Equation (3) expressed the chemical reaction in this process [36],

$$\text{O}\_2 + 2\text{H}\_2\text{O} + 4\text{e} \to 4\text{OH}^{-(3)} \tag{3}$$

During the electrodeposition process, the pH value of the bulk solution does not change, and no new materials are introduced; the silane component does not lose or gain electrons at the electrode surface. Electrodeposited films have several unique advantages compared to conventional self-assembled films [37]:


Coatings on complex non-planar geometries and controlling the thickness and composition of the nanocomposite are the significant advantages of depositing utilizing EAD (**Figure 1**).

**Figure 1.** *Electrochemical deposition of a sol-gel film [36].*

#### **2.2 Dip coating method**

Sol-gel dip coating consists of depositing a solid film by withdrawing a substrate from a sol: gravitational draining and solvent evaporation, followed by further condensation reactions. Sol-gel dip coating, compared to methods such as chemical vapor deposition (CVD), evaporation, or sputtering, does not require complex equipment and is potentially less expensive than conventional thin film-forming processes [38]. The ability to tailor the microstructure of the deposited film is the most crucial advantage of sol-gel over conventional coating methods.

The substrate from the liquid bath is drawn vertically at a speed of *U*o. By entraining the moving substrate, the liquid in a fluid mechanical boundary layer may separate above the liquid bath surface, and the outer layer returns to the bath. The fluid film terminates at a well-defined drying line by solvent evaporating and draining. The process is steady with respect to the liquid bath surface when the receding drying line velocity equals *U*o.

The concomitant draining, evaporation, and hydrolysis consolidation step represents the sol-gel transition. An integrated gel film will be left due to a withdrawn drying line moving downwards with colorful parallel interference lines. By implementing volatile solvents, in comparison to the bulk sol-gel process, the complete transition will be done in a short time. The drying and keeping of the water content are almost constantly enhanced due to the evaporation and the resulting cooling. In addition, over the surface of the wet film, a downward laminar flow of vapors forms. Inhomogeneities deposition in the film properties may occur by any turbulence or variation in the atmosphere (**Figure 2**).

A fluid mechanical equilibrium between the entrained film and the receding coating liquid is the film formation process. The equilibrium state will be affected by forces such as viscous drag and the gravity force and other forces like the surface tension, the inertial force, or the disjoining pressure.

The Landau-Levich equation describing the final liquid film thickness *h* for pure liquids considers this fundamental theoretical approach [40],

$$h = c \cdot \frac{\left(\eta U\right)^{2/3}}{\eta^{\frac{1}{6}} (\rho \mathbf{g})^{\frac{1}{3}}}\tag{4}$$

where *c*, *η*, *U*, *y*, and *ρ* are constant, liquid viscosity, withdrawal speed, the surface tension of the liquid against air, and liquid density, respectively.

Modified dip coating techniques can be used for more complex geometries, although this method is particularly suited for coating flat or rod-shaped rigid substrates [41]. A semi-continuous dip coating process for endless flexible substrates like webs or filaments, while dip coating is a typical batch process. Double-sided coating of flat substrates, especially in the production of optical filters, is one of the advantages of the dip coating method. For oxide coatings prepared from the metal salt solution, a single-layer film thickness can be deposited ranging from only a few nanometers to approximately 200 nm. With inorganic-organic hybrid materials, due to the lower shrinkage and the higher flexibility of the network film, several microns are accessible, and colloidal systems can be implemented to produce thicker films up to 1 μm.

The high-volume industrial production of ordinary optical filters using the dip coating technique. Three-layer antireflection coatings for technical glasses (e.g., displays and lighting) form the largest market segment. Dip coating methods have been implemented by several industrial brands such as the TiOr-based solar-control glass Calorex® (Irox®) and the antireflection coatings Amiran®, ConturanQ, and Mirogard®Several and well-known products emerged from these activities [41].

#### **2.3 Spin coating method**

The spin coating can rapidly deposit thin layers onto relatively flat substrates. The target surface is dispensed by coating solution; the spinning action causes the solution to spread out and leave behind the coated surface of the substrate by the chosen material very uniformly that is held by some rotatable fixture (often using a vacuum to clamp the substrate in place).

The viscous drag force precisely balances the rotational accelerations within the solution. Emslie, Bonner, and Peck (EBP) [I] first described this flow condition. Simultaneously, solvent evaporation out of the top surface of the solution is also considered by Meyerhofer [42]. Spin coating runs into two stages: viscous flow controlling and evaporation controlling. Prediction of the final coating thickness, *h*f, in terms of several key solution parameters, is according to [42]:

$$h\_f = \varkappa \left(\frac{e}{2(1-\varkappa)K}\right)^{\frac{1}{f}}\tag{5}$$

where *e*, *K*, and *x* are the solution's evaporation and flow constants and effective solids content, respectively. The evaporation and flow constants are defined as:

$$
\sigma = \mathbb{C}\sqrt{\alpha} \tag{6}
$$

$$K = \frac{\rho \alpha^2}{3\eta} \tag{7}$$

**Figure 3.**

*Procedure for spin coating method [43].*

where *ω*, *ρ*, *η*, and *C* denote the rotation rate, solution's density, viscosity, and a proportionality constant. In which *C* depends on airflow flow regime (laminar or turbulent) and solvent molecules diffusivity in air. Sol-gel film preparation by spin coating deposition typically results in a coating thickness below 1 μm (**Figure 3**).

#### **2.4 Spray coating method**

Spray coating is suitable for non-flat samples, and the thickness can be very well controlled and surface modification over large areas. Only a few studies have studied sol-gel spray coating.

Most of the previously reported research has considered the sol-gel dip coating method low-cost and accessible. However, it is not easy to control the homogeneity and thickness of the coating over the entire sample length in the case of dip coating. Furthermore, spray coating is suitable for non-flat samples, and the thickness can be very well controlled, a better alternative as it allows surface modification over large areas. A threestep process is a typical example of an organically modified silica hydrophobic coating prepared by spraying: (1) preparation of hydrophobic alcosol, (2) alcosol spraying on 100°C glass substrates, and (3) trimethylchlorosilane surface modification created by Mahadik et al. [44]. Due to low cost and lack of specialized equipment, traditional spray coating is still the most often reported method. At the same time, there are other procedures, including spray coating with plasma, thermal spray, and powder [45–47].

#### **3. Characterization techniques**

#### **3.1 Thin film X-ray diffraction**

Thin films have been considered the basic materials for modern electronic devices of metallic conductors, semiconductors, and insulators. These films should possess specific mechanical, electrical, magnetic, or optical properties for optimal device performance, which are affected strongly by the film's microstructural nature, such as crystalline or amorphous state, crystallographic orientation, crystallite size, strains, and stresses [48, 49]. Therefore, for the design and improvement of electronic devices, it is very important to characterize microstructural thin films.

The microstructure of thin films cannot be easily characterized by methods developed for bulk materials due to their small dimensions perpendicular to the surface. X-ray diffraction (XRD) is especially suitable for thin films since it is nondestructive, noncontact, and highly quantitative among the analytical methods.

*Preparation and Characterization of Thin Films by Sol-Gel Method DOI: http://dx.doi.org/10.5772/intechopen.113722*

**Figure 4.** *XRD pattern for prepared sol-gel dip coating thin film (a) amorphous TiO2:SiO2 and (b) highly crystalline TiO2: SiO2.*

By implementing the XRD test, several thin film features can be evaluated. **Figure 4** indicates XRD patterns of highly crystalline and amorphous films prepared by the sol-gel dip coating method [50], where results indicate the formation of an amorphous TiO2:SiO2 thin film (**Figure 4a**) and a highly crystalline TiO2:SiO2 (**Figure 4b**) thin film on a glass substrate. XRD results revealed that TiO2 crystals may not be grown by an increase in SiO2 content of more than 20 mol percent, while highly crystalline TiO2 has formed on the glass substrate by a lower content of SiO2 (about 15 mol%). Furthermore, by addition of SiO2 crystalline size and crystallinity of TiO2 declined, where Scherrer or Modified Scherrer equations have been used to evaluate the crystalline size according to XRD pattern and full width at half maximum (FWHM, *β*) calculation [51]:

$$D = \frac{K\lambda}{\beta \cos(\theta)}\tag{8}$$

Or modified Scherrer equation,

$$
\ln \beta = \ln \frac{K\lambda}{L} + \ln \frac{1}{\cos \theta} \tag{9}
$$

In addition, the crystalline phase of the synthesized thin film can be indicated by considering XRD results. **Figure 5** illustrate the XRD pattern of TiO2 nanocrystalline thin film prepared by different heat treatment. As shown, with an increase in

**Figure 5.** *Phase transmission of TiO2 from Anatase to Brookite Phase [52].*

temperature, the crystalline phase has been transformed from Anatase to Brookite phases. TiO2 can be prepared in three phases by different heat treatment methods, where there is the Anatase phase at a heat treatment temperature below 500°C. In contrast, the Rutile phase will form around 500–750°C, and the Brookite phase formation temperature is approximately 750–900°C.

#### **3.2 Energy dispersive x-ray spectroscopy (EDX)**

Investigation of the chemical species present in a material can be evaluated by energy-dispersive X-ray spectroscopy as a powerful technique. Analysis of the energy and intensity distribution of the X-ray signal produced by the interaction of an electron beam with a specimen has been considered the basis of the EDX method. Directed an electron beam toward the sample has been analyzed in a setup that EDX is an optional tool installed on electron microscopes. The electrons can interact with the nucleus or a specific atom's electrons by certain kinetic energy. The detection of the emitted radiation due to the loss of any amount of energy of electrons between zero and the initial energy will lead to a continuous electromagnetic spectrum that constitutes the background of the collected spectrum [53].

Ionization phenomena usually involve K shell electrons when the primary electrons interact with the atom's electrons. The electrons from L or M shells can occupy the vacancy left by the K shell electron because an atom in the excited state tends to reach the minimum energy. X-ray radiation emission is designated as *K*α, and *K*<sup>β</sup>

*Preparation and Characterization of Thin Films by Sol-Gel Method DOI: http://dx.doi.org/10.5772/intechopen.113722*

**Figure 6.** *EDX results for prepared TiO2:SiO2 thin film by dip coating sol-gel method [50].*

results from a transition between L and K or M and K shells. The emission of *K*<sup>α</sup> and *K*<sup>β</sup> X-rays identifies the elements in the analyzed sample because of the energy difference between L, M, and K levels that are well-defined for each element. In principle, a line in the continuous electromagnetic spectrum should be given by the detection of this transition level [54].

**Figure 6** shows EDX results for TiO2:SiO2 thin film coated on the glass substrate, where indicated the presence of Ti, Si, and O in the film. Also, the EDX test revealed the presence of Na, Mg, and Ca that can be related to the glass substrate due to the passing of the X-ray over the prepared thin film and the detection of glass substrate elements. EDX test can be used for mapping and evaluating the synthesized film's elements distribution.

#### **3.3 X-ray photoelectron spectroscopy**

X-ray photoelectron spectroscopy (XPS) is widely implemented in surface science techniques—an X-ray based on the photoelectric effect photon absorbed by a core or valence electron. The electron will be emitted by the larger incident photon energy than the binding energy [55]. A hemispherical electron energy analyzer spectrometer collected the emitted electrons by an electrostatic lens and performed energy analysis. The binding energy Ek of the electrons can be determined from the known photon energy *hν* and the measured kinetic energy *E*<sup>B</sup> [56],

$$E\_{\mathbf{k}} = h\nu - E\_{\mathbf{B}} - \phi \tag{10}$$

with *ϕ* as the spectrometer work function. In an XPS experiment, typical incident photon energies range from several 10s to well over 1000 eV, where the same order of kinetic energies will be considered.

The X-ray penetration depth into the sample is of the order of hundreds of nanometers or more, while the kinetic energy range used in conventional XPS studies, atoms in the sample photoelectrons elastic and inelastic interactions limited to the probe depth to a maximum of a few nanometers.

A variety of features is shown in the XPS survey spectrum in **Figure 7a**, where results indicate photoemission lines of Ga (Ga 2p1/2, Ga 2p3/2, Ga3s, Ga3p, and Ga 3d), Fe (Fe 2p1/2, Fe 2p3/2, and Fe 3p), and oxygen (O 1 s). The spin-orbit components of Ga 2p3/2 and 2p1/2 have been indicated by splitting 26.9 eV, along with a loss

#### **Figure 7.**

*GFO thin films XPS analysis, (a) different photoemissions features; (b) Ga2p core-level; (c) O1s core-level; (d) Fe2p core-level [57].*

feature at around 1136 eV Ga2p (**Figure 7b**). In addition, Ga is in a +3 oxidation state confirmed by Ga 2p3/2 peak position at 1118 eV, which is characteristic of native gallium oxide [57].

Lattice-bound oxygen is assigned by the O 1 s spectrum (**Figure 7c**) centered at 530.01 eV, while surface hydroxyl and carbonylated groups are attributed to the other contributions. The component with the most intense in 2p3/2 is at 710.8 eV, with a 13.5 eV splitting from the 2p1/2 component consistent with a Fe+3 oxidation state.

#### **3.4 Atomic force microscopic method**

An amazing technique with unprecedented resolution and accuracy is atomic force microscopy (AFM), which allows us to see and measure surface structure. The arrangement of individual atoms in a sample or the structure of individual molecules can be studied by atomic force microscope imaging. The hopping of individual atoms from a surface has been measured by scanning in an ultrahigh vacuum at cryogenic temperatures. However, even seeing biological reactions occur in real-time can be carried out in physiological buffers at 37°C. AFM does not need to be carried out under these extreme conditions [58, 59]. The crystallographic structure of materials can be used to have images containing only 5 nm of microscopic images to show about 50 atoms, or 100 μm or larger images. Almost any sample, such as the surface of a

**Figure 8.** *AFM image for TiO2:SiO2 thin film prepared by sol-gel method [61].*

ceramic material, highly flexible polymers, human cells, a dispersion of metallic nanoparticles, or individual molecules of DNA, can be imaged by AFM, but it is challenging [60]. Furthermore, AFM has various "spectroscopic" modes that measure other properties of the sample at the nanometer scale. A map of the height or topography of the surface building up as scanning a probe of the AFM goes along the sample surface.

**Figure 8** illustrates the AFM image of a synthesized 15-layer TiO2:SiO2 thin film prepared by the sol-gel method. The roughness of the prepared TiO2:SiO2 thin film has been presented in **Figure 5**, while this roughness belongs to the crystalline formation of TiO2 in the presence of amorphous SiO2. In this work, TiO2:SiO2 gel was coated on a wall of an annular photoreactor to remove oily contamination from wastewater. However, according to AFM results, TiO2:SiO2 thin film roughness has been measured as 16 nm, where the film's roughness is necessary to have proper contact between the reactant and catalyst [61].

#### **3.5 Scanning electron microscope**

The scanning electron microscope (SEM) has studied surface details of several compositions, such as metals, rock minerals, polymers, corrosion deposits, filters, ceramic membranes, foils, fractured/rough surfaces, alloys, and biological samples. Conductive or non-conductive material, either in solid or powder form, can be examined in an as-received or prepared condition by SEM technique [62, 63]. A field emission gun is installed on the SEM to investigate surface features only 1 nm apart. SEM allows large areas of a sample to remain in focus at one time, yielding 3D characteristics due to its extraordinary ability to depict large depths of field.

The performance of an electron source is expressed by two essential parameters: current density and brightness. Beam current density *J*<sup>b</sup> is given as [64]:

$$J\_{\rm b} = \frac{\text{Beam current}}{\text{Area}} = \frac{i\_{\rm b}}{\pi} \tag{11}$$

where *i*<sup>b</sup> and *d* are the current and diameter of the beam, respectively, the brightness (*β*) of the electron source would be considered as a function of the total number of electrons (current, *I*) emitted from a unit area (*A*) of the source and the solid angle (Ω) of emission subtended by those electrons. This relationship can be expressed as follows [65]:

$$\beta = \frac{\text{Current}}{\text{area} \times \text{soldangle}} = \frac{I}{A\Omega} = \frac{j\_\text{c}}{\pi a^2} \tag{12}$$

where *j*<sup>c</sup> and *α* are the current density (expressed in A/cm<sup>2</sup> ) and convergence angle of the beam in radians, respectively.

The SEM method has been used for analyzing thin films, where surface morphology and layer thickness can be evaluated by this method. TiO2:SiO2 SEM micrographs are illustrated in the **Figure 9**, where the surface morphology of 10 layers of TiO2 and TiO2:SiO2 films can be observed in **Figure 9** [61]. As indicated, films have been prepared by fractured morphology utilizing the sol-gel method. Crack formation occurs through stress and different thermal coefficients of expansion of the overlayer due to contraction and substrate during the drying and annealing processes of the films. Micro-cracks will result in better diffusion and may contribute to a higher surface area while reducing the film's durability. According to SEM images, the crystalline size of TiO2 doped by SiO2 is 32 nm [61].

#### **3.6 Transmitting electron microscope**

Ernst Ruska and Max Knoll, in 1931, invented the transmission electron microscope. The electron microscope resolution has improved steadily from around 100 nm in the early models to 0.1 nm and is even better nowadays [66]. High-resolution transmission electron microscopy (HRTEM) refers to phase-contrast imaging resolving single atoms or atomic clusters. A highly coherent source, a well-aligned system, a good detector, and a suitable sample are essential to achieve HRTEM [67].

Samples of electron microscopy typically have gratings behavior. Most electrons travel through the sample unchanged, and none may be absorbed. Wave interference forming A TEM image.

HRTEM image is formed in the image plane when two or more selected Bragg reflected beams interact (interfere) by a suitably large objective aperture to form an image. HRTEM imaging is a type of phase-contrast imaging [68]. As a result of the

**Figure 9.** *SEM images for TiO2:SiO2 multilayer thin film [61].*

*Preparation and Characterization of Thin Films by Sol-Gel Method DOI: http://dx.doi.org/10.5772/intechopen.113722*

#### **Figure 10.** *TEM images for AgInSe2 thin film prepared by sol-gel method [70].*

contrast that occurs from the distinction in the phase of the beams as a result of their interaction with the sample, it can be used to resolve the crystalline lattice, columns of atoms, or sub-Angstrom imaging of the lattice and even single atoms can be prepared in the case of the most modern aberration-corrected transmission electron microscopes. Second-phase or amorphous layers and atomic resolution, crystalline defects, and structure across boundaries can be observed by HRTEM imaging. Furthermore, in the case of interfaces in multilayer thin films, the topography information that it is aligned correctly in the direction of the electron beam on the interface is also provided [69]. Analysis of HRTEM images is complicated and can often require simulation to directly interpret the contrast present in the image, although it is relatively easy to obtain.

Sol-gel spin coating technique has been implemented to prepare highly stoichiometric AgInSe2 thin films on a p-type Si(111) substrate. Different temperatures were used to anneal these films. HRTEM images of the synthesized and annealed thin films have been shown in **Figure 10**. The HRTEM image order of the lattice spacing was indicated as 0.3 nm. Films were indexed to a pure polycrystalline chalcopyrite AgInSe2 structure, as seen in the selected area electron diffraction patterns of the AgInSe2 [70].

#### **4. Conclusion**

In this chapter, sol-gel method and coating techniques such as dip coating, spin coating, or electrochemical deposition have been investigated. Sol-gel coating methods have been considered economical and more feasible than methods such as physical vapor deposition

(PVD) or CVD, in which sol-gel has been widely utilized industrially. In addition, characterization methods for thin films have been discussed. X-ray-based methods (XRD, EDX, or XPS) were used to investigate the crystallinity and composition of the prepared thin film. Also, AFM, SEM, and TEM, which have been used to study the surface and structure of the films, were discussed in detail.

### **Author details**

Ehsan Rahmani Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

\*Address all correspondence to: ehsanrahmani@hotmail.com

© 2023 The Author(s). Licensee IntechOpen. 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.

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#### **Chapter 2**

## Theoretical Analysis of the Solid State and Optical Characteristics of Calcium Sulphide [CaS] Thin Film

*Emmanuel Ifeanyi Ugwu*

#### **Abstract**

The analysis of the calcium sulphide thin film material which is one of the families of chalcogenide groups of thin film materials was carried out in this work using a theoretical approach for which the propagated wave through the medium of the thin film that is deposited on a glass substrate is considered to be a scalar wave in nature. The thin film material is sectioned into twos, first section is termed homogeneous reference dielectric constant, *εref* where no thin film is deposited on the substrate and the second part is termed perturbed dielectric function, *Δεp*ð Þ*z* containing the deposited thin film on the glass substrate. These two terms were substituted on the defined scalar wave equation that was subsequently solved using the method of separation of variable which invariably utilized in the transformation of the equation into the second type of Volterra equation. On the other hand, Green's function approach was also introduced in order to arrive at the model equation that culminates in an expression showcasing the wave propagated through the thin film material medium. This was subsequently applied in the computation of waves, *ψ*ð Þ*z* that is propagating through the material medium for various wavelengths within the ultraviolet, visible, and near-infrared region of the electromagnetic wave spectrum for which the influence of the aforementioned dielectric constant and function were invoked. The computed values from this mechanism were in turn utilized in the analysis of the band gap, optical, and solid-state properties of the calcium sulphide (CaS) thin film materials.

**Keywords:** scalar wave, dielectric constant, analysis, calcium sulphide, thin film, wave propagation, solid state and optical properties

#### **1. Introduction**

The Chalcogenide family of thin films to which calcium Sulphide belong is one of the sulphide-based thin film that has a wide range of applications and based on that, a lot of researchers have shown so much interest in its study and as a result, both experimental and theoretical techniques are being utilized to get into deep analysis to unravel more uniqueness the thin film. Based on this various growth techniques have been utilized to develop the thin film including the CBT growth technique with an emphasis on the study of its optical and structural properties [1]. Theoretically, mathematical tools have been used for the analysis of thin films of similar types by making use of their various properties in conjunction with wave propagating through the film medium. The first of its type was the use of beam propagation technique whereby the dielectric properties were employed in studying and computing beam or field propagation through a medium with variation in small refractive index [2, 3]. The beam propagation method based on diagonalization of the Hermetician operator that generates the solution of the Helmholtz equation in media with real refractive indices [4], has been utilized in this study by some researchers while others had somehow used 2x2 propagation matrix formalism for finding the obliquely propagated electromagnetic fields in layered inhomogeneous un-axial structure which also involved bean propagation [5]. Structures such as optical fibers and optical wave guides in the presence of electro-optical perturbation have been well understood by the application of this method [6–8]. Although earlier before then, work had been going on veraciously on the study of wave propagation in a stratified media, plasma and ionosphere that gave a more clear picture of atmospherics behavior as regards wave propagating through its medium [6, 9, 10]. Van Roey in his work derived a general beam propagation relation in a number of specific cases along with the extensive simulation of wave propagation in a variety of material mediums.

Scientists have also looked at the propagation of electromagnetic field through a conducting surface [3] where the behavior of wave propagated through such material coupled with the influence of the dielectric function of the medium on such material coupled with the effect of variation of the refractive index on some species of the thin film had been analyzed as well using the same approach [11]. And a close look at the concept made it clear that recognition of the importance of the effect of the refractive index of the medium and dielectric function culminated in the reality of the creation of two velocity components that normally give rise to phase and group refractive indices as considered in the study of wave propagation [12–15]. Recently more complicated work had been embarked upon on the study of wave propagation through a modeled thin with dielectric perturbation in which WKB approximation in conjunction with numerical approach were used [16–18] along with beam propagation technique to unravel the mechanism of theoretical analysis of wave propagation through materials and based on that, lots of work had been veraciously carried out in term of the influence of dielectric constants and refractive index on beam propagating through materials [3, 5, 12, 17, 19] in other to ascertain their roles and efficacy on the use of beam propagation method and again the effect of the refractive index of the medium in the reality of the two velocity components that normally give rise to phase and group refractive indices as generally considered when it comes to the study of wave propagation because their influence on the propagated beam [13]. This had gone a long way to add and to reveal the efficacy of the theoretical approach in understanding the beam propagation mechanism in wave propagating through thin film material. This is seen to be achieved due to the flexibility of Green's function as a tool because this is what facilitated the use of the iterative process that will be involved in the computational technique in this work that has enabled one to embark on this theoretical frame work [18, 19].

*Theoretical Analysis of the Solid State and Optical Characteristics of Calcium Sulphide… DOI: http://dx.doi.org/10.5772/intechopen.112855*

#### **2. Theoretical procedures**

General wave equation

$$
\nabla^2 \boldsymbol{\mu}(\mathbf{z}) = \boldsymbol{\upmu}\_{\cdot^2}^2 \frac{\partial^2 \boldsymbol{\upmu}(\mathbf{z})}{\partial t^2} \tag{1}
$$

$$
\nabla^2 \psi(z) + a^2 \mu\_o \varepsilon\_o \psi(z) = 0 \tag{2}
$$

from which we obtain the Helmholtz form of it using the separation of variable technique which is one of the methods being used for the solution of the wave propagating through a medium in which a dielectric function as defined in our model in **Figure 1** which shown in Eq. (3).

$$
\varepsilon(\mathbf{z}) = \varepsilon\_{\mathbf{r}\mathbf{f}} + \Delta\varepsilon(\mathbf{z}) \tag{3}
$$

consisting of two parts is imposed on the wave equation. The dielectric function consists of a perturbed part, *Δε*ð Þ*z* representing the part where the thin film is deposited and the reference section where no film is deposited, *εref* . Substituting the dielectric function in Eq. (2), we obtain [18]

$$
\nabla^2 \Psi(\mathbf{z}) + \mu\_0 \varepsilon \mathbf{o} \,\alpha^2 \Psi(\mathbf{z}) = -V(\mathbf{z})\tag{4}
$$

where

$$V(\mathbf{z}) = \chi^2 \varepsilon(\mathbf{z}) \tag{5}$$

Green's function technique is used to obtain an expression for a wave propagating through the film as.

$$\Psi(z) = \int\_0^z G(z, z') V(z') \Psi(z') \tag{6}$$

The Integral

$$
\mu \left( z, z' \right) = I(z, z') = \int\_{\rho}^{z'} G(z, z') V(z') \mu(z, z' dz') \tag{7}
$$

**Figure 1.** *Scalar wave impinging upon the substrate with reference medium εref and the thin film medium* Δ*εp*ð Þ*z .*

This when critically considered is a homogeneous Volterra equation of the second type with the kernel.

$$k(z, z') = \mathbf{G}(z, z')V(z') \tag{8}$$

In this equation, the Neumann series method is not applicable to this type of equation; hence we apply Born approximation method that enables us to rewrite the equation as

$$\Psi(\mathbf{z}, \mathbf{z}') \equiv I(\mathbf{z}, \mathbf{z}') = \int\_{\boldsymbol{\sigma}}^{\mathbf{z}'} \Phi(\mathbf{z}, \mathbf{x}) V(\mathbf{x}) \Psi(\mathbf{z}, \mathbf{x}) d\mathbf{x} \tag{9}$$

where we put x in place of *z*<sup>0</sup> .

However, according to Born approximation procedure, we replace the unknown function *<sup>ψ</sup>*ð Þ *<sup>z</sup>*, *<sup>x</sup>* in the integral with a known function <sup>Φ</sup><sup>~</sup> ð Þ *<sup>z</sup>*, *<sup>x</sup>* and use it to get an approximate solution of *ψ z*, *z*<sup>0</sup> ð Þ.

That is

$$\Psi(\mathbf{z}, \mathbf{z}') = I(\mathbf{z}, \mathbf{z}') = \int\_{\boldsymbol{\theta}}^{\mathbf{z}'} \Phi(\mathbf{z}, \mathbf{x}) V(\mathbf{x}) \tilde{\Phi}(\mathbf{x}) \tag{10}$$

The sign on Φð Þ *z*, *x* is signified as an indication of the possible phase difference between the incoming wave and the outgoing wave. Thus neglecting the influence of the reflected wave in the system, we then use Green's function as in this case, we have.

$$\Phi(z, z') = \Phi(z, z') = \frac{2}{z} \sum\_{n=1}^{\infty} \frac{\sin n\pi^{z}/\_{x}}{\chi^{2} - \frac{n^{2}\pi^{2}}{x^{2}}} \tag{11}$$

This results in the solution as given

$$\begin{split} y(z, z') &= I(z, z') \\ &= -\sum\_{n=1}^{\infty} \frac{\mathcal{V}^2}{\mathcal{V}^2 - \frac{n^2 \pi^2}{z^2}} \left[ \frac{(\epsilon' + cz') \cos\left(\frac{n\pi}{z} + \frac{2\pi}{\lambda}\right) z'}{\frac{n\pi}{z} + \frac{2\pi}{\lambda}} \\ &\quad + \frac{c}{\left(\frac{n\pi}{z} + \frac{2\pi}{\lambda}\right)^2} \sin\left(\left(\frac{n\pi}{z} + \frac{2\pi}{\lambda}\right) z'\right) - \left(\frac{\epsilon' + cz'}{\frac{n\pi}{z} + \frac{2\pi}{\lambda}} \frac{c}{\left(\frac{n\pi}{z} + \frac{2\pi}{\lambda}\right)^2}\right) \right] \end{split} \tag{12}$$

*ψ λ*ð Þ vs.*λ* when z and *z*<sup>0</sup> are fixed.

In all use, we considered in the analysis the wavelength within λ = 250 nm to 1200 nm.

From the equation, it is obvious that (*ψ*ð Þ*z* tends to 0 as the dielectric constant *ε*<sup>0</sup> ! ∞,

Therefore, for fixed values of other parameters, the resultant solution can be approximated to any number of terms as may be required in relation to wave propagation terms.

*Theoretical Analysis of the Solid State and Optical Characteristics of Calcium Sulphide… DOI: http://dx.doi.org/10.5772/intechopen.112855*

This is used to obtain the absorption co-efficient using [20]

$$I = I\_o \exp \alpha \mathbf{z}$$

$$a = \mathbb{1} \langle \mathbf{n} | \ln \left( \frac{1}{T} \right) \tag{13}$$

known as Lamber-Beer- Bouguer law

The absorption coefficient is used in Eq. [21] to obtain the expression below [22].

$$\left(a\hbar\nu\right)^{2} = A\left[\hbar\nu - E\_{\text{g}}\right] \tag{14}$$

In the case of dielectric, further deduction was involved since it is known that the refractive index and dielectric function which appears in both real and imaginary parts characterize the optical properties of any material because they are related to refractive index, n, and extinction coefficient, k.

$$
\varepsilon\_r = n^2 + k^2 \tag{15}
$$

$$
\varepsilon\_i = \mathcal{D}n k \tag{16}
$$

#### **3. Results/discussion**

**Figure 1** represents a diagram showing the deposited thin film on the glass substrate which depicts a model of the thin film that is considered to represent a dielectric function with perturbed and the other part where there is no thin film we assume to be the termed reference section. This concept is mathematically represented in Eq. (3). And this equation on the other hand was used in conjunction with the general scalar wave equation to formulate a second-order differential equation in terms of dielectric function that was solved using the method of separation of variables and invariably applied to formulate Helmholtz equation as in Eq. (4). Eq. (3) was substituted in (2) in order to come up with an expression that signifies a propagating was through the thin film medium in terms of Green's function. The further deduction was made to harmonize the equations in agreement with Green's function which depicts a function that is in line with the homogeneous Volterra equation of the second type as in Eq. (7). The equation was invariably solved using the Born approximation approach that culminated in Eq. (10) that indicated the phase difference between the incident wave on the thin film and the outgoing wave of which the reflected part of the wave was ignored for the entire system in order to enable the analysis to be carried out in terms of transmitted waves as it propagates through the material thin film. The result of the solution is given in Eq. (12) which depicts *ψ λ*ð Þ as function of wavelength. The concept was finally made use of in the computation and deduction of absorption co-efficient as in Eq. (13) which formed the backbone of deduction as it concerns all the required optical and solid state properties of the material thin film as required to be analyzed in this work.

Secondly, this also was utilized in obtaining the bad gap as shown in **Figure 2** of the thin film based on the model that was presented in **Figure 1** which was presented separately in terms of all the wavelengths within the UV, Visible and near-infrared regions of electromagnetic wave spectra. The graph which depicts a plot of ð Þ *αhν* 2 as a function of wavelength within the three regions showcased the extrapolation that

**Figure 2.**

*A graph of* ð Þ *<sup>α</sup>h<sup>ν</sup>* <sup>2</sup> *as a function of wavelength for UV, visible and infrared of electromagnetic wave region (CaS) thin film.*

indicates the positions of their respective band gaps within the wavelength of the respective spectrum.

In determining the optical properties, the same process was carried out in determining the percentage transmittance, reflectance and absorbance as in **Figures 3**–**5**, which were also presented in terms of the wavelength spectrum of the considered region respectively. In the case of transmittance, percentage transmittance was used and it was discovered that within the visible and near-infrared it is zero with fluctuation up to a point at the UV region where it rose sharply while the reflectance appeared to be negative except at a particular point within the visible

*Theoretical Analysis of the Solid State and Optical Characteristics of Calcium Sulphide… DOI: http://dx.doi.org/10.5772/intechopen.112855*

**Figure 3.**

*Transmittance VS wavelength, λnm for UV, visible and infrared of electromagnetic wave region, calcium sulphide (CaS) thin film.*

**Figure 4.**

*Reflectance VS wavelength, λ for UV, visible and infrared of electromagnetic wave region; calcium sulphide (CaS) thin film.*

where it grazes the axis at zero at the point on the visible region. From observation as depicted in the graph, the absorbance seems to be negative as well.

The dielectric constants of the film were obtained by considering the fundamental electron excitation spectrum of thin films is described by means of a frequencydependent dielectric constant that is related to n and k as shown in Eqs. (15) and (16). However, the graph showing the plot dielectric constant for both real and imaginary

*Absorbance VS wavelength, λnm for UV, visible and infrared of electromagnetic wave region; calcium sulphide (CaS) thin film.*

#### **Figure 6.**

*Real dielectric constant VS wavelength, λ for UV, visible and infrared of electromagnetic wave region; calcium sulphide (CaS) thin film.*

parts respectively were plotted as a function of wavelength as considered in this work and were shown in **Figures 6** and **7** while the extinction co-efficient is depicted in **Figure 8** was also plotted in the same manner.

However, it was generally observed that the behavior of the duo appeared to be irregular in their pattern.

*Theoretical Analysis of the Solid State and Optical Characteristics of Calcium Sulphide… DOI: http://dx.doi.org/10.5772/intechopen.112855*

#### **Figure 7.**

*Imaginary dielectric constant VS wavelength, λ for UV, visible and infrared of electromagnetic wave region; calcium sulphide (CaS) thin film.*

#### **Figure 8.**

*Extinction coefficient constant VS wavelength for UV, visible and infrared of electromagnetic wave region; calcium sulphide (CaS) thin film.*


**Table 1.**

*Computed band gap as indicated by the extrapolated graphs.*

Also, the energy band gap as deduced from the figure for various wavelengths have been shown in **Table 1** based on the considered regions of the EM wave.

The electromagnetic wave spectra propagated through the thin film material. As indicated, each wavelength has a unique band gap associated with it as shown in **Table 1** just as deduced from **Figure 2**. It is observed that the band gap for nearinfrared is seen to be narrower while that of UV (i) is wider. However, the average of the duo is considered to be the actual band gap of the thin film that is 2.51 eV. At the initial stage, it was inferred from the literature based on the experimental result that the band gap of the thin film is within the range of 3.00–3.39 eV. Thus, appropriately it is reasonably considered that the computed band gap of CaS is narrower than the result from the experimental value though with just little margin of about 0.697 eV.

#### **4. Conclusion**

The analysis of the optical and solid state properties of CaS thin film has been carried out successfully using a general scalar wave equation that was made solvable by the use of Green's function technique and which finally led to the deduction of the propagation wave through the CaS thin film material. However, from the computed result and analysis in terms of the energy band gaps, it was discovered that there is a discrepancy between the values of the energy band gaps as observed in the table. This is the fact that the computed band gap is narrower than the one obtained experimentally However, the reason may not be farfetched from the assumptions and approximations that were involved during the mathematical deductions in formulating the governing equations that were used in computation which might, of course, affected the computed results of the band gaps, and perhaps the results of other graphs that showcased the optical properties as shown in graphs and also as recorded in the table some of which often appeared to be negative contrary to the experimental results in so many cases. From the computation and analysis, it was discovered that the computed band gap is narrower than the one obtained experimentally.

However, the unique feature of this work is that it has indicated that the energy band gap of any material can be studied in terms of the wavelength of the radiation propagating through the material since the wavelength of every region of the electromagnetic wave spectrum has a band gap associated with it.

*Theoretical Analysis of the Solid State and Optical Characteristics of Calcium Sulphide… DOI: http://dx.doi.org/10.5772/intechopen.112855*

### **Author details**

Emmanuel Ifeanyi Ugwu Department of Physics, Nigerian Army University, P.M.B, Biu, Nigeria

\*Address all correspondence to: ugwuei2@gmail.com; ugwuei@yahoo.com; emmanuel.ifeanyi@naub.edu.ng

© 2023 The Author(s). Licensee IntechOpen. 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.

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[15] Ugwu EI. Theoretical study of field propagation through a nonhomogeneous thin film medium using Lippmann-Schwinger equation. The International Journal of Multiphysics. 2010;**4**(4): 305-315

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[18] Martin JF, Alain D, Christian G. Alternative scheme of computing exactly *Theoretical Analysis of the Solid State and Optical Characteristics of Calcium Sulphide… DOI: http://dx.doi.org/10.5772/intechopen.112855*

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[22] Nadeem MY. Optical properties of ZnS thin film. Turkish: The Journal of Physiology. 2000;**24**:651-659

#### **Chapter 3**

## From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics

*Junjie Yang, Huiwen Deng, Jae-Seong Park, Siming Chen, Mingchu Tang and Huiyun Liu*

#### **Abstract**

Monolithic growth of III-V materials onto Si substrates is appealing for realizing practical on-chip light sources for Si-based photonic integrated circuits (PICs). Nevertheless, the material dissimilarities between III-V materials and Si substrates inevitably lead to the formation of crystalline defects, including antiphase domains (APBs), threading dislocations (TDs), and micro-cracks. These nontrivial defects lead to impaired device performance and must be suppressed to a sufficiently low value before propagating into the active region. In this chapter, we review current approaches to control the formation of defects and achieve high-quality GaAs monolithically grown on Si substrates. An APB-free GaAs on complementary-metal-oxide semiconductor (CMOS)-compatible Si (001) substrates grown by molecular beam epitaxy (MBE) only and a low TD density GaAs buffer layer with strained-layer superlattice (SLS) and asymmetric step-graded (ASG) InGaAs layers are demonstrated. Furthermore, recent advances in InAs/GaAs quantum dot (QD) lasers as efficient on-chip light sources grown on the patterned Si substrates for PICs are outlined.

**Keywords:** heteroepitaxy, III-V materials, Si, defects, integration

#### **1. Introduction**

Recently, InP and GaAs-based optical transceivers have been progressively replacing the traditional copper interconnect due to the unique properties of high transmission speed, larger bandwidth, and less cooling power required [1, 2]. Although great performances of III-V-based optoelectronic devices have been demonstrated, the cost and scalability limit the entry of their applications into the market of consumer electronics and massive production [3, 4]. In contrast, low-cost, high-bandwidth, and high-speed Si-based PICs and optoelectronic integrated circuits (OEIC) are ideal candidates to replace high-cost InP and GaAs-based PICs due to the large scalability and better thermal conductivity [3, 5–8].

However, as a critical component of PICs, a highly reliable and efficient Si-based laser is missing due to the indirect bandgap structure of Si and Ge bulk materials

[9, 10]. Fortunately, most III-V materials have superior optical properties and are ideal to be used as a laser gain medium, but a suitable integration method is needed to combine III-V materials and Si platforms [11–18]. As one of the most mature techniques, wafer bonding has been commercially used in the Si optical transceivers but left a questionable yield and cost [19–23]. Even though the integration method of direct epitaxy of III-V materials on the Si platform could cause many types of crystal defects, which leads to a substantial deterioration in the device performance, it has great potential owing to various advantages of large-scale, high yield, low-cost, and dense integration [24].

The crystal defects generated at the III-V/Si interface will trap carriers and produce extra heat to the devices by forming nonradiative recombination centers [25, 26]. Hence, a proper strategy to reduce and eliminate these crystal defects becomes the most critical condition to realize high-performance Si-based III-V optoelectronic devices. In this chapter, we will introduce the generation of different types of crystal defects in terms of different physical dimensions, followed by their corresponding solution and recently demonstrated results. After that, recent advanced works of monolithic integration of III-V QD lasers on the Si platform along with optical waveguide are discussed.

#### **2. Direct epitaxy of III-V materials on Si**

Although the direct epitaxy of III-V material on Si offers substantial benefits, issues streaming from large material dissimilarities between these two materials lead to the generation of nontrivial defects. For instance, the different polarity, large mismatch of lattice constant, and incompatible thermal expansion coefficient (CTE) result in the formation of APBs, TDs, and micro-cracks, respectively. Extensive endeavors have been dedicated to advancing the growth techniques in the last decades to tackle these three main challenges in III-V/Si heteroepitaxy and realize highperformance III-V lasers integrated into Si. In this section, the mechanisms of defect formation and strategies to suppress the defects will be discussed.

#### **2.1 Antiphase boundaries**

A planar defect called APB is formed during the heteroepitaxy of polar III-V materials on nonpolar Si (001) substrates. Si (001) vicinal surface with a small offcut angle (<1°) exhibits terraces of alternating 1 � 2 and 2 � 1 dimerization, which are separated by Si single-atomic-height (*S*) steps [27–30]. These Si *S* steps are classified into two groups, that is, *Sa* and *Sb*, depending on the dimer orientation in the upper terrace [31]. The schematic diagram of alternating *S* steps on the Si (001) surface is shown in **Figure 1**, where the *Sa* steps are straight, and the *Sb* steps are meandering due to thermal fluctuation [28]. The terrace width between the adjacent *Sa* and *Sb* steps is defined as *L*. The relationship between terrace width *L* and the offcut angle of the Si substrate *θ* is defined as

$$a = L \times \tan \theta \tag{1}$$

where *a* is the height of a single Si *S* step, corresponding to 0.136 nm.

In most zinc-blend structures, for example, III-As and III-P materials, different atoms occupy the two face-centered-cubic (FCC) sublattices. By contrast, identical *From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

**Figure 1.**

*Schematic diagram of Si (001) surface with S steps. Reprinted from reference [32] ©2021 the author under CC BY.*

atoms occupy FCC sublattices in the diamond crystal structure of Si [33]. During the heteroepitaxy of III-V materials on Si (001) substrates, the orthogonal Si dimers in adjacent terraces lead to the formation of two domains with opposite sublattice allocation, that is, antiphase domains (APDs). The interface between two APDs is an APB consisting of homopolar bonds (GadGa or AsdAs bonds) and is considered as electrically charged planar defect [34]. APBs propagate within the epilayers and act as nonradiative recombination centers and electrical leakage paths, severely degrading the optoelectronic properties of devices due to their relatively large area [34, 35]. In addition, the elastic strain associated with APBs will distort the crystal lattice and deform the DFLs. As a result, a high TD density (TDD) will be observed in the active region [32].

The presence of large-scale APBs can be characterized by using an atomic force microscope (AFM), electron scanning microscope (SEM), or transmission electron microscope (TEM). **Figure 2(a)** shows a typical AFM image of GaAs grown on Si (001) substrate with dense APBs, illustrated as curved boundaries. In practice, APBs emerge at the edge of Si *S* steps, and most of them propagate through {110} planes to the surface at low growth temperature as {110} APBs exhibit the lowest formation energy when compared with {112} and {111} APBs in both GaAs and GaP [36]. The kink of APBs into higher index planes, for instance, {111} and {112} planes, depends on the growth temperature of the epilayer. This process is crucial for the selfannihilation of APBs at the intersection [36, 37]. In stark contrast, the Si dimers are in the same orientation on the double-atomic-height (*D*) stepped Si surface. As a consequence, the nucleation of APBs is suppressed during the growth of III-V materials on Si *D* steps [25]. The APB nucleation and propagation under different circumstances are summarized in **Figure 2(b)**.

**Figure 2.**

*(a) Top view AFM image shows dense APBs on the GaAs surface. (b) Schematic diagram of APB nucleation, propagation, and annihilation on Si steps.*

A classic and common solution for suppressing APBs is to implement 4°–6° offcut Si substrates titled toward [110] direction, which preferentially forms *D* steps-dominated Si surface and thus inhibits the nucleation of APBs [28]. However, in order to be compatible with well-established CMOS processing technology, nominal Si (001) substrate with a misorientation of lower than 0.5° is required [38]. In the past decades, many techniques have been developed to achieve heteroepitaxy of APB-free III-V materials on on-axis Si (001) substrates, which will be introduced in the following contents.

#### *2.1.1 Selective area growth*

Selective area growth (SAG) allows III-V heteroepitaxy on the prepatterned Si substrates and attracts intensive scientific interest as it provides efficient defect reduction, attributed to epitaxy necking effects and aspect ratio trapping (ART) [39–41]. SAG of III-V materials on the narrow trenches with patterned vertical dielectric sidewalls (normally SiO2) ensures sufficient TD trapping if a high aspect ratio (AR) is defined. The AR is defined as the ratio of trench height *h* and width *w*:

$$AR = \frac{h}{w} \tag{2}$$

During the epitaxy of mismatched III-V on Si substrates, the misfit dislocation (MD) inevitably formed at the interface due to strain relaxation. Glissile 60° MDs tend to form segments that thread up as TDs, which propagate freely on the {111} planes in <110> directions and move upwards to the epilayer surface [42, 43]. As for the TDs propagating on the {111} planes perpendicular or parallel to the trench orientation, TDs will eventually hit the vertical dielectric sidewalls and are trapped if sufficient AR is applied, as illustrated in **Figure 3(a)** case (1) and (2). Since {111} planes form an incident angle of 54.7° with [110] direction, a minimum AR of 1.41 is required to terminate the TDs within the trench. Unlike the TDs, however, the trench only traps the planer defects lying on the {111} planes parallel to the trench orientation, as indicated by case (3) and (4) in **Figure 3**. Furthermore, V-grooved Si (001) substrates with {111} facets, formed by using wet etching, were developed to prohibit the formation of APBs even with the presence of *S* steps [25, 44], as shown in **Figure 3(b)**.

Through V-grooved Si {111} surfaces via an ART process, Li et al. successfully demonstrated an APB-free GaAs-on-V-grooved Si (GoVS) template [45]. The Si (001) substrate patterned with [110] direction SiO2 strips was etched by KOH solution to form V-grooved Si {111} facets as the etching rate of Si being the lowest in the (111) plane

#### **Figure 3.**

*(a) Schematic diagram showing TD and PD propagation within the narrow trenches with patterned vertical dielectric sidewalls. The APB nucleation is prohibited during the growth of III-V on V-grooved Si (001) substrate with {111} facets (b) even on a Si (111) S step.*

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

[44]. SAG of GaAs nanowires was performed using a metalorganic chemical vapor deposition (MOCVD) system with a two-step growth method. **Figure 4(a)** shows the initial growth of GaAs on the V-grooved substrate, and planar GaAs nanowire is observed without APBs, thanks to the Si {111} facets. Interestingly, the unique "tiara" like shape formed by Si undercut blocks the propagation of stacking faults through {111} planes, as shown in **Figure 4(b)**. After removing the SiO2 strips by a buffered oxide etch, coalesced GaAs thin film was grown to finish the template. High-quality APB-free GaAs thin film was obtained after 300 nm GaAs overgrowth, as shown in **Figure 4(c)**.

In addition, Wei et al. proposed a novel way of forming Si {111} surfaces by homoepitaxy of Si on the U-shaped patterned Si (001) substrate. The U-shaped pattern along [110] direction is formed with a period of 360 nm, ridge width of 400 nm, and depth of around 500 nm by the deep ultraviolet photolithography (DUV) and subsequent dry etching, as shown in **Figure 5(a)** [46]. The U-shaped patterns will then be dipped in a diluted hydrofluoric acid to form a hydrogenterminated surface and transferred into an IV molecular beam epitaxy (MBE) chamber for the deoxidation and subsequent homoepitaxy of 500 nm Si to form {111} facets, as shown in **Figure 5(b)**. Further deposition of Si to 550 nm leads to the merging of Si ridges and finally forms evolvement of (111)-faceted-sawtooth surface, which promotes the APB-free GaAs in the subsequent growth.

#### *2.1.2 MOCVD/MOVPE grown APB-free GaAs/Si (001)*

Although the pioneering works on SAG growth of APB-free III-V/Si (001) have been proved promising, the sophisticated processing and patterning of the Si surface

#### **Figure 4.**

*(a) Cross-sectional TEM image showing the growth of GaAs on the V-grooved Si (001) substrates. (b) Defects are trapped by the "tiara"-like shape formed by Si undercut. (c)cross-sectional SEM of grown GaAs in the GoVS template. Reprinted with permission from [45] ©2015 AIP publishing.*

#### **Figure 5.**

*(a) Cross-sectional SEM image showing a U-shaped patterned Si (001) substrate. (b) Si {111} facets formed by Si homoepitaxy. Reprinted with permission from [46] ©2015 AIP publishing.*

are costly and time-consuming. Regarding the direct growth of III-V materials on planer Si (001) substrates, forming the *D* steps-dominated Si surface is the most straightforward idea to solve the APB issue. Thus, it has also been widely investigated. The Si *D* steps can be formed by high-temperature annealing of Si (001) substrates with proper hydrogen chemical potential, attributed to the preferential and selective etching of *Sb* steps by hydrogen [34]. This process is strongly related to the width of neighboring Si terraces. According to Eq. (1), a slightly large offcut angle of >0.1° is desired to erase *Sb* steps to a sufficiently low value and form the *D* steps-dominated Si surface.

Volz *et al.* achieved APB-free GaP on Si (001) substrate with an offcut angle of 0.12° using metalorganic vapor phase epitaxy (MOVPE) [47–49]. A 500 nm Si buffer layer was first deposited, followed by postgrowth hydrogen annealing with the pressure of 950 mbar for 10 min at 975°C to obtain a *D* steps-dominated Si surface with an average terrace distance of 120 nm. Nevertheless, *S* steps still appeared as a triangle-shaped form and existed between two neighboring *D* steps, covering 15% of the surface area [37]. During the epitaxy of GaP on the Si buffer layer, APBs exist because of imperfect Si *D* steps. The distribution of APBs that resembles the underlying Si *S* steps is illustrated in **Figure 6(a)**, where the triangle-shaped *S* steps lead to the formation of APBs in two orthogonal directions [110] and [110]. The kinking and selfannihilation of APBs through energy favorable {112} is observed in the direction [110], which is perpendicular to the Si step orientation [36, 48]. The typical basal width of 180 nm for the *S* terrace yields a maximum height of 65 nm for APBs to be fully annihilated in GaP, as presented in **Figure 6(b)**. Since the triangle-shaped *S* steps become narrow along [110] direction, the decrease in basal length results in faster annihilation of APBs, which is confirmed by the TEM measurements in **Figure 6(c)**.

Based on this technique, a GaAs/GaP/Si (001) is developed as one of the most commercially successful templates for developing Si-based on-chip light sources. Many remarkable results have been reported based on this platform [50–52].

In contrast, Alcotte et al. selected a Si (001) substrate with a slightly larger miscut angle of 0.15° toward [110] direction to further enhance the etching of *Sb* steps. They demonstrated an APB-free GaAs grown on a Si (001) substrate by MOCVD without intermediate Si buffer layers [35]. Prior to growth, a Si wafer was first deoxidized in a SiConi™ chamber using an NF3/NH3 plasma. High-temperature hydrogen annealing at 850 to 950°C was then carried out to form Si *D* steps, as indicated in **Figure 7(b)**. A surface of GaAs grown on the un-optimized Si substrate is shown in **Figure 7(a)**,

#### **Figure 6.**

*(a) TEM plane view of GaP grown on pretreated Si buffer layer. Cross-sectional TEM measurement in (b) [110] and (c) [110] cross-sections showing anisotropic APDs. Reprinted with permission from [48] ©2011 AIP publishing.*

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

**Figure 7.**

*(a) AFM image of GaAs grown on an un-optimized Si substrate showing high density of APBs. (b) Si D steps formed after annealing a Si substrate under optimized conditions. (c) AFM image of a 150 nm APB-free GaAs layer grown on Si (001). Reprinted from reference [35] ©2016 the authors under CC BY.*

where a high density of APBs is visible. By utilizing an optimized Si substrate with the dominated Si *D* steps, a 150 nm APB-free GaAs epilayer was obtained with a low surface roughness of 0.8 nm for a 5 <sup>5</sup> <sup>μ</sup>m<sup>2</sup> AFM scan, as presented in **Figure 7(c)**.

#### *2.1.3 MBE grown APB-free GaAs/Si (001)*

Indeed, the above-mentioned APB-free III-V templates grown by MOCVD/ MOVPE have achieved great success in commercialization. Nevertheless, the requirement of a hydrogen source is unsuitable for migrating such methods into MBE systems. The MBE system has a unique advantage in obtaining high-quality QDs [53], which are insensitive to defects and have been regarded as one of the most promising gain media for high-performance Si-based on-chip laser sources [54]. Developing an APB-free III-V layer by a single system simplifies the growth process and is economical in the long term.

This need was first satisfied by Kwoen et al. who have successfully grown APB-free III-V lasers on on-axis Si (001) by MBE using a high-temperature Al0.3Ga0.7As nucleation layer (NL). In the study, four samples with identical structures except for the composition of Al in the first 40 nm AlxGa1-xAs NL were grown and compared by SEM and photoluminescence (PL). It was concluded that Al0.3Ga0.7As NL promoted self-annihilation of APBs and delivered the best GaAs quality. Based on this platform, InAs/GaAs-based QD lasers were developed with high operating temperature [55, 56].

Recently, Li and Yang et al. proposed a new method of using periodic Si *S* steps to redistribute the APB nucleation and promote the APB annihilation during optimized GaAs overlayer growth by a dual-MBE system [57, 58]. In their study, on-axis Si (100) substrates with unselected miscut angles of 0.15 0.1° toward <110> were deoxidized at 1200°C for 30 min in the group-IV MBE. A 100 nm Si buffer layer was first grown at 850°C by using a Si e-beam source. This was followed by five iterations of 20 nm thin Si grown at 850°C and annealed at 1200°C to reconstruct the surface and form periodic Si steps. The wafer was then transferred into the III-V chamber for subsequent growth. The schematic image showing the APB-free GaAs buffer layer structure is illustrated in **Figure 8(a)**, which started with a low temperature (LT) Al0.4Ga0.6As NL grown at 330°C, and the growth rate was 0.1 monolayers per second (MLs<sup>1</sup> ). A temperature ramping step with a ramp rate of 10°C Min<sup>1</sup> was applied afterward. At the same time of increasing temperature, GaAs was deposited

#### **Figure 8.**

*(a) Schematic image of the APB-free GaAs buffer layer structure. (b) APB-MTE formed during high-temperature annealing. Reprinted from [58] © 2022 the authors, under CC BY.*

simultaneously at a rate of 0.6 MLs<sup>1</sup> . This growth-during-ramp method was also applied in the following temperature ramping steps. Following the Al0.4Ga0.6As NL, a three-step GaAs growth technique was implemented, consisting of 190 nm LT, 180 nm mid-temperature (MT), and 340 nm high-temperature (HT) GaAs grown at 350, 420, and 580°C respectively. The temperature ramping step was inserted between these GaAs layers, and the total GaAs buffer layer thickness was 1 μm.

In contrast to the growth parameter proposed by Kwoen et al. [59], the NL was grown at LT of 330°C in this study to avoid the formation of APB-modified thermodynamic equilibrium (APB-MTE). In APB-MTE, a (110) APB tends to enlarge, resulting in the formation of two APDs with opposite polarity, as shown in **Figure 8(b)** [58, 60]. Most recently, this growth strategy has been proved efficient by Gilbert et al. as it maintains the terrace-driven nature of APBs in initial nucleation rather than nucleation-driven, leading to controllable APB burying in the GaAs overgrowth [61]. Besides, the growth-during-ramping method helps to elongate the {110} APBs while preventing the APB-MTE. In addition, a suitable high growth temperature aids in the reconfiguration of the APBs into higher index planes, ultimately promoting the annihilation of APBs.

To examine the impact of the Si buffer layer on APB annihilation, a comparative analysis of the surface morphologies was conducted between Si substrates with and without an annealed Si buffer layer, as shown in **Figure 9**. For the deoxidized Si surface, the random distribution of Si atomic steps is observed in **Figure 9(a)**. These

#### **Figure 9.**

*<sup>5</sup> <sup>5</sup> <sup>μ</sup>m<sup>2</sup> AFM image of (a) a deoxidized Si substrate and (b) a surface-reconstructed Si buffer layer. (c) 2 <sup>2</sup> <sup>μ</sup>m2 AFM image of the Si buffer layer with periodic S steps. (d) Height measurement of Si steps, showing Si surface is mainly single-stepped. Reprinted from [57] © 2020 the authors, under CC BY.*

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

undulating steps arise from the interaction between distinct stress domains on the Si surface, leading to the reduction in the overall elastic energy of the Si surface at a small offcut angle [62, 63]. In stark contrast, **Figure 9(b)** and **(c)** present the periodic *S* steps with a step height of 0.13 nm, demonstrating only Si *S* steps instead of *D* presented on the Si surface after HT annealing [64, 65].

Two samples (sample A without Si buffer layer and sample B with Si buffer layer) with identical GaAs growth methods were grown and compared to test the impact of the Si *S* steps on APB annihilation. The cross-sectional TEM measurements are taken with a viewing direction of [110] for **Figure 10(a)**–**(d)** and [110] for (e) and (f). As shown in **Figure 10(a)**–**(d)**, APBs nucleate and propagate through the energy-favored {110} planes during LT GaAs growth. The APB propagation plane is configured to higher index planes in the high-temperature growth region, contributing to APB selfannihilation. The twisted patterns that demonstrate randomly distributed APB nucleation during GaAs/Si (001) (Sample A) are observed in **Figure 10(a)**. In contrast, periodic APBs occur when GaAs are grown on the Si buffer layer (Sample B), as illustrated in **Figure 10(c)**.

In both samples, APBs tend to intersect and annihilate with each other within the high-temperature growth region. However, in **Figure 10(a)**, the randomly distributed APBs shown in sample A propagate randomly within the GaAs, making them extremely difficult to eradicate effectively. The remaining APBs thus penetrate through the whole structure, as displayed in **Figure 10(b)**. In contrast, the wellorganized APBs that nucleate on (*Sa* + *Sb*) resemble the underlying *S* steps and are closely spaced. The high growth temperature applied afterward sufficiently promotes the complete destruction of APBs within 500 nm, as shown in **Figure 10(d)**.

Furthermore, the APBs that penetrate through the whole GaAs buffer layer in sample A are noticed from [110] viewing direction, as indicated in **Figure 10(e)**. By contrast, since the Si buffer layer is populated by *S* steps in [110] direction, the APBs that nucleate on these *S* steps resemble the step orientation, leaving no APB observed in [110] viewing direction, as shown in **Figure 10(f)**. This observation differs from the aforementioned APB-free GaP/Si growth, where triangle-island-shaped *Sb* steps

#### **Figure 10.**

*Cross-sectional TEM images from [110] viewing direction showing APB nucleation and self-annihilation for (a) regional and (b) 1* μ *m range of sample a and (c) regional and (d) 1* μ *m range of sample B. TEM images from [110] viewing direction for (e) sample a and (f) sample B. reprinted from [32] ©2021 the author under CC BY.*

are left near the edge of the *D* steps. During subsequent growth of GaP on these *S* triangle islands, the APBs that resemble the underlying Si steps can be found in two orthogonal directions, that is, [110] and [110] [48, 49, 66].

The annihilation of APBs at HT is attributed to the difference in GaAs growth rate of the two domains. During the deposition of GaAs on Si, an Arsenic (As) prelayer is adopted to avoid Ga etching, and As resembles the underlying Si dimer orientation. Since Ga atoms diffuse mainly along the As dimer direction, GaAs deposited on the upper terrace of *Sa* are more likely to grow along the [110] direction (main phase), and GaAs deposited on the upper terrace of *Sb* will grow along [110] direction (antiphase), as indicated in **Figure 11(a)** [67, 68]. The main-phase GaAs grow faster than antiphase GaAs in the [110] direction, forcing neighboring APBs to intersect toward each other during temperature increases. As a result, the annihilation of terrace-driven APDs is facilitated, as shown in **Figure 11(a)**.

Interestingly, it has been reported that {110} APBs help to reduce TDs during GaAs overgrowth [58]. {110} APBs trap {111} TDs to climb along it and promote the termination of TDs with opposite Burger vector signs. In addition, the trapped TDs can glide through other {111} planes and might be captured again by other {110} APBs. This process will recur until TDs are terminated or move beyond the APBs. Consequently, the TDD level reaches 8 <sup>10</sup><sup>8</sup> cm<sup>2</sup> for GaAs grown on Si (001) substrate with periodic {110} APBs, which is half of GaAs grown on Si offcut substrate with identical growth structure. This result reveals the probability of controlling both APBs and TDs simultaneously and achieving a high-quality APB-free GaAs/Si (001) template by optimizing the GaAs growth technique in the future.

#### **2.2 Dislocations**

The second issue that hinders the direct epitaxy of III-V materials on Si is the formation of dislocations. Most III-V materials, except for GaP and aluminum phosphide (AlP), have a large lattice mismatch with Si. During the III-V-on-Si mismatched heteroepitaxy, the strain energy accumulated inside the epilayer is proportional to the epilayer thickness. Once the thickness of the strained layer exceeds a certain value, the so-called critical thickness, MDs, are formed at the interface to relax the accumulated strain. These MDs introduce missing or dangling bonds along the mismatched

#### **Figure 11.**

*(a) Schematic diagram of terrace-driven APB burying method. The area within the closed-loop APBs is considered as an antiphase, while the outside is the main phase. (b) Antiphase GaAs are buried by main-phase GaAs during the growth. Reprinted from [58]© 2022 the authors, under CC BY.*

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

interface. The commonly occurred MDs can be classified into two types: (1) edge MDs with Burgers vector lying in the interface (001) plane and perpendicular to the line direction. This type of dislocation mainly originates from Si steps and is "sessile". (2) 60° MDs with Burgers vector of 60° to the dislocation line and 45° to the substrate, and this type of dislocation is termed "glissile". Since dislocations are one-dimensional defects and cannot terminate within a crystal, 60° MDs will move toward the edge of the crystal or form segments that thread up as TDs, which propagate freely along the {111} planes and penetrate through whole epi-layers. The TEM image of MD and TD are illustrated in **Figure 12**. TDs introduce deep states and act as nonrecombination centers for carriers, which leads to short carrier lifetime, low photon emission efficiency, and impaired device performance [43].

Several strategies were developed to control TDD in the past decades, aiming to reduce TDD to a low value of <sup>10</sup><sup>6</sup> and 10<sup>5</sup> cm<sup>2</sup> , which is close to the TDD on the native substrate. For instance, inserting a Ge intermediate or SiGe-graded buffer layer effectively bridges the lattice mismatch between Si substrates and III-V [69]. Besides, the three-step GaAs growth method is commonly utilized to control TDD within the GaAs buffer layer for the GaAs-on-Si system. A thin AlAs nucleation layer grown by migration-enhanced epitaxy is also adopted to suppress three-dimensional defects raised at the III-V/Si interface [70], which is followed by MT and HT GaAs to minimize the point defects during epitaxy [54]; Thermal cycle annealing (TCA) is another effective tool as it provides extra thermal stress to enhance the motion of TDs and promote higher probability for TD interaction [71].

In addition to the previously mentioned strategies, inserting SLSs serving as dislocation filter layers (DFLs) is another effective method that can sufficiently reduce the TDD. SLSs consist of periodic lattice-mismatched thin layers without strain relaxation. The unreleased strain tends to bend TDs at the SLSs interface and forces them to move laterally toward the edge of a crystal (parallel to the interface), enhancing the probability of intersection and termination of TDs, as shown in **Figure 13**. Besides, MD segments form at the SLSs interface as TD moves, relieving the misfit and reducing the net glide force of TDs to zero [43].

#### *2.2.1 Optimization of SLSs and asymmetric step-graded filter structure*

Optimizing SLSs to improve their filtering efficiency has been extensively explored. To design a proper SLS, the strain force must be first considered. A trade-off appears as a higher strain force strengthens the filtering ability, while an over-strain

**Figure 12.** *Cross-sectional bright-field TEM image showing MDs and TDs.*

**Figure 13.**

*Cross-sectional TEM image of GaAs grown on on-axis Si (001), showing TD propagation and annihilation within four sets of In0.18Ga0.82As/GaAs DFLs.*

force leads to new defects. Thus, for the most commonly used InGaAs/GaAs system, the indium (In) composition and the thickness of GaAs space layers for InxGa1-xAs/ GaAs DFLs must be carefully designed. Tang et al. demonstrated that 18% of indium (among 16, 18, and 20%), along with a 300 nm GaAs space layer, delivered the best filter efficiency in the design of InxGa1-xAs/GaAs DFLs [72]. Besides, *in situ* thermal annealing was applied for each set of DFLs when the growth was being pulsed in the reactor. This approach further reduced the TDD, as the motion of TDs was enhanced, and thus, a higher possibility for TD self-annihilation was achieved.

Shang et al. provided a comprehensive study of optimizing DFLs on GaAs/GaP/Si (001) templates, which formed the basis for the high-temperature InAs/GaAs QD laser with an extrapolated lifetime of over 22 years [51, 71]. In this study, In0.15Ga0.85As (10 nm)/GaAs (x nm) 20 SLSs as DFLs were grown and compared. X represents values 10, 7, 5, 2, 0. A decreasing trend of filter efficiency was observed when x became lower, attributed to a higher degree of relaxation for In0.15Ga0.85As. Based on this observation, 200 nm InxGa1-xAs were further analyzed with various indium (In) compositions (10, 15, 17.5, 20, and 25%). It was concluded that 15 and 17.5% In composition delivered the best filtering efficiency, and a clear blocking effect of TDs was observed for an In composition higher than 20%. Furthermore, Shang et al. developed novel filter layers with ASG filter structure, which helps to reduce blocking effects, as shown in **Figure 14(a)**. Ten minutes of annealing at 530°C was applied for each InGaAs layer to promote tensile relaxation. Finally, TDD of 2 <sup>10</sup><sup>6</sup> cm<sup>2</sup> was achieved based on this structure, as shown in **Figure 14(b)**. This is also proven by TEM results shown in **Figure 14(c)**. Almost all TDs are blocked by this ASG filter structure, leaving the top GaAs layer with ultra-low TDD.

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

**Figure 14.**

*(a) Schematic diagram of InGaAs ASG layers. (b) ECCI image showing TDD of 2 106 cm<sup>2</sup> . (c) Cross-sectional TEM image of InGaAs ASG layers. Reprinted from [71] © 2020 the authors, under CC BY.*

#### *2.2.2 Trapping layer*

During the postgrowth cooldown period, thermal stress-induced TD motion happens as a result of the large mismatch in CTE between III-V and Si. Once TDs encounter the In-contained DWELL structure, the mechanically hardened active region forces TDs to move laterally, leaving behind the MDs at the interface and severely degrading the optical properties of QDs. To solve this issue, Selvidge et al. inserted In-contained trapping layers (TL) to displace MDs above and below active region, which dramatically improved the optical prosperities of QDs [73]. The thickness of InGaAs TLs was kept below critical thickness (7 nm) without introducing extra MDs. As shown in **Figure 15**, inserting TLs does not contribute to TD reduction, but it displaces the MD formation below it rather than the active region to minimize the decremental impact brought by MDs. TLs were also applied in the laser structure to explore its efficiency, as illustrated in **Figure 16(a)**. 7 nm In0.15Ga0.15As and In0.15Al0.15As were placed 80 nm above and below the active region sandwiched by cladding layers to minimize the effect of the electrical barrier due to bandgap alignment. From **Figure 16(b)** and **(c)**, TLs were effective for displacing MDs along it rather than on DWELL. This observation is consistent with **Figure 16(c**–**f)**, where MDs lie on the DWELL when no TLs are inserted. Most MDs lie on the TLs, and further glide of TD segments does not introduce extra MDs in the QD lasers. It was

#### **Figure 15.**

*Schematic diagrams showing MD formed (a) without and (b) with InGaAs TLs. Reprinted with permission from [73] ©2020 AIP publishing.*

#### **Figure 16.**

*(a) Schematic diagram of proposed laser structure with TLs. (b) Cross-sectional bright-field TEM image showing MD segments appear on TLs, as indicated by black arrows. (c) Zoom-in image of (b). Cross-sectional tomographic reconstruction showing (c) MDs lie on the 5th QDs in laser structure without TLs. (d) MDs lie on the TLs. (e) Part MDs lie on the TLs, and part lie on the 5th QD. Reprinted with permission from [73] ©2020 AIP publishing.*

also demonstrated that the laser with TLs exhibited half of the threshold current (even lower than state-of-art lasers on Si when higher TDD is presented in this case), a 60% increase in slope efficiency, and 3.4 times improvement in peak single facet output power, revealing the effectiveness of TLs. Such performance is comparable to Si-based QD lasers with one magnitude lower TDD. Compared with the structure consisting of thick DFLs, the insertion of thin TLs is more effective in improving laser performance without introducing a thick epilayer, which is beneficial for the yield and massive production of Si-based PICs in the long term.

Recent developments of reducing TDD in GaAs monolithically grown on Si (001) substrates by combining previously mentioned strategies are highlighted in **Table 1**.

#### **2.3 Cracks**

Controlling defect density to a sufficiently low value requires a thick buffer layer with several micrometers, which introduces the formation of micro-cracks. Because of the large mismatch in CTE between III-V materials and Si, for example, 5.73 <sup>10</sup><sup>6</sup> ° <sup>C</sup><sup>1</sup> for GaAs and 2.6 <sup>10</sup><sup>6</sup> °C<sup>1</sup> for Si, the accumulated thermal stress during the growth is relieved by forming micro-cracks and wafer warping when the epilayer cools down from high growth temperature to room temperature [79]. Theoretically, cracks form along the [110] and [1–10] directions when the elastic energy exceeds a critical value to generate two new surfaces, as shown in **Figure 17**. In addition, it is also proved that crack formation originates from other preexisting defects [80] and


*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

**Table 1.**

*Summary of recent optimization of DFL layers for GaAs monolithically grown on Si (001) substrates.*

**Figure 17.** *SEM image of cracks in orthogonal directions. Reprinted from [79] © 2022 the authors, under CC BY.*

layer thickness. For example, Yang et al. reported that the crack density increases sharply about three times when the thickness of the GaAs layer on Si increases from 5 to 6.7 μm [81]. Similar to other defects, micro-cracks are detrimental to the device's performance as they serve as scattering centers for light propagation and electrical leakage paths [81]. Additionally, the high density of micro-cracks will significantly reduce the total yield of devices [82]. Hence, controlling micro-crack is crucial for the mass production of Si-based PICs in the future.

A prolonged cooling down period with a slower cooling rate is suggested after growth to prevent the micro-cracks [79, 83]. Furthermore, SAG of III-V materials helps to prevent micro-cracks formation by alleviating thermal stress. However, dense defects, including TDs and stacking faults, will be generated near the pattern edge, degrading crystal quality. Moreover, in large patterned areas, micro-cracks remain on the sample surface [84]. Even though diverse techniques have been demonstrated, keeping the device thickness below the cracking threshold is the most economical and effective way [81].

As cracks are formed when the elastic energy exceeds a certain limitation, the thickness of the epilayers is the most prominent and essential reason for the crack formation. Yang et al. proposed the relationship between the critical cracking thickness and a dimensionless driving force number *Z* [85], which calculates the energy released per unit area for the crack:

$$G = \frac{Z\sigma^2 t}{\overline{E\_f}} \tag{3}$$

where *σ* is the stress in the thin film, t is the thin film thickness and *Ef* denotes the biaxial modulus. In a typical system where the substrate and the epilayer have similar elastic moduli, the *Z* should be within 2 to 4. The stress in the thin film can be calculated as:

$$
\sigma = \overline{E\_f} (a\_f - a\_i) \Delta T \tag{4}
$$

where *α<sup>f</sup>* and *α<sup>s</sup>* are the CTE of the thin film and the substrate, respectively. While the Δ*T* is the temperature difference between the growth temperature and the room temperature. The critical thickness for crack formation can be derived, provided that the fracture resistance *Γ* is twice the energy release rate *G* [85, 86]:

$$t\_{\mathfrak{c}} = \frac{\Gamma \overline{E\_f}}{Z \sigma^2} \tag{5}$$

Based on the mathematical model given above, the cracking threshold of GaAs is estimated as 3.9 μm when it is cooled down from the growth temperature of around 600°C to room temperature. However, for most growth of high-performance III-V compound semiconductor devices on Si, the structure was usually above 4 μm due to the utilization of a thick buffer layer to minimize the TD generated at the interface.

Furthermore, Shang et al. further improved the previous model and shed light on the relationship among dislocation density, film thickness, cooling rate, and crack formation [79]. It has been suggested that lower TDD induces higher equi-biaxial stress in the film during the cooling down period. The critical thickness is inversely proportional to the cool rate and TDD, as shown in **Figure 18**. It is suggested that with a low TDD of 1.0 �10<sup>6</sup> cm�<sup>2</sup> and a low cool rate of 1°C min�<sup>1</sup> , the critical thickness of cracking is approximately 6 μm. Therefore, a thin epilayer with a low cooling rate is of pinnacle importance to prevent micro-cracks.

Recently, Yang et al. used an optimized 300 nm Ge buffer layer to replace part of the thick GaAs buffer layer in the laser structure while keeping the TDD unchanged [82, 87]. As a result, the total thickness of the laser structure can be reduced to approach the cracking threshold without bringing any negative effects. A comparison between TD propagation for GaAs deposited directly on a Si substrate and a Ge/Si

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

#### **Figure 18.**

*Relationship among critical thickness, cooling rate, and TDD. Reprinted from [79] © 2022 the authors, under CC BY.*

virtual substrate (VS) is demonstrated in **Figure 19**. As shown in **Figure 19(a)**, a high density of defects is generated at the GaAs/Si interface, and almost <sup>10</sup><sup>9</sup> cm<sup>2</sup> TDD is observed underneath the first DFL [54]. In contrast, a much lower TDD of 6 <sup>10</sup><sup>8</sup> cm<sup>2</sup> is obtained in the 300 nm Ge buffer layer attributed to the adoption of HT TCA between 600 and 900°C, as indicated in **Figure 19(b)**. This TDD is comparable to the 1.4 μm GaAs monolithically grown on Si with one set of DFL. In addition, MDs are barely introduced in the subsequent GaAs growth since the lattice constants of Ge and GaAs are almost identical. As a result, TDD reaches 4 <sup>10</sup><sup>6</sup> cm<sup>2</sup> after applying four sets of DFLs. Based on this result, a high-quality InAs/GaAs QD laser was developed with high operation temperature, revealing the feasibility of using Ge/Si platform for reducing micro-cracks in the future.

#### **2.4 Summary**

Recent progress in controlling crystal defects during the heteroepitaxy of III-V materials on Si substrates has been reviewed in this section. Several newly developed techniques were applied for Si-based PICs, which will be discussed in the following contents.

#### **Figure 19.**

*Cross-sectional TEM images of GaAs buffer layer grown on (a) a Si substrate and (b) a Ge/Si VS. reprinted from [82] © 2021 the authors, under CC BY.*

#### **3. Photonic integrated circuits**

The idea of using Si-based PICs in which all major photonic functions are monolithically integrated on a single Si or Si-on-insulator (SOI) substrate has emerged to promote rapid advances in quantum photonics, quantum computing, LiDAR, and artificial intelligence-powered nanophotonics [4, 88]. It contributes to the better life quality of consumers with low cost due to the low material cost and large wafer size of Si [4, 89, 90]. Over the past decades, an unprecedented boom of key components of Si photonics, including Si-based modulators [91], photodetectors [92], and waveguides [93], has been witnessed. Until now, an efficient, electrically pumped Si-based laser remains a missing piece and becomes the roadblock to the commercialization of Sibased PICs.

To circumvent the inherent limitations of Si, integrating direct-bandgap III-V materials onto Si has been regarded as an attractive approach for the Si-based on-chip light source in PICs. Such integration leverages the benefits of superior optical properties of III-V materials, along with large wafer sizes and the low-cost and mature processing technology of Si. Direct epitaxy of QD-based laser on Si substrates has achieved remarkable progress [51, 54, 94, 95]. Various novel laser structures were reported with superior performance, such as distributed feedback lasers [96], comb lasers [97], photonic crystal lasers [98], topological lasers [99], etc. All key optical components integrated on a single SOI substrate are highly desired as they offer high integration density and great compatibility with the current Si microelectronics platform. Until now, the integration of III-V gain regions on SOI substrates mainly relies on wafer bonding, in which light is evanescently coupled to underlying Si waveguides [9, 20]. However, from the commercialization perspective, direct epitaxy is economically favored in terms of cost, yield, and scalability. Considering the integration of on-chip laser sources, the thick, defective buffer layer adopted for direct epitaxy of III-V materials on Si hinders the evanescent coupling of light from gain regions to underlying Si waveguides. In this case, SAG growth of laser structure on a trenched substrate and butt-coupled to the embedded, prepatterned waveguide is promising for fulfilling the last missing piece of Si-based PICs. In addition, SAG helps to alleviate the *From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

thermal stress of films, potentially preventing the formation of cracks [79]. On the other hand, such a method is nontrivial as it demands restricted design to minimize the alignment deviation between the central axis of the embedded Si waveguide and the InAs/GaAs QD active region and careful handle of polycrystal after the overgrowth of III-V on oxide.

Shang et al. recently reported the first electrically pumped continuous-wave (c.w.) InAs/GaAs QD lasers grown on a patterned 300 mm substrate [100]. In this study, the 200 nm GaP/Si template by NAsP III/V GmbH was adopted in trenches to prevent APBs [47, 66]. This was followed by a 1.6 μm GaAs buffer layer and InGaAs asymmetric graded dislocation filter layers to reduce TDD to around 1.5 <sup>10</sup><sup>7</sup> cm<sup>2</sup> . The active region consists of five stacks of InAs/GaAs DWELL structure separated by 37.5 nm GaAs space layers. The QD nucleation temperature was precisely determined using indium as an ex situ "temperature gauge" in this template to ensure high-quality QDs. As a result, room temperature with a wavelength of 1300 nm and a full width at half maximum (FWHM) of 32 meV was achieved for QDs. The as-grown 300 mm wafer from IQE with an identical growth method is shown in **Figure 20(a)**. The milky wafer surface caused by the deposited polycrystalline III-V on the oxide brought challenging tasks for device fabrication. A wet etch process for nonselective polycrystal removal facilitates the following fabrication process, as shown in **Figure 20(b)**. The top-down view of the as-cleaved laser with probe metal and the cross-sectional SEM image of the fabricated laser with a ridge width of 3.5 μm in a 20 μm trench are demonstrated in **Figure 20(c)** and **(d)**, respectively.

Finally, an electrically pumped InAs/GaAs laser was demonstrated with c.w. lasing up to 60°C, a maximum double-side power of 126.6 mW, and a threshold current of 47.5 mA. However, this work only presents a demo of an in-trench laser without demonstrating butt coupling between the laser and the embedded waveguide.

In a parallel effort, Wei et al. took a step further to test the butt coupling efficiency between their embedded InAs/GaAs QD lasers and Si waveguides. **Figure 21(a)** shows a schematic diagram of butt coupling between a trenched laser and a patterned Si waveguide. The fabricated devices are displayed in **Figure 21(b)** and **(c)**. Prior to growth, laser trenches and Si waveguides are prepatterned in an eight-inch SOI wafer,

#### **Figure 20.**

*(a) As-grown 300 mm wafer surface. (b) the fabrication process of the SAG laser. (c) As-cleaved laser with probe metal. (d) Cross-sectional SEM image of the fabricated laser in a 20* μ*m trench. ©2022 the authors under CC BY.*

#### **Figure 21.**

*(a) Schematic image of butt coupling between laser structure and Si waveguide. (b), (c) SEM and microscope images of trenched InAs/GaAs laser structure with prepatterned Si waveguide. (d)eight-inch wafer with predefined trenches and waveguides. (e) Microscope images of trenches for laser epitaxy and embedded Si waveguide. (f) and (d) patterned Si grating with 146 nm slab width and 209 nm gap for Si homoepitaxy and form Si {111} surfaces. ©2023 the authors under CC BY.*

and the periodic Si gratings are patterned inside the trench with 146 nm slab width and a 209 nm gap, as demonstrated in **Figure 21(d)** and **(e)**.

Instead of using a commercially available 200 nm GaP/Si template, Wei et al. adopted homoepitaxy of Si on the grating-patterned SOI trenches, which forms Si {111} facets to prevent the formation of APBs [46, 101]. The trenched laser is demonstrated in **Figure 22(a)**. A combination of a thin AlAs nucleation layer, a 2.1 μm GaAs

#### **Figure 22.**

*(a) Schematic image of the trenched laser structure. (b) 5 <sup>5</sup>* <sup>μ</sup>*m<sup>2</sup> AFM image of 2.1* <sup>μ</sup>*m GaAs buffer layer. (c) TDD of 2.6 <sup>10</sup><sup>7</sup> cm<sup>2</sup> is obtained for the GaAs buffer layer. (d) Cross-sectional TEM image of GaAs/Si (111) interface. (e) Comparison of PL measurement of trenched QD laser and blanket GaAs (001) laser with identical growth structure. Inset: Surface morphology of grown InAs/GaAs QDs of trenched laser. ©2023 the authors under CC BY.*

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

buffer layer consisting of InGaAs/GaAs DFLs, and GaAs/AlAs SLSs was adopted to reduce TDD to 2.6 107 cm<sup>2</sup> while maintaining low surface roughness of 0.8 nm in a <sup>5</sup> <sup>5</sup> <sup>μ</sup>m2 AFM scan, as shown in **Figure 22(b)**–**(d)**. The active region consists of seven stacks of InAs/GaAs DWELL structure separated by 39 nm GaAs space layers, sandwiched by 400 nm GaAs contact layers and Al0.4Ga0.6As cladding layers. A stepgraded AlGaAs layers were also adopted to enhance the current injection efficiency. A comparison of PL measurements between a laser with an identical structure grown on a trench and a GaAs (001) is given in **Figure 22(e)**. A similar PL intensity with a narrow FWHM of 33 nm is observed for trenched laser, attributed to high density and high uniform QDs, as shown in the inset of **Figure 22(e)**.

In this study, H3PO4:H2O2:H2O (1:2:20) wet etching was applied to remove unwanted polycrystalline III-V materials before fabrication. The trenched laser was processed with one-side cleaved and coated with a high-reflection coating. While the other side implements wet etch followed by two-step focused ion beam milling to produce high-quality facets. A High-performance trenched QD laser was fabricated with c.w. lasing up to 85°C, low threshold current of 50 mA and maximum output power of 37 mW at an injection current of 250 mA. Butt coupling efficiency between QD active region and Si waveguide was determined. A maximum power of 6.8 mW was measured at the end tip of the Si waveguide, indicating 6.7db coupling efficiency. A further improvement in coupling efficiency can be achieved by using an advanced silicon spot-size converter with precise control of the gap between the facet and the waveguide. This laser offers a prospective technique for realizing an on-chip light source for Si-based PICs.

#### **3.1 Summary**

Demonstrating high-performance trenched QD lasers shapes the faith in realizing the monolithic integration of III-V lasers for Si-based PICs as on-chip sources. It paves the way toward large-scale, high-density, low-cost PICs for the forthcoming bloom of quantum and sensing technologies.

#### **4. Conclusions**

Heteroepitaxial growth of III-V materials onto Si substrates offers an appealing approach for achieving practical Si-based on-chip light sources. Because of the large lattice mismatch between III-V materials and Si, the formation of crystal defects, including TDs, APBs, and micro-cracks, is inevitable during the epitaxy. Over the past decades, great advances in growth techniques have been made to control these defects to a reasonably low value, and state-of-the-art techniques are reviewed in this chapter. Hence, the performance of InAs QD laser grown on Si substrates progresses rapidly in terms of threshold current, maximum working temperature, and reliability. A step further is urgent to migrate these techniques into Si-based PICs, which are primed to support the growing market of automotive, sensing techniques, and quantum technologies. In order to integrate the InAs/GaAs QD light source on Si-based PICs, SAG growth of laser structure on a trenched substrate and butt-coupled to the embedded, prepatterned waveguide is regarded as a promising candidate for realizing on-chip light sources. Though only a few reports have demonstrated a demo for coupling light from trenched InAs QDs active region into the waveguide, the initial results are promising, which shapes the faith of achieving monolithic integration of III-V lasers as an on-chip light source. The realization of Si-based PICs will undoubtedly unleash the great potential of emerging technologies in the near future.

### **Acknowledgements**

This work was supported by the UK Engineering and Physical Sciences Research Council (EP/P006973/1, EP/T028475/1, EP/X015300/1).

#### **Author details**

Junjie Yang\*, Huiwen Deng, Jae-Seong Park, Siming Chen, Mingchu Tang and Huiyun Liu Department of Electronic and Electrical Engineering, University College London, London, United Kingdom

\*Address all correspondence to: zceejya@ucl.ac.uk

© 2023 The Author(s). Licensee IntechOpen. 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.

*From Challenges to Solutions, Heteroepitaxy of GaAs-Based Materials on Si for Si Photonics DOI: http://dx.doi.org/10.5772/intechopen.114062*

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#### **Chapter 4**

## Molecular Beam Epitaxy of Si, Ge, and Sn and Their Compounds

*Daniel Schwarz, Michael Oehme and Erich Kasper*

#### **Abstract**

In the past decade, the increasing need for high-performance micro- and nanoelectronics has driven the research on group IV heterostructure devices, which utilize quantum effects as dominant working principle. The compound semiconductor SiGeSn has presented itself as promising material system for group IV heterostructures due to its unique properties. Prominent applications range from the Si-integrated laser to tunneling field effect transistors for the next complementary metal oxide semiconductor generations. However, the epitaxy of heterostructures requires atomic sharp material transitions as well as high crystal quality, conditions where molecular beam epitaxy is the method of choice since it can take place beyond the thermodynamic equilibrium. Besides the numerous opportunities, the molecular beam epitaxy of SiGeSn poses various challenges, like the limited solid solubility of Sn in Si and Ge and the segregation of Sn. In this chapter, we discuss the molecular beam epitaxy of SiGeSn at ultra-low temperatures to suppress these effects.

**Keywords:** molecular beam epitaxy, group IV compounds, silicon, germanium, tin, silicon-germanium-tin, heteroepitaxy

#### **1. Introduction**

Since its inception in the 1950s, the microelectronics market has grown to one of the world's most important industries. The upcoming end of Moore's law and the steady need for faster and higher-performing devices have driven the research on novel device concepts. Particularly for devices that functionalize quantum effects and heterostructures, atomic sharp structures in the nanometer regime become more and more important and attract the interest of research.

In this context, molecular beam epitaxy (MBE) is a beloved technique since it allows atomically precise deposition control as well as the process procedure beyond the thermodynamic equilibrium. Although MBE is not the best-suited tool for mass production, its uniqueness makes MBE the method of choice for research applications.

Due to the highly developed Si-based complementary metal oxide semiconductor (CMOS) technology, the MBE of Si and other group IV compounds has become more and more important in the last few decades. Possible research topics are the Siintegrated laser [1–3], the last missing key component for optical on-chip communication, as well as novel transistor concepts for future CMOS generations [4–6].

Although the beginnings of Si-MBE reached into the late 1970s and early 1980s [7–10], its number of possible applications increased rapidly since the first synthesis of Sn-containing group IV compounds [11–15]. However, generally, the epitaxy of Sncontaining group IV compounds has proven itself quite challenging due to undesirable effects, like the temperature and strain intensified segregation of Sn [16, 17], the limited solid solubility of Sn in Ge and Si of less than 1% [18, 19], and the low melting point of Sn of 231.9°C [20]. Altogether, this reasons the necessity for the execution of the MBE of group IV compounds at ultra-low substrate temperatures in the range of approximately 160°C.

In this chapter, we not only lay the basics but also discuss the particularities of the MBE of group IV compounds. For this, Section 2 deals with the physical processes on the substrate and undesired effects during the MBE process as well as the various growth modes of heteroepitaxy. Afterwards, Section 3 presents the requirements for the basic components of a group IV MBE system. Finally, Section 4 highlights some of the most important insights of the MBE of SiGeSn.

#### **2. Basics of molecular beam epitaxy**

In a typical MBE experiment, several molecular or atomic beams are directed toward a well-oriented single crystalline substrate with beam flux densities *J* in the order of 10<sup>15</sup> cm�<sup>2</sup> s �<sup>1</sup> for matrix elements (group IV elements in our case) and lower 10<sup>12</sup> cm�<sup>2</sup> s �<sup>1</sup> for doping elements (group III for p-doping, group V for n-doping). The technical solutions for beam sources are described in the next section.

The molecules or atoms on a beam have a velocity *vL* of several hundred to thousand meters per second. That velocity defines two time scales. A variation of the beam intensity (on/off) is transferred to the substrate, which is typically in a distance of 10 to 50 cm, within a millisecond. In most cases, the transfer of beam on/off is defined by the technical design of the beam shutter construction. However, beam on/ off switching is obtained within subnanometer and nanometer dimensions of growth, routinely. This exact control of beam fluxes makes MBE a valued method for research on nanometer heterostructures.

Another important time scale is defined by the length of interaction between the arriving beam atoms and the growing layer. Very close to the surface (nanometers or less), the atoms are attracted and accelerated toward the surface. The time scale for this interaction is in the picosecond (10�<sup>12</sup> s) range.

Elastic scattering would result in a reflection of the atomic beam. The transfer of energy, momentum, and angular momentum to phonons within the picosecond time frame would result in adsorption of the atom on the surface. For single atoms with strong bonding, as in the case of group IV epitaxy, the sticking probability is near unity. This is important for good control of alloy mixing and doping with calibrated beam flux densities.

The thermal velocities *vB* are given by mean energy considerations as

$$
\upsilon\_B^2 = \frac{3k\_B}{M\_P} \cdot \frac{T\_B}{M} \tag{1}
$$

with the constants, the Boltzmann constant *kB* <sup>¼</sup> <sup>1</sup>*:*<sup>38</sup> � <sup>10</sup>�23J*=*K and the proton mass *MP* <sup>¼</sup> <sup>1</sup>*:*<sup>67</sup> � <sup>10</sup>�<sup>27</sup> kg and the variables, the beam source temperature *TB* and the atomic weight *M*. For a Si beam, one will get *vB* ¼ 1300 m*=*s with *TB* ¼ 2000 K and *M* ¼ 28.

#### **2.1 Sticking, adsorption, and desorption of atoms**

The sticking of atoms from group IV elements on a diamond-type lattice with strong bonds is unity. This is proven for Si [21] but can reasonably also be assumed for other group IV systems. The same conclusion is valid for the doping atoms from groups III and V, which are strongly bonded on lattice sites. Complete sticking allows the realization of complex designs with heterostructures and doping transitions using calibrated beam fluxes.

The arriving atom sticks on the surface as an isolated adatom which is weaker bonded to the crystal than a bulk atom.

$$\mathcal{W} = \mathcal{W}\_{\text{ad}} + \mathcal{W}\_{\text{S}} \tag{2}$$

The evaporation energy *W* of a bulk material is composed of the adsorption energy *W*ad and the additional surface energy *WS*, which is gained from the incorporation of an adatom on the kink of a surface step, as seen in the left part of **Figure 1**. The value of *W* can be extracted from the temperature-dependent vapor pressure of the matrix element. At equilibrium, the incoming flux of the vapor equals the desorbing flux density *F*eq of the epitaxial surface. The typical value of *W* amounts to several electronvolts per atom (Si: *W* ¼ 4*:*55 eV*=*atom).

The adsorption energy *W*ad depends on the surface orientation and on the reconstruction of the surface. For model calculations, often a value of 2*=*3*W* is assumed. The impinging flux *FS* of atoms is usually much higher than the desorbing flux because MBE conditions are preferably in the lower growth temperature regime. That means the supersaturation *σ* is high. We define here the supersaturation as

$$
\sigma = \frac{F\_{\text{S}}}{F\_{\text{eq}}} = \mathbf{1} \tag{3}
$$

Sometimes, the value of ln *σ* is also called supersaturation. It must be considered that supersaturation under growth conditions causes an increase in the concentration of adatoms from the equilibrium value *ns*<sup>0</sup> to an *ns*, which is dependent on the distance to the next step.

#### **Figure 1.**

*Adsorption and incorporation of an atomic beam. Left: Schematic view of a substrate surface with an adatom (striped), a surface step, and an incorporated adatom at a kink side of an atomic step (checked). Right: Binding energy diagram for the movement of an adatom in x-direction with the adsorption energy W*ad*, the bulk crystal binding energy W, and the surface diffusion barrier US.*

Steps on the surface, mainly of mono-atomic or bi-atomic height *h*, stem from three sources.

• Slight surface misorientation of the nominal surface with low index planes (Miller index: (001) planes perpendicular to the cubic axes, (111) planes perpendicular to the cubic diagonals). The preferred surface orientation for Si substrates is (001) because the interface quality between dielectrics and semiconductors is the best. Commercially available substrates typically have a misorientation angle *<sup>i</sup>* below *<sup>i</sup>* <sup>&</sup>lt;0*:*25° arc *<sup>i</sup>* <sup>≤</sup><sup>4</sup> � <sup>10</sup>�<sup>3</sup>

$$\text{arc}\,i = \frac{h}{L} \tag{4}$$

with the atomic step height *h* and the length of the terrace to the next step *L*. With *h* ¼ 0*:*14 nm, the mono-atomic step height on Si(001), one obtains terrace lengths of *L*>35 nm. That means commercial substrates already deliver a dense sequence of steps. The microscopic picture of the macroscopic growth in vertical direction is, therefore, a lateral movement of step trains. The steps move in the downward direction by the repeated incorporation of adatoms to the kink position on steps.


The critical nucleus forms by a dynamic process counterbalancing the incoming adatom flux, which is proportional to the adatom density, and the leaving adatom flux which is dependent on the nucleus size. In effect, this means an increase of steps when the surface adatom supersaturation *σ<sup>S</sup>* surpasses a value necessary for the formation of critical nuclei.

$$
\sigma\_S = \frac{n\_S}{n\_{S0}} - \mathbf{1} \tag{5}
$$

There is an important difference of these nuclei steps and steps from misorientation. The step trains from misorientation follow the inclination direction.

**Figure 2.**

*Schematic presentation of the two-dimensional nucleation. Top: Development of a stable nucleus. Bottom: Decay of a critical nucleus.*

The steps from adjacent nuclei move forward and become extinct when they meet. For each mono-atomic step, a new nuclei must be formed. The caused periodic modulation of the step density may be observed with sensitive methods like RHEED (reflection high energy electron diffraction).

#### **2.2 Growth modes of strained heteroepitaxy**

The macroscopic growth mode models, as seen in **Figure 3**, predict twodimensional (2D) growth (Frank v. d. Merve), three-dimensional (3D) growth (Volmer-Weber), or mixed 2D/3D growth (Stranski-Krastanov) from a balance of surface energies of the substrate *ES* and the film *Ef* and the interface energy *Ei* densities

$$E\_S - E\_i = E\_f \cdot \cos\Theta \tag{6}$$

The inclination angle Θ ≥0 of a 3D island is given by Eq. (6). Solutions with cos Θ ≥1 deliver 2D growth. Mixed 2D/3D growth mode is only possible for a thickness-dependent *Ei* term

Microscopic theories explain the thickness dependence of the interface energy by contributions from the elastic film strain and from the interface misfit-dislocation network. **Table 1** gives the lattice constants of the diamond-type lattice cell for the group IV elements C, Si, Ge, and Sn.

#### **Figure 3.**

*Monocrystalline growth models on a crystalline substrate (checked). Left: Two-dimensional (2D) growth according to Frank van der Merve. Middle: Three-dimensional (3D) growth according to Volmer-Weber. Right: Mixed twothree-dimensional growth according to Stranski-Krastanov.*


**Table 1.**

*Lattice constants of the group IV elements C, Si, Ge, and Sn.*

For the group IV compound SiGeSn, the lattice constant *a*0,SiGeSn depends on the compound composition and follows the relationship in Eq. (7):

$$
\sigma\_{\rm O,SiGeSn} = \sigma\_{\rm Si} \cdot \sigma\_{\rm Si} + \sigma\_{\rm Ge} \cdot \sigma\_{\rm Ge} + \sigma\_{\rm Sn} \cdot \sigma\_{\rm Sn} \tag{7}
$$

In heteroepitaxy, two materials, hence the film and the substrate, with different electrical and mechanical properties but the same crystal structure, are grown on each other. Therefore, the lattice constant of the grown film *af* usually differs from the lattice constant of the substrate *aS*. The relative lattice constant difference, according to Eq. (8), is called lattice mismatch *f*:

$$f = \frac{\mathfrak{a}\_f - \mathfrak{a}\_{\mathbb{S}}}{\mathfrak{a}\_{\mathbb{S}}} \tag{8}$$

Due to the lattice mismatch, three possible cases, as shown in **Figure 4**, are conceivable: For pseudomorphic, also known as coherent, growth, the atomic rows of the film fit exactly to the underlying rows of the substrate. In other words, the inplane lattice constant of the film *a*k,*<sup>f</sup>* adapts to the lattice constant of the substrate *aS* (see left part of **Figure 4**). However, due to the different lattice constants of the two materials, this can only take place under the formation of elastic strain of the film with the in-plane strain *ε*<sup>k</sup> ¼ �*f*.

The elastic strain energy of a pseudomorphic film is proportional to the film thickness. This pseudomorphic state holds only up to a critical thickness *tC* of the film. Above this critical thickness for strained films, dislocations are nucleated and bend to the interface for a partial relief of strain. Nanometer films and structures may be strained to much higher values, for example 1% strain in 10 nm thickness, than bulk material. This high tolerance of high strain values in nanometer structures is the base of strain engineering in electronics and photonics. Films with a thickness above the critical thickness, but which exhibit residual strain, are referred to as partially relaxed (see middle part of **Figure 4**).

In the case of complete relief of strain, the resulting film is called completely strain relaxed. The corresponding growth mode is thus called strain-relaxed growth.

#### **Figure 4.**

*Comparison of the growth modes of heteroepitaxy with the grown film (brown) on the substrate (blue) left: Pseudomorphic growth. Middle: Partial-relaxed growth. Right: Strain-relaxed growth.*

*Molecular Beam Epitaxy of Si, Ge, and Sn and Their Compounds DOI: http://dx.doi.org/10.5772/intechopen.114058*

A special case of heteroepitaxy can be performed with SiGeSn. The mixing of Si and Sn with Ge allows a decrease of the lattice constant with Si and an increase with Sn. Therefore, SiGeSn allows the decoupling of its electrical and mechanical properties from its lattice constant. Consequently, SiGeSn can be grown latticematched on Ge and even on GeSn. In order to achieve this so-called lattice-matching on Ge, a constant ratio of the Si and Sn concentration, according to Eq. (9), has to be fulfilled:

$$\frac{a\_{\rm Si}}{a\_{\rm Sn}} = \frac{a\_{\rm Ge} - a\_{\rm Sn}}{a\_{\rm Si} - a\_{\rm Ge}} = 3.67 \tag{9}$$

#### **2.3 Limits of single crystalline growth**

Considering a strongly magnified picture of the epitaxy process reveals that approx. 10<sup>15</sup> atoms*<sup>=</sup>* cm2 ð Þ<sup>s</sup> are impinging on the surface. In the MBE regime without desorption, the growth rate *R* is determined by Eq. (10):

$$R = F\_{\mathcal{S}} \cdot \mathfrak{Q} \tag{10}$$

with the beam flux density *<sup>j</sup>* and the atomic volume <sup>Ω</sup> <sup>¼</sup> <sup>2</sup> � <sup>10</sup>�<sup>23</sup> cm<sup>3</sup> for Si.

The growth rate equals a coverage of approx. one monolayer (ML) per second. This means each atom out of the 1015 atoms*<sup>=</sup>* cm<sup>2</sup> ð Þ<sup>s</sup> have to find their position on a lattice site within roughly 1 s; otherwise, the next monolayer flux would cover and fix them on unwanted sites, producing interstitials and vacancies. Exactly that is happening at very low growth temperatures of approx. 20–100°C, resulting in a growth start with single crystalline layers of high crystal defect density and subsequently an alteration to amorphous material after a critical thickness of crystalline growth at low temperatures. It has to be considered that this low-temperature growth *critical thickness* is not the same as that of the coherent growth of mismatched structures. This defect-rich growth regime is not applicable for working devices but is useful as a nucleation starter for dislocations [25] and amorphous structures.

#### **2.4 Segregation**

Through the usage of MBE, the influences of the volume diffusion of doping or alloy atoms within the Si or SiGeSn crystal can be remarkably reduced. However, the effect of surface segregation, which results in a broadening or smearing of doping profiles, can also be observed in these epitaxial layers. In order to suppress this effect, special epitaxial strategies are needed. The basic mechanism of surface segregation is an exchange of atoms from subsurface states to surface states due to the energetically favorable surface adatom position (see **Figure 5**). The segregation is quantified by the segregation length *Δs* [9], which is the ratio of the impurity surface concentration *nS* and the bulk concentration *nB*. The segregation length *Δs*, thus defined, can be converted into the dimensionless segregation coefficient *S* by dividing it by the thickness of a monolayer. Segregation leads, therefore, to an increasing impurity surface concentration *nS*, which saturates at an equilibrium where the number of segregating adatoms equals the number of incorporating adatoms. Therefore, the resulting doping profile shows an exponential increase after the beginning of the co-evaporation of dopant and lattice atoms. Consequently, the segregation length *Δs* describes the length in the growth direction from the beginning of co-evaporation to reaching equilibrium.

**Figure 5.**

*Left: Dopant atom (blue) in subsurface state. Middle: Dopant atom swaps its place with a surface crystal adatom (gray striped). Right: Further overgrowth leads to the same situation as before.*

The segregation length is typically in the order of a few nanometers but can, outside of the optimum growth parameter window, increase to several tenth to hundred nanometers.

Generally, the perfect abruptness of transitions may be obtained by a growth interruption, in which the equilibrium adatom concentration of the doping or alloy element is adjusted. These techniques are called prebuild-up for ramp-up and flash-off for an abrupt ramp-down.

The surface segregation of Sb in Si and Ge is strongly dependent on the growth temperature [9, 26–28]. In order to achieve an atomic sharp doping profile, the growth strategy, which is known as prebuild-up, can be used. For this, the adatom concentration required for equilibrium, which is typically less than a monolayer, is evaporated onto the surface before the co-evaporation begins. At the beginning of the subsequent co-evaporation, the number of incorporated adatoms per monolayer is already at the desired value.

The biggest disadvantage of the prebuild-up technique to counteract surface segregation is the remaining surface concentration of segregated atoms. Following the segregation mechanism, the surface concentration decreases linearly subsequently to the co-evaporation of dopant and matrix atoms, which leads in turn to a nonideal doping profile. Therefore, special methods are needed to get rid of the segregated surface concentration such as the flash-off method. Here, a growth interruption is used for an increase of the substrate temperature to a value where the remaining segregated atoms are being desorbed from the epitaxial surface. However, depending on the element to be desorbed, the necessary temperature for this can be relatively high and in an unfavorable range for the already grown crystal. In order to avoid the disadvantages of high temperature flash-off, the "freeze out" method may be used by which growth rate and temperature are reduced to form a delta-doping structure from the adlayer. This is specially of advantage in device structures with highly doped regions in contacts, in buried layers, and in modulation-doped quantum wells.

Besides the described prebuild-up technique, other methods can be used to suppress or counteract surface segregation. A possibility is the doping by secondary implantation (DSI) [29, 30]. In the example of Si, which is being evaporated using an electron beam evaporator (see Section 3.1.2), the molecular beam contains Si atoms as well as Si<sup>+</sup> ions. These Si<sup>+</sup> ions can then be accelerated toward the substrate using an electric field. Once these accelerated ions hit the substrate surface, they can drive segregated atoms further into the crystal and, therefore, counteract the segregation. Furthermore, special effusion cells are conceivable in which the evaporated atoms are ionized in an additional stage, whereby the dopants themselves can be accelerated toward the substrate surface [31, 32].

The presence of a third species of adatoms also influences the segregation length because the species with higher binding energy occupies the crystal positions faster. We call the third species a surfactant if it is added only to reduce the segregation length of the second species.

Particularly in the MBE of group IV compounds such as SiGeSn, segregation has a huge influence on the incorporation of Sn [16, 33]. In this case, segregation not only leads to a smearing out of the alloy composition but also to a disturbance of the epitaxy process. The consequences of Sn segregation range from an increased point defect concentration within the crystal over the formation of Sn precipitates on the surface and finally to the complete breakdown of the epitaxial process (see Section 4). Consequently, many of the previously described methods to counteract the surface segregation are not applicable for the MBE of SiGeSn which in turn justifies the necessity of ultra-low-temperature MBE of these group IV compounds.

#### **3. Molecular beam epitaxy of group IV compounds and low-dimensional structures**

#### **3.1 Molecular beam sources**

#### *3.1.1 Theory of molecular beam sources*

Different types of molecular beam sources are used in MBE systems depending on the physical properties of the material to be evaporated or sublimated. The equilibrium vapor pressure *p*<sup>0</sup> as a function of the absolute temperature *T* of the vaporization material plays an important role. From this dependency, the particle flux *F*<sup>0</sup> emitted by a surface is calculated with Eq. (11) as follows:

$$F\_0 = p\_0 \sqrt{\frac{N\_A}{2\pi M\_r k\_B T}}\tag{11}$$

with the surface temperature *T*, the molecular weight *Mr* of the considered element or molecule, the Avogadro constant *NA*, and the Boltzmann constant *kB*. From the evaporation rate *Γ*<sup>0</sup> at the surface of a melt, the area-specific particle flux can be calculated, which vaporizes an area *A* at a distance *r* and at an angle *ϑ*. The flux *FS* arriving there is inversely proportional to the square of the distance *r* and has the same characteristics as the evaporation rate to a first approximation. At some distance, the effusion cell acts like a point source of flux with a cosine distribution. The particle flux *FS* impinging on the substrate is then given with Eq. (12) as follows:

$$F\_S = \frac{\Gamma\_0}{r^2} \cos \theta = \frac{F\_0 A}{r^2} \cos \theta \tag{12}$$

The required working temperatures can be determined with these formulas. For this purpose, the vapor pressures as a function of the temperature for the corresponding elements are taken from the literature. It is additionally assumed that the typical evaporation area is 1 cm2 , and the distance between the evaporation surface and the substrate is *r* ¼ 30 cm. Furthermore, perpendicular incidence is assumed ð Þ *ϑ* ¼ 0 .

The left graph in **Figure 6** shows the results of the calculations for the matrix materials of group IV. Therefore, the necessary temperature range to achieve the required growth rates for the respective molecular beam sources can be seen in this diagram. The growth rate *R* corresponds to the right scale on the example of a Si(100) surface.

For a Si molecular beam source, a working temperature range between 1460°C≤*T* ≤ 1820°C results in growth rates of 0*:*1*Å=s*≤*R* ≤10*Å=s*. Using the melting point of Si (*T*melt,Si ¼ 1410°C), it follows that Si is evaporated instead of sublimated, which means that a crucible must be used.

In case of the growth of carbon, the working range of a molecular beam source is between 2270°C ≤*T* ≤2630°C for growth rates of 0*:*1*Å=s*≤ *R*≤10*Å=s*. However, since the melting point of carbon (*T*melt,C ¼ 3550°C) is significantly higher, carbon is only sublimated under MBE conditions. Therefore, carbon can be used directly as a filament material.

The right-hand graph of **Figure 6** shows the particle fluxes on the substrate as a function of the surface temperature of the material to be evaporated for typical group IV doping materials. In Si-based technology, only the element B is used for p-type doping. For a large variation of the doping concentration between 10<sup>16</sup> cm�<sup>3</sup> ≤ *NA* ≤ 10<sup>20</sup> cm�3, the resulting typical working temperature of a B source in the range of 1200°C≤*T* ≤1600°C, as it can be read in the vapor pressure curve. Since the melting point of B is *T*melt,B ¼ 2076°C, B belongs to the sublimated materials under MBE conditions.

The typical n-type dopants in Si technology are P and As, although Sb is also used. The respective vapor pressure curves are also shown in the right graph of **Figure 6**. The typical temperatures for the evaporation of the element P for doping concentrations between 10<sup>16</sup> cm�<sup>3</sup> ≤ *ND* ≤10<sup>20</sup> cm�<sup>3</sup> are in this regard in the range of 33°C≤*T* ≤ 97°C. This is very problematic in an ultra-high vacuum (UHV) chamber, since an effusion cell coats not only the substrate but also the rest of the chamber, specifically the chamber walls. However, these P deposits evaporate again at low temperatures, resulting in a continuous flow of P throughout the growth chamber. The result is a tremendous background doping in the epitaxial layer.

Things are looking a little better for the next group V element, As. The typical temperature range here is between 81°C≤*T* ≤ 172°C. For the conditioning of the

#### **Figure 6.**

*Particle flux on the substrate as a function of the inverse surface temperature* 1*=T of the evaporation material. Left: Typical group IV matrix materials. Right: Typical doping materials for Si-based devices. (data source: [34]).*

UHV, the entire chamber is heated at *T* ≥200°C. In the case of residual As in the chamber, it would be distributed evenly in the chamber during this conditioning, leading to a similarly increased background doping.

Consequently, the group V element Sb is typically used as n-type dopant in a Si-MBE system. The resulting working range of an Sb beam source is between 240°C≤ *T* ≤380°C. Since the melting point of Sb is *T*melt,Sb ¼ 630°C, Sb is being sublimated under MBE condition.

The choice of the appropriate molecular beam source is based on the vapor pressure curve and the melting point of the material to be evaporated. The possibilities include electron beam evaporators (EBE), effusion cells, and high-temperature sublimation cells.

#### *3.1.2 Electron beam evaporators*

Although any material can be evaporated using an EBE, their technical realization is very challenging. A schematic drawing of the main components and the functionality of a Si EBE is shown in the left part of **Figure 7**.

A W filament emits electrons which are accelerated in an electric field with typical energies between 8 and 12 keV. Since metallic impurities in the Si melt are undesirable, the electrons, emitted from the filament, are thereupon deflected at an angle of 270° using a magnetostatic field, which does not manipulate the also emitted W atoms. Due to the high reactivity of molten Si, it would attack any crucible material, which in turn leads to an excessive contamination of the melt and the molecular beam with the crucible material itself. Therefore, Si acts in an EBE as its own crucible material. For this purpose, a high-purity Si ingot is used, which is placed in a watercooled Cu crucible. The electron beam melts the Si only partially on the surface. By using an additional electromagnetic field, the electron beam can be scanned over the entire crucible to adjust the molten area. Due to the thermal properties of Si, the molten area is limited to the area directly heated by the electron beam.

#### **Figure 7.**

*Left: Schematic drawing of the main components and the functionality of an electron beam evaporator (EBE) for the evaporation of Si. Right: Marangoni convection caused turbulence in the Si melt.*

The EBE is controlled using a quadrupole mass spectrometer (QMS), which directly measures the intensity of the Si isotope with the mass number 30 in the Si molecular beam. The measurement signal is proportional to the flux or the growth rate on the substrate surface and can be used as a control parameter. A problem of heating with electrons is the Marangoni convection in the Si melt, as seen in the right part of **Figure 7**.

Since there are subareas of different temperatures with different surface tensions in the molten Si, turbulent flows arise in the melt, leading to high flux fluctuations. Although this effect can be compensated by the regulation using a QMS, the flux of an EBE underlies higher fluctuations compared to an effusion cell. However, the biggest advantage of an EBE in comparison to effusion cells is the high rate of change of the desired Si flux. The disadvantage, on the other hand, is the already mentioned fluctuation of the Si rate, which is in the range of approx. 10%.

#### *3.1.3 Effusion cells*

In an effusion cell, the crucible is heated from the outside and from below by thermal radiation. For this purpose, the crucible is surrounded by an electric heater. The production of uniform layers requires a constant flux over time. The flux from an effusion cell is determined indirectly based on the cell temperature and can be regulated by the applied heating power. The task of controlling a cell is to keep the cell temperature as constant as possible at a specified value, or to reach a new nominal temperature as quickly as possible. The regulation of the temperature of an effusion cell by the heating power must be very precise since the evaporated flux increases exponentially with the temperature.

The thermal properties of an effusion cell are the static and dynamic relationships between the conversion of electrical energy into heat, the propagation and dissipation of the thermal energy, and its effect on the evaporated flux. The material flux can only be controlled precisely if its reaction to the electrical power input is known. Since the heating element is located inside the effusion cell, the electrical heating power is initially transferred to the cell. If one neglects delays due to heat capacities, a power balance can be drawn up at any point in time: The sum of all power losses corresponds to the electrical power input. Thermal energy can be transported between two bodies by the following three mechanisms:


This results in the following heat loss mechanisms for a typical effusion cell:


The ratio of the parts in the total power depends on the temperature of the cell and, thus on the induced electrical power. For the most thermally stable operation possible, the power loss must be minimized.

A schematic drawing of the structure of an effusion cell can be seen in the left part of **Figure 8**. The evaporating material is placed in a pyrolytic BN crucible (PBN). This crucible is heated using a meander-shaped graphite heater. Side and bottom shields made of Ta minimize the thermal losses of the effusion cell. A water-carrying cooling shroud is used for a further reduction of the thermal radiation into the MBE chamber. The temperature of the crucible is measured using a thermocouple, which has to be calibrated to the actual temperature of the melt. The molecular flux can be switched on or off with a shutter.

The illustration on the right part of **Figure 8** shows a technical realization of a Ge effusion cell. The effusion cell is built on a flange with a diameter of 150 mm and has a crucible with a volume of 100 cm3 . The built-in thermocouple of an effusion cell is used to monitor and control it. Besides that, it is also possible to directly measure and control the atomic or molecular flux using a QMS. The advantage of an effusion cell is the very stable molecular flux. However, due to the good thermal isolation of the cell, the rate of change in the molecular flux is very limited, in comparison with an EBE.

#### **3.2** *In situ* **reflectometry**

The *in situ* analysis describes the measurement of various process parameters during the epitaxy process in an MBE chamber. In addition to measuring the composition of the residual gas, the actual surface temperature of the substrate, a measurement of the reflectivity of the epitaxial layers can also be carried out directly during the process. The so-called *in situ* reflectometry is interesting when the optical properties of the epitaxial layer change compared to the underlying substrate or layer

#### **Figure 8.**

*Left: Schematic scheme of an effusion cell. Right: Real Ge effusion cell on a 150 mm flange. The crucible has a volume of 100 cm<sup>3</sup> . The meander-shaped heater is made of graphite.*

stack. For example, a change from monocrystalline to amorphous growth can be observed. In the case of heteroepitaxial growth, the thickness of the growing layer can also be measured using *in situ* reflectometry.

The perpendicularly incident light beam is reflected both at the growth surface and at the interface between the substrate and the heterolayer, as it can be seen in the left part of **Figure 9**, which leads to the interference of the respective parts.

A typical measurement of the reflectivity during a growth process is shown in the right part of **Figure 9**. The growth typically begins with a Si buffer on the Si substrate. Since the optical properties do not change between the film and the substrate, the reflectivity measurements remain constant at both used wavelengths. At a time *t* ¼ 0 s, the heteroepitaxial growth of a SiGe layer begins. Therefore, the reflectivity of the epitaxial layer changes from *n*epi ¼ *n*sub ¼ *n*Si to then *n*epi ¼ *n*SiGe immediately with increasing thickness of the SiGe layer. Therefore, the already mentioned thickness interference can be observed. Using the positions of the arising maxima and minima, the corresponding thickness *d* of the epitaxial SiGe layer can be calculated using Eq. (13) and Eq. (14), respectively.

For *n*epi >*n*sub the following Eq. (13) applies for the maxima:

$$m\_{\rm epi} \cdot d = \frac{\lambda}{4} \cdot (2m + 1) \tag{13}$$

and Eq. (14) applies for the minima:

$$m\_{\rm epi} \cdot d = \frac{\lambda}{2} \cdot m \text{ with } m \in \mathbb{N} \tag{14}$$

with the wavelength *λ* of the used light.

Besides that, a weakening of the oscillations for the wavelength of 670 nm is measured. This is due to the absorption behavior of the SiGe layer. Consequently, the absorption behavior of the epitaxial-grown material can be determined from these measurements. On the other hand, at a wavelength of 950 nm, the absorption is negligible.

The technical implementation of an *in situ* reflection measurement is shown in **Figure 10**. In order to enable the necessary perpendicular incidence of light, a flange

#### **Figure 9.**

*Left: Schematic drawing of the reflectometry measurement principle. Right: Exemplary* in situ *reflection measurements at the wavelengths of 670 and 950 nm during the growth of an Si buffer and a SiGe layer on a Si substrate.*

**Figure 10.**

*Schematic drawing of the setup for* in situ *measurement of the reflectivity of the growing layer. The measuring system is attached to the growth chamber in such a way that the reflectivity can be measured under vertical incidence of light.*

with a window is mounted directly under the substrate on the growth chamber. The measurement head contains several light sources at different wavelengths and a corresponding detector. For an optimal homogeneity of the layer thickness over the entire wafer, the substrate is rotated during growth. In order to compensate for slight wobbling movements, the reflectivity measurement is synchronized with the rotation.

#### **3.3 Substrate heating and temperature measurement**

Heating of the substrate surface during the epitaxy process is necessary due to various reasons. As mentioned in Section 2.1, heating provides not only enough energy for adatoms to reach their preferred destination on the crystal surface. Furthermore, heating of the substrate prevents the adsorption of undesired elements of the residual gas and, therefore, the concentration of impurities.

As described in Section 3.1, thermal energy can be transported by three different mechanisms. Due to the lack of a transport medium as well as the necessity for substrate rotation, the mechanism of choice for the transport of thermal energy under MBE conditions is thermal radiation. The typical temperature regime for the substrate heating for the epitaxy of group IV compounds is in the range of 100°C≤*TS* ≤1200°C. According to Planck's radiation law, the corresponding radiation is, as seen in the left part of **Figure 11**, in the wavelength range of *λ*≥1100 nm. However, the absorption of typically used Si substrates is due to the bandgap of Si of *Eg* ¼ 1*:*12 eV limited to wavelengths *λ*<1100 nm (see the absorption border of Si in the left part of **Figure 11**). Therefore, the heating of Si substrates in a group IV MBE system is based not on the fundamental absorption but on the free carrier absorption.

The necessary infrared radiation for the heating of the substrates is generated using a graphite meander-based electrical heater. A schematic drawing of such a heater is shown in the right part of **Figure 11**. The measurement and control of the

**Figure 11.**

*Left: Thermal emission of a radiative heater according to Planck's radiation law. Right: Schematic drawing of a graphite meander-based electrical heater and the used thermocouple for measurement and control of the substrate temperature.*

substrate temperature is generally performed using a thermocouple, which is located behind the graphite heater. Due to the heating *via* free carrier absorption, the measurement of the thermocouple is calibrated once to the actual substrate surface temperature using a second thermocouple mounted to the surface of a calibration wafer. Since the amount of free carriers in a semiconductor can be manipulated *via* doping, the resulting calibration is dependent on the substrate doping concentration.

Despite the necessity of substrate heating, too high substrate temperatures promote undesired, epitaxy disturbing effects, especially the already in Section 2.4 described segregation. In particular, the MBE of group IV compounds suffers from the segregation of Sn [16, 33], which causes its often-reported temperature sensitivity. Furthermore, the limited solid solubility of Sn in Ge of less than 1%, the instability of the preferred α-Sn phase with its transition to β-Sn at 13.2°C, and the occurring inplane strain of GeSn on Ge amplify this effect. While not only hindering the incorporation of Sn, the segregation also leads to a high number of lattice defects, and, due to the increasing surface concentration of Sn, to β-Sn clusters and the subsequent epitaxial breakdown. All this together underlines the necessity to perform the epitaxy of SiGeSn at ultra-low substrate temperatures in the range of *TS* ≈ 160°C.

However, in this temperature regime, not only the substrate heater itself has an influence on the actual substrate temperature but also the thermal radiation of the molecular beam sources. In fact, their influence is, in this regime, the more dominant one and restricts the controllability of the substrate temperature on the base of thermocouple measurement. Therefore, an alternative method for the measurement of the actual substrate surface temperature is needed.

In this context, the mid-infrared (MIR) pyrometry in the wavelength range of 8 μm ≤*λ*≤ 14 μm has proven itself as a suitable solution. Possible realizations include mid-infrared cameras as well as single detector pyrometers. The left part of **Figure 12** shows a mid-infrared picture of an epitaxial GeSn surface. Besides that, the graph in the right part displays the comparison of the substrate temperature measured once with the thermocouple and the mid-infrared pyrometer in the moment of the growth beginning of an exemplary GeSn layer, more precisely, the opening of the Ge and Sn shutters. For this growth process, the heating power was set to *P*Heat ¼ 0 W to achieve the desired ultra-low substrate temperature.

Particularly remarkable is the observable increase of the substrate temperature by Δ*T* ¼ 30 K, which can only be explained by the thermal radiation of the molecular

*Molecular Beam Epitaxy of Si, Ge, and Sn and Their Compounds DOI: http://dx.doi.org/10.5772/intechopen.114058*

**Figure 12.**

*Left: MIR-picture of a Si substrate during a GeSn growth process. Right: Characteristics of the substrate temperature according to the calibrated thermocouple (blue) and the MIR pyrometer (red) at the beginning of a GeSn growth process.*

sources. Considering the required substrate temperature of *TS* ffi 160°C, this increase underlines the huge impact of the source radiation on the actual substrate surface temperature.

#### **4. Optimization of the molecular beam epitaxy of SiGeSn**

#### **4.1 Influence of the molecular flux distribution on SiGeSn epitaxy**

As already mentioned in Section 2.2, the electrical and mechanical properties of SiGeSn strongly depend on its composition. Furthermore, the desired condition for lattice-matched growth of SiGeSn on Ge requires a constant ratio of Si to Sn according to Eq. (9). All this underlines the necessity for an as homogeneous as possible distribution of the involved molecular fluxes of Si, Ge, and Sn. However, as already described in Section 3.1.1, the flux *FS* impinging on the substrate follows a cosine distribution of the irradiation angle. Therefore, the installation position and angle of a molecular beam source strongly influence the homogeneity of the epitaxial layer. Since only one source can be placed directly central under the substrate, the sources must be arranged in a circular and tilted manner under the substrate, which leads to an even worse distribution. This results, in turn, in the necessity of substrate rotation during growth to achieve at least circular homogeneity of the epitaxial layers. Altogether, the result is a radial-dependent change in the alloy composition, as seen in the exemplary flux distribution on a 4″ substrate, as shown in the left part of **Figure 13**.

As can be seen, the exemplary MBE system shows a divergence of the Si and the Sn flux. Particularly for SiGeSn, this means that the condition for lattice-matching is, in the best case, only fulfilled at one radius. The resulting SiGeSn film is, therefore, not completely strain-relaxed but only strain-reduced. The distribution of the residual strain *ε*k,SiGeSn of an exemplary SiGeSn layer with the lattice-matching fulfilled in the substrate center is shown in the right part of **Figure 13**.

#### **4.2 Influence of the growth temperature on the segregation of Sn**

It was already previously mentioned that the admixture of Sn to group IV compounds complicates their epitaxy. The main reason for this is the segregation of Sn,

**Figure 13.**

*Left: Relative flux deviation of Si, Ge, and Sn for an exemplary MBE system on a 4″ substrate. Right: Residual strain distribution of a SiGeSn layer with the lattice-matching fulfilled in the center of the substrate.*

which is, as already explained in Section 2.4, strongly dependent on the growth temperature. It was already reported that Sn segregation seems to be intensified when in-plane strain of the grown film comes into play, as it is the case for Sn-rich GeSn (SiGeSn with *c*Si ¼ 0;*c*Sn >8%Þ [17].

However, by the admixture of Si to GeSn, thus the epitaxy of SiGeSn, it has been shown that lattice-matched film growth on Ge can be achieved by fulfilling the condition in Eq. (9). Since the in-plane strain is then almost zero, the segregation of Sn is therefore expected to be much lower as for the epitaxy of Sn-rich GeSn. Therefore, higher substrate temperatures should be possible for the epitaxy of lattice-matched SiGeSn films, which would, in turn, lead to improved crystal quality.

The result of an intensive study to find the optimal growth temperature of latticematched, intrinsic SiGeSn is shown in the graph in **Figure 14**. For this study, the growth temperature was measured and controlled using a MIR pyrometer.

As it can be seen in the XRD spectrum on the left side, the growth of latticematched SiGeSn turns to polycrystallinity at too low growth temperatures (*TS* ¼ 160°C) and too high Sn concentrations (*c*Sn ≥ 12*:*5%) due to the reduced surface mobility of the adatoms (see Section 2.1).

#### **Figure 14.**

*Overview of the optimal growth temperature of lattice-matched SiGeSn. Green: Regions with satisfactory crystal quality, red: Regions which showed epitaxial breakdown. Orange: Regions with indications for polycrystallinity.*

In contrast to that, too high growth temperatures (*TS* ≥250°C) not only increases the surface mobility of the adatoms but also strongly intensifies the Sn segregation. Consequently, the incorporation of Sn is reduced so much that the epitaxy process is disturbed, which results in alloy decomposition. Therefore, the XRD spectrum on the right side shows not only a reflection of the SiGeSn film but also of a SiGe film, which does not contain any Sn. In this context, it is often spoken about as an epitaxial breakdown.

The compromise between these extremes can be found at growth temperatures in the range of *TS* ¼ 200°C and moderate Sn concentrations (*c*Sn ≤ 10%). Here, the surface mobility of the adatoms is high enough to enable monocrystalline growth. At the same time, the Sn segregation is well limited, so that the epitaxy process is neither disturbed nor broken down. However, if the Sn concentration exceeds *c*Sn >10%, the amount of impinging Sn atoms is so high that Sn precipitates can form even at a growth temperature of *TS* ¼ 200°C. Therefore, other approaches are necessary to achieve a good crystallinity of these Sn-rich SiGeSn compounds. A possible solution would be a reduction of the total growth rate, which would in turn reduce the amount of impinging Sn atoms. Furthermore, the precise control of Sn precipitation is being considered [33].

In contrast to that, low Sn compounds can be grown even at high growth temperatures (*TS* ≥250°C) with a satisfactory quality. Therefore, it can be concluded that the absolute amount of impinging Sn atoms seems to have a substantial influence on the resulting crystal quality at a given growth temperature.

#### **4.3 MBE of SiGeSn device structures for electronics and photonics**

The previous section reported the optimal growth temperature as the most important growth parameter, for lattice-matched, intrinsic SiGeSn. However, in most cases, not only intrinsic semiconductor regions have to be grown. In order to enable an electronic device functionality, intrinsic regions often alternate with p- or n-type doped regions. Since such regions have substantially different electrical and optical properties, the emissivity *ε* of the total layer stack, an important parameter for pyrometry, changes drastically with each material transition. Therefore, the measurement signal that changes in this way can no longer be used for control without any doubt because the actual growth temperature is no longer represented properly.

In order to prove this hypothesis, the growth process of a Ge pin diode serves as an example to investigate. Here, the growth temperature was once measured with a thermocouple and also with the MIR pyrometer. The resulting growth temperature characteristics are shown in **Figure 15**.

As it can be seen, the growth temperature, according to the thermocouple signal, remains constant at *TS* ¼ 330°C throughout the growth of the p-type doped Ge bottom layer and the intrinsic Ge region. In order to reduce the segregation of Sb (see Section 2.4) during the growth of the n-type doped Ge top layer, the growth temperature was lowered to *TS* ¼ 250°C. Here, the signal of the thermocouple follows perfectly the desired value. However, at the beginning of the intrinsic region, thus at the interface between p-type doped and intrinsic Ge, the signal of the MIR pyrometer starts to increase strongly. Although the signal then follows the drop of the setpoint, the characteristics show a completely different behavior in the n-type doped region. This can only be explained by a drastic change in the emissivity *ε* due to each newly introduced interface in the epitaxy layer stack. Consequently, other measurement methods have to be introduced for the growth of device structures, which do not

#### **Figure 15.**

*Growth temperature characteristics of a Ge pin diode measured with a thermocouple (dashed) as well as with a MIR pyrometer (solid).*

depend that much on the optical properties of the epitaxial layer stack. Another solution for this problem would be an *in situ* measurement of the emissivity *ε*, which is, in contrast, quite difficult to realize in the MIR wavelength range of 8 μm ≤*λ*≤ 14 μm.

However, the MIR pyrometer is, as explained in Section 3.3, still the most suitable method for the measurement of the actual substrate surface temperature at ultra-low growth temperatures.

#### **5. Conclusion**

This chapter has presented the fundamentals to understand the physics behind the MBE of group IV compounds. For this, important effects like adsorption, desorption, and the formation of a nucleus have been discussed in detail. Since the epitaxy of group IV compounds automatically includes heteroepitaxy, its basic growth modes, the requirements of monocrystalline growth, and other principles and effects of heteroepitaxy were presented.

Furthermore, this chapter gives a detailed insight into the main components of a group IV compound MBE system, including selection rules for the right molecular beam source suitable for the material to evaporate. Besides that, essential methods for *in situ* monitoring of the growth temperature as well as the optical properties of the epitaxial layers, specifically reflectometry and MIR pyrometry have been presented.

Considering the substantial importance of SiGeSn, especially in the current group IV research, the last part of the chapter covers several technical and physical problems of its MBE. This includes the strongly temperature-dependent segregation of Sn, thus the measurement of the actual surface temperature to suppress it, and the control of the layer composition as well as its homogeneity. In conclusion, MBE is presented as a powerful tool to realize heterostructures and devices containing them based on group IV compounds.

#### *Molecular Beam Epitaxy of Si, Ge, and Sn and Their Compounds DOI: http://dx.doi.org/10.5772/intechopen.114058*

Without a doubt, Ge and SiGeSn have shown to be serious candidates for the wavelength extension of Si photonics from the visual spectrum to the near- and midinfrared spectrum [31]. Nevertheless, breakthroughs are expected to close the gap with the excellence in material and device performance of group III/V compounds and continuous improvements are necessary to utilize the integration potential of a silicon-based structure. In the following part, we mention some of the activities that promise to have a remarkable input on the ongoing progress.


array on Si based on SPAD (single photon avalanche diode) is encouraging for infrared night vision [41]. Detector concepts based on phototransistors [42] are integration friendly for large-area arrays. The phototransistors may be based on a hetero-bipolar transistor [43] or on a field effect transistor [43].

#### **Acknowledgements**

The authors want to thank all current and former colleagues of the Institute of Semiconductor Engineering of the University of Stuttgart.

#### **Author details**

Daniel Schwarz\*, Michael Oehme and Erich Kasper Institute of Semiconductor Engineering, University of Stuttgart, Stuttgart, Germany

\*Address all correspondence to: daniel.schwarz@iht.uni-stuttgart.de

© 2023 The Author(s). Licensee IntechOpen. 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.

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Section 2
