\r\n\tThe average life expectancy of human beings is increasing the world over, a woman may end up spending almost a third of her life span in the post-menopausal period, if not more, so knowledge about menopausal health is important for a practitioner. Hence this book will be designed to deal the hormonal changes during menopause, the menopausal health problems like vasomotor symptoms, urogenital atrophy, osteoporosis and fracture, cardiovascular disease, cerebrovascular disease, psychological changes, sexual dysfunction, dementia, and cognitive disease. This will be followed by Metabolic syndrome and treatment for symptomatic women. This should sensitize the practitioner to prescribe Menopausal hormone therapy when women are symptomatic. They will be able to understand Menopausal hormone therapy benefits and risk. Practitioners will be able to prescribe Menopausal hormone therapy in breast cancer and genital cancer survivors with confidence.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"190548b14412850dfeedd82f4e37caec",bookSignature:"Prof. Hephzibah Kirubamani",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/7092.jpg",keywords:"FSH, Oestrogen, vaginal atrophy, hot flushes, Abdominal circumference, BMI, obesity, hypertension, Risks, benefits, Endometrial cancer, Cancer Cervix",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"August 7th 2019",dateEndSecondStepPublish:"August 28th 2019",dateEndThirdStepPublish:"October 27th 2019",dateEndFourthStepPublish:"January 15th 2020",dateEndFifthStepPublish:"March 15th 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"237766",title:"Prof.",name:"Hephzibah",middleName:null,surname:"Kirubamani",slug:"hephzibah-kirubamani",fullName:"Hephzibah Kirubamani",profilePictureURL:"https://mts.intechopen.com/storage/users/237766/images/system/237766.jpeg",biography:"Hephzibah Kirubamani was a former Professor of Obstetrics and Gynecology, Department of Obstetrics and Gynecology, Stanley Medical College, Tamil Nadu Dr. M.G.R. 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1. Introduction
In statistical physics only a few problems can be solved exactly. For complex problems, numerical methods can give exact results for problems that could only be solved in an approximate way. Numerical simulation can be a way to test the theory. The numerical results can be compared to the experimental results. The numerical simulation is placed between the fundamental and the experimental treatment; it has a quasi-experimental character (numerical experience). For problems of statistical physics, the most widely used simulation methods are the Monte Carlo method and the molecular dynamics method.
The first Monte Carlo simulation (MCS) was proposed by Metropolis et al. in 1953 [1]. The second Monte Carlo simulation was proposed by Wood and Parker in 1957 [2]. The obtained results were in good agreement with the experimental results of Bridgman [3] and those of Michels et al. [4]. In this method we attribute a series of initial positions chosen randomly to a system of N particles interacting through a defined potential. A sequence of particle configurations is generated by giving successive displacements to particles; we only retain configurations to ensure that the probability density is that of the chosen.
Molecular dynamics simulation (MDS) has been first introduced to simulate the behavior of fluids and solids at the molecular or atomic level. MDS was used for the first time by Alder and Wainwright in the late 1950s [5, 6] to study the interactions of hard spheres. The principle is the resolution of equations of motion for a hard sphere system in a simulation cell. The basic algorithm is Verlet’s algorithm [7].
In this chapter, we will present techniques of numerical simulations using the Monte Carlo method. We will present an application on the gas phase during plasma-enhanced chemical vapor deposition (PECVD) of thin films. The application concerns collisions between particles. Particles are in Brownian motion. Collisions, elastic or inelastic, are considered to be binary. Non-elastic collisions result in effective chemical reactions.
In Section 2, we cite some MCS and MDS works on PECVD processes. Section 3 presents general rules on numerical simulation methods. Section 4 presents how to simulate a physical problem using MCS? We present the Metropolis algorithm as a scheme to trait random configurations and different modules related to elaborate an MCS code. In Section 5, we apply the MCS on SiH4/H2 gas mixture during a PECVD process. Finally the conclusion summarizes the contents of the chapter.
2. Simulation works on the PECVD using MCS and MDS
The PECVD is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells and for film transistors and electronic devices [8, 9]. Reactions during plasma deposition are complex and are not understood completely.
Gorbachev et al. [10, 11, 12] have developed a model that is based on chemical reactions and different processes in a PECVD reactor. The model takes into account the formation of SinHm oligomers (n ≤ 5). It presents a simulation of the growth of the films. Gorbachev et al. found that Si2H5 and Si3H7 strongly influence the growth of the film [11].
Valipa et al. [13] calculated the β reactivity of the SiH3 radical on a surface of a silicon lattice plane during the growth of a-Si:H using MDS. The mechanisms of physical and chemical interactions of low temperature plasmas with surfaces can be explored using MDS [14].
For a CH4/H2 mixture, Farouk et al. used the Monte Carlo method (PIC/MC); they calculated the ionization rate of the plasma and the deposition rate of the thin layer [15]. Rodgers et al. [16] have developed three-dimensional Monte Carlo simulations of diamond (100) surface CVD. Other works on MCS are in [17, 18, 19].
In our previous works [20, 21, 22, 23, 24], we were interested in the study of the gas phase and the interaction of plasmas with the surface, for SiH4/H2 and CH4/H2 gas mixtures during PECVD processes. The used numerical simulation techniques were MCS and MDS. To complete the studies, we used the fluid model [25].
3. General rules for numerical simulation methods
The starting point of numerical simulation is a physical phenomenon; its purpose is to obtain useful physical results. Between these two points, several steps can be identified. These steps are general and they are applicable for MCS. The steps can be summarized as follows:
3.1 Definition of the physical phenomenon and main hypothesis
The physical phenomenon must be defined by the description of the dominant domain of physics. The main assumptions and simplifying approximations are necessary to understand the physical phenomenon and the design of the first model.
3.2 Definition of the mathematical model
Mathematical model requires a mathematical formulation of the problem. It may be a problem of elements or discrete object or a problem of a continuous medium; it may be a spatiotemporal problem or frequency problem and may be a deterministic or probabilistic problem.
It would be interesting to know the mathematical equations that govern the phenomenon:
The forces between particles and elements
The potential interaction
The determination of a time scale
The determination of a length scale
Definition of constant magnitudes of motion and equilibrium magnitudes
Continuity equations, balance equations, transfer equations, etc.
3.3 Elaboration of simulation code
The MCS technique has been chosen for this work; knowing its basic algorithm is necessary for elaborating the simulation. This step requires some actions:
Validation of the model on simple cases
Simulation calculation on complex phenomena
4. Algorithms and techniques for MCS
The MCS is based on a probabilistic process with a random choice of configurations and samples of the situation of the physical system. The two pedagogical examples most cited in the literature are the integration of a single variable function and Ising’s model of spin. In the following subsection, we define the integration of a single variable function. We introduce the Ising model at the end of Section 4.2.2.
4.1 Integration of function of a single variable
Calculation of the definite integral for a function f(x) of a single variable x on domain {a, b} has been proposed (Figure 1):
Figure 1.
The integral of a function f(x).
Let:
I=∫abfxdxE1
Let xi and yi be real random numbers (i = 1, 2,…, N), and let H be a real number greater than the f(x) for x belonging to the domain {a, b} (or x ∈ {a, b}).
Let r1 and r2 be two random numbers belonging to the domain {0, 1} according to a uniform distribution law. Generators (e.g., Ran, RANDOM, RANDUM, or other IMSL mathematical libraries) of random numbers can be used:
xi=a+r1b−aandyi=0+r2H−0E2
where xi and yi are random numbers (xi ∈ {a, b} and yi ∈ {0, H}).
The Monte Carlo (MC) method is based on a probabilistic process. Let N be the total number of cases chosen (possible cases). It is necessary to count the number of favorable cases (or the number of points below the curve y = f(x)); let yi ≤ f(xi)). The number of favorable cases is Nfav. When N➔∞, the value I of the integral is [26]:
I=NfavNb−aH−0.0=NfavNb−aHE3
An example [26] is the calculation of the value π by calculating the integral I on a quarter circle of unit radius (R = 1.0). The pairs of random numbers (xi, yi) satisfying the condition: xi2 + yi2 ≤ 1. The function f(x) is equal to 1−x2.
We take a = 0.0, b = 1.0, and H = 1.0.
For different values of N, we show that the numerical solution tends to π = 4I.
Although this integral is simple, it shows the strength and simplicity of the method. The technique can be generalized for the integration of multivariate functions.
We note that integration by the MC method is based on:
The choice of random configurations according to a uniform distribution law
Each configuration chosen is either favorable or unfavorable (the “or” is exclusive).
For statistical physics problems, the probabilistic choice of configurations is not always deterministic; the favorable and unfavorable cases are not exclusive. According to the Metropolis algorithm [26, 27], the steps of the simulation are:
Choice of a simulation cell of adequate shape to the studied phenomena. The size of the simulation cell is related to a scale of length characteristic of the forces and interaction potential of the studied phenomenon. This cell may contain Npc particles (and/or elements).
Choice of an initial configuration that responds to some physical and thermodynamic properties. The total or internal energy of the system is Ei.
Infinitesimal random displacement of a particle (or element of the system) and calculation of the new internal energy of the system Ef. This displacement is related to the physical magnitudes: time scale and length scale. The physical system tends toward a minimization of the internal energy of the systemwith some fluctuation. Let ΔE = Ef-Ei the fluctuation.
If ΔE ≤ 0; the new configuration is retained (favorable) and the different averages can be obtained; go to step (c).
If ΔE > 0; a random number ε is chosen such that 0 < ε < 1. Let the probability Pr equal to: Pr = exp. (−ΔE/kBT) (where kB is the Boltzmann constant and T is the temperature).
If ε < Pr, accept the move and in any case go back to step (c) for a new choice of an infinitesimal displacement (new configuration). Note that if such a trial move is rejected, the old configuration is again counted in the averaging with probability Pr.
Figure 2 shows how to choose between the selected configurations. Let ε be a random number following a uniform law; If ε1 ≤ Pr the configuration is retained, and if ε2 > Pr the configuration is rejected.
Figure 2.
Configuration choice according to Metropolis scheme.
Numerical simulation using the MC method is a very important tool for the study of static properties. The basic algorithm is based on probability notions. Understanding of the distribution function and/or interaction potentials is the heart of the calculation.
4.2.2 Thermodynamic quantities at equilibrium
In equilibrium statistical physics, the system has a certain probability that can be in any states. The probability of being in a state μ with energy H(μ) is given by the Boltzmann distribution P(μ):
Pμ=exp−Hμ/kBTZE4
where T is the absolute temperature and kB is called Boltzmann’s constant. It is conventional to denote the quantity (kBT)−1 by the symbol β. The normalizing factor Z, or partition function, is given by:
Z=∑μexp−Hμ/kBT=∑μexp−βHμE5
The average of a quantity Q fora system in equilibrium is:
<Q>=∑μQμPμ=1Z∑μQμexp−βHμE6
The internal energy U, is given by:
U=1Z∑μHμexp−βHμE7
which can be written in terms of a derivative of the partition function:
U=1Z∂Z∂β=−∂logZ∂βE8
From thermodynamics we have expressions for the specific heat C, the entropy S, and the Helmholtz free energy F:
C=∂U∂T=−kBβ2∂U∂β=−kBβ2∂2logZ∂β2E9
or
C=T∂S∂T=−β∂S∂βE10
and
S=−kBβ∂logZ∂β+kBlogZE11
and
F=U−TS=−kBlogZE12
We can calculate other parameters affecting the system.
The Monte Carlo method is an excellent technique for estimating probabilities, and we can take advantage of this property in evaluating the results. The simplest and most popular model of a system of interacting variables in statistical physics is the Ising model. It consists of spins σi which are confined to the sites of a lattice and which may have only the values (+1) and (−1). These spins interact with their nearest neighbors on the lattice with interaction constant J; they can interact with an external magnetic field B coupling to the spins. The Hamiltonian H for this model is [26]:
H=−J∑i,jσiσj−B∑iσiE13
The Ising model has been studied in one and two dimensions to obtain results of thermal properties, phase transition, and magnetic properties [26, 27, 28]. For chosen values of J and/or B, different steps may be taken for the calculations (simulation cell, initialization, configurations, boundary conditions, calculation algorithms). For any configuration, each spin takes the two possible directions. The detail of the calculation procedure is not the purpose of this chapter.
4.2.3 MCS module designs
4.2.3.1 Simulation cell and initialization
We give a system of N particles (atoms, molecules, ions or particles) placed in a cell of fixed volume, generally of cubic form. The initial positions may, depending on the case, be distributed randomly according to a certain law (uniform or otherwise) or have a given symmetry. In a fluid, a gas, or a plasma, the particles may have random positions in general; in a solid or surface, with a crystal structure, the particles take ordered positions. The choice of random initial positions allows great freedom on the choice of the number of particles in the cell.
At the first step, the particles are given velocities that are generally selected to have a zero total momentum. If the system is in thermodynamic equilibrium, the initial velocities will be randomly chosen according to a Maxwell-Boltzmann law. In the general case, the velocity distribution is according to the problem dealt with. All other phase properties can be initialized to the particles; the main thing is the conservation of the total quantities of the system.
4.2.3.2 Potentials of interaction
The particles interact with each other according to chosen interaction potentials. Since the interaction potentials are specific for each “numerical experiment,” the main part of the work consists in calculating the interaction energies for each proposed configuration.
The choice of interaction potentials is directly related to the mathematical formulation of the problem according to the state of the medium: fluid, gas, plasma, or solid. It can be Lennard-Jones potential, Coulomb potential, Debye potential, Morse potential, Stillinger-Weber potential, Born-Mayer potential, Moliere potential, or others.
4.2.3.3 Boundary conditions
In general, two main boundary conditions are used: periodic boundary conditions (PBC) and minimum image convention (MIC) [29].
To minimize the surface effect, periodic boundary conditions (PBC) [30] are invariably imposed. The simulation cell is reproduced throughout the space to form an infinite mesh. We can simulate the properties of an infinite system. The particles that we follow are in the central cell; if a particle crosses a wall with a certain velocity, its image returns with the same velocity by the opposite wall. Under these conditions, the number of particles in the central cell, and consequently the density, is constant. These conditions also allow the conservation of the energy and the momentum of the system and do not introduce periodic effects (because of the interaction between particles).
According to the hypotheses and according to the geometry of the problem, other boundary conditions are proposed [26]. For example, in order to model thin films, the simulation cells are longitudinal and parallel to the film; one uses PBC in the directions parallel to the film. In the direction normal to the film, free edge boundary conditions can be used. In such cases, it may be appropriate to also include surface fields and surface interactions. In this way, one can study phenomena such as wetting, interface localization-delocalization transitions, surface-induced ordering and disordering, etc.
The core of the program includes calculating the potential energies of particle configuration and particle collisions. The interactions and collisions between particles can be elastic or inelastic; they can be binary or collective. For computation, the interaction energy of a particle with its neighbors is carried out by refocusing a base cell on the particle. This particle only interacts with particles in this region. This is called the “minimal image convention” (MIC) [1].
4.2.3.4 Sampling of random data
Generally, a RANDOM generator of real random numbers ri belonging to the domain {0, 1} (or ri ∈ {0, 1} is available. This distribution law is uniform.
To have a real random number xi belonging to the domain {a, b} (or xi∈ab) according to a law of uniform distribution, we have:
xi=a+rib−aE14
To have a real random number xi belonging to the domain {a, b} (or xi ∈ {a,b}) according to a formula (or law) of nonuniform distribution f(x), a histogram technique is used. Let Nm be the number of intervals. If the mesh is regular (Figure 3):
Figure 3.
Random number selection according to f (x) distribution.
Δx=b−a/NmE15
We define:
fi=fxifori=0,….,mand:xi=a+i.ΔxE16
We define the sequence:
S0=0and:Si+1=Si+Δxfxi+fxi−1/2E17
and the sequence:
rx0=0etrxi=Si/SmE18
Hence each real random number ri belongs to the domain {0, 1} (where ri ∈ {0, 1}) (according to the uniform law); this number belongs to the domain {rxj-1, rxj}. It corresponds to a random value xran of the domain {xj-1, xj}; this number satisfies the formula (or the law) of nonuniform distribution f(x).
This technique can be generalized for a nonuniform distribution law f(x) with an irregular mesh Δxi, or with tabular data f(xi) with i = 1,…, m.
The technique can be generalized, too, for a discrete distribution law f(i) with i = 1,…, m.
In the literature, the reader can find simple algorithms for the choice of random numbers of some simple functions (Gaussian, etc.).
4.2.3.5 Control of the evolution of the physical system
It is necessary to find some parameters allowing the control of the smooth course of the evolution of the system. We must look for the constants of movement. For example for an isolated system, we have the conservation of the total energy and the quantity of matter.
4.2.3.6 Statistical calculations
By using the numerical simulation, it is possible to calculate many spatiotemporal quantities F(r,t). These quantities can be positions, speeds, kinetic moments, particle energies, concentrations, transport coefficients, etc. It would then be possible to calculate all other quantities related to F(r,t).
For the calculation of the averages, one can note the quantities on the space, on the time or on both. The histogram methods can be used. Static or dynamic distribution functions and spatial or temporal correlation functions can be calculated. It should be noted that the SMC is much more adequate for static properties because of the probabilistic choice of configurations.
Any calculated function or parameter F(r,t) can be used for another application in another calculation program.
4.3 Other large methods of Monte Carlo simulation
In the MCS model discussed extensively in this chapter, it’s more about collisions between particles. It’s particle-particle MCS or PP-MCS. In many problems of physics, the general idea is the same, but the applications and proposed models are numerous.
Other MCS models, named particle-in-cell MCS (PIC-MCS), are based on particle-cell interactions. In these last models, we also use a probabilistic choice of configurations and small variations in the state of the system (following the Metropolis algorithm); the interaction is between the particle with a cell, a mesh, or a drop. The parameters and variables of the cell, although local and instantaneous, are macroscopic. These parameters and variables can be thermodynamic, fluid, or electromagnetic. An example of the model based on PIC-MCS is described by Mattei et al. [31] for simulation of electromagnetic particle-in-cell collision in inductively coupled plasmas. Several works can be found in the literature on this same line of work. Other MCS models using particles may be considered. [32].
For statistical physics problem solving (such as thin film deposition problems), MCS models use experimental, numerical, or theoretical data from other methods and models. Models can be improved to hybrid models. In the hybrid models, connections between two modules can be realized. The first module is MCS; the second module is fluid, electromagnetic, or other. An example of a three-module hybrid model is presented by Mao and Bogaerts [33] to study gas mixtures in PECVD system. The three modules are MCS, fluid, and electromagnetic. The first module EM calculates the electromagnetic fields by solving Maxwell equations. These fields are used as inputs in the module MCS, where the electron density, electron temperature, electron energy distribution function, and electron impact reaction rates can be computed with a Monte Carlo procedure. Subsequently, the module fluid calculates densities and fluxes of the various plasma species (i.e., heavy particles and electrons) with continuity equations and the electrostatic field with Poisson’s equation. This electrostatic field is used as input again in the EM. This cycle is iterated until convergence. The schematic of the hybrid model is given in Figure 4.
Figure 4.
Schematic of a hybrid model of three modules used to study gas mixtures in the PECVD [33].
To solve statistical physics problems with evolutions as a function of time, kinetic models of MCS (kMCS) are used. Using kMCS, Battaile and Srolovitz [17] described kinetic phenomena of the diffusive motion of a single interstitial atom in a close-packed metal crystal. The motion of the interstitial atom is usually limited to two types: vibration of the atom around the center of the interstitial hole in which it resides and hops to nearest-neighbor interstitial sites. The atom can hop into any of the nearest-neighbor interstitial sites; it executes a random walk. In an MC simulation of this diffusion process, the new position of the interstitial atom is chosen at random from a list of the adjacent interstitial sites.
Other CVD and PECVD works on MCS are presented in Ref.s [15, 34, 35, 36, 37, 38]. They show how MCS methods can study properties of gas mixtures and properties of the growth of thin films.
5. Example of application: Monte Carlo simulation of a gas mixture in the PECVD
In this section, we present an example of PP-MCS of collisions and reactions in gas phase of SiH4/H2 mixture used in PECVD process. Some paragraphs have been treated in previous works [21, 24].
5.1 Description of the physical phenomenon
We use a MCS to study collisions and chemical reactions in gas phase of SiH4/H2 mixture used in the PECVD process. In this phase, important reactions have been identified that contribute to the production and the consumption of hydrogen (H), silylene (SiH2), and silyl (SiH3). The hydrogen consumption reactions SiH4 + H → SiH3 + H2 and SiH3 + H → SiH2 + H2 are found to play a central role in deciding the distribution of hydrogen [39].The plasma chemistry indicates that H atoms and SiH3 radicals play an important role in the a-Si:H deposition process [40]. Experimentally, it is generally accepted that SiH3 radicals dominate a-Si:H and μc-Si film growth from SiH4 plasmas in the PECVD; it is the key precursor of a-Si:H deposition [41]. The proposed MCS allowed to get the ratio SiH2/SiH3 and mean value of densities of species. It provides information on SiH4 dissociation and on the production of SiH3, H, SiH2, and Si2H6 and other important parameters.
The plasma in the PECVD reactor is weakly ionized. For our study, the mixture gas contains 22% of SiH4 and 78% of H2; the pressure is 100 mtorr, the temperature of the gas ranges from 373 to 723 K, the electron temperature is about 2.5 eV, and the electron density is 3. 108 cm−3. The process is considered to be stationary. We take into account electrons and eight neutral species (SiH4, SiH3, SiH2, H, H2, Si2H6, Si2H5, SiH). Reactions taken into account include seven electron-neutral and 14 neutral-neutral reactions. Table 1 shows the 21 reactions and rate constants Kreac. At low temperature, the neutrals interact occasionally with each other and move under the effect of thermal agitation; their velocity distribution function is Maxwell-Boltzmann distribution. Electrons have the mean velocity with kinetic energy Te.
List of gas phase reactions and corresponding rate constants [24].
Let Kreaccons and Kreacprod be the rate constants of the consumption and the production of species A. The chemical reaction for the consumption of A is as:
a·A+b·B→Kreacconsc·C+d·D
And chemical reaction for the production of A is as:
a\'·A\'+b\'·B\'→Kreacprodc\'·A+d\'·D\'
Rate production and consumption for any species A are taken as:
5.2 Description of Monte Carlo simulation technique
5.2.1 Simulation cell and phase coordinates
The MCS is based on binary collisions at the microscopic level. Elastic collisions are between all particles, and inelastic collisions (or effective collisions) are those that result in a chemical reaction. A chemical reaction needs a collision involving at least two particles (atoms, ions, electrons, or molecules). According to kinetic theory, gases consist of particles in random motion. These particles are uniformly distributed in a cell which has a parallelepiped form of sizes Lx, Ly, and Lz (Figure 5). These particles move in a straight line until they collide with other particles or the walls of their container. Dimensions and volume of Monte Carlo cell must take into consideration the mean free path of species.
Figure 5.
Form of the simulation cell.
Let ni be the density of neutral spice i (i = 1,…, 8). The first particle i is randomly chosen according to a probability of neutral species Prsp,I (nonuniform discrete distribution) given by:
Prsp,i=ni∑j=18njE20
The chosen particle takes randomly three components of space in cell ri(xi, yi, zi) according to the normal distribution (nonuniform distribution). It takes also randomly three components of velocity vi (vxi, vyi, vzi) according to Maxwell-Boltzmann distribution.
5.2.2 Treatment of elastic and inelastic collisions
Let ni and nj be the densities of species i and j in the gas and Vij the relative velocity between the two species i and j.
According to the kinetic theory of gases, we have for an incident particle i on a target particle j the average collision frequency νij as:
υij=Vijnj<σij>E21
where <sij> is the cross section of the particle j.
The mean free path <λι> of species i is:
<λi>=1nj<σij>E22
The time between two collisions τij is then:
τij=<λi>Vij=1υijE23
For chemical effective reactions (inelastic collisions) between two reactive species i and j giving products i’ and j’, the rate constant reaction verifies [45]:
kij=<σijVij·Vij>E24
General rules of collision theory are applied:
The new velocities of the colliding particles are calculated using conservation of energy and momentum for elastic collisions.
Conservation of total energy as isolated system.
Movement of the center of mass and relative motion around the center of mass.
The reader can refer to some fundamental physics books that deal with general notions of collisions and corresponding parameters [45, 46, 47, 48].
The plasma in the PECVD reactor is weakly ionized. At low temperature, particles interact occasionally with each other and move under the effect of thermal agitation. In reality, only a small fraction of collisions are effective (result in a chemical reaction) [21].
In our MCS, after traveling a random walk given by a Gaussian distribution, the first chosen particle collides with a second particle (molecule, atom, radical, or electron). The last particle j is randomly chosen according to a (i-j) collision probability Prcol,j (nonuniform discrete distribution) given by:
Prcol,j=νij∑k=19νikE25
where νij is the neutral-neutral or electron-neutral collisional frequency. The collision theory indicates that the collision between molecules can provide the energy needed to break the necessary bonds so that new bonds can be formed [49]. Particles must have sufficient energy to initiate the reaction (activation energy), so the two chosen particles must have kinetic energy equal to or greater than the barrier energy (Ea) of a gas phase reaction. The difference between the kinetic energy of the two particles and the activation energy define the kind of collision (effective or not effective).
The activation energy is given by:
Ea=−kBTlnKreac/νijE26
where the pre-exponential factor is assumed to be the collision frequency factor and Kreac is the rate constant of the gas phase reaction.
The two colliding particles (e.g., the electron and SiH4 molecule) can interact by several reactions (R1, R2, R3, and R4 in Table 1); we choose randomly one of gas phase reactions occurring according to a, nonuniform discrete distribution reaction probability Prreac (i,j):
Prreacij=Kreacij∑KreacijE27
where ∑Kreacij is the sum of all rate constants of possible reactions between i and j.
All chemical systems go naturally toward states of minimum Gibbs free energy [21, 24]. A chemical reaction tends to occur in the direction of lower Gibbs free energy. To determine the direction of the reaction that is taking place, we use the old and new values of Kreac and the equilibrium constant with reactants and product concentrations. Each set of binary collisions can be related or converted into time. As cited in section (a), Table 1 gives gas phase reactions and corresponding rate constants used in this MCS.
To continue the simulation, after the elastic collision, particle i takes new values of components velocity and new mean free path; mean free path is taken from a normal (nonuniform) distribution (Gaussian distribution). If the collision is inelastic, we have to take a new particle.
From Metropolis algorithm, the scheme of this MCS is as follows:
Choices of particle of spice i with random position, velocity, and mean free path; periodic boundary conditions are used to keep particles in the elementary cell.
Choices of random collision with a spice j.
Study of collision type (elastic, inelastic). If the collision is elastic the particle i move with a new velocity and mean free path, and we return to step (b). If the collision is inelastic particles i and j give new particles i’ and j’, according to Metropolis scheme, and we return to step (a) or (b). Periodic boundary conditions are used to keep particles in the elementary cell.
At each step, we can note the different statistics.
5.2.3 The choice of simulation parameters
Once the species are selected for the simulation model, an estimate of species densities should be made. Following the model of interaction and collisions between particles (binary, collective, etc.), a first choice of the minimum number Ni of particles of each species is made. A first estimate of the sizes (Lx, Ly, Lz) of the elementary cell is made.
The study of the types of interaction potentials and the calculation of the approximate values of the force ranges, the kinetic energies, the internal energies, and the energies of activation make it possible to correct the minimal numbers Ni of particles and the sizes (Lx, Ly, Lz) of the elementary cell.
Let kp be the number of a species, kp = 1,…, 9. The minimal numbers Qnp(kp) and the sizes (Lx, Ly, Lz) have to be discussed for statistical calculations.
For numerical programming, according to the programming language used and according to the size (or the computational capacity) of the computer, it is necessary to find a judicious choice of the tables of integer or real values and which values would be useful to save all during simulation. Let Ncol,m be the maximum number of elastic collisions per particle, and let Ncycle be the number of cycles to average the simulation calculations.
For this MCS, the numerical chosen values are in Table 2.
Cell dimensions and steps for collisions
Number of species Kp
Initial number of particles in cell
Lx (m)
4.68 10−6
1
Qnp(SiH4)
Qnp1
Ly (m)
4.68 10−6
2
Qnp(SiH3)
10
Lz (m)
20.0 10−3
3
Qnp(SiH2)
10
4
Qnp(H)
10
Ncol,m
500
5
Qnp(H2)
Qnp5
Ncycle internal cycle
2000
6
Qnp(Si2H6)
10
Ncycle external cycle
200,000
7
Qnp(SiH)
10
8
Qnp(Si2H5)
10
9
Qnp(e)
Qnp9
Table 2.
Used quantities and parameters in calculations for the gas temperature Tg = 520 K.
For radicals (e.g., SiH3), particle numbers Qnp(k) are very small; we take Qnp(k) = 10. These numbers cannot take value 1 or 0, even if a species k is in trace form in the gas. The value 0 for a species k means that any other species k’ does not make a collision with the species k; and the value 1 means that we have no collisions between particles of the same species in the cell.
Qnp1, Qnp5, and Qnp9 are calculated from the volume of cell, the pressure, the temperature, and the total number of particles in the cell (Qnp1 = 0.81187824 * 109; Qnp5 = 0.20296956 * 109; Qnp9 = 131).
5.2.4 Calculation of statistical properties and some results of the calculations
As we have chosen a stationary regime, we must reach the values and properties at equilibrium. The results of the simulation show this trend. In MCS, averaged values, distribution functions, autocorrelation functions, and correlation functions can be calculated. To ensure rapid convergence of calculations, it would be useful to look for statistically symmetric (or stationary or unsteady) parameters [26, 50].
As an example for our MCS calculation, we have:
The number of Si2H6, SiH, and Si2H5 particles reaching the surface is negligible.
Let Ns,i and Ns, H2 be the densities of a species i and H2 reaching the surface. The ratios Ns,i/Ns, H2 are too small (Table 3).
Let Ns,i be the density of a species i reaching the surface and Nv,i the density of same species i in volume. The ratios Ns,i/Nv,i are too small (Table 4); the surface effect is negligible.
The reactions begin with the dissociation (consumption) of H2 and SiH4 by R5, R1, and R2 reactions.
The production of SiH3 is done by R8, and then there is production of SiH2 by R12.
The reaction R2: SiH4 + e → SiH2 + 2H + e plays the central role in SiH4 dissociation by electron impact [24]. This result is compatible with [39].
The second important chemical reaction in the SiH4 dissociation is R1: SiH4 + e → SiH3 + H + e [24]. This result is compatible with that of Perkins et al. [51] and that of Doyle et al. [52].
Type
H2
SiH4
H
SiH3
SiH2
Ns,i/Ns, H2
1
0.23
1.67 10−4
8.60 10−5
9.86 10−6
Table 3.
Ratios Ns,i/Ns, H2 of particles reaching the surface compared to H2.
Type
SiH4
SiH3
SiH2
v, j
6.695 10−6
7.965 10−6
775 10−6
Table 4.
Ratios Ns,i/Nv,i of particles reaching the surface compared to volume.
6. Conclusions
MCS is a widely used method in statistical physics to study thermodynamic, structural, or phase properties. It is based on random and probabilistic processes. The purpose of this chapter is to present the technique for general use in physics for the study of thin film deposition problems. The technique can be generalized to other fields of science: biology, economics, transportation, and social sciences.
We started by presenting general rules for numerical simulation methods. Metropolis algorithm has been considered as the basic algorithm. After, we presented the different steps for the realization of a MCS code. We chose the particle-particle model MCS (PP-MCS) to explain the different steps and procedures to be applied in the deposition of thin layers by PECVD processes. We have shown that this technique can be generalized to the particle-in-cell MCS (PIC-MCS) case or kinetic MCS (kMCS), as it can be joined with other modules to give hybrid models. It is important to know how to choose random configurations from the laws or probability distributions in the system.
A numerical application is presented for collisions in a SiH4/H2 gas mixture in the PECVD process. A preliminary work of determination of the chemical reactions between molecules and radicals is made. A choice of the simulation cell is made, and the definition of the probabilities of the collisions between peers is made. The Metropolis algorithm makes it possible to follow the various elastic and inelastic collisions; it also makes it possible to make the statistics of the interactions with the surface. The results are compatible with [39, 51, 52].
Other questions may be asked to account for molecular ions, surface and volume kinetics, or thin film formation. The techniques and different models of the MCS (PP-MCS, MCS-PIC, kMCS) allow taking care of these questions.
The interconnection of the MCS with other models (MDS, hybrid model, fluid model, electromagnetic model, etc.) would allow answering more questions. The methods can be applied to other specialties than the physical sciences.
\n',keywords:"MCS, potential, reaction rates, collisions, thin film deposition",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/68593.pdf",chapterXML:"https://mts.intechopen.com/source/xml/68593.xml",downloadPdfUrl:"/chapter/pdf-download/68593",previewPdfUrl:"/chapter/pdf-preview/68593",totalDownloads:503,totalViews:0,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"March 25th 2019",dateReviewed:"July 11th 2019",datePrePublished:"August 19th 2019",datePublished:"December 18th 2019",dateFinished:null,readingETA:"0",abstract:"Many physical phenomena can be modeled using Monte Carlo simulation (MCS) because it is a powerful tool to study thermodynamic properties. MCS can be used to simulate interactions between several particles or bodies in the presence of local or external fields. The main idea is to create a high number of different random configurations; statistics can be taken according to appropriate algorithms (Metropolis algorithm). In this chapter, we present basic techniques of MCS as the choice of potential, reaction rates, simulation cell, random configurations, and algorithms. We present some principal ideas of MCS used to study particle-particle collisions in the gas and in plasmas. Other MCS techniques are presented briefly. A numerical application is presented for collisions in gas phase during thin film deposition by plasma-enhanced chemical vapor deposition (PECVD) processes. Parameters and results of the simulation are studied according to a chosen reactor and mixture.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/68593",risUrl:"/chapter/ris/68593",book:{slug:"theory-application-and-implementation-of-monte-carlo-method-in-science-and-technology"},signatures:"Fethi Khelfaoui and Oumelkheir Babahani",authors:[{id:"299501",title:"Prof.",name:"Fethi",middleName:null,surname:"Khelfaoui",fullName:"Fethi Khelfaoui",slug:"fethi-khelfaoui",email:"fethi.khelfaoui@gmail.com",position:null,institution:{name:"Université Kasdi Merbah Ouargla",institutionURL:null,country:{name:"Algeria"}}},{id:"300166",title:"Dr.",name:"Oumelkheir",middleName:null,surname:"Babahani",fullName:"Oumelkheir Babahani",slug:"oumelkheir-babahani",email:"babahaniok@hotmail.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Simulation works on the PECVD using MCS and MDS",level:"1"},{id:"sec_3",title:"3. General rules for numerical simulation methods",level:"1"},{id:"sec_3_2",title:"3.1 Definition of the physical phenomenon and main hypothesis",level:"2"},{id:"sec_4_2",title:"3.2 Definition of the mathematical model",level:"2"},{id:"sec_5_2",title:"3.3 Elaboration of simulation code",level:"2"},{id:"sec_7",title:"4. Algorithms and techniques for MCS",level:"1"},{id:"sec_7_2",title:"4.1 Integration of function of a single variable",level:"2"},{id:"sec_8_2",title:"4.2 Principle of the MCS model",level:"2"},{id:"sec_8_3",title:"4.2.1 Calculation algorithm (Metropolis algorithm)",level:"3"},{id:"sec_9_3",title:"4.2.2 Thermodynamic quantities at equilibrium",level:"3"},{id:"sec_10_3",title:"4.2.3 MCS module designs",level:"3"},{id:"sec_10_4",title:"4.2.3.1 Simulation cell and initialization",level:"4"},{id:"sec_11_4",title:"4.2.3.2 Potentials of interaction",level:"4"},{id:"sec_12_4",title:"4.2.3.3 Boundary conditions",level:"4"},{id:"sec_13_4",title:"4.2.3.4 Sampling of random data",level:"4"},{id:"sec_14_4",title:"4.2.3.5 Control of the evolution of the physical system",level:"4"},{id:"sec_15_4",title:"4.2.3.6 Statistical calculations",level:"4"},{id:"sec_18_2",title:"4.3 Other large methods of Monte Carlo simulation",level:"2"},{id:"sec_20",title:"5. Example of application: Monte Carlo simulation of a gas mixture in the PECVD",level:"1"},{id:"sec_20_2",title:"5.1 Description of the physical phenomenon",level:"2"},{id:"sec_21_2",title:"5.2 Description of Monte Carlo simulation technique",level:"2"},{id:"sec_21_3",title:"5.2.1 Simulation cell and phase coordinates",level:"3"},{id:"sec_22_3",title:"5.2.2 Treatment of elastic and inelastic collisions",level:"3"},{id:"sec_23_3",title:"Table 2.",level:"3"},{id:"sec_24_3",title:"Table 3.",level:"3"},{id:"sec_27",title:"6. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equation of state calculations by fast computing machines. The Journal of Chemical Physics. 1953;21:1087-1092. DOI: 10.1063/1.1699114'},{id:"B2",body:'Wood WW, Parker FR. Monte Carlo equation of state of molecules interacting with the Lennard-Jones potential. The Journal of Chemical Physics. 1957;27:720-733. 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DOI: 10.1002/ctpp.2150360102'},{id:"B44",body:'Amanatides E, Stamou S, Mataras D. Gas phase and surface kinetics in plasma enhanced chemical vapor deposition of microcrystalline silicon: The combined effect of RF power and hydrogen dilution. Journal of Applied Physics. 2001;90:5786-5798. DOI: 10.1063/1.1413241'},{id:"B45",body:'Moison M, Pelletier J. Physique Des Plasmas Collisionnels: Application Aux décharges Haute fréquence. France: EDP Sciences; 2006'},{id:"B46",body:'Delcroix J-L, Bers A. Physique Des Plasmas 1. Paris: Inter Editions/CNRS Editions; 1994'},{id:"B47",body:'Atkins PW, de Paula J. Chimie Physique. 4th ed. De Boeck; 2015. 973 p. ISBN-10: 2804166511'},{id:"B48",body:'Atkins PW. Eléments de Chimie Physique. De Boeck Université; 1998. 512 p. ISBN-10: 2744500100'},{id:"B49",body:'Moore JT, Hren C, Mikulecky PJ. U Can: Chemistry I for Dummies. Wiley; 2015. 456 p. ISBN: 978-1-119-07940-8'},{id:"B50",body:'Allen MP, Tildesley DJ. Computer Simulation of Liquids. Oxford: Clarendon Press; 1987'},{id:"B51",body:'Perkins GGA, Austin ER, Lampe FW. The 147-nm photolysis of monosilane. Journal of the American Chemical Society. 1979;101:1109-1115'},{id:"B52",body:'Doyle JR, Doughty DA, Gallagher A. Silane dissociation products in deposition discharges. Journal of Applied Physics. 1990;68:4375'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Fethi Khelfaoui",address:"fethi.khelfaoui@gmail.com;, khelfaoui.fe@univ-ouargla.dz",affiliation:'
Physics Department, RPPS Laboratory, Faculty of Mathematics and Matter Sciences, Kasdi Merbah Ouargla University, Algeria
Physics Department, RPPS Laboratory, Faculty of Mathematics and Matter Sciences, Kasdi Merbah Ouargla University, Algeria
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Behar, Ch. Kabakchiev, I. Garvanov and H. Rohling",authors:[{id:"2768",title:"Dr.",name:"Christo",middleName:null,surname:"Kabakchiev",fullName:"Christo Kabakchiev",slug:"christo-kabakchiev"},{id:"18669",title:"Dr.",name:"Vera",middleName:null,surname:"Behar",fullName:"Vera Behar",slug:"vera-behar"},{id:"18671",title:"Dr.",name:"Ivan",middleName:null,surname:"Garvanov",fullName:"Ivan Garvanov",slug:"ivan-garvanov"},{id:"18672",title:"Prof.",name:"Hermann",middleName:null,surname:"Rohling",fullName:"Hermann Rohling",slug:"hermann-rohling"}]},{id:"14034",title:"Practical Monte Carlo Based Reliability Analysis and Design Methods for Geotechnical Problems",slug:"practical-monte-carlo-based-reliability-analysis-and-design-methods-for-geotechnical-problems",signatures:"Jianye Ching",authors:[{id:"19783",title:"Prof.",name:"Jianye",middleName:null,surname:"Ching",fullName:"Jianye Ching",slug:"jianye-ching"}]},{id:"14035",title:"A Monte Carlo Framework to Simulate Multicomponent Droplet Growth by Stochastic Coalescence",slug:"a-monte-carlo-framework-to-simulate-multicomponent-droplet-growth-by-stochastic-coalescence",signatures:"Lester Alfonso, Graciela Raga and Darrel Baumgardner",authors:[{id:"18046",title:"Prof.",name:"Lester",middleName:null,surname:"Alfonso",fullName:"Lester Alfonso",slug:"lester-alfonso"},{id:"22501",title:"Dr.",name:"Graciela",middleName:null,surname:"Raga",fullName:"Graciela Raga",slug:"graciela-raga"},{id:"22502",title:"Dr.",name:"Darrel",middleName:null,surname:"Baumgardner",fullName:"Darrel Baumgardner",slug:"darrel-baumgardner"}]},{id:"14036",title:"Monte Carlo Simulation of Room Temperature Ballistic Nanodevices",slug:"monte-carlo-simulation-of-room-temperature-ballistic-nanodevices",signatures:"Ignacio Íñiguez-de-la-Torre, Tomás González, Helena Rodilla, Beatriz G. 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Al-Harthi",authors:[{id:"22395",title:"Prof.",name:"Mamdouh A.",middleName:null,surname:"Al-Harthi",fullName:"Mamdouh A. Al-Harthi",slug:"mamdouh-a.-al-harthi"}]},{id:"14039",title:"Monte Carlo Simulations in Solar Radio Astronomy",slug:"monte-carlo-simulations-in-solar-radio-astronomy",signatures:"G. Thejappa and R. J. MacDowall",authors:[{id:"21608",title:"Dr.",name:"Thejappa",middleName:null,surname:"Golla",fullName:"Thejappa Golla",slug:"thejappa-golla"}]},{id:"14040",title:"Using Monte Carlo Simulation for Prediction of Tool Life",slug:"using-monte-carlo-simulation-for-prediction-of-tool-life",signatures:"Sayyad Zahid Qamar, Anwar Khalil Sheikh, Tasneem Pervez and Abul Fazal M. Arif",authors:[{id:"21687",title:"Dr.",name:"Sayyad Zahid",middleName:null,surname:"Qamar",fullName:"Sayyad Zahid Qamar",slug:"sayyad-zahid-qamar"},{id:"21688",title:"Prof.",name:"Anwar Khalil",middleName:null,surname:"Sheikh",fullName:"Anwar Khalil Sheikh",slug:"anwar-khalil-sheikh"},{id:"21689",title:"Prof.",name:"Abul Fazal M.",middleName:null,surname:"Arif",fullName:"Abul Fazal M. Arif",slug:"abul-fazal-m.-arif"},{id:"21690",title:"Prof.",name:"Tasneem",middleName:null,surname:"Pervez",fullName:"Tasneem Pervez",slug:"tasneem-pervez"}]},{id:"14041",title:"Loss of Load Expectation Assessment in Electricity Markets using Monte Carlo Simulation and Neuro-Fuzzy Systems",slug:"loss-of-load-expectation-assessment-in-electricity-markets-using-monte-carlo-simulation-and-neuro-fu",signatures:"H. Haroonabadi",authors:[{id:"20037",title:"Dr.",name:"Hossein",middleName:null,surname:"Haroonabadi",fullName:"Hossein Haroonabadi",slug:"hossein-haroonabadi"}]},{id:"14042",title:"Automating First- and Second-order Monte Carlo Simulations for Markov Models in TreeAge Pro",slug:"automating-first-and-second-order-monte-carlo-simulations-for-markov-models-in-treeage-pro",signatures:"Benjamin P. Geisler",authors:[{id:"19631",title:"Dr.",name:"Benjamin",middleName:"Peter",surname:"Geisler",fullName:"Benjamin Geisler",slug:"benjamin-geisler"}]},{id:"14043",title:"Monte Carlo Simulations of Adsorbed Molecules on Ionic Surfaces",slug:"monte-carlo-simulations-of-adsorbed-molecules-on-ionic-surfaces",signatures:"Abdulwahab Khalil Sallabi",authors:[{id:"22986",title:"Prof.",name:"A",middleName:null,surname:"Slabi",fullName:"A Slabi",slug:"a-slabi"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"70902",title:"Virtual Reality: A Tool for Improving the Teaching and Learning of Technology Education",doi:"10.5772/intechopen.90809",slug:"virtual-reality-a-tool-for-improving-the-teaching-and-learning-of-technology-education",body:'
1. Introduction
Technical Vocational Education and Training (TVET) is a globally recognized process for preparing people for dynamic engagement in occupations of functional value. It is an effective source of skilled workforce. It is an effective tool for employment generation, wealth creation and crime reduction. UNESCO [1] defined TVET as all forms and aspects of education that are technical or vocational in nature and skill oriented, provided either in educational institutions or under their authority, by public authorities and private sectors or through other forms of organised education, formal, informal or non-formal, aiming to ensure that all members of the community have access to the pathways of lifelong learning. TVET is defined as an integral part of general education which prepares its recipients for occupational fields and effective participation in the world of work. It is an aspect of lifelong learning and a preparation for responsible citizenship, which helps to promote environmentally sound sustainable development and facilitate poverty alleviation. The goal of TVET is to fight indolence, develop skills, provide knowledge and build attitudes required for entry and progressing in any chosen occupation.
However, TVET today faces huge demands globally due to high level of unemployment. Access to skill acquisition is low in relation to the potential trade. High educational entry requirements exclude the majority of youths and young adults. Female participation is relatively low in TVET and concentrated in female-dominated occupations. Geographical imbalances also exist—with low enrolments in rural and low-income areas [2]. The quality of TVET graduates has been portrayed as extremely low, as the majority graduate without employable skills. They lacked the applied technical skills necessary for solving problems and enhancing business productivity and knowledge required by industry. Therefore, they cannot take advantage of available employment opportunities; neither can they create employment, due to gross skill deficiency [3]. Low performance of candidates on terminal examinations is symptomatic of low quality. And symptoms of faulty TVET training include mismatches between supply and demand, employer complaints and low employment rates for graduates. For TVET to achieve its envisaged objectives, it must be properly strengthened (UNESCO, [4]; United Nations, [5]).
The infrastructure needed to deliver quality and practical oriented TVET courses requires huge investment in capital. Both hard and soft infrastructure is needed to prop up the system. Challenges of attaining quality TVET programmes have been discovered to include lack of required TVET facilities, poor funding of TVET programmes and the use of obsolete facilities. Inadequate funding may have been indicted in the poor infrastructural support needed to drive quality delivery of TVET courses [3]. This limitation frustrates the integration of entrepreneurship and practical skills in TVET programmes especially in developing countries. The lack of support infrastructure and infrastructural failures results to high transaction costs which makes delivery very expensive, and since economy has not been friendly, inefficiency has prevailed.
Puyate [6] pointed out that the present state of vocational and technical education facilities is very poor; there is no planned means of maintenance of the already broken-down equipment or means of purchasing new ones, and there is little or no concern on the part of government, teachers and students for the improvement of the present state of teaching facilities. This limits effective skill acquisition by students leading to production of unskilled TVET graduates who cannot fit into gainful employment. Surveys show that only about 40% of TVET institutions of higher learning have laboratory or workshop space for technical education programmes and that the other 60% do not have laboratory or workshop space and that this reflects the low quality of technology programmes in higher institutions. He further noted that these few universities that have laboratories experience acute shortage of laboratory equipment and supplies. Puyate (4) concluded that this situation is partly responsible for the reason why it has been increasingly difficult to run experiments effectively for students and made the teaching and research in science and technology difficult, and therefore the country was producing insufficient and ill-prepared technical education graduates necessary for driving the technological and socio-economic development of this nation. Uwaifo [7] lamented that due to inadequacy of instructional facilities, only a small proportion of the students benefit from the current pedagogical system used in developing countries like Nigeria, especially in technical and vocational education. Unavailability of facilities has caused the use of ineffective methods of teaching and learning. There is dearth of ICT facilities for the training of students. Access to affordable and reliable Internet connectivity is only available in a few institutions, faculties and offices, and power fluctuations and deficient bandwidth have considerably reduced reliability of the access and made things difficult [7].
There are basically two branches of TVET: the technical and vocational areas. Effective teaching and learning of any branch of technical and vocational education can be made easier and interesting through the use of appropriate and adequately provided learning facilities as well as the adoption of the right teaching and learning methods. Inadequacies in teaching, as well as laboratory and workshop facilities, have contributed in no small measure to the diminution of the quality of technical education graduates. Uwaifo [7] lamented that only a small proportion of the students benefit from the current system used in technical and vocational education, proving that only those who learn easily if information is in written or spoken form (verbalizers) can learn in the present situation. This calls for a more effective method in an encouraging environment. Virtual reality has been found effective for learning in different fields and for different types of learners.
2. Virtual reality
Virtual reality is a computer-generated, three-dimensional, multimedia environment. Virtual reality is an environment produced by a computer that looks and seems real to the person experiencing it [8]. It means experiencing things through computers when such things did not really exist [9]. It is a simulation of a real or imagined environment that can be experienced visually in the three dimensions of width, height and depth and that may additionally provide an interactive experience visually in full real-time motion with sound and feedback [10]. Virtual reality, therefore, is a computer-simulated, game-based learning environment, which appears real and gives learners the opportunity to interact with the learning materials and share learning experiences with both their teachers and other learners. In virtual reality, human participants can engage and manipulate simulated physical elements in the environment and interact with fictional or simulated components. Virtual reality allows the user to perform actions and observe their consequences but without penalties as experienced in real situations.
Virtual reality can be traced back to the nineteenth century. The term “virtual reality” was first used in the mid-1980s when Jaron Lanier, founder of VPL Research, began to develop the gear, including goggles and gloves, needed to experience what he called “virtual reality.” But before then, some technologists were developing simulated environments. A major landmark was made in 1956 when the Sensorama was built. Morton Heilig was interested in using it for the Hollywood motion picture industry. He wanted people to get the feeling of being in the movie. The Sensorama experience simulated a real city environment, which one could ride through on a motorcycle. The rider experiences a multisensory stimulation, which provides the opportunity to see the road, hear the engine, feel the vibration and smell the motor’s exhaust in the designed virtual world. In 1960, Heilig patented a head-mounted display device, called the Telesphere Mask.
In 1965, another inventor, Ivan Sutherland, built upon the foundational work of Heilig to achieve “the Ultimate Display,” a head-mounted device that he suggested would serve as a “window into a virtual world.” The 1970s and 1980s were a heady time in the field. Optical advances in the 1970s and 1980s produced haptic devices and other instruments that would allow you to move around in the virtual space. For example, in the mid-1980s, the Virtual Interface Environment Workstation (VIEW) system was built by NASA to combine a head-mounted device with gloves to enable the haptic interaction.
The evolution of virtual reality has provided means of carrying out experiments which would not otherwise be possible owing to availability, accessibility and cost of equipment, tools and materials, as well as safety of human and material resources. Although virtual reality does not replace real objects, it helps to carry out experiments before it is done in the real world. It has been proven to contain a feature which appeals to every faculty of learning. Virtual reality can be used to simulate a real environment for training, education and an imagined environment for interaction [9]. Virtual reality proved effective when used to augment physical facilities for learning in many fields, like teaching architecture [11]; teaching physics [12]; welder training [13]; teaching painting [14]; teaching physical education [15, 16, 17, 18]; training in fire safety [19]; teaching safety rules [20, 21, 22]; teaching electric power supply systems [23]; teaching biology [24]; and teaching electronic circuit construction [3], among many others. In virtual reality, students can work at their own pace to master the skills needed, get periodic feedback and have the opportunity to correct their mistakes without loss of materials, damage to equipment and injury to human beings and materials [25]. Virtual reality provides an opportunity to accurately and realistically simulate dangerous or risky situations and make them safe for learning before engaging in the real situation. Virtual reality can deconstruct complex procedures into convenient actions with each student learning at a different pace [26]. It helps in visualisation of complex concepts and theories as well as exploration of virtual scenarios in the form of real-world settings. It stimulates interaction, ensures that learning is fun and enjoyable and permits cost-effectiveness [27]. Virtual reality encourages students’ participation, reduces distractions and increases attention span of students. By doing so, learning of technology education may become a more interactive process, playful and experimental—like the action-oriented approach of learning. The fondness of young people on computer games gave credence to the adoption of virtual reality as an educational tool [3, 28, 29] for teaching and learning of technology education.
There are two principal ways of using virtual reality in the classroom. The first way involves a traditional desktop set-up. This form of virtual reality is called desktop, fish tank [30, 31] or simply non-immersive virtual reality [3] and used interchangeably in this study. Desktop virtual reality is presented on an ordinary computer screen and is usually explored by keyboard, mouse, wand, joystick or touch screen [32, 33]. The second way is the immersive system. Immersive virtual reality is presented on multiple, room-size screens or through a stereoscopic, head-mounted display unit [34]. Additional specialized equipment such as a data glove enables the participant to interact with the virtual environment through normal body movements. Sensors on the head unit and data glove track the viewer’s movements during exploration and provide feedback. This environment may take the form of a series of large screens or a complete cave automatic virtual reality system [35].
Desktop virtual reality is quite affordable as compared to immersive virtual reality, thereby making the choice suitable for studies in medium-income economies as experienced in developing countries. Besides, there is no overwhelmingly conclusive evidence that immersive systems are more effective in educational applications than their non-immersive counterparts [34]. Rather, the non-immersive virtual reality is much more mature and widely used in different educational areas as compared to the immersive virtual reality which is cumbersome, expensive and occupies much space [36]. Studies have shown that desktop virtual reality technology can enhance academic achievement [3, 37, 38, 39, 40]. Moreover, there are unresolved questions relating to health and safety issues, such as motion sickness, simulator sickness and perceptual shift that arise in the use of immersive virtual reality systems [41, 42, 43]. Literature revealed headaches, nausea, balance upsets and other physical effects of head-mounted device systems. One other concern is the potential side effects and after effects of virtual reality exposure. Some other effects could include cybersickness, a type of motion sickness caused by the virtual reality experience, perceptual-motor disturbances, flashbacks and generally lowered arousal [44]. Desktop virtual reality is user friendly. Woodford [9] emphasised that desktop virtual reality is collaborative, unlike its immersive counterparts. Collaboration is a vital aspect of effective learning in skill-related fields like technology education.
Youngblut [36] conducted an extensive survey research on educational uses of virtual reality technology. Youngblut’s study found unique capabilities of virtual reality in boosting academic achievement. This study showed potential educational effectiveness even for students with special needs. The role of the teacher changed from director of learning activities to facilitator. It was reported that students enjoyed using predeveloped applications and developing their own virtual worlds. The majority of the teachers in the studies reviewed said they would use virtual reality technology if it were affordable, available and easy to use for students and teachers. Chen [45] carried out an experimental study titled “Virtual Space and Its Effects on Learning.” The aim of the study was to find out how virtual reality can influence the learning of technology skills. The study showed that virtual reality is an effective tool for teaching and learning skills. However, Chen [45] asserts that although virtual reality is recognized as an impressive learning tool, there are still many issues that need further investigation including identifying the appropriate theories and/or models to guide its design and development, finding out whether its use can improve the intended performance and understanding and investigating ways to reach more effective learning when using this technology and its impact on learners with different aptitudes. Lee et al. [24] researched on learning effectiveness in a desktop virtual reality-based learning environment. The learning effectiveness was measured through three specific purposes: academic performance, perceived learning and satisfaction. There was a significant difference in the academic performance, perceived learning and satisfaction between the two groups. It was concluded that the virtual reality instructional programme positively affected the students’ academic achievement and their perceived learning quality and satisfaction. The study of Lee et al. [24] helped to justify the desktop virtual reality for this study.
Onele [46] carried out a study on effects of teaching methods in virtual reality on the interest and academic achievement of electronic technology education students in Nigerian universities. It adopted a pretest-posttest quasi-experimental design. ElectricVLab designed and supplied by Quality Assurance International LLC, Massachusetts, in the USA, was used to provide the virtual learning setting for students to learn electronic technology education. The study found that student achieved high with virtual reality; there was no significant difference between the achievement of male students in demonstration and their counterparts in peer tutoring class. However, female students in peer tutoring class achieved significantly higher than their counterparts in the demonstration class. Moreover, students from both classes indicated high interest in the study of electronic technology education using virtual reality. The research identified a significant interaction effect between teaching methods.
It is true that virtual reality has existed for decades; its use is new to education, especially in developing countries. Research on applications of virtual reality technology to education is in its infancy, especially in Africa [47], and for teaching and learning in industrial-related training like technology education [3]. Such a situation presents both challenges and opportunities for instructors and researchers interested in virtual reality technology. One of those challenges is the selection of right teaching methods when virtual reality is involved. Some of the studies were on how to arrange lessons, how these arrangements affect students’ behaviour, and in the long term, how they affect students’ academic achievement. Yet, there does not seem to be a sufficiently conclusive and prescriptive body of research to guide the instructional method and classroom facilitation of virtual reality technologies [3, 48, 49, 50, 51]. Researchers lamented dearth of empirical evidences to help instructors make the right choice of teaching methods in virtual reality [52, 53, 54]. Thus, researchers and educators interested in classroom uses and methods in virtual reality technologies do not yet have either a sound theoretical framework or a strong body of empirical data from controlled experiments with which to work. Anderson [55] believes that the use of virtual reality as a learning environment will require a thorough pedagogical consideration by educators in order to choose the most appropriate and suitable teaching methods, especially for teaching and learning of technology education.
\n',keywords:"virtual reality, technology education, virtual environment, virtual reality components, educational technology",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/70902.pdf",chapterXML:"https://mts.intechopen.com/source/xml/70902.xml",downloadPdfUrl:"/chapter/pdf-download/70902",previewPdfUrl:"/chapter/pdf-preview/70902",totalDownloads:219,totalViews:0,totalCrossrefCites:0,dateSubmitted:"September 14th 2019",dateReviewed:"December 9th 2019",datePrePublished:"January 23rd 2020",datePublished:"January 14th 2021",dateFinished:"January 23rd 2020",readingETA:"0",abstract:"This work dealt with technology education, its expectations and present state, especially in developing countries. It looked at virtual reality: its development, types, uses and how it can be applied to improve teaching and learning. It also looked at different works that compared virtual reality, and other educational technology tools were reviewed. Advantages of virtual reality were highlighted; these will include both social and academic issues. Immersive and non-immersive virtual reality for education were briefly discussed, looking at the applicability of each to teaching and learning, ease of use, cost-effectiveness and health implications.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/70902",risUrl:"/chapter/ris/70902",signatures:"Onele Nicholas Ogbonna",book:{id:"8697",title:"Virtual Reality and Its Application in Education",subtitle:null,fullTitle:"Virtual Reality and Its Application in Education",slug:"virtual-reality-and-its-application-in-education",publishedDate:"January 14th 2021",bookSignature:"Dragan Cvetković",coverURL:"https://cdn.intechopen.com/books/images_new/8697.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"101330",title:"Dr.",name:"Dragan",middleName:"Mladen",surname:"Cvetković",slug:"dragan-cvetkovic",fullName:"Dragan Cvetković"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"311949",title:"Dr.",name:"Nicholas Ogbonna",middleName:"Ogbonna",surname:"Onele",fullName:"Nicholas Ogbonna Onele",slug:"nicholas-ogbonna-onele",email:"nicelinks@yahoo.com",position:null,institution:{name:"Ebonyi State University",institutionURL:null,country:{name:"Nigeria"}}}],sections:[{id:"sec_1",title:"1. 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The impact of internet virtual physics laboratory instruction on the achievement in physics, science process skills and computer attitudes of 10th-grade students. Journal of Science Education and Technology. 2007;16(5):451-461'},{id:"B13",body:'Porter NC, Cote JA, Gifford TD, Lam W. Virtual reality welder training. Journal of Ship Production. 2005;22:126-138'},{id:"B14",body:'Heckman J, Joseph R. Virtual reality painter training becomes real. Metal Finishing. 2003;101(5):22-26'},{id:"B15",body:'Holden MK. Virtual environments for motor rehabilitation: Review. Cyberpsychology & Behavior. 2004;2005(8):187-211'},{id:"B16",body:'Keshner EA. Virtual reality and physical rehabilitation: A new toy or a new research and rehabilitation tool? Journal of NeuroEngineering and Rehabilitation. 2004;1:8-9'},{id:"B17",body:'Zaretsky M. Zaretsky Dossier for Teaching. 2011. Retrieved from: https://issuu.com/mzaretsky/docs/dossier-teaching-2011'},{id:"B18",body:'Zhang L, Liu Q. 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