Plasma & Microwave Technology

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CHAPTER II: PLASMA & MICROWAVE TECHNOLOGY

Introduction

The goal of this chapter is to familiarise the reader with the relevant aspects of plasma- and microwave technologies, as well as introduce the core methods and mathematical descriptions needed for microwave plasma modelling. Some key terms and definitions are first described in Section 2.2, followed by the most common plasma-chemical reactions described in Section 2.3, which are expanded upon in Appendix A. A brief overview of various plasma sources is given in Section 2.4, followed by a brief introduction into the core concepts of microwave components and design in Section 2.5. The overall modelling and simulation method for plasmas is described briefly in Section 2.6, followed by a more specific description of microwave plasma modelling in Section 2.7. The domain equations are expanded upon in Appendix C. Plasma diagnostics are discussed in Section 2.8.

Plasma Definitions & Terms

As temperature increases, states of matter “decompose” to less structured, more chaotic systems. A solid lattice changes to less tightly-bound liquid movements, which further changes to unbound gas molecules, governed by collisions. The gas phase further changes to a collection of charged ions and neutral particles which behave differently from their atomically neutral counterparts. The latter is known as the plasma state and it is often pointed out that over 95 % of the visible universe is in the plasma state. In physics and engineering, a plasma must conform to three main conditions [34]:

• Quasi-neutrality ( ≃  );
• ionisation of the gas ( →  ⁺ +  ); and
• exhibition of collective behaviour i.e. the motions depend on both local -and remote conditions.

 Plasma Temperatures
A gas in thermal equilibrium contains particles of all velocities ( ), and follows a typical Maxwell-Boltzmann distribution, described by Equation (2.1) and shown visually in Figure 2.1.
The width of this distribution is characterised by a constant value for in Equation (2.1), and this is what temperature refers to in plasma physics (Figure 2.2). Plasmas can have different temperatures for different species, e.g. electron temperature, ion temperature, neutral particle temperatures, each described by a Maxwell-Boltzmann distribution.
The properties of a plasma vary with electron density and temperature. These parameters change, based on the type of energy supply and the amount of energy transferred to the plasma. A plasma is considered to be in local thermodynamic equilibrium (LTE) when the electron temperatures are close to the heavier particle temperatures. LTE also requires chemical reactions to be governed by collisions only and not by radiative processes, that collision phenomena have to be micro-reversible, and that diffusion time must be sufficient for particles to reach equilibrium [37]. LTE requires higher collisional exchanges, higher densities and higher pressures, and hence requires higher power delivered to the plasma [37].
Numerous plasmas exist far from thermodynamic equilibrium (non-thermal), however, and are characterised by multiple temperatures related to different plasma particles. This can also be described as a departure from the Boltzmann-distribution patterns for the density of excited atoms. It is, however, the electron temperature in particular that often differs significantly from that of heavier particles [37]. Non-thermal plasmas are usually generated at low pressures and low power levels. Thermal plasmas are usually characterised by higher electron densities, whereas non-thermal plasmas are more selective (lower electron densities). These characteristics affect the engineering aspects and application areas of these two types of plasmas.

Plasma-Chemical Reactions

Reaction rates are affected by reaction cross-sections, probabilities and electron energy-distribution functions. The reaction rate is a result of integration of the reaction cross-section over the relevant distribution function [35]. The most relevant elementary plasma-chemical reactions are discussed here.

Ionisation Processe

Ionisation is a key process in plasma chemistry and entails the conversion of neutral atoms or molecules into electrons and positive ions. In electronegative gases with high electron affinity (e.g. O2, Cl2, SF6, UF6), negative ions are also formed. Ionisation processes are subdivided into five different groups, and are briefly described in Appendix A. Electrons are the first to gain energy from electric fields due to their low mass, and transmit the energy to other components through collisions. This energy is used for ionisation, excitation and dissociation processes. Rates are therefore dependent on the number of electrons with adequate energy to initiate a reaction. This is described by means of the electron energy-distribution function (EEDF) which is the probability density for an electron to have a particular energy, ϵ [35]. The EEDF strongly depends on the electric field strength (and hence electron temperature) as well as gas composition in the plasma.
The average electron energy can be determined by Equation (2.3). In most plasmas, E_ave varies between 1 eV and 5 eV. Ion energies can also be described by an energy-distribution function, and at low pressures they are often similar to the Maxwellian distribution function above, with ion temperature, , close to the gas temperature, [35].

Elastic & Inelastic Collisions

Elementary processes can generally be divided into two categories: Elastic and inelastic. During elastic collisions the internal energies do not change, the kinetic energy is conserved, and it results in only geometric scattering & redistribution of kinetic energy. Inelastic collisions, however, change kinetic energy into internal energy. These processes can be described by six collision parameters, reported in Appendix B.

Coulomb Collisions

Electron-electron, electron-ion and ion-ion scattering processes are all classified as coulomb collisions. Energy transfer between these particles during elastic collisions is only possible in the form of kinetic energy.

Plasma Sources

Excitation frequencies influence the behaviour of the electrons and ions in a plasma, and the different plasma sources can be classified according to the excitation mode [37]:

• Direct current (DC) discharges;
• radio frequency (RF) discharges; and
• microwave discharges.

DC Discharges

Plasma in DC discharges are generally created in closed discharge vessels using interior electrodes. Numerous types of discharges can be obtained by varying the applied voltage and discharge current [38, 39]. Different types of DC discharges are categorised in Figure 2.4.
The pulsed mode DC discharges have the advantages of higher operating power, additional performance control and more homogeneous film deposition [39]. The pulsed power supply, however, is more complex in design and affects reproducibility of the process [37].

RF Discharges

Plasmas can be generated at high power levels using RF discharges. Despite the higher cost, different types of RF discharges are gaining increasing popularity due to the absence of direct contact between the plasma and electrode(s). Many of these discharge systems are electrodeless and therefore electrode-related problems are not a major concern [40]. The RF electric field interactions with the plasma can be either inductive or capacitive. The inductively coupled plasma (ICP) is excited and maintained using a coil in close proximity to a gas stream. High-frequency electric current is passed through the coil, where a magnetic field is induced along the axis of the discharge tube. The resulting electric field accelerates the electrons and thus maintains the plasma [37]. Alternatively, capacitively coupled plasmas (CCPs) generate higher values for the electric fields than ICPs do. As in a capacitor, the electric field is now the primary effect. These higher electric field values make it possible to generate non-LTE plasmas that are used in material treatment such as electronics [40].

Microwave Discharges

Microwave systems are electrodeless, and the same principle applies to all variations. Microwaves are guided along the system, through some form of metallic waveguide, and transmit energy directly to the plasma gas electrons. Whereas RF discharges operate with wavelengths of approximately 22 m, microwave plasmas are sustained by electromagnetic waves in the centimeter range, which is comparable to the size of the physical system [37]. This form of plasma generation will be discussed further in the following sections.

Microwave Components & Design

Transmission lines, such as waveguides, and their corresponding cavities represent significant aspects in many practical radio-frequency systems. In this section the fundamentals of waveguide design will be introduced, as well as their electromagnetic field propagation characteristics. Also, the significance in varying geometries (rectangular and cylindrical) will be discussed and compared, and ultimately the design and characteristics of their corresponding cavities. This process includes discussions of cut-off frequencies, attenuation constants and quality factors used to describe cavities.

Transverse Electromagnetic Modes

Electromagnetic field configurations are known as modes. Analysing these fields within any region is dependent upon solving the Maxwell field equations in a coordinate system appropriate to the region. For any particular problem various field configurations, or solutions, exist that satisfy the wave equations, Maxwell’s equations, and the boundary conditions [41]. In several regions of practical importance, such as waveguides, the dimensions and field excitation only allow for a single mode capable of propagation [42]. As a result, the electromagnetic field at most points in space is characterized by the amplitudes of this one dominant mode type. The three general modes are Transverse Electromagnetic (TEM), Transverse Electric (TE) and Transverse Magnetic (TM). In the TEM mode both the electric and magnetic fields are perpendicular to the direction of propagation, however no TEM solutions exist for hollow rectangular waveguides [43].

Acknowledgements
Abstract 
Research Outputs
Peer-reviewed Articles 
Conference Proceedings 
Submitted Articles 
List of Figures
List of Tables 
Nomenclature 
Acronyms and Abbreviations 
1 Introduction 
1.1 Background
1.2 Problem Statement
1.3 Objective
1.4 Experimental Scope
1.5 Thesis Overview
2 Plasma & Microwave Technology 
2.1 Introduction
2.2 Plasma Definitions & Terms
2.2.1 Plasma Temperatures
2.3 Plasma-Chemical Reactions
2.3.1 Ionisation Processes
2.3.2 Elastic & Inelastic Collisions
2.3.3 Coulomb Collisions
2.4 Plasma Sources
2.4.1 DC Discharges
2.4.2 RF Discharges
2.4.3 Microwave Discharges
2.5 Microwave Components & Design
2.5.1 Transverse Electromagnetic Modes
2.5.2 Rectangular Waveguides
2.5.3 Power
2.5.4 Attenuation
2.5.5 Resonant Cavities
2.6 Modelling & Simulation of Plasma Processes
2.7 Microwave Plasma Modelling
2.8 Plasma Diagnostics
2.8.1 Spectroscopy
2.8.2 Probe Measurements
2.8.3 Thermocouple
2.8.4 Langmuir Probes
2.8.5 Enthalpy Probes
2.9 Summary
3 Silicon Carbide: Properties, Synthesis & Deposition
3.1 Introduction
3.2 History
3.3 Crystalline forms
3.4 SiC Layer Defects
3.5 Commercial production of SiC
3.6 Physical properties
3.7 Methyltrichlorosilane
3.8 Microwave synthesis
3.9 Thermal vs. Plasma Enabled CVD of SiC
3.10 SiC as a nuclear ceramic
3.11 Summary
4 Spouted Beds Reactor Design, Operation & Modelling
4.1 Introduction
4.2 Introduction to Spouted Beds
4.3 Cone and Inlet Design
4.4 Solids Properties
4.5 Gas Flow Rate & Bed Depth
4.6 Applications
4.7 Microwave Plasma-enabled Spouted Bed CVD Reactors
4.8 Summary .
5 Experimental 
5.1 Introduction
5.2 Calibration
5.3 Equipment/Apparatus
5.4 Design of Experiment
5.5 Method/Procedure
5.6 Characterisation Equipment
5.7 Summary
6 Results & Discussion
6.1 Introduction
6.2 Experimental Results: Deposition and Growth Rates
6.3 Contour Plots and Optimisation
6.4 Response Surface Methodology (RSM) and ANOVA Analysis
6.5 Electron Microscopy and Optical Colour Mapping
6.6 Particle Size: TEM
6.7 Elemental Composition: EDX, XPS, TGA and FTIR
6.8 Crystallographic Structure: XRD
6.9 Surface Area & Porosity
6.10 Heat Treatment/Annealing
6.11 Summary
7 Modelling & Simulation 
7.1 Introduction
7.2 Geometry & Key Parameters
7.3 Simulation Model
7.4 Modelling Software
7.5 Results and Discussions
7.6 Summary
8 Conclusions & Recommendations
8.1 Summary
8.2 Conclusions
8.3 Recommendations
9 Reference List 
Appendices
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