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PlasmaModuleUsersGuide.pdf
Contents
Chapter 1: Introduction
About the Plasma Module 14
Overview of the User’s Guide 24
Chapter 2: Data Required for Plasma Modeling
Data Requirements 28
Importing Collision Cross-Section Data 34
Chapter 3: The Boltzmann Equation, Two-Term Approximation Interface
The Boltzmann Equation, Two-Term Approximation Interface 40
Theory for the Boltzmann Equation, Two-Term Approximation Interface 48
Chapter 4: The Drift Diffusion Interface
The Drift Diffusion Interface 58
Theory for the Drift Diffusion Interface 70
Chapter 5: The Heavy Species Transport Interface
The Heavy Species Transport Interface 80
Theory for the Heavy Species Transport Interface 104
Chapter 6: Plasma Interfaces
The Plasma Interface 126
The Plasma, Time Periodic Interface 143
The Inductively Coupled Plasma Interface 160
The Microwave Plasma Interface 163
Plasma Reactors Theory 164
Capacitively Coupled Plasmas 167
DC Discharges 181
Theory for Inductively Coupled Plasmas 184
Theory for Microwave Plasmas 188
Theory for Global Models 197
Chapter 7: Equilibrium Discharges Interfaces
The Equilibrium DC Discharge Interface 204
The Combined Inductive/DC Discharge Interface 211
The Equilibrium Inductively Coupled Plasma Interface 218
Equilibrium Discharges Theory 222
Summary of the Equilibrium Discharge Interfaces Features 228
Chapter 8: AC/DC Interfaces
The Electrostatics Interface 230
The Electric Currents Interface 253
The Electrical Circuit Interface 274
Theory for the Electrostatics Interface 291
Theory for the Electric Currents Interface 296
Theory for the Electrical Circuit Interface 298
Connecting to Electrical Circuits 308
SPICE Import and Export 312
Chapter 9: Fluid Flow Interface
The Single-Phase Flow, Laminar Flow Interface 316
Theory for the Single-Phase Flow Laminar Interface 339
Introduction
About the Plasma Module
Why Plasma is Used in Modeling
How the Plasma Module Helps Improve Your Modeling
Plasma Module Nomenclature
The Plasma Module Physics Interface Guide
Common Physics Interface and Feature Settings and Nodes
Where Do I Access the Documentation and Application Libraries?
The Documentation and Online Help
The Application Libraries Window
Contacting COMSOL by Email
COMSOL Access and Technical Support
COMSOL Online Resources
Overview of the User’s Guide
Table of Contents, Glossary, and Index
Data Requirements for Plasma Modeling
AC/DC Interfaces
Fluid Flow Interfaces
Boltzmann Equation, Two-Term Approximation Interface
Drift Diffusion Interface
The Heavy Species Interface
The Plasma Interfaces
The Equilibrium Discharge Interfaces
Data Required for Plasma Modeling
Data Requirements
Electron Impact Reactions
detailed balance
Reaction
Surface Reaction
Species
Importing Collision Cross-Section Data
Cross-Section Data File Format
Importing Cross Sections
The File Format
References for the Plasma Module Cross-Section Data Requirements
The Boltzmann Equation, Two-Term Approximation Interface
The Boltzmann Equation, Two-Term Approximation Interface
Settings
Electron Energy Distribution Function settings
Dependent Variables
Global Nodes for the Boltzmann Equation, Two-Term Approximation Interface
Boltzmann Model
Boltzmann Settings
Mole Fraction Settings
results
Initial Values
Initial Values
Cross Section Import
Electron Impact Reaction
Collision
Cross Section Data
Theory for the Boltzmann Equation, Two-Term Approximation Interface
The Electron Energy Distribution Function
Maxwellian EEDF
Druyvesteyn EEDF
Generalized EEDF
Boltzmann Equation, Two-Term Approximation
References for the Boltzmann Equation, Two-Term Approximation Interface
The Drift Diffusion Interface
The Drift Diffusion Interface
Settings
Electron Properties
Stabilization
Discretization
Dependent Variables
Domain, Boundary, and Pair Nodes for the Drift Diffusion Interface
Drift Diffusion Model
Model Inputs
Electron Density and Energy
Mean electron energy specification
Units
DC Electron Mobility
Initial Values
Initial Values
Electron Production Rate
Electron Production Rate
General Power Deposition
General Power Deposition
Velocity
Velocity
Inductive Power Deposition
Inductive Power Deposition
Microwave Power Deposition
Microwave Power Deposition
Insulation
Electron Density and Energy
Electron Density and Energy
Wall
General Wall Settings
Electron Density Wall Settings
Electron Energy Wall Settings
Flux
Flux
Electron Outlet
Theory for the Drift Diffusion Interface
Introduction to Drift Diffusion Theory
Electron Transport Theory
Source Coefficients
Stabilization
Tensor Transport Properties
The Wall Boundary Condition
The Insulation Boundary Condition
The Electron Density and Energy Boundary Condition
Reference for the Drift Diffusion Interface
The Heavy Species Transport Interface
The Heavy Species Transport Interface
Settings
Out-of-Plane Thickness (2D, 1d Axisymmetric, and 1D)
Transport Settings
Reactor
Electron Energy Distribution Function Settings
CHEMKIN Import for Species Property
Stabilization
surface chemistry
Discretization
Domain, Boundary, and Pair Nodes for the Heavy Species Transport Interface
Cross Section Import
Diffusion and Migration
Model Inputs
Density
Total Mass flow
Mean electron energy
Electron Impact Reaction
Reaction Formula
Collision Type
Collision
Cross Section Data
Arrhenius Parameters
Kinetic Expressions
Source Coefficient Data
Reaction
Domain Selection
Reaction Formula
reaction parameters
Species
Domain Selection
Species Formula
General Parameters
Electron Parameters
Species Thermodynamic Parameters
Mobility and Diffusivity Expressions
Mobility Specification
Surface Reaction
Reaction Formula
Reaction Parameters
secondary emission parameters
Surface Species
Species Formula
General Parameters
Surface Species Parameters
Bulk Species Parameters
Flux
Inlet
Inlet
Outflow
Symmetry
Theory for the Heavy Species Transport Interface
About the Transport Equations
Multicomponent Diffusion Equations
Additional Quantities of Interest
Auxiliary Relations
Source Coefficients
Thermodynamic Properties
Species Transport Properties
Mixture Transport Properties
Scaling
Stabilization
Surface Reactions
Flux Matching
flux matching for each Species
flux matching for the total mass flux
flux matching for the total HEAT flux
About Surface Species
Limitations of the Heavy Species Transport Equations
Global Model
Closed reactor
Constant mass
Constant pressure
Global Model Surface reactions
References for the Heavy Species Transport Interface
Plasma Interfaces
The Plasma Interface
Settings
Out-of-Plane Thickness (2D, 1d Axisymmetric, and 1D)
Transport Settings
Plasma Properties
Reactor
Electron Energy Distribution Function
CHEMKIN Import for Species Property
Stabilization
discretization
Dependent Variables
Domain, Boundary, Edge, Point, and Pair Nodes for the Plasma Interface
Plasma Model
Model Inputs
Electron Density and Energy
Mean electron energy specification
Units
Density
Total Mass flow
Mean electron energy
EEDF Inputs
Initial Values
Initial Values
Species Constraint Group
The Plasma, Time Periodic Interface
Settings
Out-of-Plane Thickness (2D, 1d Axisymmetric, and 1D)
Transport Settings
Plasma Properties
Electron Energy Distribution Function
extra dimension settings
Secondary Emission Model
Stabilization
discretization
Dependent Variables
Domain, Boundary, Edge, Point, and Pair Nodes for the Plasma, Time Periodic Interface
Species Group
Species Constraint Group
Dielectric Contact
Ground
Metal Contact
Surface Charge Accumulation
Terminal
Zero Charge
Periodic Excitation
Circuit Options
parallel rc circuit
l–network
reversed L–Network
The Inductively Coupled Plasma Interface
Settings
Plasma Conductivity Coupling
compute tensor plasma conductivity
coupled interfaces
Electron Heat Source
coupled interfaces
Collisionless Heating Coupling
coupled interfaces
The Microwave Plasma Interface
Settings
Plasma Reactors Theory
Capacitively Coupled Plasmas
The Importance of 1D Modeling
Electric Excitation
Meshing Guidelines
Using Consistent Source Frequencies and Period Settings
Choosing the Number of Elements in the Extra Dimension
Pulsed Discharges
Choosing the Correct Space on Which to Solve for the Heavy Species
ion transport in pulsed discharges
Validity of Fluid Models
Complex Chemistries and Electronegative Discharges
Solver Settings
DC Discharges
Introduction to DC Discharge Theory
DC Discharge Boundary Conditions
Tips for Modeling DC Discharges
Theory for Inductively Coupled Plasmas
Introduction to Inductively Coupled Plasmas
Domain Equations for the Inductively Coupled Plasma Interface
Theory for Microwave Plasmas
Introduction
Wave Heated Discharge Theory
Ambipolar Fields
te and tm mode propagation
TE mode
TM mode
ECR reactors
Resonance Zone
Deposited and Reflected Power
Modeling Suggestions
Solver Settings
Plasma Conductivity in the Presence of a Static Magnetic Field
References
Theory for Global Models
Introduction
Heavy Species
Electron Density and Electron Energy Density
EEDF computed from the Boltzmann equation in the two-term approximation
References for the Heavy Species Transport Interface
Equilibrium Discharges Interfaces
The Equilibrium DC Discharge Interface
Settings for Physics Interfaces and Coupling Features
Physics Interface and Coupling Features
Equilibrium Discharge Heat Source
Settings
Heat Source Components
Equilibrium Discharge Heat Source
Flow Coupling
Settings
Flow Coupling
Equilibrium Discharge Boundary Heat Source
Settings
Electrode Properties
Electron Current
Ion Current
Source Position
Equilibrium Discharge Boundary Heat Source
The Combined Inductive/DC Discharge Interface
Settings for Physics Interfaces and Coupling Features
Physics Interface and Coupling Features
Static Current Density Component
Settings
Static Current Density Component
Induction Current Density Component
Settings
Induction Current Density Component
Lorentz Force
Settings
Lorentz Force
The Equilibrium Inductively Coupled Plasma Interface
Settings for Physics Interfaces and Coupling Features
Physics Interface and Coupling Features
Equilibrium Discharges Theory
Domain equations
transport properties
Boundary equations
Summary of the Equilibrium Discharge Interfaces Features
References
AC/DC Interfaces
The Electrostatics Interface
Settings
Cross-Section Area (1D components)
Thickness (2D components)
Physics-Controlled Mesh
Manual Terminal Sweep Settings
Dependent Variables
Discretization
Domain, Boundary, Edge, Point, and Pair Nodes for the Electrostatics Interface
About the Boundary Conditions
Available Nodes
Charge Conservation
Material Type
Electric Field
Initial Values
Initial Values
Space Charge Density
Space Charge Density
Zero Charge
Ground
Boundary, Edge, or Point Selection
Constraint Settings
Electric Potential
Boundary, Edge, or Point Selection
Electric Potential
Circuit Settings
Constraint Settings
Surface Charge Density
Surface Charge Density
External Surface Charge Accumulation
Material Type
External Surface Charge Accumulation
Electric Displacement Field
Electric Displacement Field
Periodic Condition
Boundary Selection
Periodic Condition
Constraint Settings
Thin Low Permittivity Gap
Thin Low Permittivity Gap
Surface Charge Accumulation
Surface Charge Accumulation
Dielectric Shielding
Material Type
Electric Shielding
Terminal
Terminal
Constraint Settings
Floating Potential
Floating Potential
Constraint Settings
Distributed Capacitance
Distributed Capacitance
Line Charge
Edge Selection
Line Charge
Line Charge (on Axis)
Line Charge (on Axis)
Line Charge (Out-of-Plane)
Point Selection
Line Charge (Out-of-Plane)
Point Charge
Point Selection
Point Charge
Point Charge (on Axis)
Point Selection
Point Charge (on Axis)
Change Cross Section
Change Cross Section
Change Thickness (Out-of-Plane)
Change Thickness (Out-of-Plane)
Charge Conservation, Piezoelectric
Electric Displacement
Metal Contact
Terminal
Quick Circuit Settings
Constraint Settings
Dielectric Contact
Surface Charge Type
Distributed Capacitance
Electrostatic Point Dipole
Electrostatic Point Dipole
The Electric Currents Interface
Settings
Physics-Controlled Mesh
Cross-Section Area (1D)
Thickness (2D)
Manual Terminal Sweep Settings
Dependent Variables
Discretization
Domain, Boundary, Edge, Point, and Pair Nodes for the Electric Currents Interface
About the Boundary Conditions
Available Nodes
Current Conservation
Material Type
Conduction Current
Electric Field
Initial Values
Initial Values
External Current Density
External Current Density
Current Source
Current Source
Electric Insulation
Floating Potential
Floating Potential
Constraint Settings
Boundary Current Source
Boundary Current Source
Normal Current Density
Normal Current Density
Distributed Impedance
Distributed Impedance
Terminal
Terminal
Constraint Settings
Contact Impedance
Contact Impedance
Sector Symmetry
Pair Selection
Sector Settings
Constraint Settings
Line Current Source
Edge Or Point Selection
Line Current Source
Line Current Source (on Axis)
Line Current Source (On Axis)
Point Current Source
Point Selection
Point Current Source
Point Current Source (on Axis)
Point Selection
Point Current Source
Piezoresistive Material
Piezoresistive Material Property
The Electrical Circuit Interface
Device names
Settings
Resistance in Parallel to PN Junctions
Create unique nodes for new devices
Electrical Circuit Toolbar
Ground Node
Ground Connection
Voltmeter
DEVICE NAME
Node Connections
Ampère Meter
DEVICE NAME
Node Connections
Device Parameters
Resistor
DEVICE NAME
Node Connections
Device Parameters
Capacitor
DEVICE NAME
Node Connections
Device Parameters
Inductor
DEVICE NAME
Node Connections
Device Parameters
Voltage Source
DEVICE NAME
Node Connections
Device Parameters
Current Source
DEVICE NAME
Node Connections
Device Parameters
Voltage-Controlled Voltage Source
DEVICE NAME
Node Connections
Device Parameters
Voltage-Controlled Current Source
DEVICE NAME
Node Connections
Device Parameters
Current-Controlled Voltage Source
DEVICE NAME
Node Connections
Device Parameters
Current-Controlled Current Source
DEVICE NAME
Node Connections
Device Parameters
Subcircuit Definition
Subcircuit Pins
Subcircuit Instance
DEVICE NAME
Node Connections
NPN BJT and PNP BJT
DEVICE NAME
Node Connections
Model Parameters
n-Channel MOSFET and p-Channel MOSFET
DEVICE NAME
Node Connections
Model Parameters
Mutual Inductance
DEVICE Parameters
Transformer
Node Connections
DEVICE Parameters
Diode
DEVICE NAME
Node Connections
Model Parameters
External I vs. U
DEVICE NAME
Node Connections
External Device
External U vs. I
DEVICE NAME
Node Connections
External Device
External I-Terminal
DEVICE NAME
Node Connections
External Terminal
SPICE Circuit Import
SPICE Circuit Export
Theory for the Electrostatics Interface
Charge Relaxation Theory
First Case: t >> t
Second Case: t <
Electrostatics Equations
The Electrostatics Interface in Time Dependent or Frequency Domain Studies
Theory for the Electric Currents Interface
Electric Currents Equations in Steady State
Dynamic Electric Currents Equations
Theory for the Electrical Circuit Interface
Electric Circuit Modeling and the Semiconductor Device Models
Bipolar Transistors
MOSFET Transistors
Diode
Reference for the Electrical Circuit Interface
Connecting to Electrical Circuits
About Connecting Electrical Circuits to Physics Interfaces
Connecting Electrical Circuits Using Predefined Couplings
Connecting Electrical Circuits by User-Defined Couplings
Determining a Current or Voltage Variable Name
Solving
Postprocessing
SPICE Import and Export
SPICE Import
SPICE Export
Reference
Fluid Flow Interface
The Single-Phase Flow, Laminar Flow Interface
The Laminar Flow Interface
Settings
Physical Model
Dependent Variables
Advanced Settings
Discretization
Fluid Properties
Model Inputs
Fluid Properties
Volume Force
Initial Values
Initial Values
Wall
Boundary Condition
Wall Movement
Constraint Settings
Inlet
Boundary Condition
Velocity
Pressure Conditions
Mass Flow
Fully Developed Flow
Constraint Settings
Outlet
Boundary Condition
Pressure Conditions
Velocity
Fully Developed Flow
Constraint Settings
Symmetry
Boundary Selection
Constraint Settings
Open Boundary
Boundary Conditions
Boundary Stress
Boundary Condition
Constraint Settings
Vacuum Pump
Parameters
Static Pressure Curve Data
Units
Static Pressure Curve Interpolation
Location in user interface
Periodic Flow Condition
Pressure Difference
Constraint Settings
Orientation of Source
Flow Continuity
Pressure Point Constraint
Pressure Constraint
Constraint Settings
Point Mass Source
Source Strength
Line Mass Source
Selection
Source Strength
Gravity
Acceleration of Gravity
Theory for the Single-Phase Flow Laminar Interface
General Single-Phase Flow Theory
2D Axisymmetric Formulations
Compressible Flow
Weakly Compressible Flow
The Mach Number Limit
Incompressible Flow
The Reynolds Number
Theory for the Wall Boundary Condition
Slip
Sliding Wall
Slip Velocity
Prescribing Inlet and Outlet Conditions
Inlet Conditions
Outlet Conditions
Alternative Formulations
Mass Flow
Pointwise Mass Flux
Mass Flow Rate
Standard Flow Rate
Fully Developed Flow (Inlet)
Fully Developed Flow (Outlet)
No Viscous Stress
Normal Stress Boundary Condition
Pressure Boundary Condition
Vacuum Pump Boundary Condition
Defining a Device at an Outlet
Mass Sources for Fluid Flow
Point Source
Line Source
Numerical Stability — Stabilization Techniques for Fluid Flow
Streamline Diffusion
Crosswind Diffusion
Isotropic Diffusion
Solvers for Laminar Flow
Nonlinear Solver
Linear Solver
Time-Dependent Solvers
Pseudo Time Stepping for Laminar Flow Models
Discontinuous Galerkin Formulation
Particle Tracing in Fluid Flow
References for the Single-Phase Flow, Laminar Flow Interfaces
Index
Plasma Module
User’s Guide
P l a s m a M o d u l e U s e r ’ s G u i d e
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Part number: CM021401
C o n t e n t s
C h a p t e r 1 : I n t r o d u c t i o n
About the Plasma Module
14
Why Plasma is Used in Modeling . . . . . . . . . . . . . . . . . 14
How the Plasma Module Helps Improve Your Modeling . . . . . . . . 15
Plasma Module Nomenclature . . . . . . . . . . . . . . . . . . 16
The Plasma Module Physics Interface Guide. . . . . . . . . . . . . 18
Common Physics Interface and Feature Settings and Nodes . . . . . . 20
Where Do I Access the Documentation and Application Libraries? . . . . 20
Overview of the User’s Guide
24
C h a p t e r 2 : D a t a R e q u i r e d f o r P l a s m a M o d e l i n g
Data Requirements
28
Electron Impact Reactions . . . . . . . . . . . . . . . . . . . 28
Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Surface Reaction . . . . . . . . . . . . . . . . . . . . . . . 30
Species . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Importing Collision Cross-Section Data
34
Cross-Section Data File Format . . . . . . . . . . . . . . . . . 34
The File Format . . . . . . . . . . . . . . . . . . . . . . . 35
References for the Plasma Module Cross-Section Data Requirements . . . 37
C h a p t e r 3 : T h e B o l t z m a n n E q u a t i o n ,
T w o - T e r m A p p r o x i m a t i o n I n t e r f a c e
The Boltzmann Equation, Two-Term Approximation Interface
Global Nodes for the Boltzmann Equation, Two-Term Approximation
40
C O N T E N T S | 3
Interface. . . . . . . . . . . . . . . . . . . . . . . . . 43
Boltzmann Model. . . . . . . . . . . . . . . . . . . . . . . 44
Initial Values . . . . . . . . . . . . . . . . . . . . . . . . 45
Cross Section Import . . . . . . . . . . . . . . . . . . . . . 46
Electron Impact Reaction. . . . . . . . . . . . . . . . . . . . 46
Theory for the Boltzmann Equation, Two-Term Approximation
Interface
48
The Electron Energy Distribution Function . . . . . . . . . . . . . 48
Boltzmann Equation, Two-Term Approximation . . . . . . . . . . . 49
References for the Boltzmann Equation, Two-Term Approximation
Interface. . . . . . . . . . . . . . . . . . . . . . . . . 55
C h a p t e r 4 : T h e D r i f t D i f f u s i o n I n t e r f a c e
The Drift Diffusion Interface
58
Domain, Boundary, and Pair Nodes for the Drift Diffusion Interface . . . 61
Drift Diffusion Model . . . . . . . . . . . . . . . . . . . . . 62
Initial Values . . . . . . . . . . . . . . . . . . . . . . . . 65
Electron Production Rate . . . . . . . . . . . . . . . . . . . 65
General Power Deposition . . . . . . . . . . . . . . . . . . . 65
Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Inductive Power Deposition. . . . . . . . . . . . . . . . . . . 66
Microwave Power Deposition . . . . . . . . . . . . . . . . . . 66
Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Electron Density and Energy . . . . . . . . . . . . . . . . . . 67
Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Electron Outlet . . . . . . . . . . . . . . . . . . . . . . . 69
Theory for the Drift Diffusion Interface
70
Introduction to Drift Diffusion Theory . . . . . . . . . . . . . . 70
Electron Transport Theory . . . . . . . . . . . . . . . . . . . 72
Source Coefficients . . . . . . . . . . . . . . . . . . . . . . 74
Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . 75
Tensor Transport Properties . . . . . . . . . . . . . . . . . . 75
4 | C O N T E N T S
The Wall Boundary Condition . . . . . . . . . . . . . . . . . . 76
The Insulation Boundary Condition . . . . . . . . . . . . . . . . 77
The Electron Density and Energy Boundary Condition . . . . . . . . 77
Reference for the Drift Diffusion Interface . . . . . . . . . . . . . 78
C h a p t e r 5 : T h e H e a v y S p e c i e s T r a n s p o r t I n t e r f a c e
The Heavy Species Transport Interface
Domain, Boundary, and Pair Nodes for the Heavy Species Transport
80
Interface. . . . . . . . . . . . . . . . . . . . . . . . . 85
Cross Section Import . . . . . . . . . . . . . . . . . . . . . 86
Diffusion and Migration . . . . . . . . . . . . . . . . . . . . 86
Electron Impact Reaction. . . . . . . . . . . . . . . . . . . . 88
Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Species . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Surface Reaction . . . . . . . . . . . . . . . . . . . . . . . 97
Surface Species . . . . . . . . . . . . . . . . . . . . . . 100
Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Outflow . . . . . . . . . . . . . . . . . . . . . . . . . 102
Symmetry . . . . . . . . . . . . . . . . . . . . . . . . 103
Theory for the Heavy Species Transport Interface
104
About the Transport Equations . . . . . . . . . . . . . . . . 104
Multicomponent Diffusion Equations . . . . . . . . . . . . . . 105
Additional Quantities of Interest . . . . . . . . . . . . . . . . 109
Auxiliary Relations . . . . . . . . . . . . . . . . . . . . . 109
Source Coefficients . . . . . . . . . . . . . . . . . . . . . 110
Thermodynamic Properties . . . . . . . . . . . . . . . . . . 111
Species Transport Properties . . . . . . . . . . . . . . . . . 112
Mixture Transport Properties . . . . . . . . . . . . . . . . . 113
Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Stabilization . . . . . . . . . . . . . . . . . . . . . . . . 115
Surface Reactions . . . . . . . . . . . . . . . . . . . . . 115
Flux Matching . . . . . . . . . . . . . . . . . . . . . . . 117
About Surface Species . . . . . . . . . . . . . . . . . . . . 118
C O N T E N T S | 5
Limitations of the Heavy Species Transport Equations . . . . . . . . 119
Global Model . . . . . . . . . . . . . . . . . . . . . . . 119
References for the Heavy Species Transport Interface . . . . . . . . 122
C h a p t e r 6 : P l a s m a I n t e r f a c e s
The Plasma Interface
Domain, Boundary, Edge, Point, and Pair Nodes for the Plasma
126
Interface. . . . . . . . . . . . . . . . . . . . . . . . 134
Plasma Model . . . . . . . . . . . . . . . . . . . . . . . 135
Initial Values . . . . . . . . . . . . . . . . . . . . . . . 140
Species Constraint Group . . . . . . . . . . . . . . . . . . 141
The Plasma, Time Periodic Interface
Domain, Boundary, Edge, Point, and Pair Nodes for the Plasma,
143
Time Periodic Interface . . . . . . . . . . . . . . . . . . 150
Species Group . . . . . . . . . . . . . . . . . . . . . . . 151
Species Constraint Group . . . . . . . . . . . . . . . . . . 152
Dielectric Contact . . . . . . . . . . . . . . . . . . . . . 152
Ground . . . . . . . . . . . . . . . . . . . . . . . . . 152
Metal Contact . . . . . . . . . . . . . . . . . . . . . . . 153
Surface Charge Accumulation . . . . . . . . . . . . . . . . . 154
Terminal . . . . . . . . . . . . . . . . . . . . . . . . . 155
Zero Charge . . . . . . . . . . . . . . . . . . . . . . . 155
Periodic Excitation . . . . . . . . . . . . . . . . . . . . . 156
Circuit Options . . . . . . . . . . . . . . . . . . . . . . 156
The Inductively Coupled Plasma Interface
160
Plasma Conductivity Coupling . . . . . . . . . . . . . . . . . 161
Electron Heat Source . . . . . . . . . . . . . . . . . . . . 161
Collisionless Heating Coupling. . . . . . . . . . . . . . . . . 161
6 | C O N T E N T S
The Microwave Plasma Interface
Plasma Reactors Theory
163
164
Capacitively Coupled Plasmas
167
The Importance of 1D Modeling . . . . . . . . . . . . . . . . 170
Electric Excitation . . . . . . . . . . . . . . . . . . . . . 170
Meshing Guidelines . . . . . . . . . . . . . . . . . . . . . 171
Using Consistent Source Frequencies and Period Settings . . . . . . 171
Choosing the Number of Elements in the Extra Dimension . . . . . . 173
Pulsed Discharges . . . . . . . . . . . . . . . . . . . . . 175
Choosing the Correct Space on Which to Solve for the Heavy
Species . . . . . . . . . . . . . . . . . . . . . . . . 176
Validity of Fluid Models . . . . . . . . . . . . . . . . . . . 177
Complex Chemistries and Electronegative Discharges . . . . . . . . 179
Solver Settings . . . . . . . . . . . . . . . . . . . . . . . 180
DC Discharges
181
Introduction to DC Discharge Theory. . . . . . . . . . . . . . 181
DC Discharge Boundary Conditions . . . . . . . . . . . . . . 182
Tips for Modeling DC Discharges . . . . . . . . . . . . . . . 183
184
Theory for Inductively Coupled Plasmas
Introduction to Inductively Coupled Plasmas . . . . . . . . . . . 184
Domain Equations for the Inductively Coupled Plasma Interface . . . . 187
188
Theory for Microwave Plasmas
Introduction . . . . . . . . . . . . . . . . . . . . . . . 188
Wave Heated Discharge Theory . . . . . . . . . . . . . . . . 188
Plasma Conductivity in the Presence of a Static Magnetic Field . . . . 195
References . . . . . . . . . . . . . . . . . . . . . . . . 196
Theory for Global Models
197
Introduction . . . . . . . . . . . . . . . . . . . . . . . 197
References for the Heavy Species Transport Interface . . . . . . . . 202
C O N T E N T S | 7
C h a p t e r 7 : E q u i l i b r i u m D i s c h a r g e s I n t e r f a c e s
The Equilibrium DC Discharge Interface
204
Equilibrium Discharge Heat Source . . . . . . . . . . . . . . . 206
Flow Coupling . . . . . . . . . . . . . . . . . . . . . . . 208
Equilibrium Discharge Boundary Heat Source . . . . . . . . . . . 209
The Combined Inductive/DC Discharge Interface
211
Static Current Density Component . . . . . . . . . . . . . . . 214
Induction Current Density Component . . . . . . . . . . . . . 215
Lorentz Force . . . . . . . . . . . . . . . . . . . . . . . 216
The Equilibrium Inductively Coupled Plasma Interface
Equilibrium Discharges Theory
218
222
Summary of the Equilibrium Discharge Interfaces Features
228
References . . . . . . . . . . . . . . . . . . . . . . . . 228
C h a p t e r 8 : A C / D C I n t e r f a c e s
The Electrostatics Interface
Domain, Boundary, Edge, Point, and Pair Nodes for the
230
Electrostatics Interface . . . . . . . . . . . . . . . . . . 232
Charge Conservation . . . . . . . . . . . . . . . . . . . . 235
Initial Values . . . . . . . . . . . . . . . . . . . . . . . 236
Space Charge Density . . . . . . . . . . . . . . . . . . . . 236
Zero Charge . . . . . . . . . . . . . . . . . . . . . . . 236
Ground . . . . . . . . . . . . . . . . . . . . . . . . . 236
Electric Potential . . . . . . . . . . . . . . . . . . . . . . 237
Surface Charge Density . . . . . . . . . . . . . . . . . . . 238
External Surface Charge Accumulation . . . . . . . . . . . . . 239
Electric Displacement Field . . . . . . . . . . . . . . . . . . 239
Periodic Condition . . . . . . . . . . . . . . . . . . . . . 240
Thin Low Permittivity Gap . . . . . . . . . . . . . . . . . . 241
8 | C O N T E N T S
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