Beyond enabling new capabilities, plasma-based techniques, characterized by quantum radicals of feed gases, hold the potential to enhance and improve many processes and applications. Following in the tradition of its popular predecessor, Plasma Electronics, Second Edition: Applications in Microelectronic Device Fabrication explains the fundamental physics and numerical methods required to bring these technologies from the laboratory to the factory.
Emphasizing computational algorithms and techniques, this updated edition of a popular monograph supplies a complete and up-to-date picture of plasma physics, computational methods, applications, and processing techniques. Reflecting the growing importance of computer-aided approaches to plasma analysis and synthesis, it showcases recent advances in fabrication from micro- and nano-electronics, MEMS/NEMS, and the biological sciences.
A helpful resource for anyone learning about collisional plasma structure, function, and applications, this edition reflects the latest progress in the quantitative understanding of non-equilibrium low-temperature plasma, surface processing, and predictive modeling of the plasma and the process. Filled with new figures, tables, problems, and exercises, it includes a new chapter on the development of atmospheric-pressure plasma, in particular microcell plasma, with a discussion of its practical application to improve surface efficiency.
The book provides an up-to-date discussion of MEMS fabrication and phase transition between capacitive and inductive modes in an inductively coupled plasma. In addition to new sections on the phase transition between the capacitive and inductive modes in an ICP and MOS-transistor and MEMS fabrications, the book presents a new discussion of heat transfer and heating of the media and the reactor.
Integrating physics, numerical methods, and practical applications, this book equips you with the up-to-date understanding required to scale up lab breakthroughs into industrial innovations.

Preface to the First Edition xv

Preface to the Second Edition xvii

About the Authors xix

List of Figures xxi

List of Tables xxxiii

Chapter 1 Introduction 1

1.1 Plasma and Its Classification 1

1.2 Application of Low Temperature Plasma 2

1.3 Academic Fusion 3

References 5

Chapter 2 Phenomenological Description of the Charged Particle Transport 7

2.1 Transport in Real (Configuration) Space 7

      2.1.1 Momentum Balance of Electrons 8

      2.1.2 Energy Balance of Electrons 9

2.2 Transport in Velocity Space 12

      2.2.1 Electron Velocity Distribution and Swarm Parameters 13

      2.2.2 Ion Velocity Distribution and Mean Energy 20

2.3 Thermal Equilibrium and its Governing Relations 23

      2.3.1 Boltzmann Distribution in Real Space 23

      2.3.2 Maxwell Distribution in Velocity Space 24

References 28

Chapter 3 Macroscopic Plasma Characteristics 29

3.1 Introduction 29

3.2 Quasi Neutrality 29

3.3 Charge separation In Plasmas 30

      3.3.1 Spatial Scale of Charge-Separation 30

      3.3.2 Time Scale for Charge-Separation 31

3.4 Plasma Shielding 32

      3.4.1 Debye Shielding 32

      3.4.2 Metal Probe in a Plasma 33

3.5 Particle Diffusion 36

      3.5.1 Ambipolar Diffusion 36

      3.5.2 Spatial and Time Scale of Diffusion 37

3.6 Bohm Sheath Criterion 39

      3.6.1 Bohm Velocity 29

      3.6.2 Floating Potential 40

References 41

Chapter 4 Elementary Processes in Gas Phase and on Surfaces 43

4.1 Particles and Waves 44

      4.1.1 Particle Representation in Classical and Quantum Mechanics 44

      4.1.2 Locally Isolated Particle Group and Wave Packets 46

4.2 Collisions and Cross Sections 48

      4.2.1 Conservation Laws in Collisions 49

      4.2.2 Definition of Collision Cross Sections 51

      4.2.3 The Distribution of Free Paths 55

      4.2.4 Representation of Collisions in Laboratory and CM Reference Frames 56

4.3 Classical Collision Theory 59

      4.3.1 Scattering in Classical Mechanics 60

      4.3.2 Conditions for the Applicability of the Classical Scattering Theory 66

4.4 Quantum Theory Of Scattering 66

      4.4.1 Differential Scattering Cross Section σ(θ) 68

      4.4.2 Modified Effective Range Theory in Electron Scattering 73

4.5 Collisions Between Electrons And Neutral Atoms/Molecules 74

      4.5.1 Resonant Scattering 75

4.6 Electron–Atom Collisions 77

      4.6.1 Energy Levels of Atoms 77

      4.6.2 Electron–Atom Scattering Cross Sections 79

4.7 Electron–Molecule Collisions 83

      4.7.1 Rotational, Vibrational, and Electronic Energy Levels of Molecules 84

      4.7.2 Rotational Excitation 85

      4.7.2.1 Rotational Energy Levels 85

      4.7.2.2 Rotational Excitation Cross Sections 88

      4.7.3 Vibrational Excitation 89

      4.7.3.1 Vibrational Energy Levels 89

      4.7.3.2 Vibrational Cross Sections 91

      4.7.4 Electronic Excitation and Dissociation 92

      4.7.4.1 Electronic States of Molecules 92

      4.7.4.2 Cross Sections for Electronic Excitation of Molecules 94

      4.7.5 Electron Collisions with Excited Atoms and Molecules 94

4.8 Nonconservative Collisions of Electrons With Atoms and Molecules 98

      4.8.1 Electron-Induced Ionization 98

      4.8.2 Electron Attachment 100

      4.8.2.1 Dissociative Electron Attachment 101

      4.8.2.2 Nondissociative Electron Attachment 103

      4.8.2.3 Ion Pair Formation 104

      4.8.2.4 Electron Attachment to Excited Molecules 104

      4.8.2.5 Rate Coefficients for Attachment 105

      4.8.3 Electron–Ion and Ion–Ion Recombination 106

      4.8.4 Electron–Ion and Electron–Electron Collisions 108

4.9 Heavy Particle Collisions 109

      4.9.1 Ion–Molecule Collisions 110

      4.9.1.1 Charge Transfer, Elastic, and Inelastic Scattering of Ions 112

      4.9.1.2 Ion–Molecule Reactions 114

      4.9.2 Collisions of Fast Neutrals 115

      4.9.3 Collisions of Excited Particles 115

      4.9.3.1 Chemi-Ionization and Penning Ionization 120

      4.9.4 Collisions of Slow Neutrals and Rate Coefficients 120

      4.9.4.1 Quenching and Transport of Excited States 123

      4.9.4.2 Kinetics of Rotational and Vibrational Levels 124

4.10 Photons in Ionized Gases 125

      4.10.1 Emission and Absorption of Line Radiation 127

      4.10.2 Resonant Radiation Trapping 128

4.11 Elementary Processes at Surfaces 129

      4.11.1 Energy Levels of Electrons in Solids 132

      4.11.2 Emission of Electrons from Surfaces 132

      4.11.2.1 Photo-Emission 133

      4.11.2.2 Thermionic Emission 133

      4.11.2.3 Field-Induced Emission 136

      4.11.2.4 Potential Ejection of Electrons from Surfaces by Ions and Excited Atoms 139

      4.11.3 Emission of Ions and Neutrals from Surfaces 140

      4.11.3.1 Surface Neutralization 141

      4.11.3.2 Surface Ionization 143

      4.11.4 Adsorption 145

References 147

Chapter 5 The Boltzmann Equation and Transport Equations of Charged Particles 147

5.1 Introduction 147

5.2 The Boltzmann Equation 147

      5.2.1 Transport in Phase Space and Derivation of the Boltzmann Equation 148

5.3 Transport Coefficients 150

5.4 The Transport Equation 154

      5.4.1 Conservation of Number Density 155

      5.4.2 Conservation of Momentum 155

      5.4.3 Conservation of Energy 156

5.5 Collision Term In The Boltzmann Equation 157

      5.5.1 Collision Integral 157

      5.5.2 Collision Integral between an Electron and a Gas Molecule 158

      5.5.2.1 Elastic Collision Term Jelas 159

      5.5.2.2 Excitation Collision Term Jex 161

      5.5.2.3 Ionization Collision Term Jion 162

      5.5.2.4 Electron Attachment Collision Term Jatt 163

5.6 Boltzmann Equation For Electrons 164

      5.6.1 Spherical Harmonics and Their Properties 164

      5.6.2 Velocity Distribution of Electrons 167

      5.6.2.1 Velocity Distribution under Uniform Number Density: g0 168

      5.6.2.2 Velocity Distribution Proportional to ∇rn(r, t): g1 169

      5.6.3 Electron Transport Parameters 176

References 179

Chapter 6 General Properties of Charged Particle Transport in Gases 181

6.1 Introduction 181

6.2 Electron Transport In DC Electric Fields 181

      6.2.1 Electron Drift Velocity 182

      6.2.2 Diffusion Coefficients 184

      6.2.3 Mean Energy of Electrons 187

      6.2.4 Excitation, Ionization, and Electron Attachment Rates 187

6.3 Electron Transport in Radio Frequency Electric Fields 188

      6.3.1 Relaxation Time Constants 190

      6.3.2 Effective Field Approximation 195

      6.3.3 Expansion Procedure 198

      6.3.4 Direct Numerical Procedure 202

      6.3.5 Time-Varying Swarm Parameters 206

6.4 Ion Transport In Dc Electric Fields 208

References 210

Chapter 7 Modeling of Nonequilibrium (Low Temperature) Plasmas 213

7.1 Introduction 213

7.2 Continuum Models 214

      7.2.1 Governing Equations of a Continuum Model 215

      7.2.2 Local Field Approximation (LFA) 218

      7.2.3 Quasi-Thermal Equilibrium (QTE) Model 219

      7.2.4 Relaxation Continuum (RCT) Model 220

      7.2.5 Phase Space Kinetic Model 222

7.3 Particle Models 224

      7.3.1 Monte Carlo Simulations (MCSs) 225

      7.3.2 Particle-in-Cell (PIC) and Particle-in-Cell/Monte Carlo Simulation (PIC/MCS) Models 227

7.4 Hybrid Models 229

7.5 Circuit Model 229

      7.5.1 Equivalent Circuit Model in CCP 230

      7.5.2 Equivalent Circuit Model in ICP 231

      7.5.3 Transmission-Line Model (TLM) 231

7.6 Electromagnetic Fields and Maxwell’s Equations 233

      7.6.1 Coulomb’s Law, Gauss’s Law, and Poisson’s Equation 234

      7.6.2 Faraday’s Law 234

      7.6.3 Ampere’s Law 235

      7.6.4 Maxwell’s Equations 236

References 236

Chapter 8 Numerical Procedure of Modeling 239

8.1 Time Constant of the System 139

      8.1.1 Collision-Oriented Relaxation Time 240

      8.1.2 Plasma Species-Oriented Time Constant 241

      8.1.3 Plasma-Oriented Time Constant/Dielectric Relaxation Time 243

8.2 Numerical Techniques To Solve The Time Dependent Drift-Diffusion Equation 243

      8.2.1 Time-Evolution Method 244

      8.2.1.1 Finite Difference 245

      8.2.1.2 Digitalization and Stabilization 247

      8.2.1.3 Time Discretization and Accuracy 248

      8.2.2 Scharfetter–Gummel Method 251

      8.2.3 Cubic Interpolated Pseudoparticle Method 253

      8.2.4 Semi-Implicit Method for Solving Poisson’s Equation 253

8.3 Boundary Conditions 253

      8.3.1 Ideal Boundary — Without Surface Interactions 253

      8.3.1.1 Dirichlet Condition 253

      8.3.1.2 Neumann Condition 254

      8.3.1.3 Periodicity Condition 255

      8.3.2 Electrode Surface 256

      8.3.2.1 Metallic Electrode 256

      8.3.2.2 Dielectric Electrode 257

      8.3.3 Boundary Conditions with Charge Exchange 257

      8.3.4 Boundary Conditions with Mass Transport 258

      8.3.4.1 Plasma Etching 258

      8.3.4.2 Plasma Deposition 259

      8.3.4.3 Plasma Sputtering 259

      8.3.5 Moving Boundary under Processing 260

References 261

Chapter 9 Capacitively Coupled Plasma

9.1 Radio Frequency Capacitive Coupling 263

9.2 Mechanism of Plasma Maintenance 263

      9.2.1 Low-Frequency Plasma 266

      9.2.2 High-Frequency Plasma 268

      9.2.3 Electronegative Plasma 271

      9.2.4 Very High-Frequency Plasma 274

      9.2.5 Two-Frequency Plasma 276

      9.2.6 Pulsed Two-Frequency Plasma 279

References 283

Chapter 10 Inductively Coupled Plasma 285

10.1 Radio Frequency Inductive Coupling 285

10.2 Mechanism of Plasma Maintenance 285

      10.2.1 E-mode and H-mode 285

      10.2.2 Mechanism of Plasma Maintenance 287

      10.2.3 Effect of Metastables 288

      10.2.4 Function of ICP 293

10.3 Phase Transition Between E-Mode and H-Mode in an ICP 294

10.4 Wave Propagation in Plasmas 295

      10.4.1 Plasma and Skin Depth 295

      10.4.2 ICP and the Skin Depth 299

References 301

Chapter 11 Magnetically Enhanced Plasma 303

11.1 Direct Current Magnetron Plasma 303

11.2 Unbalanced Magnetron Plasma 307

11.3 Radio Frequency Magnetron Plasma 307

11.4 Magnetic Confinements Of Plasmas 310

11.5 Magnetically Resonant Plasmas 311

References 313

Chapter 12 Plasma Processing and Related Topics 315

12.1 Introduction 315

12.2 Physical Sputtering 315

      12.2.1 Target Erosion 321

      12.2.2 Sputtered Particle Transport 322

12.3 Plasma Chemical Vapor Deposition 324

      12.3.1 Plasma CVD 325

      12.3.2 Large-Area Deposition with High Rate 327

12.4 Plasma Etching 329

      12.4.1 Wafer Bias 331

      12.4.1.1 On Electrically Isolated Wafers (without Radio-Frequency Bias) 332

      12.4.1.2 On Wafers with Radio-Frequency Bias 332

      12.4.2 Selection of Feed Gas 333

      12.4.3 Si or Poly-Si Etching 334

      12.4.4 Al Etching 335

      12.4.5 SiO2 Etching 337

      12.4.6 Feature Profile Evolution 343

      12.4.7 Plasma Bosch Process 346

      12.4.8 Charging Damage 346

      12.4.8.1 Surface Continuity and Conductivity 350

      12.4.8.2 Charging Damage to Lower Thin Elements in ULSI 350

      12.4.9 Thermal Damage 351

      12.4.10 Specific Fabrication of MOS Transistor 351

      12.4.10.1 Gate Etching 352

      12.4.10.2 Contact Hole Etching 354

      12.4.10.3 Low-K Etching 356

      12.4.11 MEMS Fabrication 357

References 359

Chapter 13 Atmospheric Pressure, Low Temperature Plasma 359

13.1 High Pressure, Low Temperature Plasma 359

      13.1.1 Fundamental Process 360

      13.1.2 Historical Development 361

13.2 Micro Plasma 361

      13.2.1 Radiofrequency Atmospheric Micro-Plasma Source 361

      13.2.2 Gas Heating in a Plasma 361

      13.2.3 Effect of Local Gas Heating 363

References 366

Index 369

Zoran Lj. Petrovic obtained his Master’s degree in the Department of Applied Physics, Faculty of Electrical Engineering in the University of Belgrade, and earned his Ph.D from Australian National University. He is the Head of the Department of Experimental Physics in the Institute of Physics, University of Belgrade. He has taught postgraduate courses in microelectronics, plasma kinetics and diagnostics and was a visiting professor in Keio University (Yokohama, Japan). He has received the Nikola Tesla award for technological achievement and the Marko Jaric Award for Great Achievement in Physics. He is a full member of the Academy of Engineering Sciences of Serbia and Serbian Academy of Sciences and Arts where he chairs the department of engineering science. Zoran Petrovic is a fellow of American Physical Society, vice president of the National Scientific Council of Serbia, and president of the Association of Scientific Institutes of Serbia. He is a member of editorial boards of Plasma Sources Science and Technology and Europena Physical Journal D. He has authored or co-authored over 220 papers in leading international scientific journals, and has given more than 90 invited talks at professional conferences. His research interests include atomic and molecular collisions in ionized gases, transport phenomena in ionized gases, gas breakdown, RF and DC plasmas for plasma processing, plasma medicine, positron collisions and traps, and basic properties of gas discharges.

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