PRINCIPLES OF PLASMA DISCHARGES AND MATERIALS PROCESSING
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1 PRINCIPLES OF PLASMA DISCHARGES AND MATERIALS PROCESSING Second Edition MICHAEL A. LIEBERMAN ALLAN J, LICHTENBERG WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC PUBLICATION
2 CONTENTS PREFACE xrrii PREFACE TO THE FIRST EDITION xxi SYMBOLS AND ABBREVIATIONS xxv PHYSICAL CONSTANTS AND CONVERSION FACTORS xxxiii PRACTICAL FORMULAE xxxv INTRODUCTION Materials Processing / Plasmas and Sheaths / 6 Plasmas / 6 Sheaths / Discharges / 14 Radio Frequency Diodes / 14 High-Density Sources / Symbols and Units / 20 2 BASIC PLASMA EQUATIONS AND EQUILIBRIUM Introduction / 23
3 vi CONTENTS 2.2 Field Equations, Current, and Voltage / 24 Maxwell's Equations / 24 2,3 The Conservation Equations / 28 Boltzmann's Equation / 28 Macroscopic Quantities / 30 Particle Conservation / 30 Momentum Conservation / 31 Energy Conservation / 34 Summary / Equilibrium Properties / 35 Boltzmann's Relation / 37 Debye Length / 38 Quasi-neutrality / 40 Problems / 41 3 ATOMIC COLLISIONS Basic Concepts / 43 Elastic and Inelastic Collisions / 43 Collision Parameters / 44 Differential Scattering Cross Section / Collision Dynamics / 49 Center-of-Mass Coordinates / 49 Energy Transfer / 52 Small Angle Scattering / 53 3,3 Elastic Scattering / 55 Coulomb Collisions / 55 Polarization Scattering / Inelastic Collisions / 63 Atomic Energy Levels / 63 Electric Dipole Radiation and Metastable Atoms / 67 Electron Ionization Cross Section / 70 Electron Excitation Cross Section / 72 Ion--Atom Charge Transfer / 73 Ion-Atom Ionization / Averaging Over Distributions and Surface Effects / 78 Averaging Over a Maxwellian Distribution / 78 Energy Loss per Electron--Ion Pair Created / 81 Surface Effects / 82 Problems / 83
4 CONTENTS VII 4 PLASMA DYNAMICS Basic Motions / 87 Motion in Constant Fields / 87 E x B Drifts / 90 Energy Conservation / Nonmagnetized Plasma Dynamics / 93 Plasma Oscillations / 93 Dielectric Constant and Conductivity / 95 Ohmic Heating / 97 Electromagnetic Waves / 99 Electrostatic Waves / Guiding Center Motion / 102 Parallel Force / 104 Adiabatic Constancy of the Magnetic Moment / 105 Drift Due to Motion Along Field Lines (Curvature Drift) / 106 Drift Due to Gyration (Gradient Drift) / 107 Polarization Drift / Dynamics of Magnetized Plasmas / 110 Dielectric Tensor / 110 The Wave Dispersion / Waves in Magnetized Plasmas / 113 Principal Electron Waves / 115 Principal Waves Including Ion Dynamics / 118 The CMA Diagram / Wave Diagnostics / 123 Interferometer / 123 Cavity Perturbation / 126 Wave Propagation / 127 Problems / DIFFUSION AND TRANSPORT Basic Relations / 133 Diffusion and Mobility / 133 Free Diffusion / 134 Ambipolar Diffusion / Diffusion Solutions / 136 Boundary Conditions / 136
5 will CONTENTS Time-Dependent Solution j 138 Steady-State Plane-Parallel Solutions / 139 Steady-State Cylindrical Solutions / Low-Pressure Solutions / 144 Variable Mobility Model / 144 Langmuir Solution f 146 Heuristic Solutions / Diffusion Across a Magnetic Field / 149 Ambipolar Diffusion / Magnetic Multipole Confinement / 155 Magnetic Fields / 155 Plasma Confinement / 157 Leak Width w / 159 Problems / DIRECT CURRENT (DC) SHEATHS Basic Concepts and Equations / 165 The Collisionless Sheath / 167 6,2 The Bohm Sheath Criterion / 168 Plasma Requirements / 169 The Presheath / 170 Sheath Potential at a Floating Wall / 172 Collisional Sheaths / 173 Simulation Results / The High-Voltage Sheath / 175 Matrix Sheath / 175 Child Law Sheath / Generalized Criteria for Sheath Formation / 178 Electronegative Gases / 179 Multiple Positive Ion Species / High-Voltage Collisional Sheaths / Electrostatic Probe Diagnostics / 185 Planar Probe With Collisionless Sheath / 187 Non-Maxwellian Electrons / 189 Cylindrical Probe With a Collisionless Sheath / 191 Double Probes and Emissive Probes / 195 Effect of Collisions and DC Magnetic Fields / 198 Probe Construction and Circuits / 199
6 CONTENTS ix Probes in Time-Varying Fields / 201 Problems / CHEMICAL REACTIONS AND EQUILIBRIUM Introduction / Energy and Enthalpy / Entropy and Gibbs Free Energy / 216 Gibbs Free Energy / Chemical Equilibrium / 221 Pressure and Temperature Variations / Heterogeneous Equilibrium / 226 Equilibrium Between Phases / 226 Equilibrium at a Surface / 229 Problems / MOLECULAR COLLISIONS Introduction / Molecular Structure / 236 Vibrational and Rotational Motion / 237 Optical Emission / 239 Negative Ions / Electron Collisions With Molecules / 241 Dissociation / 243 Dissociative Ionization / 245 Dissociative Recombination / 246 Example of Hydrogen / 247 Dissociative Electron Attachment / 24'1 Polar Dissociation / 250 Metastable Negative ions / 251 Electron Impact Detachment / 251 Vibrational and Rotational Excitations / 252 Elastic Scattering / Heavy-Particle Collisions / 253 Resonant and Nonresonant Charge Transfer / 255 Positive-Negative Ion Recombination / 256 Associative Detachment / 258 Transfer of Excitation / 260 Rearrangement of Chemical Bonds / 262
7 x CONTENTS Ion--Neutral Elastic Scattering / 263 Three-Body Processes / Reaction Rates and Detailed Balancing / 265 Temperature Dependence / 266 The Principle of Detailed Balancing / 267 A Data Set for Oxygen / Optical Emission and Actinometry / 274 Optical Emission / 275 Optical Actinometry / 277 O Atom Actinometry / 278 Problems / CHEMICAL KINETICS AND SURFACE PROCESSES Elementary Reactions / 285 Relation to Equilibrium Constant / Gas-Phase Kinetics / 289 First-Order Consecutive Reactions / 290 Opposing Reactions / 292 Bimolecular Association With Photon Emission / 293 Three-Body Association / 295 Three-Body Positive-Negative Ion Recombination / 297 Three-Body Electron-Ion Recombination / Surface Processes / 299 Positive Ion Neutralization and Secondary Electron Emission / 299 Adsorption and Desorption / 303 Fragmentation / 308 Sputtering / Surface Kinetics / 311 Diffusion of Neutral Species / 311 Loss Rate for Diffusion / 312 Adsorption and Desorption / 315 Dissociative Adsorption and Associative Desorption / 316 Physical Adsorption / 316 Reaction With a Surface / 317 Reactions on a Surface / 318 Surface Kinetics and Loss Probability / 319 Problems / 320
8 CONTENTS Xi 10 PARTICLE AND ENERGY BALANCE IN DISCHARGES Introduction / Electropositive Plasma Equilibrium / 330 Basic Properties / 330 Uniform Density Discharge Model / 333 Nonuniform Discharge Model / 336 Neutral Radical Generation and Loss Electronegative Plasma Equilibrium / 340 Differential Equations / 342 Boltzmann Equilibrium for Negative Ions / 345 Conservation Equations / 348 Validity of Reduced Equations / Approximate Electronegative Equilibria / 350 Global Models / 351 Parabolic Approximation For Low Pressures / 354 Flat-Topped Model For Higher Pressures / Electronegative Discharge Experiments and Simulations / 359 Oxygen Discharges / 360 Chlorine Discharges / Pulsed Discharges / 369 Pulsed Electropositive Discharges / 370 Pulsed Electronegative Discharges / 376 Neutral Radical Dynamics / 380 Problems / 381 1i CAPACITIVE DISCHARGES Homogeneous Model / 388 Plasma Admittance / 390 Sheath Admittance / 391 Particle and Energy Balance / 395 Discharge Parameters / Inhomogeneous Model / 399 Collisionless Sheath Dynamics / 400 Child Law / 402 Sheath Capacitance / 403 Ohmic Heating / 404 Stochastic Heating / 405 Self-Consistent Model Equations / 406
9 Al CONTENTS Scaling / 410 Collisional Sheaths / 411 Low and Moderate Voltages / 413 Ohmic Heating in the Sheath / 413 Self-Consistent Collisionless Heating Models / 414 Dual-Frequency and High-Frequency Discharges / 416 Electronegative Plasmas / Experiments and Simulations / 418 Experimental Results / 419 Particle-in-Cell Simulations / 423 Role of Secondaries / 428 Implications for Modeling / Asymmetric Discharges / 430 Capacitive Voltage Divider / 430 Spherical Shell Model / Low-Frequency RF Sheaths / Ion Bombarding Energy at Electrodes / Magnetically Enhanced Discharges / Matching Networks and Power Measurements 452 Power Measurements / 456 Problems / INDUCTIVE DISCHARGES High-Density, Low-Pressure Discharges / 462 Inductive Source Configurations / 462 Power Absorption and Operating Regimes / 464 Discharge Operation and Coupling / 466 Matching Network / ,2 Other Operating Regimes / 470 Low-Density Operation / 470 Capacitive Coupling / 471 Hysteresis and Instabilities / 473 Power Transfer Efficiency / 476 Exact Solutions / Planar Coil Configuration / Helical Resonator Discharges / 483 Problems / 487
10 CONTENTS All 13 WAVE-HEATED DISCHARGES Electron Cyclotron Resonance Discharges / 492 Characteristics and Configurations 492 Electron Heating / 497 Resonant Wave Absorption / 501 Model and Simulations / 507 Plasma Expansion / 509 Measurements / Helicon Discharges / 513 Helicon Modes / 514 Antenna Coupling / 517 Helicon Mode Absorption / 520 Neutral Gas Depletion / Surface Wave Discharges / 527 Planar Surface Waves / 528 Cylindrical Surface Waves / 530 Power Balance / 530 Problems / DIRECT CURRENT (DC) DISCHARGES Qualitative Characteristics of Glow Discharges / 535 Positive Column / 536 Cathode Sheath / 537 Negative Glow and Faraday Dark Space / 537 Anode Fall / 537 Other Effects / 538 Sputtering and Other Configurations / Analysis of the Positive Column / 539 Calculation of T` / 540 Calculation of E and no / 541 Kinetic Effects / Analysis of the Cathode Region / 543 Vacuum Breakdown / 544 Cathode Sheath / 546 The Negative Glow and Faraday Dark Space / ,4 Hollow Cathode Discharges / 551 Simple Discharge Model / 552 Metal Vapor Production in a Hollow Cathode Discharge / 555
11 x1v CONTENTS 14.5 Planar Magnetron Discharges / 559 Limitations of Glow Discharge Sputtering Source / 559 Magnetron Configuration / 560 Discharge Model / Ionized Physical Vapor Deposition / 564 Problems / ETCHING Etch Requirements and Processes / 571 Plasma Etch Requirements / 572 Etch Processes / Etching Kinetics / 579 Surface Kinetics / 579 Discharge Kinetics and Loading Effect / 583 Chemical Framework / Halogen Atom Etching of Silicon / 586 Pure Chemical F-Atom Etching / 587 Ion Energy-Driven F-Atom Etching / 589 CF4 Discharges / 592 Oz and H2 Feedstock Additions / 596 Cl-Atom Etching / Other Etch Systems / 600 F and CF, Etching of SiO2 / 600 Si3Na Etching / 602 Aluminum Etching / 602 Copper Etching / 603 Resist Etching Substrate Charging / 606 Gate Oxide Damage / 607 Grounded Substrate / 607 Nonuniform Plasmas / 608 Transient Damage During Etching 611 Electron Shading Effect / 612 Radiofrequency Biasing / 613 Etch Profile Distortions / 614 Problems / 616
12 CONTENTS xv 16 DEPOSITION AND IMPLANTATION Introduction / Plasma-Enhanced Chemical Vapor Deposition / 621 Amorphous Silicon / 622 Silicon Dioxide / 625 Silicon Nitride / Sputter Deposition / 630 Physical Sputtering / 630 Reactive Sputtering / Plasma-Immersion Ion Implantation (PIII) / 634 Collisionless Sheath Model / 636 Collisional Sheath Model / 641 Applications of PIII to Materials Processing / 644 Problems / DUSTY PLASMAS Qualitative Description of Phenomena / Particle Charging and Discharge Equilibrium / 651 Equilibrium Potential and Charge / 651 Discharge Equilibrium / Particulate Equilibrium / Formation And Growth Of Dust Grains / Physical Phenomena And Diagnostics / 668 Strongly Coupled Plasmas / 668 Dust Acoustic Waves / 669 Driven Particulate Motion / 670 Laser Light Scattering / Removal or Production of Particulates / 673 Problems / KINETIC THEORY OF DISCHARGES Basic Concepts / 679 Two-Term Approximation / 680 The Kroolc Collision Operator / 680 Two-Term Collisional Kinetic Equations / 681 Diffusion and Mobility / 684 Druyvesteyn Distribution / 685 Electron Distribution in an RF Field / 686
13 xvi CONTENTS Effective Electrical Conductivity / Local Kinetics / Nonlocal Kinetics / Quasi-Linear Diffusion and Stochastic Heating / 699 Quasi-linear Diffusion Coefficient / 700 Stochastic Heating / 703 Relation to Velocity Kick Models 704 Two Term Kinetic Equations / Energy Diffusion in a Skin Depth Layer / 706 Stochastic Heating / 706 Effective Collision Frequency / 708 Energy Distribution / Kinetic Modeling of Discharges / 711 Non-Maxwellian Global Models / 711 Inductive Discharges / 712 Capacitive Discharges f 715 Problems / 719 APPENDIX A. COLLISION DYNAMICS 723 Coulomb Cross Section / 725 APPENDIX B. THE COLLISION INTEGRAL 727 Boltzmann Collision integral / 727 Maxwellian Distribution / 728 APPENDIX C. DIFFUSION SOLUTIONS FOR VARIABLE MOBILITY MODEL 731 REFERENCES 735
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