Post on 26-Jun-2020
PRINCIPLES OF PLASMADISCHARGES ANDMATERIALSPROCESSING
Second Edition
MICHAEL A. LIEBERMANALLAN J, LICHTENBERG
WILEY-INTERSCIENCE
A JOHN WILEY & SONS, INC PUBLICATION
CONTENTS
PREFACE
xrrii
PREFACE TO THE FIRST EDITION
xxi
SYMBOLS AND ABBREVIATIONS
xxv
PHYSICAL CONSTANTS AND CONVERSION FACTORS
xxxiii
PRACTICAL FORMULAE
xxxv
INTRODUCTION
1
1 .1
Materials Processing / 11 .2
Plasmas and Sheaths / 6Plasmas / 6Sheaths / 11
1 .3 Discharges / 14Radio Frequency Diodes / 14High-Density Sources / 18
1 .4
Symbols and Units / 20
2 BASIC PLASMA EQUATIONS AND EQUILIBRIUM
23
2.1 Introduction / 23
vi CONTENTS
2 .2
Field Equations, Current, and Voltage / 24
Maxwell's Equations / 24
2,3
The Conservation Equations / 28Boltzmann's Equation / 28Macroscopic Quantities / 30
Particle Conservation / 30Momentum Conservation / 31Energy Conservation / 34Summary / 35
2.4
Equilibrium Properties / 35Boltzmann's Relation / 37Debye Length / 38Quasi-neutrality / 40
Problems / 41
3 ATOMIC COLLISIONS
43
3.1
Basic Concepts / 43Elastic and Inelastic Collisions / 43Collision Parameters / 44Differential Scattering Cross Section / 46
3.2
Collision Dynamics / 49Center-of-Mass Coordinates / 49Energy Transfer / 52Small Angle Scattering / 53
3,3
Elastic Scattering / 55Coulomb Collisions / 55Polarization Scattering / 58
3.4
Inelastic Collisions / 63Atomic Energy Levels / 63Electric Dipole Radiation and Metastable Atoms / 67Electron Ionization Cross Section / 70Electron Excitation Cross Section / 72Ion--Atom Charge Transfer / 73Ion-Atom Ionization / 78
3 .5
Averaging Over Distributions and Surface Effects / 78Averaging Over a Maxwellian Distribution / 78Energy Loss per Electron--Ion Pair Created / 81Surface Effects / 82
Problems / 83
CONTENTS VII
4 PLASMA DYNAMICS
87
4 .1
Basic Motions / 87Motion in Constant Fields / 87E x B Drifts / 90Energy Conservation / 91
4.2
Nonmagnetized Plasma Dynamics / 93Plasma Oscillations / 93Dielectric Constant and Conductivity / 95Ohmic Heating / 97Electromagnetic Waves / 99Electrostatic Waves / 141
4.3
Guiding Center Motion / 102Parallel Force / 104Adiabatic Constancy of the Magnetic Moment / 105Drift Due to Motion Along Field Lines
(Curvature Drift) / 106Drift Due to Gyration (Gradient Drift) / 107Polarization Drift / 108
4.4
Dynamics of Magnetized Plasmas / 110Dielectric Tensor / 110The Wave Dispersion / 112
4.5
Waves in Magnetized Plasmas / 113Principal Electron Waves / 115Principal Waves IncludingIon Dynamics / 118The CMA Diagram / 121
4.6
Wave Diagnostics / 123Interferometer / 123Cavity Perturbation / 126Wave Propagation / 127
Problems / 129
5 DIFFUSION AND TRANSPORT
133
5 .1
Basic Relations / 133Diffusion and Mobility / 133Free Diffusion / 134Ambipolar Diffusion / 135
5 .2
Diffusion Solutions / 136Boundary Conditions / 136
will CONTENTS
Time-Dependent Solution j 138Steady-State Plane-Parallel Solutions / 139
Steady-State Cylindrical Solutions / 142
5.3
Low-Pressure Solutions / 144Variable Mobility Model / 144Langmuir Solution f 146Heuristic Solutions / 147
5 .4
Diffusion Across a Magnetic Field / 149Ambipolar Diffusion / 152
5 .5
Magnetic Multipole Confinement / 155
Magnetic Fields / 155Plasma Confinement / 157Leak Width w / 159
Problems / 160
6 DIRECT CURRENT (DC) SHEATHS
165
6.1
Basic Concepts and Equations / 165The Collisionless Sheath / 167
6,2
The Bohm Sheath Criterion / 168Plasma Requirements / 169The Presheath / 170Sheath Potential at a Floating Wall / 172Collisional Sheaths / 173Simulation Results / 174
6.3
The High-Voltage Sheath / 175Matrix Sheath / 175Child Law Sheath / 176
6.4
Generalized Criteria for Sheath Formation / 178Electronegative Gases / 179Multiple Positive Ion Species / 182
6.5
High-Voltage Collisional Sheaths / 1846 .6
Electrostatic Probe Diagnostics / 185Planar Probe With Collisionless Sheath / 187Non-Maxwellian Electrons / 189Cylindrical Probe With a Collisionless Sheath / 191Double Probes and Emissive Probes / 195Effect of Collisions and DC Magnetic Fields / 198Probe Construction and Circuits / 199
Probes in Time-Varying Fields / 201Problems / 203
7 CHEMICAL REACTIONS AND EQUILIBRIUM
207
7.1 Introduction / 2077 .2
Energy and Enthalpy / 2087 .3
Entropy and Gibbs Free Energy / 216Gibbs Free Energy / 219
7.4
Chemical Equilibrium / 221Pressure and Temperature Variations / 224
7.5
Heterogeneous Equilibrium / 226Equilibrium Between Phases / 226Equilibrium at a Surface / 229
Problems / 231
8 MOLECULAR COLLISIONS
235
8.1 Introduction / 2358.2
Molecular Structure / 236Vibrational and Rotational Motion / 237Optical Emission / 239Negative Ions / 240
8.3
Electron Collisions With Molecules / 241Dissociation / 243Dissociative Ionization / 245Dissociative Recombination / 246Example of Hydrogen / 247Dissociative Electron Attachment / 24'1Polar Dissociation / 250Metastable Negative ions / 251Electron Impact Detachment / 251Vibrational and Rotational Excitations / 252Elastic Scattering / 253
8 .4
Heavy-Particle Collisions / 253Resonant and Nonresonant Charge Transfer / 255Positive-Negative Ion Recombination / 256Associative Detachment / 258Transfer of Excitation / 260Rearrangement of Chemical Bonds / 262
CONTENTS ix
x CONTENTS
Ion--Neutral Elastic Scattering / 263Three-Body Processes / 264
8 .5
Reaction Rates and Detailed Balancing / 265Temperature Dependence / 266The Principle of Detailed Balancing / 267A Data Set for Oxygen / 270
8 .6
Optical Emission and Actinometry / 274Optical Emission / 275Optical Actinometry / 277O Atom Actinometry / 278
Problems / 279
9 CHEMICAL KINETICS AND SURFACE PROCESSES
285
9 .1
Elementary Reactions / 285Relation to Equilibrium Constant / 288
9.2
Gas-Phase Kinetics / 289First-Order Consecutive Reactions / 290Opposing Reactions / 292Bimolecular Association With Photon Emission / 293Three-Body Association / 295Three-Body Positive-Negative Ion Recombination / 297Three-Body Electron-Ion Recombination / 298
9.3
Surface Processes / 299Positive Ion Neutralization and Secondary
Electron Emission / 299Adsorption and Desorption / 303Fragmentation / 308Sputtering / 308
9.4
Surface Kinetics / 311Diffusion of Neutral Species / 311Loss Rate for Diffusion / 312Adsorption and Desorption / 315Dissociative Adsorption and Associative Desorption / 316Physical Adsorption / 316Reaction With a Surface / 317Reactions on a Surface / 318Surface Kinetics and Loss Probability / 319
Problems / 320
CONTENTS Xi
10 PARTICLE AND ENERGY BALANCE IN DISCHARGES
327
10.1 Introduction / 32710.2
Electropositive Plasma Equilibrium / 330Basic Properties / 330Uniform Density Discharge Model / 333Nonuniform Discharge Model / 336Neutral Radical Generation and Loss
33810.3
Electronegative Plasma Equilibrium / 340Differential Equations / 342Boltzmann Equilibrium for Negative Ions / 345Conservation Equations / 348Validity of Reduced Equations / 349
10.4
Approximate Electronegative Equilibria / 350Global Models / 351Parabolic Approximation For Low Pressures / 354Flat-Topped Model For Higher Pressures / 358
10.5
Electronegative Discharge Experiments and Simulations / 359Oxygen Discharges / 360Chlorine Discharges / 366
10.6
Pulsed Discharges / 369Pulsed Electropositive Discharges / 370Pulsed Electronegative Discharges / 376Neutral Radical Dynamics / 380
Problems / 381
1i CAPACITIVE DISCHARGES
387
11 .1
Homogeneous Model / 388Plasma Admittance / 390Sheath Admittance / 391Particle and Energy Balance / 395Discharge Parameters / 397
11.2
Inhomogeneous Model / 399Collisionless Sheath Dynamics / 400Child Law / 402Sheath Capacitance / 403Ohmic Heating / 404Stochastic Heating / 405Self-Consistent Model Equations / 406
Al CONTENTS
Scaling / 410Collisional Sheaths / 411Low and Moderate Voltages / 413Ohmic Heating in the Sheath / 413Self-Consistent Collisionless Heating Models / 414
Dual-Frequency and High-Frequency Discharges / 416Electronegative Plasmas / 417
11 .3
Experiments and Simulations / 418Experimental Results / 419Particle-in-Cell Simulations / 423Role of Secondaries / 428Implications for Modeling / 429
11 .4
Asymmetric Discharges / 430Capacitive Voltage Divider / 430Spherical Shell Model / 432
11 .5
Low-Frequency RF Sheaths / 43411 .6
Ion Bombarding Energy at Electrodes / 44111 .7
Magnetically Enhanced Discharges / 44911 .8
Matching Networks and Power Measurements
452Power Measurements / 456
Problems / 457
12 INDUCTIVE DISCHARGES
461
12.1
High-Density, Low-Pressure Discharges / 462Inductive Source Configurations / 462Power Absorption and Operating Regimes / 464Discharge Operation and Coupling / 466Matching Network / 469
12,2
Other Operating Regimes / 470Low-Density Operation / 470Capacitive Coupling / 471Hysteresis and Instabilities / 473Power Transfer Efficiency / 476Exact Solutions / 476
12.3
Planar Coil Configuration / 47712.4
Helical Resonator Discharges / 483Problems / 487
CONTENTS All
13 WAVE-HEATED DISCHARGES
491
13.1
Electron Cyclotron Resonance Discharges / 492Characteristics and Configurations
492Electron Heating / 497Resonant Wave Absorption / 501Model and Simulations / 507Plasma Expansion / 509Measurements / 512
13.2
Helicon Discharges / 513Helicon Modes / 514Antenna Coupling / 517Helicon Mode Absorption / 520Neutral Gas Depletion / 525
13.3
Surface Wave Discharges / 527Planar Surface Waves / 528Cylindrical Surface Waves / 530Power Balance / 530
Problems / 532
14 DIRECT CURRENT (DC) DISCHARGES
535
14.1
Qualitative Characteristics of Glow Discharges / 535Positive Column / 536Cathode Sheath / 537Negative Glow and Faraday Dark Space / 537Anode Fall / 537Other Effects / 538Sputtering and Other Configurations / 539
14.2
Analysis of the Positive Column / 539Calculation of T` / 540Calculation of E and no / 541Kinetic Effects / 542
14.3
Analysis of the Cathode Region / 543Vacuum Breakdown / 544Cathode Sheath / 546The Negative Glow and Faraday Dark Space / 550
14,4
Hollow Cathode Discharges / 551Simple Discharge Model / 552Metal Vapor Production in a Hollow Cathode Discharge / 555
x1v CONTENTS
14.5
Planar Magnetron Discharges / 559Limitations of Glow Discharge
Sputtering Source / 559Magnetron Configuration / 560Discharge Model / 561
14 .6
Ionized Physical Vapor Deposition / 564Problems / 563
15 ETCHING
571
15.1
Etch Requirements and Processes / 571Plasma Etch Requirements / 572Etch Processes / 576
15.2
Etching Kinetics / 579Surface Kinetics / 579Discharge Kinetics and Loading Effect / 583Chemical Framework / 585
15 .3
Halogen Atom Etching of Silicon / 586Pure Chemical F-Atom Etching / 587Ion Energy-Driven F-Atom Etching / 589CF4 Discharges / 592Oz and H2 Feedstock Additions / 596Cl-Atom Etching / 598
15.4
Other Etch Systems / 600F and CF, Etching of SiO2 / 600Si3Na Etching / 602Aluminum Etching / 602Copper Etching / 603Resist Etching
60415.5
Substrate Charging / 606Gate Oxide Damage / 607Grounded Substrate / 607Nonuniform Plasmas / 608Transient Damage During Etching
611Electron Shading Effect / 612Radiofrequency Biasing / 613Etch Profile Distortions / 614
Problems / 616
CONTENTS xv
16 DEPOSITION AND IMPLANTATION
619
16.1 Introduction / 61916.2
Plasma-Enhanced Chemical Vapor Deposition / 621Amorphous Silicon / 622Silicon Dioxide / 625Silicon Nitride / 629
16.3
Sputter Deposition / 630Physical Sputtering / 630Reactive Sputtering / 632
16.4
Plasma-Immersion Ion Implantation (PIII) / 634Collisionless Sheath Model / 636Collisional Sheath Model / 641Applications of PIII to Materials Processing / 644
Problems / 646
17 DUSTY PLASMAS
649
17.1
Qualitative Description of Phenomena / 64917.2
Particle Charging and Discharge Equilibrium / 651Equilibrium Potential and Charge / 651Discharge Equilibrium / 656
17.3
Particulate Equilibrium / 65817.4
Formation And Growth Of Dust Grains / 66217.5
Physical Phenomena And Diagnostics / 668Strongly Coupled Plasmas / 668Dust Acoustic Waves / 669Driven Particulate Motion / 670Laser Light Scattering / 671
17.6
Removal or Production of Particulates / 673Problems / 675
18 KINETIC THEORY OF DISCHARGES
679
18.1
Basic Concepts / 679Two-Term Approximation / 680The Kroolc Collision Operator / 680Two-Term Collisional Kinetic Equations / 681Diffusion and Mobility / 684Druyvesteyn Distribution / 685Electron Distribution in an RF Field / 686
xvi CONTENTS
Effective Electrical Conductivity / 687
18.2
Local Kinetics / 68918.3
Nonlocal Kinetics / 693
18.4
Quasi-Linear Diffusion and Stochastic Heating / 699Quasi-linear Diffusion Coefficient / 700Stochastic Heating / 703Relation to Velocity Kick Models
704Two Term Kinetic Equations / 704
18.5
Energy Diffusion in a Skin Depth Layer / 706Stochastic Heating / 706Effective Collision Frequency / 708Energy Distribution / 709
18.6
Kinetic Modeling of Discharges / 711Non-Maxwellian Global Models / 711Inductive Discharges / 712Capacitive Discharges f 715
Problems / 719
APPENDIX A. COLLISION DYNAMICS
723
Coulomb Cross Section / 725
APPENDIX B. THE COLLISION INTEGRAL
727
Boltzmann Collision integral / 727Maxwellian Distribution / 728
APPENDIX C. DIFFUSION SOLUTIONS FOR VARIABLEMOBILITY MODEL
731
REFERENCES
735