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