PRINCIPLES OF PLASMA DISCHARGES AND MATERIALS PROCESSING

By ANDREW GONZALEZ

CONTENTS INTRODUCTION MATERIALS PROCESSING / PLASMAS AND SHEATHS / PLASMAS / SHEATHS / DISCHARGES / RADIO FREQUENCY DIODES / HIGH-DENSITY SOURCES / SYMBOLS AND UNITS / BASIC PLASMA EQUATIONS AND EQUILIBRIUM INTRODUCTION / FIELD EQUATIONS, CURRENT, AND VOLTAGE / MAXWELL’S EQUATIONS / THE CONSERVATION EQUATIONS / BOLTZMANN’S EQUATION / MACROSCOPIC QUANTITIES / PARTICLE CONSERVATION / MOMENTUM CONSERVATION / ENERGY CONSERVATION / SUMMARY / EQUILIBRIUM PROPERTIES / BOLTZMANN’S RELATION / DEBYE LENGTH / QUASI-NEUTRALITY / PROBLEMS / ATOMIC COLLISIONS BASIC CONCEPTS / ELASTIC AND INELASTIC COLLISIONS / COLLISION PARAMETERS / DIFFERENTIAL SCATTERING CROSS SECTION / COLLISION DYNAMICS / CENTER-OF-MASS COORDINATES / ENERGY TRANSFER / SMALL ANGLE SCATTERING / ELASTIC SCATTERING / COULOMB COLLISIONS / POLARIZATION SCATTERING / INELASTIC COLLISIONS / ATOMIC ENERGY LEVELS / ELECTRIC DIPOLE RADIATION AND METASTABLE ATOMS / ELECTRON IONIZATION CROSS SECTION / ELECTRON EXCITATION CROSS SECTION / ION–ATOM CHARGE TRANSFER / ION–ATOM IONIZATION / AVERAGING OVER DISTRIBUTIONS AND SURFACE EFFECTS / AVERAGING OVER A MAXWELLIAN DISTRIBUTION / ENERGY LOSS PER ELECTRON–ION PAIR CREATED / SURFACE EFFECTS / PLASMA DYNAMICS BASIC MOTIONS / MOTION IN CONSTANT FIELDS / E B DRIFTS / NONMAGNETIZED PLASMA DYNAMICS / PLASMA OSCILLATIONS / DIELECTRIC CONSTANT AND CONDUCTIVITY / OHMIC HEATING / ELECTROMAGNETIC WAVES / ELECTROSTATIC WAVES / GUIDING CENTER MOTION / PARALLEL FORCE / ADIABATIC CONSTANCY OF THE MAGNETIC MOMENT / DRIFT DUE TO MOTION ALONG FIELD LINES (CURVATURE DRIFT) / DRIFT DUE TO GYRATION (GRADIENT DRIFT) / POLARIZATION DRIFT / DYNAMICS OF MAGNETIZED PLASMAS / DIELECTRIC TENSOR / THE WAVE DISPERSION / WAVES IN MAGNETIZED PLASMAS / PRINCIPAL ELECTRON WAVES / PRINCIPAL WAVES INCLUDING ION DYNAMICS / THE CMA DIAGRAM / WAVE DIAGNOSTICS / INTERFEROMETER / CAVITY PERTURBATION / WAVE PROPAGATION / DIFFUSION AND TRANSPORT BASIC RELATIONS / DIFFUSION AND MOBILITY / FREE DIFFUSION / AMBIPOLAR DIFFUSION / DIFFUSION SOLUTIONS / BOUNDARY CONDITIONS / TIME-DEPENDENT SOLUTION / STEADY-STATE PLANE-PARALLEL SOLUTIONS / STEADY-STATE CYLINDRICAL SOLUTIONS / LOW-PRESSURE SOLUTIONS / VARIABLE MOBILITY MODEL / LANGMUIR SOLUTION / HEURISTIC SOLUTIONS / DIFFUSION ACROSS A MAGNETIC FIELD / MAGNETIC MULTIPOLE CON?NEMENT / MAGNETIC FIELDS / PLASMA CON?NEMENT / LEAK WIDTH W / DIRECT CURRENT (DC) SHEATHS BASIC CONCEPTS AND EQUATIONS / THE COLLISIONLESS SHEATH / THE BOHM SHEATH CRITERION / PLASMA REQUIREMENTS / THE PRESHEATH / SHEATH POTENTIAL AT A FLOATING WALL / COLLISIONAL SHEATHS / SIMULATION RESULTS / THE HIGH-VOLTAGE SHEATH / MATRIX SHEATH / CHILD LAW SHEATH / GENERALIZED CRITERIA FOR SHEATH FORMATION / ELECTRONEGATIVE GASES / MULTIPLE POSITIVE ION SPECIES / HIGH-VOLTAGE COLLISIONAL SHEATHS / ELECTROSTATIC PROBE DIAGNOSTICS / PLANAR PROBE WITH COLLISIONLESS SHEATH / NON-MAXWELLIAN ELECTRONS / CYLINDRICAL PROBE WITH A COLLISIONLESS SHEATH / DOUBLE PROBES AND EMISSIVE PROBES / EFFECT OF COLLISIONS AND DC MAGNETIC FIELDS / PROBE CONSTRUCTION AND CIRCUITS / PROBES IN TIME-VARYING FIELDS / CHEMICAL REACTIONS AND EQUILIBRIUM ENERGY AND ENTHALPY / ENTROPY AND GIBBS FREE ENERGY / GIBBS FREE ENERGY / CHEMICAL EQUILIBRIUM / PRESSURE AND TEMPERATURE VARIATIONS / HETEROGENEOUS EQUILIBRIUM / EQUILIBRIUM BETWEEN PHASES / EQUILIBRIUM AT A SURFACE / MOLECULAR COLLISIONS MOLECULAR STRUCTURE / VIBRATIONAL AND ROTATIONAL MOTION / OPTICAL EMISSION / NEGATIVE IONS / ELECTRON COLLISIONS WITH MOLECULES / DISSOCIATION / DISSOCIATIVE IONIZATION / DISSOCIATIVE RECOMBINATION / EXAMPLE OF HYDROGEN / DISSOCIATIVE ELECTRON ATTACHMENT / POLAR DISSOCIATION / METASTABLE NEGATIVE IONS / ELECTRON IMPACT DETACHMENT / VIBRATIONAL AND ROTATIONAL EXCITATIONS / HEAVY-PARTICLE COLLISIONS / RESONANT AND NONRESONANT CHARGE TRANSFER / POSITIVE–NEGATIVE ION RECOMBINATION / ASSOCIATIVE DETACHMENT / TRANSFER OF EXCITATION / REARRANGEMENT OF CHEMICAL BONDS / ION–NEUTRAL ELASTIC SCATTERING / THREE-BODY PROCESSES / REACTION RATES AND DETAILED BALANCING / TEMPERATURE DEPENDENCE / THE PRINCIPLE OF DETAILED BALANCING / A DATA SET FOR OXYGEN / OPTICAL EMISSION AND ACTINOMETRY / OPTICAL ACTINOMETRY / O ATOM ACTINOMETRY / CHEMICAL KINETICS AND SURFACE PROCESSES ELEMENTARY REACTIONS / RELATION TO EQUILIBRIUM CONSTANT / GAS-PHASE KINETICS / FIRST-ORDER CONSECUTIVE REACTIONS / OPPOSING REACTIONS / BIMOLECULAR ASSOCIATION WITH PHOTON EMISSION / THREE-BODY ASSOCIATION / THREE-BODY POSITIVE–NEGATIVE ION RECOMBINATION / THREE-BODY ELECTRON–ION RECOMBINATION / SURFACE PROCESSES / POSITIVE ION NEUTRALIZATION AND SECONDARY ELECTRON EMISSION / ADSORPTION AND DESORPTION / FRAGMENTATION / SPUTTERING / SURFACE KINETICS / DIFFUSION OF NEUTRAL SPECIES / LOSS RATE FOR DIFFUSION / DISSOCIATIVE ADSORPTION AND ASSOCIATIVE DESORPTION / PHYSICAL ADSORPTION / REACTION WITH A SURFACE / REACTIONS ON A SURFACE / SURFACE KINETICS AND LOSS PROBABILITY / PARTICLE AND ENERGY BALANCE IN DISCHARGES ELECTROPOSITIVE PLASMA EQUILIBRIUM / BASIC PROPERTIES / UNIFORM DENSITY DISCHARGE MODEL / NONUNIFORM DISCHARGE MODEL / NEUTRAL RADICAL GENERATION AND LOSS / ELECTRONEGATIVE PLASMA EQUILIBRIUM / DIFFERENTIAL EQUATIONS / BOLTZMANN EQUILIBRIUM FOR NEGATIVE IONS / CONSERVATION EQUATIONS / VALIDITY OF REDUCED EQUATIONS / APPROXIMATE ELECTRONEGATIVE EQUILIBRIA / GLOBAL MODELS / PARABOLIC APPROXIMATION FOR LOW PRESSURES / FLAT-TOPPED MODEL FOR HIGHER PRESSURES / ELECTRONEGATIVE DISCHARGE EXPERIMENTS AND SIMULATIONS / OXYGEN DISCHARGES / CHLORINE DISCHARGES / PULSED DISCHARGES / PULSED ELECTROPOSITIVE DISCHARGES / PULSED ELECTRONEGATIVE DISCHARGES / NEUTRAL RADICAL DYNAMICS / CAPACITIVE DISCHARGES HOMOGENEOUS MODEL / PLASMA ADMITTANCE / SHEATH ADMITTANCE / PARTICLE AND ENERGY BALANCE / DISCHARGE PARAMETERS / INHOMOGENEOUS MODEL / COLLISIONLESS SHEATH DYNAMICS / CHILD LAW / SHEATH CAPACITANCE / STOCHASTIC HEATING / SELF-CONSISTENT MODEL EQUATIONS / SCALING / LOW AND MODERATE VOLTAGES / OHMIC HEATING IN THE SHEATH / SELF-CONSISTENT COLLISIONLESS HEATING MODELS / DUAL-FREQUENCY AND HIGH-FREQUENCY DISCHARGES / ELECTRONEGATIVE PLASMAS / EXPERIMENTS AND SIMULATIONS / EXPERIMENTAL RESULTS / PARTICLE-IN-CELL SIMULATIONS / ROLE OF SECONDARIES / IMPLICATIONS FOR MODELING / ASYMMETRIC DISCHARGES / CAPACITIVE VOLTAGE DIVIDER / SPHERICAL SHELL MODEL / LOW-FREQUENCY RF SHEATHS / ION BOMBARDING ENERGY AT ELECTRODES / MAGNETICALLY ENHANCED DISCHARGES / MATCHING NETWORKS AND POWER MEASUREMENTS / POWER MEASUREMENTS / INDUCTIVE DISCHARGES HIGH-DENSITY, LOW-PRESSURE DISCHARGES / INDUCTIVE SOURCE CON?GURATIONS / POWER ABSORPTION AND OPERATING REGIMES / DISCHARGE OPERATION AND COUPLING / MATCHING NETWORK / OTHER OPERATING REGIMES / LOW-DENSITY OPERATION / CAPACITIVE COUPLING / HYSTERESIS AND INSTABILITIES / POWER TRANSFER EF?CIENCY / EXACT SOLUTIONS / PLANAR COIL CON?GURATION / HELICAL RESONATOR DISCHARGES / WAVE-HEATED DISCHARGES ELECTRON CYCLOTRON RESONANCE DISCHARGES / CHARACTERISTICS AND CON?GURATIONS / ELECTRON HEATING / RESONANT WAVE ABSORPTION / MODEL AND SIMULATIONS / PLASMA EXPANSION / MEASUREMENTS / HELICON DISCHARGES / HELICON MODES / ANTENNA COUPLING / HELICON MODE ABSORPTION / NEUTRAL GAS DEPLETION / SURFACE WAVE DISCHARGES / PLANAR SURFACE WAVES / CYLINDRICAL SURFACE WAVES / POWER BALANCE / DIRECT CURRENT (DC) DISCHARGES QUALITATIVE CHARACTERISTICS OF GLOW DISCHARGES / POSITIVE COLUMN / CATHODE SHEATH / NEGATIVE GLOW AND FARADAY DARK SPACE / ANODE FALL / OTHER EFFECTS / SPUTTERING AND OTHER CON?GURATIONS / ANALYSIS OF THE POSITIVE COLUMN / CALCULATION OF TE / CALCULATION OF E AND N0 / KINETIC EFFECTS / ANALYSIS OF THE CATHODE REGION / VACUUM BREAKDOWN / THE NEGATIVE GLOW AND FARADAY DARK SPACE / HOLLOW CATHODE DISCHARGES / SIMPLE DISCHARGE MODEL / METAL VAPOR PRODUCTION IN A HOLLOW CATHODE DISCHARGE / PLANAR MAGNETRON DISCHARGES / LIMITATIONS OF GLOW DISCHARGE SPUTTERING SOURCE / MAGNETRON CON?GURATION / DISCHARGE MODEL / IONIZED PHYSICAL VAPOR DEPOSITION / ETCHING ETCH REQUIREMENTS AND PROCESSES / PLASMA ETCH REQUIREMENTS / ETCH PROCESSES / ETCHING KINETICS / DISCHARGE KINETICS AND LOADING EFFECT / CHEMICAL FRAMEWORK / HALOGEN ATOM ETCHING OF SILICON / PURE CHEMICAL F-ATOM ETCHING / ION ENERGY-DRIVEN F-ATOM ETCHING / CF4 DISCHARGES / O2 AND H2 FEEDSTOCK ADDITIONS / CL-ATOM ETCHING / OTHER ETCH SYSTEMS / F AND CFX ETCHING OF SIO2 / SI3N4 ETCHING / ALUMINUM ETCHING / COPPER ETCHING / RESIST ETCHING / SUBSTRATE CHARGING / GATE OXIDE DAMAGE / GROUNDED SUBSTRATE / NONUNIFORM PLASMAS / TRANSIENT DAMAGE DURING ETCHING / ELECTRON SHADING EFFECT / RADIOFREQUENCY BIASING / ETCH PRO?LE DISTORTIONS / DEPOSITION AND IMPLANTATION PLASMA-ENHANCED CHEMICAL VAPOR DEPOSITION / AMORPHOUS SILICON / SILICON DIOXIDE / SILICON NITRIDE / SPUTTER DEPOSITION / PHYSICAL SPUTTERING / REACTIVE SPUTTERING / PLASMA-IMMERSION ION IMPLANTATION (PIII) / COLLISIONLESS SHEATH MODEL / COLLISIONAL SHEATH MODEL / APPLICATIONS OF PIII TO MATERIALS PROCESSING / DUSTY PLASMAS QUALITATIVE DESCRIPTION OF PHENOMENA / PARTICLE CHARGING AND DISCHARGE EQUILIBRIUM / EQUILIBRIUM POTENTIAL AND CHARGE / DISCHARGE EQUILIBRIUM / PARTICULATE EQUILIBRIUM / FORMATION AND GROWTH OF DUST GRAINS / PHYSICAL PHENOMENA AND DIAGNOSTICS / STRONGLY COUPLED PLASMAS / DUST ACOUSTIC WAVES / DRIVEN PARTICULATE MOTION / LASER LIGHT SCATTERING / REMOVAL OR PRODUCTION OF PARTICULATES / KINETIC THEORY OF DISCHARGES TWO-TERM APPROXIMATION / THE KROOK COLLISION OPERATOR / TWO-TERM COLLISIONAL KINETIC EQUATIONS / DRUYVESTEYN DISTRIBUTION / ELECTRON DISTRIBUTION IN AN RF FIELD / EFFECTIVE ELECTRICAL CONDUCTIVITY / LOCAL KINETICS / NONLOCAL KINETICS / QUASI-LINEAR DIFFUSION AND STOCHASTIC HEATING / QUASI-LINEAR DIFFUSION COEF?CIENT / RELATION TO VELOCITY KICK MODELS / TWO TERM KINETIC EQUATIONS / ENERGY DIFFUSION IN A SKIN DEPTH LAYER / EFFECTIVE COLLISION FREQUENCY / ENERGY DISTRIBUTION / KINETIC MODELING OF DISCHARGES / NON-MAXWELLIAN GLOBAL MODELS / INDUCTIVE DISCHARGES / CAPACITIVE DISCHARGES / CHAPTER MATERIALS PROCESSING CHEMICALLY REACTIVE PLASMA DISCHARGES ARE WIDELY USED TO MODIFY THE SURFACE PROP- ERTIES OF MATERIALS PLASMA PROCESSING TECHNOLOGY IS VITALLY IMPORTANT TO SEVERAL OF THE LARGEST MANUFACTURING INDUSTRIES IN THE WORLD PLASMA-BASED SURFACE PROCESSES ARE INDISPENSABLE FOR MANUFACTURING THE VERY LARGE SCALE INTEGRATED CIRCUITS (ICS) USED BY THE ELECTRONICS INDUSTRY SUCH PROCESSES ARE ALSO CRITICAL FOR THE AEROSPACE, AUTOMOTIVE, STEEL, BIOMEDICAL, AND TOXIC WASTE MANAGEMENT INDUSTRIES MATERIALS AND SURFACE STRUCTURES CAN BE FABRICATED THAT ARE NOT ATTAINABLE BY ANY OTHER COMMER- CIAL METHOD, AND THE SURFACE PROPERTIES OF MATERIALS CAN BE MODI?ED IN UNIQUE WAYS FOR EXAMPLE, 0 2-MM-WIDE, 4-MM-DEEP TRENCHES CAN BE ETCHED INTO SILICON ?LMS OR SUBSTRATES (FIG 1 1) A HUMAN HAIR IS 50–100 MM IN DIAMETER, SO HUNDREDS OF THESE TRENCHES WOULD ?T ENDWISE WITHIN A HUMAN HAIR UNIQUE MATERIALS SUCH AS DIAMOND ?LMS AND AMORPHOUS SILICON FOR SOLAR CELLS HAVE ALSO BEEN PRODUCED, AND PLASMA- BASED HARDENING OF SURGICALLY IMPLANTED HIP JOINTS AND MACHINE TOOLS HAVE EXTENDED THEIR WORKING LIFETIMES MANYFOLD IT IS INSTRUCTIVE TO LOOK CLOSER AT INTEGRATED CIRCUIT FABRICATION, WHICH IS THE KEY APPLICATION THAT WE DESCRIBE IN THIS BOOK AS A VERY INCOMPLETE LIST OF PLASMA PRO- CESSES, ARGON OR OXYGEN DISCHARGES ARE USED TO SPUTTER-DEPOSIT ALUMINUM, TUNGSTEN, OR HIGH-TEMPERATURE SUPERCONDUCTING ?LMS; OXYGEN DISCHARGES CAN BE USED TO GROW SIO2 ?LMS ON SILICON; SIH2CL2=NH3 AND SI(OC2H5)4=O2 DISCHARGES ARE USED FOR THE PLASMA-ENHANCED CHEMICAL VAPOR DEPOSITION (PECVD) OF SI3N4 AND SIO2 ?LMS,