Plasma electronics: applications in microelectronic device fabrication

336 Pages·2006·4.335 MB·English

by  T. Makabe, Z. Petrovic

Plasma ElEctronics:
applications in microelectronic
Device Fabrication
© 2006 by Taylor & Francis Group, LLC
Series in Plasma Physics
Series Editor:
Steve Cowley, Imperial College, UK and UCLA, USA
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© 2006 by Taylor & Francis Group, LLC
Series in Plasma Physics
PlaSma ElEctronicS:

applications in microelectronic
Device Fabrication
t makabe
Keio University, Japan
Z Petrovic´
Institute of Physics Belgrade, Serbia
New York London
© 2006 by Taylor & Francis Group, LLC
Published in 2006 by
CRC Press
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© 2006 by Taylor & Francis Group, LLC
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International Standard Book Number-10: 0-7503-0976-8 (Hardcover)
International Standard Book Number-13: 978-0-7503-0976-9 (Hardcover)
Library of Congress Card Number 2005056888
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Library of Congress Cataloging-in-Publication Data
Makabe, T. (Toshiaki).
Plasma electronics : applications in microelectronic device fabrication / by T. Makabe and I. Petrovic
p. cm. -- (Series in plasma physics)
Includes bibliographical references and index.
ISBN 0-7503-0976-8
1. Plasma engineering. I. Title. II. Series.
TA2020.M35 2005
621.044--dc22 2005056888
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Preface
Overthepastthreedecadeslow-temperatureplasmaapplicationshavebeen
extendedfromprimarilylightingtothefabricationofmicroelectronicdevices
andnewmaterials,farexceedingourexpectations.Radiofrequencyplasmas
rangingfrom105 Hzto109 Hz,inparticular,arenowusedtoprocessmetal-
lic,semiconductor,anddielectricmaterialsforthefabricationofultralarge-
scale integrated (ULSI) circuits and to deposit various kinds of functional
thin films and to modify the surface properties. Without plasma-produced
ions and dissociated neutral radicals for etching and deposition on wafers,
microelectronicsmanufacturingforULSIcircuitwouldsimplybeunfeasible.
The advent of ULSI fabrication has greatly changed how the field of plasma
science is approached and understood. Low-temperature non-equilibrium
plasmas are sustained mainly by electron impact ionization of a feed gas
drivenbyanexternalradiofrequencypowersource.Theselow-temperature
plasmas acquire characteristics intrinsic to the feed gas molecules as deter-
minedbytheiruniqueelectron-collisioncross-sectionsets.Thisuniqueness
meansthatplasmasmustbeunderstoodusingquantum,atomic,andmolecu-
larphysics.Thedisparatetimeandspatialscalesinvolvedinlow-temperature
plasma processing (submeter to nanometer and seconds to nanoseconds)
makes plasma processing an inherently stiff problem. The characteristics of
low-temperatureplasmascontrastmarkedlywithhighlyionizedequilibrium
plasmasthatareensemblesofchargedparticleswhosebehaviorcanbeun-
derstoodthroughtheirlong-rangeCoulombinteractionsandcollectiveeffects
andcharacterizedbyplasmafrequency,Debyelength,andelectrontempera-
ture.Thefundamentalcollisionandreactionprocessesoccurringbothingas
phase and on surface in low-temperature plasmas are the bases for under-
standingtheirbehaviorandexploitingthemforpracticalapplications.
In the emerging nanotechnology era, device design, reliability, and the
design of integrated plasma processes for their fabrication are tightly cou-
pled. Being able to predict feature profile evolution under the influence of
spatio-temporallyvaryingplasmasisindispensablefortheprogressofnano-
technology.Predictionofplasmadamageanditsmitigationarealsocrucial
prediction&mitigationare2processandwillbeperformedthroughaseries
of vertically integrated numerical modeling and simulations ranging from the
reactorscaletothosecognizantofdeviceelementssubtendingtheplasma.
Motivatedbytheimportantroleofplasmasintechnologyandtheneedfor
simulationstounderstandtheassociatedcomplexprocesses,weemphasize
© 2006 by Taylor & Francis Group, LLC
in this book academic fusion among atomic and molecular physics, surface
physics, the Boltzmann transport theory, electromagnetic theory, and com-
putationalscienceasplasmaelectronics.Wedothistodescribeandpredict
thespaceandtimecharacteristicsoflow-temperatureplasmasandassociated
processingintrinsictospecificfeedgases.Anunderlyingthemethroughthis
work is computer-aided plasma analysis and synthesis, with emphasis on
computationalalgorithmsandtechniques.
ThisbookisbasedonaseriesoflecturespresentedatKeioUniversityas
part of its graduate program. The university’s interest in the subject matter
and feedback were essential parts of developing this text. We believe that the
book is well suited as an instrument for self-instruction through its topical
exercisesandproblemsarrangedineachchapter.
It is a pleasure to acknowledge our debt to David Graves and Robert
Robson, who have helped in a variety of ways during the long period of
our research life composing plasma electronics. Finally, we are indebted to
T.Yagisawaforfigurepreparationandhisattentiontodetail.
ToshiakiMakabeandZoranLj.Petrovic
KeioUniversity
© 2006 by Taylor & Francis Group, LLC
Contents
1 Introduction..........................................................1
1.1 PlasmaandItsClassification.....................................1
1.2 ApplicationofLow-TemperaturePlasma.........................2
1.3 AcademicFusion................................................3
References............................................................4
2 PhenomenologicalDescriptionoftheCharged
ParticleTransport....................................................5
2.1 TransportinReal(Configuration)Space..........................5
2.1.1 MomentumBalanceofElectrons..........................6
2.1.2 EnergyBalanceofElectrons...............................7
2.2 TransportinVelocitySpace.....................................10
2.2.1 ElectronVelocityDistributionand
SwarmParameters.......................................10
2.2.2 IonVelocityDistributionandMeanEnergy...............18
2.3 ThermalEquilibriumandItsGoverningRelations...............20
2.3.1 BoltzmannDistributioninRealSpace....................21
2.3.2 MaxwellDistributioninVelocitySpace...................22
References...........................................................25
3 MacroscopicPlasmaCharacteristics.................................27
3.1 Introduction....................................................27
3.2 Quasi-Neutrality................................................27
3.3 Charge-SeparationinPlasmas...................................28
3.3.1 SpatialScaleofCharge-Separation.......................28
3.3.2 TimeScaleforCharge-Separation........................29
3.4 PlasmaShielding...............................................30
3.4.1 DebyeShielding.........................................30
3.4.2 MetalProbeinaPlasma..................................31
3.5 ParticleDiffusion...............................................34
3.5.1 AmbipolarDiffusion.....................................34
3.5.2 SpatialandTimeScaleofDiffusion.......................35
3.6 BohmSheathCriterion..........................................37
3.6.1 BohmVelocity...........................................37
3.6.2 FloatingPotential........................................38
References...........................................................39
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4 ElementaryProcessesinGasPhaseandonSurfaces.................41
4.1 ParticlesandWaves.............................................42
4.1.1 ParticleRepresentationinClassicaland
QuantumMechanics.....................................42
4.1.2 LocallyIsolatedParticleGroupandWavePackets........44
4.2 CollisionsandCrossSections...................................46
4.2.1 ConservationLawsinCollisions.........................47
4.2.2 DefinitionofCollisionCrossSections.....................49
4.2.3 TheDistributionofFreePaths............................53
4.2.4 RepresentationofCollisionsinLaboratoryand
CMReferenceFrames....................................54
4.3 ClassicalCollisionTheory.......................................57
4.3.1 ScatteringinClassicalMechanics.........................58
4.3.2 ConditionsfortheApplicabilityoftheClassical
ScatteringTheory........................................64
4.4 QuantumTheoryofScattering..................................64
4.4.1 DifferentialScatteringCrossSectionσ(θ).................66
4.4.2 ModifiedEffectiveRangeTheoryin
ElectronScattering.......................................71
4.5 CollisionsbetweenElectronsandNeutral
Atoms/Molecules..............................................72
4.5.1 ResonantScattering......................................73
4.6 Electron–AtomCollisions.......................................75
4.6.1 EnergyLevelsofAtoms..................................75
4.6.2 Electron–AtomScatteringCrossSections.................77
4.7 Electron–MoleculeCollisions...................................81
4.7.1 Rotational,Vibrational,andElectronicEnergy
LevelsofMolecules......................................81
4.7.2 RotationalExcitation.....................................83
4.7.2.1 RotationalEnergyLevels........................83
4.7.2.2 RotationalExcitationCrossSections.............84
4.7.3 VibrationalExcitation....................................87
4.7.3.1 VibrationalEnergyLevels.......................87
4.7.3.2 VibrationalCrossSections.......................88
4.7.4 ElectronicExcitationandDissociation....................89
4.7.4.1 ElectronicStatesofMolecules....................89
4.7.4.2 CrossSectionsforElectronicExcitation
ofMolecules....................................91
4.7.5 ElectronCollisionswithExcitedAtoms
andMolecules...........................................92
4.8 NonconservativeCollisionsofElectronswithAtoms
andMolecules..................................................95
4.8.1 Electron-InducedIonization..............................95
4.8.2 ElectronAttachment.....................................97
4.8.2.1 DissociativeElectronAttachment................99
4.8.2.2 NondissociativeElectronAttachment...........100
© 2006 by Taylor & Francis Group, LLC
4.8.2.3 IonPairFormation............................101
4.8.2.4 ElectronAttachmenttoExcitedMolecules.....101
4.8.2.5 RateCoefficientsforAttachment..............102
4.8.3 Electron–IonandIon–IonRecombination..............103
4.8.4 Electron–IonandElectron–ElectronCollisions..........105
4.9 HeavyParticleCollisions.....................................105
4.9.1 Ion–MoleculeCollisions...............................106
4.9.1.1 ChargeTransfer,Elastic,andInelastic
ScatteringofIons ............................. 106
4.9.1.2 Ion–MoleculeReactions.......................109
4.9.2 CollisionsofFastNeutrals.............................110
4.9.3 CollisionsofExcitedParticles..........................111
4.9.3.1 Chemi-IonizationandPenningIonization.....112
4.9.4 CollisionsofSlowNeutralsandRateCoefficients......116
4.9.4.1 QuenchingandTransportofExcitedStates....116
4.9.4.2 KineticsofRotationaland
VibrationalLevels.............................118
4.10 PhotonsinIonizedGases.....................................119
4.10.1 EmissionandAbsorptionofLineRadiation...........119
4.10.2 ResonantRadiationTrapping.........................122
4.11 ElementaryProcessesatSurfaces.............................123
4.11.1 EnergyLevelsofElectronsinSolids...................124
4.11.2 EmissionofElectronsfromSurfaces...................127
4.11.2.1 Photo-Emission.............................127
4.11.2.2 ThermionicEmission ....................... 128
4.11.2.3 Field-InducedEmission.....................129
4.11.2.4 PotentialEjectionofElectronsfromSurfaces
byIonsandExcitedAtoms..................132
4.11.3 EmissionofIonsandNeutralsfromSurfaces..........135
4.11.3.1 SurfaceNeutralization......................136
4.11.3.2 SurfaceIonization...........................136
4.11.4 Adsorption...........................................138
References..........................................................140
5 TheBoltzmannEquationandTransportEquationsof
ChargedParticles..................................................143
5.1 Introduction..................................................143
5.2 TheBoltzmannEquation.....................................143
5.2.1 TransportinPhaseSpaceandDerivationofthe
BoltzmannEquation...................................144
5.3 TransportCoefficients........................................146
5.4 TheTransportEquation.......................................150
5.4.1 ConservationofNumberDensity......................151
5.4.2 ConservationofMomentum...........................151
5.4.3 ConservationofEnergy................................153
5.5 CollisionTermintheBoltzmannEquation....................153
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5.5.1 CollisionIntegral.......................................153
5.5.2 CollisionIntegralbetweenanElectronanda
GasMolecule...........................................154
5.5.2.1 ElasticCollisionTerm J ......................155
elas
5.5.2.2 ExcitationCollisionTerm J ...................158
ex
5.5.2.3 IonizationCollisionTerm J ...................158
ion
5.5.2.4 ElectronAttachmentCollisionTerm J ........ 159
att
5.6 BoltzmannEquationforElectrons..............................160
5.6.1 SphericalHarmonicsandTheirProperties ..............160
5.6.2 VelocityDistributionofElectrons.......................163
5.6.2.1 VelocityDistributionunderUniform
NumberDensity:g0............................164
5.6.2.2 VelocityDistributionProportionalto
∇ n(r,t):g1.....................................165
r
5.6.3 ElectronTransportParameters..........................170
References..........................................................174
6 GeneralPropertiesofChargedParticleTransportinGases.........175
6.1 Introduction...................................................175
6.2 ElectronTransportinDC-ElectricFields........................175
6.2.1 ElectronDriftVelocity..................................175
6.2.2 DiffusionCoefficients...................................178
6.2.3 MeanEnergyofElectrons...............................180
6.2.4 Excitation,Ionization,andElectron
AttachmentRates.......................................181
6.3 ElectronTransportinRadio-FrequencyElectricFields..........184
6.3.1 RelaxationTimeConstants..............................184
6.3.2 EffectiveFieldApproximation..........................189
6.3.3 ExpansionProcedure...................................192
6.3.4 DirectNumericalProcedure............................195
6.3.5 Time-VaryingSwarmParameters.......................199
6.4 IonTransportinDC-ElectricFields.............................201
References..........................................................203
7 ModelingofNonequilibrium(Low-Temperature)Plasmas.........205
7.1 Introduction...................................................205
7.2 ContinuumModels............................................207
7.2.1 GoverningEquationsofaContinuumModel............207
7.2.2 LocalFieldApproximation(LFA).......................210
7.2.3 Quasi-ThermalEquilibrium(QTE)Model...............211
7.2.4 RelaxationContinuum(RCT)Model....................212
7.2.5 PhaseSpaceKineticModel..............................214
7.3 ParticleModels................................................216
7.3.1 MonteCarloSimulations(MCSs) ....................... 216
7.3.2 Particle-in-Cell(PIC)andParticle-in-Cell/MonteCarlo
Simulation(PIC/MCS)Models.........................219
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