Periodic materials and interference lithography for photonics, phononics and mechanics

333 Pages·2009·4.797 MB·English

by  Martin Maldovan, Edwin L Thomas

Martin Maldovan and
Edwin L. Thomas
Periodic Materials and
Interference Lithography
for Photonics, Phononics and Mechanics

MartinMaldovanand
EdwinL.Thomas
PeriodicMaterialsand
InterferenceLithography
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Martin Maldovan and
Edwin L. Thomas
Periodic Materials and
Interference Lithography
for Photonics, Phononics and Mechanics
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ISBN:978-3-527-31999-2
V
Contents
Preface XI
Introduction XIII
Theory 1
1 StructuralPeriodicity 3
1.1 NonperiodicversusPeriodicStructures 4
1.2 Two-dimensionalPointLattices 6
1.3 Three-dimensionalPointLattices 10
1.3.1 PrimitiveandNonprimitiveUnitCells 14
1.4 MathematicalDescriptionofPeriodicStructures 16
1.5 FourierSeries 20
1.5.1 FourierSeriesforTwo-dimensionalPeriodicFunctions 20
1.5.2 FourierSeriesforThree-dimensionalPeriodicFunctions 23
1.5.3 ArbitraryUnitCells 25
FurtherReading 26
Problems 26
2 PeriodicFunctionsandStructures 29
2.1 Introduction 30
2.2 CreatingSimplePeriodicFunctionsinTwoDimensions 31
2.2.1 TheSquareLattice 31
2.2.2 TheTriangularLattice 38

2.3 CreatingSimplePeriodicFunctionsinThreeDimensions 41
2.3.1 TheSimpleCubicLattice 44
2.3.2 TheFace-centered-cubicLattice 47
2.3.3 TheBody-centered-cubicLattice 51
2.4 CombinationofSimplePeriodicFunctions 59
Problems 61
3 InterferenceofWavesandInterferenceLithography 63
3.1 ElectromagneticWaves 64
PeriodicMaterialsandInterferenceLithography.M.MaldovanandE.Thomas
Copyright2009WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-31999-2
VI Contents
3.2 TheWaveEquation 65
3.3 ElectromagneticPlaneWaves 68
3.4 TheTransverseCharacterofElectromagneticPlaneWaves 69
3.5 Polarization 72
3.5.1 LinearlyPolarizedElectromagneticPlaneWaves 73
3.5.2 CircularlyPolarizedElectromagneticPlaneWaves 74
3.5.3 EllipticallyPolarizedElectromagneticPlaneWaves 75
3.6 ElectromagneticEnergy 75
3.6.1 EnergyDensityandEnergyFluxforElectromagneticPlaneWaves 77
3.6.2 Time-averagedValues 77
3.6.3 Intensity 80
3.7 InterferenceofElectromagneticPlaneWaves 81
3.7.1 Three-dimensionalInterferencePatterns 86
3.8 InterferenceLithography 89
3.8.1 PhotoresistMaterials 89
3.8.2 TheInterferenceLithographyTechnique 92
3.8.3 DesigningPeriodicStructures 93
FurtherReading 94
Problems 94
4 PeriodicStructuresandInterferenceLithography 97
4.1 TheConnectionbetweentheInterferenceofPlaneWavesandFourier
Series 98
4.2 SimplePeriodicStructuresinTwoDimensionsViaInterference
Lithography 100
4.3 SimplePeriodicStructuresinThreeDimensionsViaInterference
Lithography 104
FurtherReading 110
Problems 111
Experimental 113
5 FabricationofPeriodicStructures 115
5.1 Introduction 116
5.2 LightBeams 116
5.3 M ultipleGratingsandtheRegistrationChallenge 118
5.4 BeamConfiguration 119
5.4.1 UsingFourBeams 119
5.4.2 UsingaSingleBeam(PhaseMaskLithography) 120
5.5 PatternTransfer:MaterialPlatformsandPhotoresists 122
5.5.1 NegativePhotoresists 124
5.5.2 PositivePhotoresists 126
5.5.3 Organic–InorganicHybridsResists 128
5.6 PracticalConsiderationsforInterferenceLithography 128
Contents VII
5.6.1 PreservingPolarizationsandDirections 128
5.6.2 Contrast 131
5.6.3 Drying 132
5.6.4 Shrinkage 133
5.6.5 Backfilling – CreatingInversePeriodicStructures 133
5.6.6 VolumeFractionControl 134
5.7 ClosingRemarks 135
FurtherReading 136
Applications 139
6 PhotonicCrystals 141
6.1 Introduction 142
6.2 One-dimensionalPhotonicCrystals 143
6.2.1 FinitePeriodicStructures 143
6.2.2 InfinitePeriodicStructures 147
6.2.3 FiniteversusInfinitePeriodicStructures 150
6.3 Two-dimensionalPhotonicCrystals 151
6.3.1 ReciprocalLatticesandBrillouinZonesinTwoDimensions 152
6.3.2 BandDiagramsandPhotonicBandGapsinTwoDimensions 157
6.3.3 PhotonicBandGapsinTwo-dimensionalSimplePeriodic
Structures 160
6.4 Three-dimensionalPhotonicCrystals 162
6.4.1 ReciprocalLatticesandBrillouinZonesinThreeDimensions 164
6.4.2 BandDiagramsandPhotonicBandGapsinThreeDimensions 168
6.4.3 PhotonicBandGapsinThree-dimensionalSimplePeriodic
Structures 170
FurtherReading 176
Problems 179
7 PhononicCrystals 183
7.1 Introduction 184
7.1.1 ElasticWavesinHomogeneousSolidMaterials 184
7.1.2 AcousticWavesinHomogeneousFluidMaterials 187
7.2 PhononicCrystals 188
7.3 One-dimen sionalPhononicCrystals 190
7.3.1 FinitePeriodicStructures 190
7.3.2 InfinitePeriodicStructures 194
7.4 Two-dimensionalPhononicCrystals 198
7.4.1 VacuumCylindersinaSolidBackground 198
7.4.2 SolidCylindersinAir 202
7.4.3 PhononicBandGapsinTwo-dimensionalSimplePeriodic
Structures 205
7.5 Three-dimensionalPhononicCrystals 207
VIII Contents
7.5.1 SolidSpheresinaSolidBackgroundMaterial 208
FurtherReading 210
Problems 213
8 PeriodicCellularSolids 215
8.1 Introduction 216
8.2 One-dimensionalHooke’sLaw 218
8.3 TheStressTensor 219
8.4 TheStrainTensor 221
8.4.1 Expansion 225
8.4.2 GeneralDeformation 226
8.4.3 ResolvingaGeneralDeformationasStrainPlusRotation 227
8.5 Stress–StrainRelationship:TheGeneralizedHooke’sLaw 229
8.6 TheGeneralizedHooke’sLawinMatrixNotation 230
8.7 TheElasticConstantsofCubicCrystals 232
8.7.1 Young’sModulusandPoisson’sRatio 233
8.7.2 TheShearModulus 235
8.7.3 TheBulkModulus 237
8.8 TopologicalDesignofPeriodicCellularSolids 238
8.9 FiniteElementProgramtoCalculateLinearElasticMechanical
Properties 243
8.10 LinearElasticMechanicalPropertiesofPeriodicCellularSolids 243
8.11 Twelve-connectedStretch-dominatedPeriodicCellularSolidsvia
InterferenceLithography 247
8.12 FabricationofaSimpleCubicCellularSolidviaInterference
Lithography 249
8.13 PlasticDeformationofMicroframes 250
FurtherReading 252
9 FurtherApplications 255
9.1 ControllingtheSpontaneousEmissionofLight 256
9.2 LocalizationofLight:MicrocavitiesandWaveguides 259
9.3 SimultaneousLocalizationofLightandSoundinPhotonic–Phononic
Crystals:NovelAcoustic–OpticalDevices 264
9.4 NegativeRefractionandSuperlenses 268
9.5 MultifunctionalPeriodicStructures:MaximumTransportofHeatand

Electricity 272
9.6 Microfluidics 273
9.7 ThermoelectricEnergy 275
9.7.1 PeltierEffect 275
9.7.2 ThomsonEffect 276
9.7.3 SeebeckEffect 277
FurtherReading 278