index [rd.springer.com]978-1-4419-6312-3/1.pdf · elastic deformation elastic constants (see...

7
275 A Al. See Aluminum Alumina, 6, 7 Aluminum interconnect, 77, 87–90, 95, 96, 98, 99, 105–107, 111–113 properties, 9, 37, 38, 41, 47, 65, 71, 85, 87–90, 95, 100, 106, 111, 113, 115, 180, 190, 196, 197, 200, 201, 204, 205, 209, 244, 256 Aluminum alloy properties, 197 Aluminum alloy 2080 T8 properties, 197 Anisotropy, 33, 115 Aspect ratio fiber, 175, 180, 265 line structure, 81, 89 solder joint, 134 unit-cell model, 175 Atomistic modeling, 110, 264 Axisymmetric model, 30, 35, 37, 64, 172, 178, 180, 184, 195, 215, 232, 236, 237, 249, 257 B Back stress, 46 Ball grid arrays, 6 Barrier layers. See Interconnect Bauschinger effect, 17, 44, 196 BCB properties, 85, 92 Biological material, 265, 266 Biomimetic material, 265 Boltzmann’s constant, 58 Bone, 265, 266 Burger’s vector, 58 C C. See Carbon Carbon, 5, 99, 227 Cementite, 227 Ceramic matrix composite, 203–205, 208 Chromium, 43 Circuit board, 7, 8, 125, 149–150, 153, 155, 162, 163 Coefficient of thermal expansion of composites, 202, 203, 208 Collagen fibril, 265, 266 Composite Al/SiC, 179, 181, 185, 188, 194, 197, 201, 202, 206, 213, 244–246, 256 ceramic matrix, 202–208, 255 elastic properties, 180, 185, 205, 266 foam reinforced, 213 hexagonal array model, 174, 177, 185 interpenetrating, 202–208, 213, 255 long (continuous)-fiber reinforced, 170, 185 metal-ceramic, 199, 207, 208, 236, 255 metal matrix, 9, 180, 190, 192, 202–208, 211, 218, 221, 226, 247, 254, 255 microlayered, 236 multilayered (see Multilayers) nanolayered, 236 particle reinforced, 177, 181–183, 211, 213, 218, 247, 253, 254, 267 phase contiguity, 202, 203, 255 plastic properties, 185, 190, 232 polymer matrix, 265 short-fiber reinforced, 180, 184 square array model, 187–190, 200 thermal expansion, 200–202, 207, 208, 212, 213, 255 unit-cell model, 174, 208, 254 viscoelastic matrix, 199, 213–219 Index

Upload: others

Post on 13-Jan-2020

11 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Index [rd.springer.com]978-1-4419-6312-3/1.pdf · Elastic deformation elastic constants (see Elastic constants) generalized Hooke’s law, 173 linear elasticity, 15, 25 strain energy,

275

AAl. See AluminumAlumina, 6, 7Aluminum

interconnect, 77, 87–90, 95, 96, 98, 99, 105–107, 111–113

properties, 9, 37, 38, 41, 47, 65, 71, 85, 87–90, 95, 100, 106, 111, 113, 115, 180, 190, 196, 197, 200, 201, 204, 205, 209, 244, 256

Aluminum alloyproperties, 197

Aluminum alloy 2080 T8properties, 197

Anisotropy, 33, 115Aspect ratio

fiber, 175, 180, 265line structure, 81, 89solder joint, 134unit-cell model, 175

Atomistic modeling, 110, 264Axisymmetric model, 30, 35, 37, 64,

172, 178, 180, 184, 195, 215, 232, 236, 237, 249, 257

BBack stress, 46Ball grid arrays, 6Barrier layers. See InterconnectBauschinger effect, 17, 44, 196BCB

properties, 85, 92Biological material, 265, 266Biomimetic material, 265Boltzmann’s constant, 58Bone, 265, 266Burger’s vector, 58

CC. See CarbonCarbon, 5, 99, 227Cementite, 227Ceramic matrix composite, 203–205, 208Chromium, 43Circuit board, 7, 8, 125, 149–150, 153, 155,

162, 163Coefficient of thermal expansion

of composites, 202, 203, 208Collagen

fibril, 265, 266Composite

Al/SiC, 179, 181, 185, 188, 194, 197, 201, 202, 206, 213, 244–246, 256

ceramic matrix, 202–208, 255elastic properties, 180, 185, 205, 266foam reinforced, 213hexagonal array model, 174, 177, 185interpenetrating, 202–208, 213, 255long (continuous)-fiber reinforced,

170, 185metal-ceramic, 199, 207, 208, 236, 255metal matrix, 9, 180, 190, 192, 202–208,

211, 218, 221, 226, 247, 254, 255microlayered, 236multilayered (see Multilayers)nanolayered, 236particle reinforced, 177, 181–183, 211,

213, 218, 247, 253, 254, 267phase contiguity, 202, 203, 255plastic properties, 185, 190, 232polymer matrix, 265short-fiber reinforced, 180, 184square array model, 187–190, 200thermal expansion, 200–202, 207, 208,

212, 213, 255unit-cell model, 174, 208, 254viscoelastic matrix, 199, 213–219

Index

Page 2: Index [rd.springer.com]978-1-4419-6312-3/1.pdf · Elastic deformation elastic constants (see Elastic constants) generalized Hooke’s law, 173 linear elasticity, 15, 25 strain energy,

276 Index

Composite material. See CompositeConstitutive model (behavior, response),

13, 20–21, 32–33, 56–57, 62, 70, 132–133, 161, 263–264, 267

Copperinterconnect, 77, 87, 90–95, 98,

99, 103, 104, 115, 116, 164properties, 85, 92, 95, 98, 100, 106, 111,

157Creep

activation energy, 21, 57mechanisms (see Deformation

mechanisms)power-law, 21, 58, 61steady-state, 21, 56stress exponent, 21, 57

CTE. See Coefficient of thermal expansionCu. See CopperCurvature

thermoelastic deformation of bi-layers, 25–28

wafer curvature method for stress measurement, 42, 43

Cu6Sn

5, 267

Cyclic deformationreversed yielding, 17, 18, 24, 207, 208

DDamage model, 267, 268, 271Damage parameter, 269Deformation

cyclic, 8, 126, 151, 152, 163, 164, 220–227, 241, 255

elastic (see Elastic deformation)incompressible, 15mechanisms (see Deformation

mechanisms)plastic (see Plastic deformation)rate-dependent (see Time-dependent

deformation)thermoelastic, 25–28, 52time-dependent (see Time-dependent

deformation)Deformation mechanisms

diffusional creep (flow), 18, 21, 59–62, 113, 114

dislocation glide, 21, 58power-law breakdown, 58power-law creep, 21, 58

Delamination, 6, 77, 155, 244Delrin

properties, 157Diamond, 65, 236–238

Dielectriclow-k (see Low-k dielectric)

Diffusional creep. See Deformation mechanisms

Discrete dislocation dynamics, 264Dislocations, 18, 21, 33, 43, 46, 57–59, 92,

110, 231, 264Dorn constant, 58Drucker model of constrained plastic

deformation, 183, 264Dual phase structure, 8Ductility, 220, 227–231

EElastic constants

biaxial modulus, 27, 39, 42, 46bulk modulus, 16, 200, 216indentation-derived, 65–69, 71,

231, 235, 237, 238, 246, 256, 257

plane strain modulus, 28, 30Poisson’s ratio, 3, 16, 25, 28, 29, 31, 37,

39, 47, 63, 65, 82–85, 128, 141, 148, 149, 170, 173–175, 179, 196, 197, 201, 215, 222, 229, 232, 237, 238, 249, 254, 267

relation for isotropic materials, 15shear modulus, 16, 58, 173, 200, 216Young’s modulus, 3, 16, 17, 25, 27,

29, 31, 37, 47, 63, 65, 66, 71, 82, 83, 128, 140, 148, 170, 172, 173, 175, 177, 179, 196, 197, 200, 201, 215, 222, 229, 232, 237, 238, 246, 249, 254, 267

Elastic deformationelastic constants (see Elastic constants)generalized Hooke’s law, 173linear elasticity, 15, 25strain energy, 16

Elasticity. See Elastic deformationElastic modulus. See Elastic constantsElastic shake-down, 194Electromigration, 6, 77, 85, 92, 95, 97, 109Electronic packaging

circuit board, 7, 8, 149–151, 153, 155, 162, 163

encapsulation (see Encapsulation)flip-chip package, 149heat sink, 6, 7, 125, 126, 163heat spreader, 125, 126solder (see Solder)solder joint (see Solder)thermal interface material, 125, 126, 163

Page 3: Index [rd.springer.com]978-1-4419-6312-3/1.pdf · Elastic deformation elastic constants (see Elastic constants) generalized Hooke’s law, 173 linear elasticity, 15, 25 strain energy,

277Index

underfill, 125, 147–155, 162, 163

Encapsulant. See EncapsulationEncapsulation

aging, 159–162properties, 157, 160viscoelastic response, 160

Epoxywith hollow-sphere fillers,

218–219mica filled epoxy resin, 156properties, 175, 215, 216silica filled epoxy resin, 214with solid fillers, 216–218

Equilibrium equations, 14Eutectic, 8, 134, 220, 227Eutectoid, 227

FFatigue, 6, 8, 39, 127, 140,

220, 225Fe. See IronFe

3C. See Cementite

Ferrite (in carbon steels), 227Ferrite core (in transformer)

properties, 156–162Finite element analysis

axisymmetric, 413D, 156, 203unit-cell model, 174, 175,

208, 254Finite element method.

See Finite element analysisFinite element model.

See Finite element analysisFlip-chip package, 149Free body diagram, 138

GGas constant, 21, 60Generalized Hooke’s law, 173Generalized plane strain, 38, 52,

70, 79, 81, 88, 111, 115, 171, 174, 175, 185, 208, 254

Glass fiberproperties, 175

Glass transition temperature, 22, 33

Grainscolumnar grains, 60, 61, 70grain size, 21, 42, 59, 62, 114, 263non-equiaxed grain structure, 87

HHall–Petch relation, 220Hardness

relation with yield strength, 233–236Hashin–Shtrikman bounds, 177,

179, 200Heat sink, 6, 7, 125, 126, 163Heterogeneity, 8, 169, 231, 253, 257Heterogeneous materials, 168–257Hooke’s law, 15Hydroxyapatite, 265Hysteresis loop, 18, 51, 54, 92,

195, 223

IInclusion particle, 196–198Indentation

coefficient of friction, 65, 233, 236, 249contact stiffness, 237, 247elastic modulus measurement, 63hardness, 63, 65–69, 71, 231, 232, 234,

236, 237, 244, 246indentation-induced damage, 244indenter (see Indenter)load–displacement curve, 63–65,

237, 238Oliver and Pharr method, 63pile-up, 64, 69, 233, 245plastic zone, 67, 68reduced modulus, 63, 65sink-in, 64, 233substrate effect, 65, 69, 244, 246, 247unloading, 63, 66–69, 237–241, 243, 244,

246, 247Indenter

Berkovich, 65, 232circular, 248conical, 64, 65, 232diamond, 65, 236–238rigid, 233, 249

Indicial notation, 13Interconnect

aluminum, 87–90, 105, 106, 111barrier layers, 90, 92, 98, 115copper, 90–95, 104, 1153D integration, 116L and T shaped, 95, 96, 115multilevel, 5, 6, 99, 116pre-existing debond, 107via, 99, 100, 116

Interfacedelamination (debond, decohesion), 6, 77sliding, 9

Page 4: Index [rd.springer.com]978-1-4419-6312-3/1.pdf · Elastic deformation elastic constants (see Elastic constants) generalized Hooke’s law, 173 linear elasticity, 15, 25 strain energy,

278 Index

Intermetallicinclusion particle in aluminum, 196layer in solder, 140, 267particle in solder, 229, 230

Interpenetrating composite, 203–208, 213, 255Iron, 196, 227Isostrain condition, 170, 176Isostress condition, 170Isotropic hardening, 17, 18, 69, 70, 163, 190,

208, 210, 237, 255Isotropy

transverse isotropy, 173, 254

JJoule heat, 125, 126

KKelvin-Voigt model. See Viscoelastic responseKerner model, 200Kinematic hardening, 17, 18, 44, 46, 69, 70,

90, 163, 164, 194, 196, 255Kronecker delta, 18

LLa. See LanthanumLanthanum, 227Lap-shear testing, 127, 129, 131, 137, 140,

162, 228, 267LaSn

3

properties, 228–230Lead, 8, 126, 140, 220–222, 225–227Lead(Pb)-free solder. See SolderLoad transfer, 138, 179, 183Low-k dielectric

air gap technology, 116BCB, 92, 94, 95, 99–105SiCOH, 99–105SiLK™, 93

MMaterial

biological, 265, 266biomimetic, 265choice of constitutive models, 13, 32–33,

62, 70, 263–264, 267classes of engineering materials, 32, 180,

208, 255natural, 265

Maxwell model. See Viscoelastic responseMEMS. See Microelectromechanical systems

Metal interconnect. See InterconnectMetal matrix composite, 9, 180, 190, 202–208,

211, 218, 221, 226, 247, 254, 255Microbeam

bending moment, 50, 52mechanical deflection, 48–52, 70thermal deflection, 52–54triangular beam configuration, 52

Microcrack, 141, 159, 225Micro-device. See Microelectronic deviceMicroelectromechanical systems, 1, 4, 48, 56,

125Microelectronic device, 1, 5–8, 90, 111, 116,

214Microelectronic packaging. See Electronic

packagingMicroelectronics, 4, 10, 77, 115, 125, 264, 265Micro-indentation. See IndentationMicromachine, 4–5, 78Micromachined cantilever beam.

See MicrobeamMicroprocessor, 5, 6, 77, 125, 126Microvoid, 141, 225, 271Mismatch

thermal expansion, 1, 5, 6, 8, 23–28, 35, 37, 40, 42, 52, 59, 77, 163, 198, 205, 214

Modulus. See Elastic constantsMultilayers

under indentation, 236, 244metal-ceramic, 231, 236–247, 256metal-metal, 231, 245, 256overall elastic response, 169–173, 232,

238, 243, 244, 246, 247, 254yield strength, 233

Multi-phase material, 8, 9

NNanoindentation. See IndentationNanolayered composite, 236, 244Natural material, 265

OOptoelectronics, 125Orthotropic material, 173, 204Osteon, 265

PParticle crowding, 252, 253Passivation, 40, 43, 54, 60, 87–89, 95, 98Pb. See Lead

Page 5: Index [rd.springer.com]978-1-4419-6312-3/1.pdf · Elastic deformation elastic constants (see Elastic constants) generalized Hooke’s law, 173 linear elasticity, 15, 25 strain energy,

279Index

Pearlite, 227Plastic deformation

Bauschinger effect, 17, 44, 196cyclic response, 52, 70, 194–196, 255equivalent (effective) plastic strain, 19, 20,

35, 37, 49, 53–55, 67, 87, 91, 95–97, 102, 141–143, 145, 146, 149, 151, 182, 183, 188, 197, 206, 207, 224, 225, 227, 229, 230, 239, 241, 251, 269–271

incremental flow theory, 19during indentation unloading, 241, 256isotropic hardening, 17, 18, 70, 163, 190,

208, 210, 237, 255kinematic hardening, 17, 18, 44, 46, 70,

90, 164, 194, 196, 255perfectly plastic, 16, 17, 30, 39, 40, 44, 66,

128, 141, 222, 229, 232, 236Ramberg-Osgood relation, 17strain hardening, 16, 17, 19, 20, 35, 43–47,

69–71, 92, 128, 181, 194, 195, 197, 242, 255, 256, 264, 267

strain hardening exponent, 17, 197strain rate hardening, 20, 144, 145, 268,

271strain rate sensitivity, 21stress–strain relation, multiaxial, 20stress–strain relation, uniaxial, 16–18, 20,

22, 28, 29, 45, 128, 141, 226, 227, 248–250, 268

viscoplastic response, 20–21von Mises yield criterion, 19, 30,

234, 240yield strength, 16–20, 30, 33, 39, 40,

42–45, 66, 71, 85, 135, 141, 143, 222, 224, 227, 229, 233, 237, 241, 255, 263, 267

Plasticity. See Plastic deformationPolyimide, 47, 48Polysulfide

properties, 157, 158Power electronics, 6, 7Printed circuit board. See Circuit board

QQuartz

properties, 43, 59, 60

RRaman spectroscopy, 78Ramberg-Osgood relation, 17Rare-earth element, 227

Rate-dependent deformation. See Time-dependent deformation

Reliability, 1–3, 5, 6, 8, 11, 78, 90, 95, 98, 110, 116, 126, 147, 156, 162, 163, 220, 263

Residual stress, 4, 5, 24, 69, 156, 190–195, 202, 204–208, 254, 255

Reuss model, 170Rigid body, 1Rule-of-mixtures, 174, 205, 231, 254

SSaint-Venant’s principle, 35Scanning electron microscopy, 4, 8, 140SEM. See Scanning electron microscopySemiconductor, 35, 116, 125, 163, 220Shake-down, 194Si. See SiliconSiC. See Silicon carbideSiCOH

properties, 85, 102–105Silica. See Silicon oxideSilica glass. See Silicon oxideSilicon

properties, 100, 111, 155Silicon carbide

properties, 9, 179, 236Silicon chip, 5–7, 116, 125, 126, 149–150,

162, 163Silicone coating

properties, 156, 157, 159, 160, 162

Silicon nitrideproperties, 4

Silicon oxideproperties, 4, 43, 82, 103

SiNx. See Silicon nitride

SiO2. See Silicon oxide

SiOx. See Silicon oxide

Sn. See TinSn-3.5Ag alloy, 128, 134, 136Sn-1.0Ag-0.1Cu alloy, 141, 145,

148, 267Sn-3Ag-0.5Cu alloy, 140, 141Sn-based solder

properties, 227, 229Sn-Pb alloy

colony, 221lamellar structure, 220–227Pb-rich phase (properties), 8, 220–222,

226, 227Sn-rich phase (properties),

224, 226

Page 6: Index [rd.springer.com]978-1-4419-6312-3/1.pdf · Elastic deformation elastic constants (see Elastic constants) generalized Hooke’s law, 173 linear elasticity, 15, 25 strain energy,

280 Index

Soldercracking (fracture, failure), 6–8, 77,

140–142, 220, 225, 267–271damage, 126, 140–142, 147, 149, 151, 220,

225–227, 230, 267–271deformation, 6, 8, 125–142, 144–154,

162–164, 220, 222, 229, 230, 267drop impact, 7, 8intermetallic layer, 140, 267lap-shear testing, 129, 131, 137, 140, 162,

228, 267lead (Pb)-bearing, 126lead (Pb)-free, 126plastic band (localization), 141, 142, 147,

163, 227Sn-3.5Ag, 128, 134, 136Sn-1.0Ag-0.1Cu, 141, 145, 148, 267Sn-3Ag-0.5Cu, 140, 141Sn-Pb (see Sn-Pb alloy)Sn-rich (Sn-based), 126, 140, 226, 227,

229, 269Solder joint. See SolderStandard linear solid model. See Viscoelastic

responseStoney’s equation, 40, 69Strain

dilatational, 15engineering expression for shear,

15, 127engineering strain, 30equivalent (effective) plastic strain,

20, 35, 37, 49, 53–55, 67, 70, 86, 87, 91, 93–97, 102, 107, 108, 115, 141–143, 145, 146, 148–153, 181–184, 186, 188, 189, 192, 193, 197, 199, 206, 207, 223–230, 239–242, 251, 268–271

generalized plane strain, 38, 52, 70, 79, 81, 88, 111, 115, 171, 174, 175, 185, 208, 254

infinitesimal, 13, 14plane strain, 2, 3, 15, 28, 30, 38, 52, 70,

79–81, 88, 111, 115, 128, 171, 174, 175, 185, 187, 188, 196, 197, 200, 202, 208, 221, 229, 249, 254, 255, 257, 267

true strain, 29, 30, 181, 191–193Strain energy density, 16Strain gradient plasticity, 264Stress

deviatoric, 18, 19, 23, 32, 87, 103engineering stress, 30equi-biaxial, 27, 39–43, 58, 59, 80, 81

hydrostatic, 16, 19, 23, 68, 88–92, 95–98, 100, 101, 104–108, 111–114, 142, 144, 157–159, 181–184, 191, 192, 205, 239–241, 271

maximum principal, 14, 31, 32, 103, 104, 153–155, 157–162

mean, 16plane stress, 15, 25, 27, 30, 49, 52, 70, 249principal, 14, 31, 32, 39, 240tensor, 13–15, 18, 19, 32, 103, 112true stress, 29, 30, 181, 191von Mises effective, 19, 31, 32, 38, 39, 47,

48, 70, 142, 144, 153–155, 223, 224, 241, 242, 268, 271

Stress gradient, 5, 52, 68, 87, 106, 109, 112, 113

Stress-induced voiding. See Stress voidingStress triaxiality, 271Stress voiding

saturation void fraction, 111–113void growth, 109, 113, 114, 116void nucleation, 92, 105, 271

Stretchable electronics, 47Structural hierarchy, 265, 266

TTa. See TantalumTaN. See Tantalum nitrideTantalum, 5Tantalum nitride

properties, 90, 115Thermal cycling, 61, 70, 90, 116, 141, 163,

209, 255Thermal expansion

bi-layers, 27, 52coefficient of (see Coefficient of thermal

expansion)of composites, 200, 202, 203, 205–208,

255strain-stress relation, 1, 28

Thermal management, 125, 163, 203Thermal oxide, 79Thermal residual stress, 190–195, 202,

204–208, 254, 255Thermo-mechanical fatigue, 140, 220, 225Thin film

on compliant substrate, 47–48continuous, 10, 35–71, 77–79, 81, 113etching, 79free-standing, 37, 47, 56, 264multilayers (see Multilayers)passivated, 40, 43, 44, 46, 55–57patterned, 10, 77, 84

Page 7: Index [rd.springer.com]978-1-4419-6312-3/1.pdf · Elastic deformation elastic constants (see Elastic constants) generalized Hooke’s law, 173 linear elasticity, 15, 25 strain energy,

281Index

stress in lines, 81, 82, 84, 90stress measurement by wafer curvature, 42unpassivated, 43, 60

Time-dependent deformationcreep, 6, 21–23, 113, 114strain rate hardening, 20strain rate sensitivity, 21stress relaxation, 22, 113, 114viscoelastic (see Viscoelastic response)viscoplastic, 20–21

TiN. See Titanium nitrideTin, 8, 126, 220Titanium nitride (TiN), 90Transformer

encapsulation (see Encapsulation)ferrite core, 156–162

Transistor, 5, 77Transverse isotropy, 173, 254Twin (twinning), 18, 46

UUnderfill, 125, 147–155Universal gas constant. See Gas constant

VVia. See InterconnectViscoelastic matrix Composite, 213

Viscoelastic responsecharacteristic relaxation time, 216Kelvin-Voigt model, 22, 23linear viscoelasticity, 2, 216Maxwell model, 22, 23nonlinear viscoelasticity,

160–162relaxed modulus, 216standard linear solid model, 23, 215unrelaxed modulus, 216viscosity, 22, 215

Viscoplastic response. See Plastic deformation

Voiding, 6, 77, 95, 97, 99, 101, 103, 105, 109, 111–114

Voigt model, 170von Mises effective stress, 19, 31, 32,

38, 39, 47, 48, 70, 142, 144, 153–155, 223, 224, 233, 241, 242, 268, 271

von Mises yield criterion, 30, 155

XX-ray diffraction, 47, 78, 92

YYielding. See Plastic deformation