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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
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
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
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
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
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
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
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