Index
analytical model, 76–7
ANSYS, 16
antireflective coating, 218
Arrhenius temperature dependence, 7
atomic flux, 73
atomic layer deposition, 215
back-end-of-line metal layer, 214
back-end-of-line process, 159
Black’s Law, 175
Blech condition, 305–6
Blech equation, 103
Blech product, 12
Bragg monochromatic diffraction, 79
Bragg’s Law, 140
Cahn-Hilliard equation, 34
Cahn-Nye crystal bending model, 156
charge-couple device (CCD), 138
classical continuum modeling, 47–8
‘coincident site lattices, ’, 249
microstructural changes, 143–58
active slip system, slip deformation modeling in grain 2, subgrain boundary formation, 156
Cu electromigration test structures by Intel Corporation, 146
deviatoric stress versus temperature graphs suggest plastic deformation, 154
electromigration loading, 149–52
EM-induced plastic deformation in Al(Cu) interconnects, 153
experimental, 145–7
fluorescence mapping, 147
grain orientation mapping, 1.6 μm passivated Cu lines, using synchrotron-based X-ray microdiffraction, 148
in-plane orientation effects, 154–8
initial microstructure, 147–9
Laue diffraction spots evolution, 150
Laue reflection spots, 155
linewidth effects, 152–4
plastic deformation axis, electron flow direction in crystal, 157
quantitative measurement, 151
scanning white-beam X-ray microdiffraction experiment diagram, 146
inflated current density exponent n, 176–82
Joule heating effect versus electromigration-induced plasticity, 179–82
microstructure evolution and electromigration, 135–84
electromigration-induced microstructural changes, 143–58
future trends, 184
plasticity and materials degradation mechanisms, 158–74
reliability, 175–84
synchrotron-based scanning X-ray submicron diffraction (mSXRD), 137–43
plasticity-amplified diffusion in electromigration, 168–74
bamboo grains illustration with dislocation cores, 169
calculated diffusivities as temperature function between interface diffusion path and dislocation cores, 173
Cu interconnects diffusion values, 173
diffusivities comparison as temperature function, 172
grain boundary diffusion values, 170
grain containing same-sign edge dislocations, 168
materials degradation mechanisms, 172–4
parameters/terms values, 171
plasticity and materials degradation mechanisms, 158–74
electromigration-induced microstructural changes in Cu interconnects: texture effects, 159–68
plasticity-amplified diffusion in electromigration, 168–74
reliability, 175–84
current exponent n illustration, extrapolated lifetime impact, 183
EM test data/results from Cu interconnect lines, 178
EM test results, 181
inflated current density exponent n, 176–82
Kirchheim and Kaeber’s experimental MTF data, 177
overestimating device lifetime danger, 183–4
scaling effects on electromigration reliability, 190–208
effect of via scaling on EM reliability, 194–200
future trends, 206–8
mass transport during electromigration, 193–4
methods to improve EM lifetime, 202–5
multi-linked statistical tests for via reliability, 200–3
texture effects, 159–61
Cu Laue diffraction spots and typical densities of GNDs, 165
experimental, 159–61
in situ electromigration experiments, 162
Laue diffraction images, cathode end of line after 36h testing, 163
plasticity, 161–5
SEM images and schematic drawings, Cu interconnect test structures, 160
space/contour intensity plot of dielectric effects, 164
texture comparison, Cu lines, 167
texture effects, 165–8
voiding during electromigration, 113–132
future trends, 130–2
immortality, 125–30
void growth, 117–25
void nucleation, 114–17
X-ray microbeam analysis, 97–112
electromigration-induced strains in conductor lines, 103–8
samples and X-ray microdiffraction methods, 100–3
covergent-beam electron diffraction, 98
critical stress, 116
crystal bending, 143
crystal polygonisation, 143
Cu/dielectric cap interface, 122–3
Cu/metal cap interface, 122–3
current-carrying conductor, 56
‘damascene’ approach, 213
defective element, 66
diffuse interface approach, 34–6
dissolution, 279–82
drift velocity equation, 224
‘dual-damascene’ integration scheme, 214
dual damascene process, 100
Einstein-Nernst diffusion equation, 53
electric current, 54
electrical resistance, 291–2
electrodeposition, 100
EM-induced strains in conductor lines, 103–8
average deviatoric strains, EM and Cu control lines, 107
Cu line resistance at various temperatures, 108
deviatoric strains in EM-1 line after 120 and 123 h current stressing at 270 °C, 106
electron wind force and back flow strain gradient, 103–4
measurements in Cu conductor lines, 105–7
passivation layers role, 104–5
root mean square (RMS) deviations, deviatoric strains, EM lines and control lines, 107
strain evolution comparison, Al and Cu conductor lines, 107–8
thermal interplay, 105
Eshelby and 2D finite-element model findings, 83–90
2D approximate models, Eshelby model and finiteelement model geometry, 83
electromigration-induced volumetric strain distribution, 87
measured deviatoric, elastic strains comparison, 88
measured elastic, out-of-plane strain comparison, 89
measured vs predicted directions of deviatoric and elastic strain, 85
Wang et al. (1998) data results, 90
Wang et al. (1998) experiment findings, 89–90
Zhang et al. (2008) experiment findings, 83–9
experimental, modeling, simulation findings, 79–90
experiments, 79–82
measured elastic deviatoric strain components, 82
measured elastic strain comparison, 81
schematic cross-section, two AI lines, 80
failure in nanoscale copper interconnects, 211–50
flip-chip solder joints, 285–323
advanced electronic packaging, 285–6
future trends, 322–3
high current density applications, 286–8
Joule heating-enhanced dissolution, 294–303
review scope, 289
stress-related degradation, 303–12
thermomigration behavior under a thermal gradient, 312–19
voiding failure, 289–94
future trends, 130–2
interconnect dimension shrinkage, 130
low-k dielectrics, 130–2
reservoir effects at cathode end, 131
immortality, 125–30
criteria, 125–7
SEM cross-section image of void formation, 129
short length effects in copper interconnects, 127–30
straight via-to-via line with void nucleation, 128
straight via-to-via line without void nucleation, 126
microstructural evolution of lead-free and lead-tin solders, 271–82
dissolution and recrystallisation, 279–82
grain reorientation and rotation, 278–9
intermetallic compound formation, 272–4
void formation, 274–7
whisker and hillock formation, 277–8
microstructure evolution of copper interconnects, 135–84
electromigration-induced microstructural changes, 143–58
future trends, 184
plasticity and materials degradation mechanisms, 158–74
reliability, 175–84
synchrotron-based scanning X-ray submicron diffraction (mSXRD), 137–43
modeling, simulation and X-ray microbeam studies, 70–91
approaches, 73–9
experimental, modeling, simulation findings, 79–90
modeling and simulation approaches, 73–9
analytical model, 76–7
finite-element model, 77–9
governing equations, 73–6
three possible diffusion paths illustration, 75
motivation for PD application, 46
PD applicability, 46
samples and X-ray microdiffraction methods, 100–3
copper conductor line samples, 100
Cu line, optical and SEM image, and schematic sketch crosssection, 101
Cu line SEM image and Cu fluorescence map, 102
polychromatic X-ray beam in X-ray microdiffraction experiments, 102
strain measurements, 100–3
white beam deviatoric strain measurements uncertainties, 103
X-ray microbeam diffraction and heating stage, 102
X-ray microdiffraction experiments, 100
synchrotron-based scanning X-ray submicron diffraction (μSXRD), 137–43
void growth, 117–25
mechanisms, 119–22
metal capping layer effect, 122–3
pre-existing voids effects in copper interconnects, 123–5
SEM images of 0.61μm and 2.25μm wide fabricated Cu interconnects, 124
SEM images of unpassivated Cu interconnects showing edge displacement void growth, 121
SEM images of unpassivated Cu interconnects showing surface grain thinning, 120
TEM cross-section image of Cu interconnect coated with CoWP capping layer, 123
theory, 117–19
void nucleation, 114–17
Al and Cu interconnect architecture, 115
aluminium and copper interconnects differences, 116–17
SEM cross-section images of failed 0.2μm-wide SiN-capped Cu interconnects, 118
theory, 114–15
times-to-failure for 0.2μm and 0.6μm-wide SiN-capped Cu interconnects, 117
voiding, copper interconnects, 113–132
future trends, 130–2
immortality, 125–30
void growth, 117–25
void nucleation, 114–17
X-ray microbeam analysis, copper interconnects, 97–112
electromigration (EM)-induced strains in conductor lines, 103–8
Laue white beam X-ray diffraction pattern from Cu grain, 99
samples and X-ray microdiffraction methods, 100–3
SEM images, Cu conductor line after EM test, 98
electromigration driving force, 6
electromigration modeling, 3–39
analytical methods, 5–15
apparent n value evolution with experimental j × L conditions, 14
Blech effect, 11–13
drift velocity evolution with current density, 15
interconnect line length distribution, 15
lifetime prediction method consequences, 13–15
mass transport equation, 5–11
relative vacancy concentration distribution at different diffusion time, 8
SEM observation of void size evolution, 13
stress build-up for different time steps, 10
void cross-section via 3 metal 3 interconnect, 6
diffusion path application and texture effects, 28–30
model and boundary conditions, 28–9
results, 29–30
morphological void evolution, 30–8
diffuse interface approach, 34–6
sharp interface approach, 31–4
void growth application, 36–8
numerical methods, 15–38
diffusion path application and texture effects, 28–30
dynamical void growth, 17
hydrostatic stress evolution in 20μm length copper line, 25
hydrostatic stress evolution in 200μm length copper line, 25
mechanical constitutive equation, 20–3
morphological void evolution, 30–8
N concentration evolution, 26
real circuit layout case application, 26–7
resistance evolution during copper interconnect electromigration testing, 18
resistance evolution during electromigration test, 37
schematic illustration of boundary conditions, 23
simplified power grid layout illustration, 27
stress evolution equation of metal lines, 23–6
vacancy concentration evolution, 30
vacancy concentration field, 29
vacancy profile comparison, single metal line and power grid case, 27
vacancy transport constitutive equation, 18–20
void cross-section in copper, simulated void growth sequence, 37
void escaping from grain boundary, 34
void surface area evolution, 33
von Mises component map, 28
peridynamics approach, 45–68
classical continuum modeling and EM, 47–8
comparison and contrast to MD, 51–3
computational requirements, 63–7
constitutive parameters and temperatures used in calculations, 60
differential volumes interaction, 50
EM master equation, 53–4
enhanced optical images of copper, 57
examples, 56–63
finite element modeling, 48
mathematical basics, 49–51
mathematical specifics, 55–6
microelastic PD model for quasibrittle material, 51
modeling assumptions, 54–5
molecular dynamics (MD) and EM, 47
multiphysics fields and equations for PD, 52
PD model calculation results, 62
PD model reasons, 48
scanning electron micrographs, open circuit induced by EM, 46
SEM micrograph of wide copper damascene line, 57
voltage and temperature variation of modeled conductor, 61
stress evolution equation, metal lines, 23–6
model and boundary conditions, 23–4
results, 24–6
electron backscattering diffraction, 98
electron microscopy techniques, 139
‘electron wind, ’, 212
electron wind force, 287
EM lifetime, 206
energy dispersive X-ray spectroscopy, 56
equilibrium mechanical equation, 20
Eshelby inclusion theory, 77
extreme ultraviolet (EUV) lithography, 137
Fickian diffusion, 6
finite difference method, 32
EM, 48
advanced electronic packaging, 285–6
variation in pad diameter, pitch and line width, 286
electromigration, 285–323
high current density applications, 286–8
challenges in assembly and packaging, 287
Joule heating-enhanced dissolution, 294–303
current stressing, 294–5
solder interconnect melting due to aluminium diffusion, 296–303
UBM layers dissolution, 295–8
stress-related degradation, 303–12
characteristics of solder strips, 306
fractographs of Sn3.5Ag1.0Cu solder joints, 311
hillock and valley formation in tin-lead solder joint, 304
marker movement and stress gradient as a function of location, 307
mechanical deformation and degradation under current stressing, 308–12
modulus variation of Sn3.5Ag1.0Cu solder joints, 309
morphology, 303–8
SEM image of solder joints after mechanical shear testing, 310
U field fringe of an Sn4Ag0.5Cu solder joint, 308
V field fringe of an Sn4Ag0.5Cu solder joint, 309
whisker growth at the anode, 305
thermomigration behaviour under a thermal gradient, 312–19
tin-based lead-free solder interconnects, 317–19
tin-lead solder interconnects, 312–17
voiding failure, 289–94
EM reliability parameters, 294
lifetime statistics and EM reliability, 292–4
nucleation and void growth, 289–92
SEM image of Sn3.5Ag1.0Cu solder joints, 290
variation in voltage as a function of time, 292
Weibull cumulative distribution, 293
focused ion beam method, 317
Fourier thermal equation, 20
Fourier transform, 67
geometrically necessary dislocations, 140
grain reorientation, 278–9
grain rotation, 278–9
Green’s function method, 63–4
inter-layer dielectrics, 159
interconnect signal latency, 219
intermetallic compound formation, 272–4
AuSn4 formation, 274
polarity effect during current stressing, 273
International Technology Roadmap for Semiconductors, 285
current stressing, 294–5
thermal infrared measurement for the chip side, 295
solder interconnect melting due to aluminium diffusion, 298–303
current density distribution in the Al interconnect, 302
elemental mapping of the interface between a solder and UBM, 299
SEM image of Sn3.5Ag1.0Cu solder joints, 301
UBM layers dissolution, 295–8
Cu pillar bump with solder cap, 297
elemental mapping at the UBM/IMC interface in a Sn3Ag1.5Cu solder joint, 296
Laue white-beam diffraction, 79
dissolution and recrystallisation, 279–82
recrystallised Zn nanosheet grains in a Sn9Zn solder after current stressing, 281
microstructural evolution, 271–82
grain reorientation and rotation, 278–9
intermetallic compound formation, 272–4
AuSn4 formation, 275
polarity effect during current stressing, 273
void formation, 274–7
simulated resistance change, 276
whisker and hillock formation, 277–8
line edge roughness (LER), 218
‘M1, ’, 214
mass transport equation, 5–11
mean time to failure, 292
median time to failure, 175
metallic corrosion shorting, 212
molecular dynamics, 47
Monte Carlo simulation, 200
Moore’s law, 130
Nabarro–Herring model, 304–5
blocking rate-limiting EM pathways, 236–45
Cu interconnect coated with CoWP, 238
expected lifetime trending using ITRS-2009 parameters, 243
post-EM analysis of Cu interconnect with CoWP capping, 240
SiNx capped dielectric over Cu metal, 239
copper microstructure impact, 245–50
microstructure development in damascene copper interconnects, 245–7
microstructure impact on copper EM, 247–50
electromigration failure, 211–50
electromigration scaling by generation, 220–36
calculated drift velocities for hypothetical 32 nm interconnect, 234
estimated atomic fraction for given EM pathway as function of technology node, 230–1
exploded view of major EM pathways, 227
grain boundary angles and averaged grain sizes with interconnect microvolume, 229
pathway dependent Cu electromigration diffusion and kinetic parameters, 232
relative impact of critical void volume on EM lifetime, 226
void formation at the cathode end must reach certain size to generate interconnect failure, 225
process solutions being developed, 211–20
canonical copper interconnect and technology scaling, 212–15
copper-based interconnect technology, 211–12
dual-damascene interconnect structure, 213
expected interconnect resistivity as function of technology node, 217
issues and evolution of canonical copper interconnect, 215–20
ITRS values used to predict EM drift velocities at each technology node, 216
suppression by metal capping, 220–45
Nernst–Einstein equation, 272
Nernst–Einstein relation, 223
passivation layers, 104–5
peak streaking, 143
peridynamics, 49–53
computational requirements, 63–7
Green’s function method, PD model of EM computational efficiency, 63–4
mathematical application of causal Green’s function, 64–7
electromigration modeling, 45–68
classical continuum modeling and EM, 47–8
comparison and contrast to MD, 51–3
computational requirements, 63–7
EM master equation, 53–4
examples, 56–63
finite element modeling, 48
mathematical basics, 49–51
mathematical specifics, 55–6
modeling assumptions, 54–5
molecular dynamics (MD) and EM, 47
PD model reasons, 48
examples, 56–63
PD model implementation, 58–63
problems, 56–8
Poisson coefficient, 16
Poisson’s ratio, 77
effects on electromigration reliability of copper interconnects, 190–208
effect of via scaling on EM reliability, 194–200
EM test structures schematic, 195
future trends, 206–8
mass transport during electromigration, 193–4
normalised EM lifetime as function of cross-sectional area of Cu line, 190
progressive and abrupt resistance increases for typical single-linked downstream EM test structure, 195
ratio of median lifetime for each technology node relative to 0.13 μm technology, 207
EM lifetime and failure mode with downstream electron flow, 195–8
CDF plots of single-linked downstream EM tests of 125 and 175 nm wide M1 lines, 197
CDF plots of single-linked downstream EM tests of M1 lines with different widths, 197
EM-failed sample in downstream tests with line width of 125 nm, 197
void formation for downstream electron flow, 196
EM lifetime and failure mode with upstream electron flow, 198–200
large cathode void in M2 trench, 200
resistance traces of 90 nm wide EM samples in upstream EM test, 199
resistance traces of 125 nm wide EM samples in upstream EM test, 199
methods to improve EM lifetime, 202–5
CDF plots of M2 Cu interconnects with different caps, 203
different Cu/cap interfaces, 204
EM failed samples showing different voiding locations, 205
normalised resistance traces for large grain and CoWP capped samples, 205
typical resistance traces of mode I and mode II failures, 204
multi-linked statistical tests for via reliability, 200–3
CDF plots of upstream EM test structures as function of line width, 201
EM lifetime data for upstream M2 electron flows, 202
scanning electron microscopy (SEM), 56
selective electroless deposition (SED), 237–8
sharp interface approach, 31–4
SiGexNy process, 242
silicidation, 242
Soret effect, 224
steady-state stress gradient, 104
stochastic model, 15
stress gradient, 54
stress-migration, 211–12
synchrotron-based scanning X-ray submicron diffraction (mSXRD), 137–43
beamline 7.3.3 experimental endstation, 139
beamline 7.3.3 schematic layout, 139
beamline components and layout, 138–40
crystal bending, polygonisation and rotation, 142–3
crystal planes set in undeformed, bent/curved polygonised states, Laue diffraction peaks, in CCD detector space, 142
side view, experimental setup with 2-D CCD detector, 140
single white-beam CCD image, multiple sets of Laue diffraction peaks from Cu polycrystalline, 141
two crystal bodies in undeformed, bent/curved polygonised states, laue diffraction peaks, in CCD detector space, 144
white beam mSXRD as local plasticity probe, 140–2
synchrotron X-ray microdiffraction, 136–7
system-on-chip (SOC) integration, 220
tetraethyl erthosilicate (TEOS), 215
thermal strain, 105
thermomigration, 288
solder interconnect under thermal gradient, 312–19
tin-based lead-free solder interconnects, 317–19
tin-lead solder interconnects, 312–17
time-to-failure, 292
thermomigration, 317–19
line-type test structure, 320
micrograph of a Sn3.5Ag solder joint, 318
SEM images of Ni/Sn58Bi/Cu solder joints, 321
thermomigration, 312–17
SEM images of a row of tin-lead solder joints, 313
SEM images of cross-sectional planes for unpowered solder joints, 316
temperature distribution before current stressing, 315
transmission electron microscopy (TEM), 79
‘TRUNC()’ See truncation function
truncation function, 228
under bump metallurgy, 272
Joule heating-enhanced dissolution, 294–303
current stressing, 294–5
solder interconnect melting due to aluminium diffusion, 298–303
UBM layers dissolution, 295–8
vacancy concentration, 8
vacancy exchange mechanism, 5
void formation, 274–7
application, 36–8
simulated resistance change, 276
void growth theory, 117–19
void nucleation theory, 114–15
voiding, 56
copper interconnects, 113–132
future trends, 130–2
immortality, 125–30
void growth, 117–25
void nucleation, 114–17
voiding failure, 289–94
EM reliability parameters, 294
lifetime statistics and EM reliability, 292–4
nucleation and void growth, 289–92
SEM image of Sn3.5Ag1.0Cu solder joints, 290
variation in voltage as a function of time, 292
Weibull cumulative distribution, 293
X-ray diffraction (XRD) technique, 137
electromigration, copper interconnects, 97–112
electromigration (EM)-induced strains in conductor lines, 103–8
samples and X-ray microdiffraction methods, 100–3
X-ray microbeam modeling and simulation, electromigration, 70–91
approaches, 73–9
experimental, modeling, simulation findings, 79–90
X-ray microbeam simulation and modeling, electromigration, 70–91
approaches, 73–9
experimental, modeling, simulation findings, 79–90
X-ray microdiffraction analysis software (XMAS), 142
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