C
Cahn-Hilliard equation,
34
Cahn-Nye crystal bending model,
156
charge-couple device (CCD),
138
chemical mechanical polishing, ,
100,
214
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
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
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
plasticity and materials degradation mechanisms,
158–74
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
current exponent
n illustration, extrapolated lifetime impact,
183
EM test data/results from Cu interconnect lines,
178
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
mass transport during electromigration,
193–4
methods to improve EM lifetime,
202–5
multi-linked statistical tests for via reliability,
200–3
Cu Laue diffraction spots and typical densities of GNDs,
165
in situ electromigration experiments,
162
Laue diffraction images, cathode end of line after 36h testing,
163
SEM images and schematic drawings, Cu interconnect test structures,
160
space/contour intensity plot of dielectric effects,
164
texture comparison, Cu lines,
167
voiding during electromigration,
113–132
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
crystal polygonisation,
143
Cu/dielectric cap interface,
122–3
Cu/metal cap interface,
122–3
current-carrying conductor,
56
E
Einstein-Nernst diffusion equation,
53
electrical resistance,
291–2
electrochemical deposition,
213,
246
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
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
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
advanced electronic packaging,
285–6
high current density applications,
286–8
Joule heating-enhanced dissolution,
294–303
stress-related degradation,
303–12
thermomigration behavior under a thermal gradient,
312–19
interconnect dimension shrinkage,
130
reservoir effects at cathode end,
131
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
whisker and hillock formation,
277–8
microstructure evolution of copper interconnects,
135–84
electromigration-induced microstructural changes,
143–58
plasticity and materials degradation mechanisms,
158–74
synchrotron-based scanning X-ray submicron diffraction (mSXRD),
137–43
modeling, simulation and X-ray microbeam studies,
70–91
experimental, modeling, simulation findings,
79–90
modeling and simulation approaches,
73–9
finite-element model,
77–9
governing equations,
73–6
three possible diffusion paths illustration,
75
motivation for PD application,
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
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
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
times-to-failure for 0.2μm and 0.6μm-wide SiN-capped Cu interconnects,
117
voiding, copper interconnects,
113–132
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,
electromigration modeling,
3–39
apparent
n value evolution with experimental
j ×
L conditions,
14
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,
SEM observation of void size evolution,
13
stress build-up for different time steps,
10
vacancy accumulation at cathode, ,
11
void cross-section via 3 metal 3 interconnect,
diffusion path application and texture effects,
28–30
model and boundary conditions,
28–9
morphological void evolution,
30–8
diffuse interface approach,
34–6
sharp interface approach,
31–4
void growth application,
36–8
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
enhanced optical images of copper,
57
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
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
electron backscattering diffraction,
98
electron microscopy techniques,
139
energy dispersive X-ray spectroscopy,
56
equilibrium mechanical equation,
20
Eshelby inclusion theory,
77
extreme ultraviolet (EUV) lithography,
137
F
finite difference method,
32
finite element method,
16,
105
advanced electronic packaging,
285–6
variation in pad diameter, pitch and line width,
286
high current density applications,
286–8
challenges in assembly and packaging,
287
Joule heating-enhanced dissolution,
294–303
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
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
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
N
Nabarro–Herring model,
304–5
nanoscale copper interconnects
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
S
effects on electromigration reliability of copper interconnects,
190–208
effect of via scaling on EM reliability,
194–200
EM test structures schematic,
195
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
steady-state stress gradient,
104
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