Post on 19-Feb-2021
Interaction of electric field on metal ions
Force on metal ions (Cu+) resulting from momentum transfer from the conduction electrons
Anode+
Cathode-
E-
-
-
Cu+-
Fwind Ffield
Hillocks
Voids
Grain boundaries
Whiskers
Metal2 Cu
Metal1 Cu e
Via Depletion
Ta/TaNliner layer
Low-kdielectric
SiN, NSiCcap layer
Void
Metal2 CuTa/TaNliner layer
Low-kdielectric
SiN, NSiCcap layerMetal1 Cu
e
Line Depletion
Void
Growth of voids
Increase of local current density
Increase of Joule heating
Increase of temperature
Stress Migration
due to mechanical stress
Thermal Migration
due to thermal gradient
Electrolytic electromigration Solid state electromigration
Migration in Solid-State Materials
Electromigration
due to electrical field
Solid-state electromigration
Chemical Diffusion
due to concentration gradient
-(a) (b)
(c)
0,01
0,1
1
10
100
-40 0 25 60 80 100 125 150 175
Temperature T [Celsius]
Consumer electronics
Automotive electronics
Jmax(T) / Jmax(T = 25°C Jmax(T) compared to Jmax(Tref = 25°C) acc. Eq. (2.1)
(c)(a) (b)
Min. Max.
Current density
Amorphous
Polycrystalline
Near-bamboo
Bamboo
Monocrystalline
No crystal lattice or grain boundaries
Grain boundaries dominate
Featuring both crystal lattice and grain boundaries
Crystall lattice dominates
Crystall lattice and lattice defects define characteristics
Diffusion process Activation energy in eV
Aluminum Copper
Bulk diffusion 1.2 2.3
Grain-boundary diffusion 0.7 1.2
Surface diffusion 0.8 0.8
Triple pointBlocking
grain
(a) Dielectric deposition (b) Trench etching
(c) Metal deposition (d) Metal removal
Silicon substrate
Dielectric (e.g., SiO2)
Dielectric (e.g., SiO2)
Metal(Cu)
Surface coatingDielectric cap
Diffusion barrierMetal liner
Example Frequency
Controlling the background lighting for a computer screen 10 mHz
Frame rate on a PC monitor 60 Hz
Sampling frequency for audio signals 44 kHz
Carrier frequency for radio frequency identification (RFID) 13.56 MHz
Processor clock frequency 3 GHz
MTF (AC)MTF (DC)
103
102
101
10010
-2
10-1
100
101
102
103
104
105
106
107
108
Frequency in Hz
Structural widthSkin depth
2016 2020 2024Year
10-5
10-6
10-7
Size
in m
10-8
10-9
Cu
Dielectric (e.g., SiO2)
T
Vacancy
Atom
σ
Vacancy
Atom
Tensile stressCompressive stress
a
b
Vacancy
Atom
Tensile stress Compressive stress
a
b
Vacancy
Atom
Tensile stress Compressive stress
D
∆c
c
TM
SM
EM
T
σ
j
− +EMTM
SM
T
σ
Vacancy
Atom
Tσ
− +EMTM
SM
Current (e−)
Via
Void
Current (e−)Void
a
TSV
VoidCurrent (e−)
b
Alternating CurrentVoid
c
Die 2
Die 1 TSV
Mechanicalfailure
Mobility changes
Φ1, j1 Φ3, j3
Φ4, j4
Φ2, j2
Φ5, j5
I1,2
ModelLayout
I2,4
I4,5
I2,3
ModelLayout
Clock frequencyProblem size
Rel
ativ
e ch
ange
1
10
20
30
40
2016 2018 2020 2022 2024 2026
Year
Technology
PatternLibrary
Simulation(FEM)
Schematic
Placement,Routing, …
Circuit Layout
Physical Design
0 3.31.1 2.2
j / j0
0 3.31.1 2.2
j / j0
0.97 1.031.0
j / j0
Current density
Atomic flux
Flux divergence
Mechanical stress
Steady state Void nucleation
Lifetime
Void growth
Check for limit
Basic currentdensity simulation
Void growthsimulation
Atomic fluxsimulation
Incorporation ofmechanical stress
-1.0 1.00
ΔJ / ΔJmax
e–
Metal 1
Via
Metal 2
-1.0 1.00
σ / σmax
σ / σmax
x in µm
Metal
Conductive Stripe
-1.0 1.00
σ / σmax
σ / σmax
x in µm
Metal
Conductive Stripe
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