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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