ElectromigrationElectromigration

충북대학교 전자정보대학 김영석

2 11 92011.9

1

Ref: J. Lienig

Metal: Parasitic Resistance/CapacitanceSheet Resistance of Metal square/1.0 Ω≈

Typical Parasitic Capacitances of Metals

Typical parasitics in both long- and short-channel CMOS processes, Baker

전자정보대학 김영석 2

Metal: Signal DelayEx: Resistance and Delay of metal1 1mm long and 200nm wide

mR

nmnmwnmmml drawndrawn

50010001.0450/200,000,2050/1

Ω=⋅Ω

=

====μ

FF

CperimeterCareaCmsquare

fringeplate

/79)402000(/23)201000(

2.0

2

⋅+⋅=μ

psfFRCtfF

maFmmmaFmm

d 28162500350350162

/79)4.02000(/23)2.01000( 2

=⋅Ω⋅===

⋅++⋅⋅= μμμμμμ

psfFRCtd 2816250035.035.0 =Ω==

전자정보대학 김영석 3

Metal: Current LimitationsElectromigration: Too much current => Electrons Migrate

E 1

mmAJal μ/1=

Ex 1

AAWJIlIwm drawnμλ

150)150()/1()?,3 ,05.0 max ===

Ex 2

AmmmAWJIsol al μμμ 150)15.0()/1() max =⋅=⋅=

AIsol

Vcmlwm dropdrawn

150 )

? ,1 ,3 ,05.0

max =

====

μ

μλ

VAmmsquareIRVdrop 1150

15.0000,10/1.0max =⋅⋅Ω=⋅= μμμ

전자정보대학 김영석 4

Electromigration TheoryElectromigration Theory

5전자정보대학 김영석

Electromigration: DefinitionElectromigration is the forced movement of metal ions due to an electric field

금속에 전류가 흐를 때 일어나는 금속 이온의 이동 현상

6전자정보대학 김영석

Electromigration: HistoryDiscovered by Gerardin in 1861

Black’s equation to predict the Metal Failure in 1969

)exp()FailuretoTimeMean( EAMTTF a

Western Digital desktop drives in 1980s : Failure in a year or so

)exp()FailuretoTimeMean (kTJ

MTTF a

n

=

Western Digital desktop drives in 198 s : Failure in a year or so

=> Found Improper Design Rules in an IC controller

(Hard Disk Drives require 1 – 2 Amperes of Current)

7전자정보대학 김영석

Electromigration: TheoryFtotal = Fdirect + Fwind

Fdirect : Direct Electrostatic Force from the Electric Field

Fwind : Force on metal ions from momentum transfer from the conduction electrons (Electron Wind)conduction electrons (Electron Wind)

Fdirect << Fwind due to High Current conduction => Metal Atoms (Ions) go to the Anode

8전자정보대학 김영석

Electromigration: TheoryMass Balance Continuity Equation: describes the atom concentration evolution through some interconnect segment

0JN=⋅∇+

∂

fluxatomictotal:ionconcentrat atom:

0

JJJJJN

Jt

+++=

∇+∂

current electricby inducedflux atomic:

fluxatomictotal:

jkT

NqZDJ

JJJJJ

c

NTc

=

+++= σ

ρ

gradient by temp inducedflux atomic:2

ND

TkTNDQJT

Ω

⋅∇−=

gradiention concentratby inducedflux atomic:

stress mechnicalby inducedflux atomic:

NDJ

HkT

NDJ

N ⋅∇−=

⋅∇Ω

=σ

Electromigration due to Electric Field, Mechanical Stress, Thermal G adientGradient

9전자정보대학 김영석

Electromigration: TheoryEffects of Electromigration in Metal Interconnects

Depletion of Atoms (Voids)

• Slow reduction of connectivity

I t t F il• Interconnect Failure

Deposition of Atoms (Hillocks, Whisker)

• Short CutsShort Cuts

10전자정보대학 김영석

Black’s EquationMean time to Failure of a single wire due to electromigration

Black’s Emirical Equation

)exp()FailuretoTimeMean( EAMTTF a

A: Cross section area dependent constant

)exp()FailuretoTimeMean (kTJ

MTTF a

n

=

A: Cross section area dependent constant

Jn: Current density

Ea: Activation energy for electromigration

(0.7eV for grain boundary in aluminium)

K: Boltzmann constant

T: Ab l t t tT: Absolute temperature

Jn and T are Deciding Factors

11전자정보대학 김영석

Black’s Equation: DataJ=1x105A/cm2

=1mA/um

T=100

lif >10life>10year

12전자정보대학 김영석

Temperature Dependency of Max Current DensityA temp rise of 100K in Al reduces the max. Current Density by about 90%

13전자정보대학 김영석

Atomic TransportAl, Cu Interconnects are Polycrystalline, i.e., consists of Grains of Lattice

Atomic Transport occurs at metal-dielectric interface (surface), grain boundariesgrain boundaries

Grain, Grain Boundary, Triple Point

Triple point(1 inbound, 2 outbounds) : Void

T i le oint(2 inbound 1 outbounds) : HillockTriple point(2 inbound, 1 outbounds) : Hillock

14전자정보대학 김영석

Activation EnergiesAl

Ea,grain=0.7eV

Ea,bulk=1.2eV

E f 0 8 VEa,surface=0.8eV

Dominant Diffusion: Grain/Surface

CuCu

Ea,grain=1.2eV

Ea,bulk=2.3eV

Ea,surface=0.8eV

Dominant Diffusion: Surface

15전자정보대학 김영석

Electromigration-Aware DesignDesign

16전자정보대학 김영석

Maximum Tolerable Current DensitiesConventional metal wires (house wires)

Al ~ 19,100A/cm2

Cu ~ 30,400A/cm2

> R hi lti t t d t J l h ti=> Reaching melting temperature due to Joule heating

(Melting Temp of Al/Cu : 933K/1358K )

Metal Interconnet on ICs

Al ~ 200,000A/cm2

Cu ~ 1,000,000A/cm2

=> Reaching Failure due to Electromigration before reaching melting temperaturemelting temperature

/1:rationElectromig Alfor GuideDesign IC :Ex mmAJal = μ

22' /000,2005.0/1 5.0 thicknessmetal Assume

cmAmmAJm

al ==

=

μ

μ

17전자정보대학 김영석

Bamboo WiresSmaller Grains => Vulnerable to Electromigration

What if we reduce wire width < grain size ?

Resistive to Electromigration

B b Wi (N Wi ) G i B d i li di lBamboo Wires (Narrow Wires) : Grain Boundaries lie perpendicular to width => No boundary diffusion => Less Electromigration

18전자정보대학 김영석

Immortal Wires (Blech Length)High Current => Electromigration

But, length < Blech Length

Mechanical Stress by Hillcocks and Voids counteracts ElectromigrationElectromigration

19전자정보대학 김영석

Wires and Vias and Corner BendsAl Wire width < 1mA/um

Current Density of Tungsten Via is higher => Use Multiple Vias

Multiple Vias must be organized such that resulting current is distributed as evenly as possibledistributed as evenly as possible

Avoid 90-degree corner bends : use 135-degree bends

20전자정보대학 김영석

EM-Aware (Analog) Physical Design Flow

21전자정보대학 김영석

EM-Aware (Analog) Physical Design FlowCurrent-Driven Routing

Routing with current-correct wire widths and via sizes

Minimization of wire area

C t D it V ifi tiCurrent-Density Verification

Automatic verification of actual current densities within arbitrarily shaped layout structuresy p y

Current-Driven Layout Decompaction

Post-routing adjustment of layout segments according to their t l d itactual density

Homogenization of the current flow

22전자정보대학 김영석

SummaryElectromigration: Migration of atoms due to momentum transfer from conduction electrons

Al : Grain Boundary Diffusion, Cu : Surface Diffusion

Decisive Factors to ElectromigrationDecisive Factors to Electromigration

Current Density

Temperaturep

Soutions

Cu instead of Al : Jmax(Cu) ~ 5*Jmax(Al)

Bamboo Structures, Blech Length

23전자정보대학 김영석