electromigration.ppt [호환 모드] -...
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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