fatigue damage in solder joint interconnects - presentation

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Fatigue damage modeling in solder interconnects using a cohesive zone approach Adnan Abdul-Baqi, Piet Schreurs, Marc Geers AIO-Meeting: 03-06-2003 Supported by Philips

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Page 1: Fatigue damage in solder joint interconnects - presentation

Fatigue damage modeling in solder interconnects

using a cohesive zone approach

Adnan Abdul-Baqi, Piet Schreurs, Marc Geers

AIO-Meeting: 03-06-2003

Supported by Philips

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Page 2: Fatigue damage in solder joint interconnects - presentation

Outline

• Introduction

• Geometry and loading

• Cohesive zone method:

– Cohesive zone formulation

– Cohesive tractions

– Damage evolution law

– One dimensional example

• Results:

– Damage distribution

– Corresponding total effective damage and reaction force

– Life-time prediction in comparison with empirical models

• Conclusions

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Page 3: Fatigue damage in solder joint interconnects - presentation

Printed circuit board (PCB)

• Solder joints providemechanical& electricalconnection between the siliconchip and the printed circuit board.

• Repeated switching of the device→ temperature fluctuations→ fatigue of thesolder joints→ device failure.

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Page 4: Fatigue damage in solder joint interconnects - presentation

Solder bump

• Interconnects failure contributes by up to20 % to device failure.

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Page 5: Fatigue damage in solder joint interconnects - presentation

Tin-Lead solder

Typical Tin-Lead microstructure (A. Matin).

• Simplified microstructure is chosen for the simulations:

– Physically: rapid coarsening→ continuous change.

– Numerically: Large number of degrees of freedom→ time consuming.

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Page 6: Fatigue damage in solder joint interconnects - presentation

Geometry and loading: solder bump

x

0.1

mm

0.1 mmx

y

U

Lead

Tin

• Plane strain formulation, thickness= 1 mm.

• Elastic properties:Tin (E = 50 GPa,ν = 0.36), Lead(E = 16 GPa,ν = 0.44) .

• Loading: cyclic mechanical withUmaxx = 1µm.

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Page 7: Fatigue damage in solder joint interconnects - presentation

Cohesive zone method: cohesive zone?

continuum element

1 2

3 4

∆ cohesive zone

continuum element

t

n

• Cohesive zones are embedded between continuum elements.

• Constitutive behavior: specified through a relation betweentheseparation∆ (initially = 0) and a correspondingtractionT(∆).

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Page 8: Fatigue damage in solder joint interconnects - presentation

Cohesive zone method: stiffness matrix and nodal force vector

• The cohesive zone nodal displacement vector is constructed in the local frameof reference (t,n):

uT = {u1t , u

1n, u

2t , u

2n, u

3t , u

3n, u

4t , u

4n}.

• The relative displacement vector∆ is then calculated as:

∆ =

∆t

∆n

= Au

whereA is a matrix of the shape functions:

A =

−h1 0 −h2 0 h1 0 h2 0

0 −h1 0 −h2 0 h1 0 h2

and

h1 =1

2(1− η), h2 =

1

2(1 + η).

The parameterη is defined at the cohesive zone mid plane and varies between−1 at nodes (1,3) and1 at nodes (2,4).

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Page 9: Fatigue damage in solder joint interconnects - presentation

• The cohesive zone internal nodal force vector and stiffness matrix are now writ-ten as:

f =∫S

ATT dS =l

2

∫ +1

−1ATT dη

K =∫S

ATBA dS =l

2

∫ +1

−1ATBA dη

whereS is the cohesive zone area,l is the cohesive zone length andB is thecohesive zone constitutive tangent operator given by:

B =

∂Tt

∂∆t

∂Tt

∂∆n

∂Tn

∂∆t

∂Tn

∂∆n

.

• Finally, K andf are transformed to the global frame of reference (x,y).

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Page 10: Fatigue damage in solder joint interconnects - presentation

Cohesive tractions: monotonic loading

−1 0 1 2 3 4 5 6

−2

−1

0

1

(a)

∆n/δ

n

Tn/σ

max

−3 −2 −1 0 1 2 3

−1

0

1

(b)

∆t/δ

tT

t/τm

axCohesive zone monotonic normal(a) and shear(b) tractions.

• Characteristics:peak tractionandcohesive energy.

• The softening branch is the energy dissipation source.

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Page 11: Fatigue damage in solder joint interconnects - presentation

Cohesive tractions: cyclic loading

• A linear relation is assumed between the cohesive traction and the correspondingcohesive opening:

Tα = kα(1−Dα)∆α

wherekα is the initial stiffness andα is either the local normal (n) or tangential(t) direction in the cohesive zone plane.

• Energy dissipation is accounted for by thedamage variableD.

• The damage variable is supplemented with anevolution law:

D = f (∆,∆, T,D, ...).

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Page 12: Fatigue damage in solder joint interconnects - presentation

Cyclic loading: damage evolution

• Evolution law (motivated by Roe and Siegmund, 2003):

Dα = cα|∆α| (1−Dα + r)m

|Tα|1−Dα

− σf

wherecα, r,m are constants andσf is the cohesive zone endurance limit.

• Satisfies main experimental observations on cyclic damage:

– Damage increases with the number of cycles.

– The larger the load, the larger the induced damage.

– Damage is larger in the presence of mean stress/strain.

– Load sequencing: cycling at a high stress level followed by a lower level(H–L) causes more damage than when the order is reversed (L–H).σf = 0 −→ linear damage accumulation (Miner’s law).

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Page 13: Fatigue damage in solder joint interconnects - presentation

Uniaxial cyclic tension-compression example

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Geometry:L = 20µm,R = 10µm.Loading: axial sinusoidal displacementU with amplitude of0.2µm.Continuum:E = 30 GPa,ν = 0.25.Cohesive zone:k = 106 GPa/mm, c = 100 mm/N, σf = 150 MPa, r = 10−3,m = 3.

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Page 14: Fatigue damage in solder joint interconnects - presentation

Initial cohesive stiffness

High initial stiffness→ minimize artificial enhancement of the overall compliance.

For a bar containingn equally spaced cohesive zones:

σ =(U − n∆)

LE,

T = k(1−D)∆.

Stress continuity→ σ = (U/L)E∗, whereE∗ is given as:

E∗ =

1− 1kLnE (1−D) + 1

E.To ensure a negligible enhancement of the overall compliance→ nE

kL << 1.

In a two-dimensional model the condition is estimated byEkl << 1, wherel ≈ L/n

is the average cohesive zone length.

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Page 15: Fatigue damage in solder joint interconnects - presentation

0 200 400 600 800 1000−0.15

−0.1

−0.05

0

0.05

0.1

0.15

N (cycles)

F (

N)

(b)

−0.05 0 0.05 0.1 0.15 0.2−400

−200

0

200

400

∆ (µ m)

T (

MPa

)

(a)

(a) Reaction force vs. cycles to failure.(b) Cohesive traction vs. opening.

• Assumption: damage does not occur under compression:

– Physically: infinite compressive strength.

– Numerically: minimizes inter-penetration (overlapping) of neighboring con-tinuum elements under compression.

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Page 16: Fatigue damage in solder joint interconnects - presentation

F versusN : experimental (Erik de Kluizenaar: Philips).

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Page 17: Fatigue damage in solder joint interconnects - presentation

0 20 40 60 80 100−0.15

−0.1

−0.05

0

0.05

0.1

0.15

N (cycles)

F (N

)

(a)

0 500 1000 1500 2000−0.15

−0.1

−0.05

0

0.05

0.1

0.15

N (cycles)

F (N

)

(b)

Different damage parameters:(a) r = 10−3,m = 1. (b) r = 0,m = 3.

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Page 18: Fatigue damage in solder joint interconnects - presentation

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

N (cycles)

D

(a)

εmean

= 0 ε

mean = 0.5 %

0 100 200 300 4000

0.2

0.4

0.6

0.8

1

N (cycles)

D

(b)

H−LL−H

(a) Mean strain effect.(b) Load sequencing effect.

H–L: 200 cycles atεmax = 1 % followd by 200 cycles atεmax = 0.5 %

L–H: 200 cycles atεmax = 0.5 % followd by 200 cycles atεmax = 1 %

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Page 19: Fatigue damage in solder joint interconnects - presentation

Cohesive parameters: solder bump

czg1

czg2

czg3

czg4

• Initial cohesive zone stiffnesskα = 106 GPa/mm.

– Sufficiently high compared to continuum stiffness. Identical for all cohesivezone groups.

• Damage coefficientcα in [mm/N]: czg1 : 0, czg2 : 25, czg3 : 100, czg4 : 0.

• σfα = 0 MPa, r = 10−3.

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Page 20: Fatigue damage in solder joint interconnects - presentation

Computational time reduction

• Loading is applied incrementally.

• For large number of cycles→ time consuming.

• Computational time reduction: only selected cycles are simulated.

• Time reduction of more than90 % in some cases.

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Page 21: Fatigue damage in solder joint interconnects - presentation

Results: damage distribution

N = 500; Deff

= 0.14 N = 1000; Deff

= 0.22

Damage distribution in the solder bump at different cycles.Red linesindicatedamaged cohesive zones (Di

eff ≥ 0.5).

Dieff = (Di

n2

+ Dit2 −Di

nDit)

1/2

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Page 22: Fatigue damage in solder joint interconnects - presentation

N = 2000; Deff

= 0.31 N = 8000; Deff

= 0.4

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Page 23: Fatigue damage in solder joint interconnects - presentation

0 2000 4000 6000 80000

0.1

0.2

0.3

0.4

0.5

N (cycles)

Def

f

The total effective damage versus the number of cycles.

Thetotal effective damageis calculated by averaging over all cohesive zones:

Deff =1

S

N∑iDi

eff Si

whereDieff is the effective damage at cohesive zone (i).

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Page 24: Fatigue damage in solder joint interconnects - presentation

0 2000 4000 6000 8000−8−6−4−2

02468

N (cycles)

F x (N

)

The reaction force versus the number of cycles.

• Slow softening followed by rapid softening (Kanchanomai et al., 2002)

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Page 25: Fatigue damage in solder joint interconnects - presentation

S-N curve

1 2 3 4 5 6−3

−2.5

−2

−1.5

−1

−0.5

log(2Nf)

log(

ε max

)FEM linear fit

Applied strainεmax versus the number of reversals to failure2Nf .

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Page 26: Fatigue damage in solder joint interconnects - presentation

• Finite element data can be fitted with theCoffin-Mansonmodel:

εmax = a(2Nf)b

a: fatigue ductility coefficientb: fatigue ductility exponent

• Failure criteria:50% reduction in the reaction force−→ a = 0.83, b = −0.49.

• Reduction of25% or 75%→ same value ofb.

• Change by±50 % in the Young’s modulii→ same value ofb.

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Page 27: Fatigue damage in solder joint interconnects - presentation

Effect of the elastic parameters

0.5 0.75 1 1.25 1.50

1

2

3

4

E/Er

Nf/N

fr

Variation ofNf withE at εmax = 1%. Fitting curve:Nf/Nrf = (E/Er)−1.83.

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Page 28: Fatigue damage in solder joint interconnects - presentation

Conclusions

• Evolution law captures main cyclic damage characteristics.

• The model’s prediction of the solder bump life-time agrees with the Coffin-Manson model.

• More efficient computational time reduction scheme:−→ simulation of larger number of cycles.−→ more realistic microstructure.

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Page 29: Fatigue damage in solder joint interconnects - presentation

Movie ...

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Page 30: Fatigue damage in solder joint interconnects - presentation

Thank you

Questions?

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