Ratcheting deformation
in thin film structures
Z. SUO
Princeton University
Work with
MIN HUANG, Rui Huang, Jim Liang, Jean Prevost
Princeton University
Q. MA, H. Fujimoto, J. He
Intel Corporation
Interconnect Structures
•Complex architecture
•Small feature sizes
•Diverse materials
Intel: 130nm technology
ibm.com
Thermal Cycling: Qualification Test
~1000 cycles
Temperature
150 °C
125 °C
-55°C
125°C
-40 °C
Time
•Make-and-break
•Time consuming, a bottleneck
•Multiple failure modes
•Little understanding of mechanisms
•New materials
Flip-chip structure
Package substrate
(1.1mm thick, 30-40mm size)
~1000 cycles
Underfil/fillet (150um thick)
Solder bumps (100 um diameter, 150 um spacing)
Silicon die (0.7mm thick, 10-15mm size)
Underfill
SiN (0.45um thick)
Al-Cu
2um thick
Polyimide
(4 um thick)
Lower level interconnects (10-15 um thick)
Silicon
•SiN film cracking
•Metal pad crawling
-55°C
125°C
500 cycles between -55°C and 125°C
Plan view
Edge view
Courtesy of Dr. J.B. Han , Agilent Technologies Singapore
Empirical Observations of Cracking
•
•
•
•
Organic substrate
At die corners
Silicon die
After temperature cycles
In SiN film over Al pads, but not in SiN film over silica
More likely when Al pad is wide
Flip-chip structure
Package substrate
(1.1mm thick, 30-40mm size)
Questions
Underfil/fillet (150um thick)
Solder bumps (100 um diameter, 150 um spacing)
Silicon die (0.7mm thick, 10-15mm size)
Underfill
• Why cycling?
SiN does not fatigue.
SiN (0.45um thick)
Al-Cu
2um thick
Polyimide
(4 um thick)
Lower level interconnects (10-15 um thick)
Silicon
• Why cracking?
*Shear stress is limited by the yield strength
of polymer, say 100 MPa.
*Breaking strength of SiN is 1000 MPa.
Ratcheting Plastic Deformation
Huang, Suo, Ma, Fujimoto, J. Mater. Res., 15, 1239 (2000)
Temperature
30~40 mm
150 °C
Organic substrate
125 °C
Silicon die
1.1 mm
0.7 mm
-55 °C
Time
150 µm thick
polymer layer
Biased Shear Stress
polymer
0.5 µm SiN
2 µm
Aluminum pad
10~100 µm
Silica and low level interconnects (10~15µm thick)
Silicon
•Biased shear stress, from organic substrate
•Metal yields, from CTE mismatch with SiO2
Stress builds up in SiN. STEADY STATE
First cycle
τ0
SiN passivation film
τ0
τ0
τ0
Metal pad
Many cycles, STEADY STATE
τ0
SiN passivation film
τ0
τ0
Metal pad
t
σ
τ0
σ
L
2σt = τ 0 L
σ=
τ 0L
2t
Ratchet and Pawl
Cyclic motion
One-directional motion
Metal Pad Crawling
Polyimide
Al pad
SiN
Al pad
Silica
After ~1000 thermal cycles
Polyimide
SiN
Al pad
Al pad
Silica
Large plastic deformation over many thermal cycles
Finite Element Simulation
1 cycle
10 cycles
50 cycles
100 cycles
Shear stress in metal relaxes
as temperature cycles
Shear Stress in Al pad decreased as thermal cycle
6.00E+07
5.00E+07
1
1
Shear stress in Al pad (Pa)
4.00E+07
τm
3.00E+07
10
10
2.00E+07
50
50
1.00E+07
100
100
0.00E+00
0
5
10
15
20
25
30
35
40
45
50
-1.00E+07
-2.00E+07
-3.00E+07
-4.00E+07
Position (µ )
τ0
SiN passivation film
τ0
Metal pad
τm
τ0
Membrane stress in SiN builds up
as temperature cycles
Stress built up in SiN film as thermal cycle
σ
2.5E+09
2.0E+09
100 & Liquid Model
Normal stress in SiN film (Pa)
1.5E+09
σ
50
1.0E+09
10
5.0E+08
1
0.0E+00
0
10
20
30
-5.0E+08
-1.0E+09
-1.5E+09
-2.0E+09
-2.5E+09
Position (µ )
40
50
Metal pad geometry. Slots.
SiO2
Al
Temperature
150 °C
125 °C
-40 °C
Time
• Direct finite element calculations for 3D, many
cycles take VERY long time.
3D Structure
σ xy
σ xx
σ yx +
τ mx
∂σ yx
τ 0y
∂y
τ my
σ yx
σ yy +
dy
τ 0x
σ xy
∂σ yy
∂y
z
dy
y
∂σ xx
∂σ xy σ xx + ∂x dx
+
dx
∂x
Steady-state: σ
Shear stress in metal vanishes
Elastic plane stress problem
x
yy
τ my
τ mx
τ 0y
τ0x
v
u
passivation film
metal
substrate
Slot!
Further Issues
• Why cycle, again? Why not just plastic collapse?
• Number of cycles to approach the steady state.
εp
Blanket film
3
stress
Y
4 dε = −(α m − α s )dT
p
2
E
strain
5
σ
Aluminum
1
Silicon
σ
2
+Y
1
3
−Y
E (α m − α s )
dσ = −
dT
1−ν
5
(
4
TL
)
E(TH − TL ) α f − α s ⎧> 2, cyclic plasticity
⎨
shakedown
(1 − ν )Y
⎩< 2,
TH
T
Why Crawling?
Temperature
Organic Substrate
150 °C
Silicon die
125 °C
-55 °C
Time
τ0
Metal film
Silicon
stress
σ
τ0
σ
film
σ
τ0
τ0
σ
Y
Strain
increment
σ
E
strain
Huang, Suo, Ma, Acta Materialia, 49, 3039-3049 (2001)
Elastic-Plastic Model
stress
Y
σ, ε
p
τ0, γp
σ, εp
E
film
Strain
increment
τ0
σ
σ, εp
σ, εp
strain
Matching strains
of film & substrate
J2 flow theory
τ0
dε ijp
Shear strain increment
(
)
dε p = − α f − α s dT
= sij dλ
dγ
p
dε p dγ p
=
σ / 3 2τ 0
=−
6τ 0
σ
(α f − α s )dT
σ 2 + 3τ 02 = Y 2
Yield condition
E (α f − α s )(TH − TL )
Four-color map
(1 −ν )Y
Cyclic
Plasticity
Crawling
Plastic
Collapse
2
2
Shakedown
0
τ0
1
3
Y
Stress and strain change with temperature
t
C’
F•
E
0
•
C
A
TL
σ
Y 2 − 3τ 0
b)
2
α Al > α Si
1
(α
c)
f
−αs )
C(C’)
D
TH T
E
2
F
B
•
γp
TL
TH
C’
D
1
σi A
− Y 2 − 3τ 0
A B
E
D
a)
Al
Si
εp
E (α f − α s )
E
F
∆γ
d)
D
1 −ν
C(C’)
B F
TL
TH T
0
(
6τ 0 (α f − α s )
A
TL
1
B
)
Y 2 − 3τ 0
C
2
TH T
12(1 − ν )τ 0 ⎡ E α f − α s (TH − TL ) ⎤
Strain per cycle ∆γ =
− 2⎥
⎢
2
2
E
⎣ (1 − ν ) Y − 3τ 0
⎦
p
p
Ratcheting-Creep Analogy
τ
E m (α m − α s )(TH − TL )
<2
(1 − ν m )Y
Normalized shear stress, τm/Y
Y1
3
3
E m (α m − α s )(TH − TL )
=2
(1 − ν m )Y
E m (α m − α s )(TH − TL )
>2
(1 − ν m )Y
linear approximation
(
)
12(1 − ν )τ 0 ⎡ E α f − α s (TH − TL ) ⎤
∆γ =
− 2⎥
⎢
2
2
E
⎣ (1 − ν ) Y − 3τ 0
⎦
p
0
p
∆
γ
Strain per cycle ∆γ
Normalized ratcheting strain rate,
p
Y (1 − ν m ) / E m
dγ
dγ
⇔
dN
dt
Number of cycles to reach steady-state
τ0
σ
u
substrate
Elastic passivation film
Equilibrium
Elasticity
∂σ
h
= τ − τ0
∂x
∂u
σ = Ep
∂x
∂u
∂ 2u Hτ 0
=D 2 −
∂N
η
∂x
L
L
passivation film
metal film H
h
Ratcheting metal film
η ∂u
τ=
H ∂N
−1
Em ⎛ Em ∆α∆T
η=
− 2⎞
⎠
12 ⎝
Y
D=
EHh
η
−1
L2 L2 Em ⎛ Em ∆α∆T
N0 ~
~
− 2⎞
⎠ Huang,Suo, Ma, J Mech.Phys. Solids. 50, 1079 (2002)
Y
D Hh E p ⎝
Concomitant crack extension and underlayer ratcheting
σ
Tensile Film
Ratcheting Layer
Rigid Substrate
Hhσ 2
da
= 0.6
dN
ηGc
−1
⎡
⎤
Em
Em ∆α∆T
η=
− 2⎥
⎢
12(1 − vm ) ⎣ (1 − vm )Y
⎦
J. Liang, R. Huang, J.H. Prevost, Z. Suo, submitted
Conclusions
• Thermal cycling test is a bottleneck.
• Ratcheting: cyclic temperature, aided by
biased shear stress, causes uni-directional
deformation.
• Stress relaxes in metal, and builds up in SiN.
• Ductile, low k dielectrics may ratchet.
• Need thin film data on large plastic
deformation over many cycles, and long time.
www.princeton.edu/~suo