Cracking in Interconnects
due to Thermal Ratcheting
Zhen Zhang, Zhigang Suo
Division of Engineering and Applied Sciences
Harvard University
Jean H. Prévost
Department Civil and Environmental Engineering
Princeton University
MRSEC
Flip-chip structure
Cyclic loading test
Temperature
1500C
Packaging temperature
1250C
Loading
range
-550C
Time
Plan view of SiN
Organic
substrate
underfill
Silicon die
Underfill
SiN (0.45mm thick)
Al-Cu
2mm thick
Polyimide
(4 mm thick)
Lower level interconnects (10-15 mm thick)
Silicon
What is the origin of high stress?
Ratcheting Plastic Deformation
Packaging and loading
Organic Substrate
Temperature
underfill
1500C
Silicon die
1250C
-550C
Biased Shear Stress
Packaging temperature
Loading
range
Time
Polymeric underfill
0.5 µm SiN
2 µm
Al or Cu
10~100 µm
Silica and low level interconnects (10~15µm thick)
Silicon
Huang, Suo, Ma, Fujimoto, J. Mater. Res., 15, 1239 (2000)
Ratcheting Plastic Deformation
First cycle
t0
t0
t0
tm
tm biased shear stress
SiN film
s
Al / Cu pad
gp
Metal yields every cycle !
t0
Many cycles
t0
s
membrane stress
due to CTE mismatch
t0
m pad
Al /tCu
Stress builds up in SiN
s
t0
tm
s
What is the crack behavior?
2D Shear Lag Model
ty
Elastic film
tx0
z
stress
s0
0
Y
y
x
E
strain
Elastic-plastic sublayer
Elastic substrate
Gradual loss of constraint
Stress relaxes in crack wake, but intensifies at crack tip.
Two challenges for simulation
• Crack growth
• Plasticity
X-FEM
Linear creep analogy
Extended Finite Element Method (X-FEM)
Nodal Enrichment functions:
– Displacement jumps
– Singular crack tip field
Benefits:
– Relative coarse mesh
– No remeshing required for
crack growth simulations
Time-saving
Moës, Dolbow, Belytschko, Int. J. Num Math. Eng, 46, 131 (1999).
Linear Ratcheting-Creep Analogy
Uni-directional shear stress t
gp
Cyclic loading
Temperature
s
cyclic membrane stress
125
°C
-55
°C
s
metal film
stress
Y
E
substrate
Cycle
strain
1 cycle
t
dg p t

dN  R
 Em T

Em
where  R 

2


12(1  vm )  (1  vm )Y

Y
3
1
Ratcheting-Creep analogy
dg p
dg

dN
dt
Linear
Time-saving
approximation
Strain per cycle
g p / N
Huang, Suo, Ma, Acta Materialia, 49, 3039-3049 (2001)
Semi-infinite Stationary Crack in Blanket Film
KI
s0
s0
Length scale l  hHEN  R
l(N)
s0
K ~ s 0 N 1/ 4
Creep
l(N)
Ratchet
N
• Both creep and ratcheting calculation show the same trend.
• Comparison of time cost:
• Creep: 1hr 20min
• Ratchet: 22 hr
K
K
Finite Stationary Crack in Blanket Film
s0
Early stage l<<a
Infinite crack limit
Final stage l>>a
K  1.05s 0  NEHh /  
1/ 4
Griffith crack limit
2a
K  s0  a
KI
s0  a
s0
Early
stage
Evolving
l~a
l
l 
 f  , 
a
a 
2a
K
s0
Creep
Ratchet
Normalized cycles NEHh /  a 2
Final
stage
s0
l>>a
2a
Crack Propagation in a Blanket Film
s0
Initiation
Preparation
Transient
Propagation
Steady-state
KI
s0 
s0
da
da

s0
V
 / Nc
Normalized cycles
2
Cycle scale N c 
E Hh
Kss
N / Nc


Length scale    K ss 
 s0 
2
Simulation of Cracks Propagation in Interconnects
Initial state
Tensile
stress
After 100 cycles
t0
Compressive
region
Cyclic loading
Temperature
150
°C
125
°C
-55
°C
Packaging temperature
Loading
range
Time
Summary
High
temperature
packaging
Ratcheting
deformation
in metal layer
Thermal
cyclic
loading
High stress
in SiN
passivation film
Cracking in
interconnects
X-FEM + Linear creep analogy
Simulation of cracking in interconnects becomes feasible