APPLIED PHYSICS LETTERS 88, 072102 共2006兲
Current crowding-induced electromigration in SnAg3.0Cu0.5 microbumps
Kuo Ning Chiang,a兲 Chien Chen Lee, and Chang Chun Lee
Advanced Microsystem Packaging and Nano-Mechanics Research Laboratory, Department of Power
Mechanical Engineering, National Tsing Hua University, HsinChu, Taiwan
Kuo Ming Chen
United Microelectronics Corporation, Package Engineering Department, Science Industrial Park,
HsinChu, Taiwan
共Received 14 October 2006; accepted 20 January 2006; published online 13 February 2006兲
To determine the relevance of current crowding to electromigration in the SnAg3.0Cu0.5 solder
bump, a three-dimensional dual bumps simulation model was designed to demonstrate how current
crowding can enhance the local atomic flux along the electron flow path. The finding of void
formation occurred at the entrance points to the cathode sides and the enhancement of the growth
and clustering of the intermetallic compound at the outgoing points of the anode sides along the
electron flow path were verified experimentally. The tilting effect is obvious at the anode/chip side.
The experimental mean-time-to-failure was observed, and Black’s equation with Joule heating effect
were investigated as well. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2173710兴
Under high current density, electromogration is a common failure in interconnects, which is a combination of thermal and electrical on mass motion.1 A higher temperature
and a higher current density enhances the rate of mass transportation. There are many papers in recent literature on the
current crowding phenomenon around the regions where the
traces connect to the solder bump interface, which accelerates of the depletion of solder bump.2–9 Numerical simulations of the current density distribution and the increased
temperature around the current crowding region in the solder
bump have also been studied.10,11 However the starting point
of void formation and the intermetallic compound 共IMC兲 accumulated polarity effect of the solder bump needs more
study.
Black’s equation has been successful in characterizing
the operating life of aluminum and copper traces on a chip.12
Some papers have been published on the concept of modification of the mean-time-to-failure 共MTTF兲 prediction in the
solder bump.13 However, the MTTF comparison between experimental measurement, the published Black’s equation and
the modified Black’s equation is needed to provide a deeper
understanding of electromigration-induced failure in the solder bump.
The aim of this study is to investigate the electromigration of SnAg3.0Cu0.5 solder bumps. This study designed a
three-dimensional dual bumps simulation model and designed a corresponding test vehicle to verify the numerical
findings. Furthermore, the experimental MTTF in the temperature range from 125 to 165 ° C has been investigated
with current densities of 0.74 to 1.68⫻ 104 A / cm2. It was
discovered that the Joule heating effect obviously affects the
real temperature in the solder bump and as such affects the
MTTF of the solder bump.
The cross-sectional schematic diagram of the solder
bump used for the electromigration experiments is illustrated
in Fig. 1. For the test chip with SnAg3.0Cu0.5, the under bump
metallurgy 共UBM兲 on the chip side consists of 0.8 ␮m Cu,
0.3 ␮m Ni共V兲, and 0.4 ␮m Ti. The bumped chip was
a兲
Electronic mail: knchiang@pme.nthu.edu.tw
mounted on a BT substrate, with consisted of 0.05 ␮m Au,
3 ␮m Ni, and 32 ␮m Cu. To measure the real solder bump
temperature due to the current stressing, the temperature coefficient of resistance 共TCR兲 calculation was applied to obtain the actual temperature of the current stressed bump. The
real temperature of the solder bump can be monitored in situ.
This electrical method for junction temperature measurement
is a direct noncontact technique since it utilizes the function
itself as the temperature sensor.
This study investigated the current crowding distribution
in a dual solder bumps system. Figure 2 shows the solid
model of the solder bumps. The resistivities of the material
used in this simulation as Al, Cu, SnAg3.0Cu0.5, Ti, Ni共V兲,
Ni, and Au were 2.74, 1.68, 10.4, 54, 63.2, 7.4, and
2.35 ␮⍀ cm, respectively. The test temperatures were 125,
150, and 165 ° C, respectively, and the current densities were
7.38⫻ 103, 1.21⫻ 104 and 1.68⫻ 104 A / cm2, respectively.
For the purpose of investigating the starting point of the void
formation and the IMC accumulation location and it’s composition, scanning electron microscopy 共SEM兲 and energy
dispersive x-ray 共EDX兲 were used.
Black’s equation successfully characterized the operational life of aluminum and copper traces on a chip, which is
typically expressed as
FIG. 1. 共Color online兲 Schematic diagram of the bump used in this study.
The direction of the electron flow is indicated by arrows.
0003-6951/2006/88共7兲/072102/3/$23.00
88, 072102-1
© 2006 American Institute of Physics
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072102-2
Appl. Phys. Lett. 88, 072102 共2006兲
Chiang et al.
TABLE I. MTTF comparison between measured, oven temperature calculated, and real temperature calculated MTTF under the test conditions of current
densities and temperatures.
Experiment
Modified Black’s equation:
MTTF= 3.13E1J−2.11e共0.88/kT兲
Published Black’s equation:
MTTF= 2.38E3J−2.52e共0.85/kT兲
Current 共mA兲
T oven 共°C兲
MTTF 共h兲
MTTF 共h兲
Deviation 共%兲
T real 共°C兲
MTTF 共h兲
Deviation 共%兲
220
360
500
500
500
165
165
165
150
125
2089
637
261
694
2594
2198
634
277
615
2664
5.22
−0.47
6.13
−11.38
2.70
Average: 0.44
169.5
174.8
175.9
159.4
135.1
2176
585
277
661
2707
4.16
−8.16
6.13
−4.76
4.36
Average: 0.35
MTTF = A
冉 冊
1
Q
,
n exp
J
KT
共1兲
where A is constant, J is the average current density
共A / cm2兲, n is an experimentally derived current density exponent, Q is an experimentally derived activation energy
共eV兲, K is Boltzman constant 共8.617E-5 eV/ K兲, and T is
average bump temperature 共K兲. Under a constant current accompanied by varied temperature stressing, the activation
energy can be obtained by the following equation:
ln共MTTF兲 = ln共A兲 − n ln共J兲 +
冉 冊
Q
.
KT
共2兲
If we treat ln共MTTF兲 as the Y axis, and 共1 / KT兲 as the X axis,
then the slope Q can be obtained. Furthermore, if under a
constant temperature accompanied with varied current stressing, we treat ln共MTTF兲 as the Y axis, and ln共J兲 as the X axis,
then the slope n can be obtained.
However, during the current stressing in solder bumps,
Joule heating may cause a temperature increase. TCR is a
direct noncontact technique since it utilizes the function itself as the temperature sensor. Although methods, such as
infrared, can be used to measure junction temperatures, their
application is limited to junctions that are directly visible.
The calculation of TCR is typically expressed as
TCR =
冉
R1 − R0
R0
冊冉
冊
1
,
T1 − T0
共3兲
where T0 is the reference temperature, T1 is the real temperature, R0 is the resistance in T0, and R1 is the resistance in T1.
While calculating the n, the MTTF needs to be modified as
冋冉 冊冉
MTTFoven = MTTFreal exp
Q
KT
1
Toven
−
1
Treal
冊册
,
共4兲
under a constant temperature accompanied with varied current stressing. If we treat ln共MTTFoven兲 as the Y axis, and
ln共J兲 as the X axis, then the slope n can be obtained.
Table I shows the MTTF comparison between measured,
oven temperature calculated, and real temperature calculated
MTTF under the test conditions of current densities and temperatures. The values listed in Table I are the averaged values
of 13 samples tested. Normally, the real temperature will be
around 10 ° C higher than that of the oven temperature under
1.68⫻ 104 A / cm2. By substituting the real temperature due
to Joule heating, and the maximum current density due to
current crowding, for the average ones, then the modified
Black’s equation is obtained. The more the actual solder
bump temperature is applied, the smaller the discrepancy of
the averaged MTTF. This result implies that the Joule
heating effect needs to be taken into consideration when
conducting the MTTF calculation.
Maximum current density was simulated by finite element method 共FEM兲, which provides a better understanding
of local heat as well as current crowding. Figure 3 shows the
simulation results, indicating the serious current crowding
distribution in solder bumps. This study found that the current crowding phenomena was main reason to hasten the
solder bump electromigration failure. There is a very large
current density change at the contact between the bump and
the UBM. This change leads to current crowding, and higher
current density at the entry points and exit points of the
solder bump. The current crowding phenomena enhances the
void formation at the entry points of the cathode side of the
FIG. 3. 共Color online兲 Current density distribution in the cross section of the
FIG. 2. 共Color online兲 Tilted view of the three-dimensional dual solder
dual solder bumps model. Current crowding occurs in the vicinity of the
bumps finite element model.
junction of the bumps and the UBM.
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072102-3
Appl. Phys. Lett. 88, 072102 共2006兲
Chiang et al.
FIG. 4. Cross-sectional SEM images of solder bumps after at 125 ° C with
an applied current of 共a兲 0 mA, and 共b兲 1.68⫻ 104 A / cm2 for 1431 h. Voids
formed at the entry points of both cathode/chip and cathode/substrate sides
of the solder bumps along the electron flow path. IMC grew, tilted, and
clustered at the outgoing points of both anode/chip and anode/substrate sides
along the electron flow path.
solder bumps; and enhances the atomic tilted and clustered at
the exit points of the anode side.
A corresponding test vehicle was designed and implemented to verify the simulation results. Figure 4共a兲 shows
the cross-section SEM image of dual solder bumps without
current applied at 125 ° C, and Fig. 4共b兲 shows the cross
section of the dual solder bumps after current stressing at
1.68⫻ 104 A / cm2 at 125 ° C for 1431 h. The SEM image
verified the void formed at the entry points of both the
cathode/chip and the cathode/substrate sides of the solder
bumps along the electron flow path. The IMC grew and accumulated at the outgoing points of both anode/chip and
anode/substrate sides along the electron flow path. Under this
current stressing condition, the ratio of the operating temperature over the melting temperature of SnAg3.0Cu0.5 solder
bump is more than 80%; a value which is much higher than
that of Al trace, Cu trace, and UBM. Therefore, the starting
point of the void formation occurred at the entry points of
both the cathode/chip and the cathode/substrate sides of the
solder bumps. The tilting effect indicates that electromigration enhances IMC tilt and clustering at the anode, especially
at the anode/chip side. A large amount of IMC was found,
tilted, clustered, and attached to the UBM on the chip side.
The EDX results indicated that the IMC was 共Ni, Cu兲3Sn4.
The Ni and Cu atoms in the IMC seemed to have migrated
from the metallization layers on the substrate side along the
electron flow path.
In summary, the impact of Joule heating on electromigration was investigated. Through the TCR calculation, the
real temperature in the solder bump was obtained. It was
found that the Joule heating effect had an obvious effect on
the MTTF of solder bumps. The current density distributions
observed from the finite element analysis showed that the
void formation occurred at the entrance points of both
cathode/chip and cathode/substrate sides of solder bumps,
and that it enhanced the growth and clustering of IMC at the
outgoing points of both anode/chip and anode/substrate sides
along the electron flow path. The tilting effect is quite obvious, especially at the anode/chip side.
The authors would like to express their appreciation to
Frank Kuo in SPIL for his great help in the preparation of the
experimental test vehicles, and Abel Tan for his great help on
the set up of the equipment for the analyses.
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