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Microelectronics Reliability 52 (2012) 735–743
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Microelectronics Reliability
journal homepage: www.elsevier.com/locate/microrel
Failure mechanism of FBGA solder joints in memory module subjected to
harmonic excitation
Yusuf Cinar a, Jinwoo Jang a, Gunhee Jang a,⇑, Seonsik Kim b, Jaeseok Jang b, Jinkyu Chang b, Yonghyun Jun b
a
b
Department of Mechanical Engineering, Hanyang University, 17, Haengdang-dong, Seongdong-gu, Seoul 133-791, Republic of Korea
Memory Division, Samsung Electronics Co. Ltd., San #16, Banwol-Ri, Taean-Eup, Hwasung-City, Gyeonggi-Do 445-701, Republic of Korea
a r t i c l e
i n f o
Article history:
Received 7 October 2010
Received in revised form 2 November 2011
Accepted 23 November 2011
Available online 20 December 2011
a b s t r a c t
This paper investigates the failure mechanism of Fine-pitch Ball Grid Array (FBGA) solder joints of memory modules due to harmonic excitation by the experiments and the ﬁnite element method. A ﬁnite element model of the memory module was developed, and the natural frequencies and modes were
calculated and veriﬁed by experimental modal testing. Modal damping ratios are also obtained and used
in the forced vibration analysis. The experimental setup was developed to monitor resistance variation of
FBGA solder joints due to the harmonic excitation under Joint Electron Devices Engineering Council
(JEDEC) standard service conditions. Experiments showed that the failure of the solder joints of the memory module under vibration mainly occurs due to resonance. Forced vibration analysis was performed to
determine the solder joints having high stress concentration under harmonic excitation. It showed that
failure occurs due to the relative displacement between PCB and package and solder joints are the most
vulnerable part of the memory module under vibration. It also showed that cracked solder joints in the
experiments match those in the simulations with the highest stress concentration.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Memory modules are composed of a number of packages or dynamic random access memory integrated circuits modules
mounted on a printed circuit board (PCB), designed for use in personal computers, workstations, and servers. There are various
types of memory modules, such as Single In-Line Memory Module
(SIMM), Dual In-Line Memory Module (DIMM), and Small Outline
Dual In-Line Memory Module (SO-DIMM). Packages are mounted
on PCBs through solder balls called ball grid arrays (BGAs). Solder
balls are further used to provide the electrical signals between
package chips and the PCB. Memory modules are exposed to vibration over various frequency ranges [1], which may result in the
malfunction of products. Reliability and performance of memory
modules are standardized by the Joint Electron Devices Engineering Council (JEDEC). Performance and fatigue life time of the memory modules mostly depend on the solder joints. According to a
report released by a semiconductor company, solder joint cracks
reﬂected approximately 40% of total failure of memory modules.
Therefore, it is important to understand the dynamic behavior of
memory modules, as well as the behavior of solder joints subjected
to vibration.
⇑ Corresponding author. Address: PREM, Department of Mechanical Engineering,
Hanyang University, 17, Haengdang-dong, Seongdong-gu, Seoul 133-791, Republic
of Korea. Tel.: +82 2 2299 5685; fax: +82 2 2292 3406.
E-mail address: [email protected] (G. Jang).
0026-2714/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.microrel.2011.11.015
Many researchers have investigated the fatigue life reliability of
packages or memory modules due to thermal load by experiment
and simulation [2–4]. Once vibration was realized to be one of
the dominant failures for electronic components, the electronic
packaging industry began to show interest in understanding its
failure mechanism under vibration. Basaran and Chandaroy [5]
presented a study based on a viscoplastic model to compute damage mechanics of a solder joint with Pb40/Sn60 solder alloys under
different dynamic load conditions. They showed that fatigue life of
solder alloys is greatly affected by dynamic loads and the frequency ranges of applied loads. Kim et al. [6] investigated the high
cycle vibration fatigue life characteristics of Pb-free and Pb packages under various mixed mode stresses by experiment and FEM.
They observed the failure process of a solder ball at low frequency
during the fatigue test by using an optical microscope. Wu [7] utilized the global–local modeling concept to calculate von Mises
stress in solder joints of interest under random vibration loading.
Then, she predicted the fatigue life of solder joints by using a damage model, called the Basquin power-law relation. Che and Pang [8]
studied ﬂip chip solder joints under out-of-plane sinusoidal vibration load with constant and varying amplitudes and they used
Miner’s cumulative damage law to estimate fatigue life of ﬂip chip
solder joints. Zhou et al. [9,10] investigated the vibration durability
of Sn3.0Ag0.5Cu (SAC305) and Sn37Pb solder interconnects under
narrow-band harmonic vibration and random vibration. They
found that SAC305 interconnects have lower fatigue durability
than Sn37Pb interconnects. However, prior researchers did not
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Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
Fig. 1. A DDR3 SDRAM type memory module: (a) front view, (b) back view and (c) side view.
Table 1
Dimensions of bare PCB and packages of a memory module.
Components
Number of components (EA)
Dimensions in mm (L W H)
Bare PCB
Package
Package register
1
36
1
133.35 30.00 1.295
11.00 7.50 0.77
13.50 8.00 0.779
investigate failure mechanism of the solder joint in terms of resistance variation over high frequency ranges, as well as the most vulnerable solder joint of the memory module under vibration.
This paper investigates the failure mechanism of Fine-pitch Ball
Grid Array (FBGA) solder joints in daisy chains assembled memory
module with double-sided packages due to harmonic excitation by
using the experiments and the ﬁnite element method. The experimental setup was developed to monitor resistance variation of
FBGA solder joints due to the harmonic excitation of the JEDEC
standard service condition 1 [11]. A ﬁnite element model of the
memory module was developed, and the natural frequencies and
modes were calculated and veriﬁed by experimental modal testing.
Forced vibration analysis was performed to correlate the cracked
solder joints in experiments with the solder joint of high stress
concentration in simulation.
There are two types of solder balls used in the packages and the
package register. The solder balls of the packages and the package
register have diameters of 0.4 mm and 0.3 mm and heights of
2. Analysis model
Fig. 1 shows a double-data-rate three synchronous dynamic
random access memory (DDR3 SDRAM) type memory module used
in this research. It is mainly composed of a PCB, packages and package register, and solder balls. The PCB is composed of 10 layers of
copper conductor and FR-4, while the packages and package register are composed of many integrated circuits (ICs). This memory
module has 36 packages and 1 package register. Table 1 shows
the mechanical dimensions of PCB, package, and package register.
Fig. 2. BGA patterns of package and package register: (a) package and (b) package
register.
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Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
Fig. 3. Finite element model of a memory module: (a) front view, (b) back view and (c) side view.
Table 2
Material properties of each component of a memory module.
Component
Material type
Density (kg m3)
Young’s modulus (MPa)
Poisson’s ratio (–)
Element type
Element number
Bare PCB
Package
Package register
Solder ball
FR4
–
–
Sn–Ag–Cu
2200.5
1920.5
2389.1
7094.0
22,000
12,000
12,000
44,113
0.40
0.40
0.40
0.36
Brick
Brick
Brick
Brick
78,368
77,184
6964
46,337
Fig. 4. Experimental setup for modal testing.
0.3079 mm and 0.3026 mm, respectively. Solder balls are modeled
as an octagonal structure with sixteen elements. The BGAs of the
package and package register have different patterns, as shown
in Fig. 2. The red square1 in package and package register in
Fig. 2 shows their orientation in memory module in Fig. 1.
1
For interpretation of color in Figs. 1–3,8,9, the reader is referred to the web
version of this article.
3. Free vibration analysis
A ﬁnite element model of the memory module was developed,
as shown in Fig. 3. Table 2 shows the material type, properties, element type and number of each component. The PCB, packages,
package register, and solder balls are modeled by the linear brick
elements with eight nodes, and each node has three degrees of
freedom. The total number of elements was 208,853. In the ﬁnite
element model, packages, solder balls and PCB were connected
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Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
Table 3
Simulated, measured natural frequencies and damping ratios of the memory module.
Mode number
Mode
Mode
Mode
Mode
Mode
Mode
1
2
3
4
5
6
Simulation
Experiment
f (Hz)
f (Hz)
877.86
1306.2
1993.6
2847.3
3949.2
5067.3
885
1260
1890
2705
3760
4820
Error (%)
Damping ratio (%)
0.81
3.67
5.48
5.26
5.03
5.13
1.61
1.35
1.09
1.05
0.972
0.172
by node sharing. DDR type memory modules are usually inserted
in a slot in a motherboard so that the ﬁnite element model is assumed to have a ﬁxed boundary condition of two short sides and
one long side and a free boundary condition of one long side. The
natural frequencies and mode shapes were calculated by using
ANSYS.
Experimental modal testing was performed to verify the proposed simulated results. Fig. 4 shows the experimental setup for
the modal testing. An impact hammer was used to excite a memory module. The responses on the memory module were measured
at 18 points by using a laser Doppler vibrometer (sensor) and
PULSE 3560C (signal analyzer). The mode shapes were determined
by using the STAR modal system. Table 3 shows the comparison
between the simulated and experimental natural frequencies of
the memory module. Fig. 5 shows the comparison between the
simulated and experimental mode shape of vibration modes 1, 2,
and 3 of the memory module. Table 3 and Fig. 5 show that the simulated natural frequencies and the mode shapes match well with
the experimental ones.
4. Experiment to detect failure mechanism of memory module
Failure mechanism of the solder joints can be observed by monitoring the resistance increase of the memory module with daisy
chain assembly, because failure of solder joints due to crack increase resistance. Except package register, every package on the
memory module was assembled with daisy chains. The daisy
chains of the packages in the front and back side of the memory
module were connected in series. Total resistance of daisy chain
of the memory module was measured to be around 35–40 X. A
failure of the solder joint is assumed to occur when total resistance
reaches greater than 100 X [9].
An experimental setup was developed to detect failure mechanism of the memory module, as shown in Fig. 6. An EDS50-150
type electro-dynamic shaker was used to excite the memory module ﬁxed on a jig. The variation in input acceleration proﬁle was
measured by an accelerometer on the top of the shaker and was
controlled by VibrationVIEW software, shown on the right side in
Fig. 6. A potential of 2.5 V was supplied to the memory module
with daisy chain assembly from a power supply. Variations in
acceleration on top of the shaker, current, and voltage were measured simultaneously in real time, and then acceleration and resistance (voltage/current) were obtained using an oscilloscope. Three
sides of memory module were ﬁxed to the jig mounted on the top
of a shaker, shown in Fig. 6, to maintain the same boundary conditions as a DDR memory module.
The memory module in this research was excited by the JEDEC
service condition [11]. Fig. 7 shows the variation of input force in
terms of acceleration. The harmonic excitation was applied to the
memory module in a constant peak displacement (1.5 mm) from
20 Hz to 80 Hz (cross-over frequency). A constant acceleration level was then applied between 80 Hz and 2000 Hz. A complete
sweep of the test frequency range, which goes from 20 Hz to
Fig. 5. Comparison of simulated and experimental results of three modes (a) mode
1, (b) mode 2 and (c) mode 3.
2000 Hz and back to 20 Hz, is repeated in a logarithmic manner
every 4 min. The sweep rate is 1 decade/min. Harmonic excitation
is applied in the out-of-plane direction (Z direction) because pretests showed that the solder joints are more vulnerable in the Z
direction than in the X and Y directions.
Fig. 8 shows the variation in resistance in the developed experiment. Red dotted lines in Fig. 8 show the ﬁrst, second, and third
natural frequencies of the memory module corresponding to 885,
1260, and 1890 Hz. Total resistance of the memory module with
the daisy chain was measured to be around 35–40 X before experiment is performed. Failure mechanism due to resistance variation
under vibration is presented in Fig. 8. Fig. 8a shows that the resistance of the memory module did not change until 12 min. The
resistance slightly increased around the 1st natural frequency of
the memory module between 12 and 14 min, as shown in the left
plot of Fig. 8b. While the sweep frequency was returning to 20 Hz
from 2000 Hz, the resistance increased around its 1st natural frequency again between 14 and 16 min, as shown in the right plot
of Fig. 8b. Fig. 8c shows that the resistance continuously increased
around the 1st, 2nd, and 3rd natural frequencies of the memory
Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
739
Fig. 6. Experimental setup to monitor failure mechanism.
method and mode superposition. The damped global ﬁnite element
equation of the memory module due to harmonic excitation is given by
€ðtÞg þ ½CfxðtÞg
_
½Mfx
þ ½KfxðtÞg ¼ fPðtÞg
ð1Þ
where [M], [C], [K] and {P(t)} are the mass, damping, stiffness matri€ðtÞg, fxðtÞg
_
ces and excitation force vector, and fx
and {x(t)} are the
nodal acceleration, velocity and displacement vectors. In the large
sized problem, the direct integration technique to obtain the forced
response is not the computationally efﬁcient method [12]. The
forced response, {x(t)}, can be approximated by using the mode
superposition method as follows:
fxðtÞg n
X
f/i gfzi ðtÞg
ð2Þ
i¼1
Fig. 7. Variation of acceleration input of JEDEC service condition 1.
module between 28 and 32 min. Finally, the resistance of the
memory module at the 1st natural frequency increased bigger than
100 X between 44 and 48 min, as shown in Fig. 8d. Crack growth
reduces stiffness of the memory module, which decreases natural
frequency of the memory module. As the experiment goes by, frequency range at which resistance increases near natural frequencies gradually becomes wider as shown in Fig. 8.
In this work, the same experiment was performed for six memory modules with daisy chains. Time to failure is approximately
45–55 min, and packages near the ﬁxed boundary shown in
Fig. 5 were the frequently failed packages. One of the most frequently failed packages is the package 5 and 33 shown in Fig. 1.
Crack propagation is also found in package 1. Fig. 9 shows the
cross-sectional view of the solder ball of packages 1 and 5 of the
memory module after the molding, cutting, and polishing process.
The crack in the solder ball is located near the PCB side.
5. Finite element forced vibration analysis
The dynamic response of a memory module subjected to harmonic excitation was investigated by using the ﬁnite element
where {/i} is the i-th mode vector which is the eigenvector calculated by the free vibration analysis. {zi(t)} and n are modal displacement and the number of modes to be used in calculation of the
displacement vector, {x(t)}, respectively. Substituting Eqs. (2) into
(1) and rearranging it after multiplying with {/i}T, the decoupled
n equations of motion are obtained as follows:
½UT ½M½Uf€zg þ ½UT ½C½Ufz_ g þ ½UT ½K½Ufzg ¼ ½UT fPg
ð3Þ
Then Eq. (3) can be written in terms of modal coordinates as
follows:
€zi þ 2xi ni z_ i þ x2i zi ¼ Q i ði ¼ 1 . . . nÞ
ð4Þ
where xi and ni donate natural frequency and damping ratio of
i-th mode, respectively. Eq. (4) becomes a set of n decoupled differential equations for the damped system and the solution in
terms of modal coordinate, zi, can be obtained by using the time
integration. Then the displacement, {x(t)}, can be calculated with
the Eq. (2).
Frequency response of a memory module was obtained experimentally, and the half power method was used to calculate modal
damping ratios of the memory module from Eq. (5) for its six
modes shown in Table 3 [13]. They were inserted into Eq. (4).
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Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
Fig. 8. Variation of the resistance of the memory module during the harmonic excitation of the JEDEC service condition 1: (a) from 0 to 12 min, (b) from 12 to 16 min, (c) from
28 to 32 min and (d) from 44 to 48 min.
ni ¼
1 Dx
2 xi
_
ð5Þ
where Dx is the width of the frequency response curve at the half
power level.
The harmonic excitation force of JEDEC service condition 1 can
be written as follows:
pðtÞ ¼ p ðtÞ sin xðtÞ
ð6Þ
In the case of logarithmic sweep, the variation of frequency with respect to time is given by
xðtÞ ¼ xs 23:3219St=60
ð7Þ
Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
741
Fig. 11. Convergence of the displacement of the package 1 with the increase of
mode number.
Fig. 9. Crack of the solder ball: (a) N6 solder joint of package 5 and (b) A1 solder
joint of package 1.
where xs is the starting frequency and S is the sweep rate in decade
per minute. The sweep rate in JEDEC service condition 1 is deﬁned
as 1 decade/min. Combining Eqs. (7) and (6) yields the force function for the logarithmic sweep as follows [14]:
_
pðtÞ ¼ p ðtÞ
_
60xs 3:3219St=60
1 þb
2
S lnð2Þ
ð8Þ
where p ðtÞ ¼ Mn a0 g and Mn, a0 and g are the nodal mass, applied
acceleration corresponding to JEDEC service condition 1 which is
20G and gravitational acceleration, respectively and b represents
phase.
Fig. 10 shows the ﬁnite element model for the forced vibration
analysis. Two short sides and one long side of the ﬁnite element
model were rigidly coupled with a nodal mass, while the base excitation in Fig. 7 is applied. The solution zi of Eq. (4) is obtained by
using numerical integration with an integration time step of
2.5 105 s. Numerical integration was performed around the natural frequencies over 2 s with the starting frequency of 830 Hz,
1222 Hz and 1852 Hz for the ﬁrst three modes of memory module,
respectively. The accuracy of the mode superposition depends on
how many modes are superposed to calculate the response, as
shown in Eq. (2). Convergence of the proposed method was veriﬁed
by increasing the superposed mode numbers. Displacement response on any location on the ﬁnite element model of memory
module due to increasing number of modes can be observed to
determine the number of modes to superpose in the calculation.
The package 1 is selected to verify the accuracy of the proposed
method. Fig. 11 shows the calculated axial displacement on the
package 1 near the ﬁrst natural frequency of the memory module,
indicating that 40 or more than 40 modes are sufﬁcient to guarantee the accuracy. But increasing number of superposed modes increases computation time, therefore 50 modes was selected to
calculate the response under vibration. Package 5 is one of the
most failed packages from the experiments. Therefore displacement variation on package 5 of the memory module is obtained
and shown in Fig. 12 for comparison. As shown, the biggest displacement occurs at the ﬁrst natural frequency for package 5. Displacement variation around modes 2 and 3 are relatively small, as
shown in Fig. 12b and c.
Under the harmonic excitation in Z direction, Fig. 13 shows displacement distribution and von Mises stress distribution at the
ﬁrst resonance frequency for the section view of package 5 (P5)
and package 15 (P15) and their symmetric packages (package 33
(P33) and package 24 (P24)) on the back side of the memory module shown as yellow dotted border in Fig. 3a and b. Table 4 shows
the absolute and relative Z displacements for P5-N6 (near ﬁxed
edge) and P15-J6 (near free edge) solder joints at the ﬁrst resonance frequency. Though the absolute displacements at the free
edge of memory module near P15 and P24 is bigger than that at
the ﬁxed edge as shown in Fig. 13a, the relative displacements at
Fig. 10. Finite element model of a memory module for harmonic analysis.
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Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
Fig. 13. Displacement and stress distribution on the 1st natural frequency for the
section view of yellow dotted border in Fig. 3a: (a) Distribution of Z directional
displacement and (b) von Mises stress distribution.
Table 4
Absolute and relative displacements of P5-N6 and P15-J6 solder joints.
Solder
joint
P5-N6
P15-J6
Absolute displacement
(mm)
PCB
Package
0.0500323
0.3488220
0.0500238
0.3488210
Relative displacement (PCB-package)
(mm)
0.0000085
0.0000010
Fig. 12. Variations of displacement on package 5 with time: (a) the response
around the 1st natural frequency, (b) the response around the 2nd natural
frequency and (c) the response around the 3rd natural frequency.
the ﬁxed edge of memory module near P5 and P33 is bigger than
that at the free edge as shown in Table 4. It results in bigger von
Mises stress on the solder joints of packages (P5 and P33) near
the ﬁxed boundary than that near free edge as shown in Fig. 13b.
The von Mises stress was calculated to determine the stress distribution on package 5 and the vulnerable solder balls where failure may occur. Stress distribution in the BGA for package 5 at
the ﬁrst natural frequency is represented in Fig. 14. The two solder
balls with the highest stress concentration are N1 and N6 on package 5, while the cracked solder ball during the experiment was N6,
whose location is shown with a red star (right corner of P5) in
Fig. 1a. Fig. 15 shows the variation in the von Mises stress of solder
balls P5-N1 and P5-N6, due to changes in excitation frequency.
Stress level is averaged at the node between solder ball and PCB
interface. As shown, their stress levels are similar and higher than
the rest of the solder balls in BGA of package 5. Fig. 16 shows the
stress distribution of the solder ball at P5-N6 and the adjacent
PCB and package. As shown, the stress concentration occurs at
the solder ball just over the PCB, which matches with the cracked
location of the solder ball in Fig. 9a.
Fig. 14. Stress distribution of BGA for package 5.
6. Conclusion
This paper presents an investigation of failure mechanism of
FBGA solder joints of memory modules due to harmonic excitation
by using the experimental and ﬁnite element methods. The experimental setup was developed to monitor and to characterize the
failure mechanism of FBGA solder joints due to the harmonic excitation of JEDEC standard service condition 1. Results showed that
the crack of the solder joints of the memory module under vibration mainly occurs due to resonance. A ﬁnite element model of
the memory module was developed, and the natural frequencies
and modes were calculated and veriﬁed by experimental modal
testing. Forced vibration analysis was performed to determine
Y. Cinar et al. / Microelectronics Reliability 52 (2012) 735–743
743
placement between PCB and package and solder joints are the most
vulnerable part of the memory module under vibration. It also
showed that cracked solder joints in the experiments match those
in the simulations with the highest stress concentration. Furthermore, the most vulnerable part of the memory module under
vibration was found to be the solder joint near the PCB.
The proposed experiment and simulation will be applied to develop robust memory module designs and solder joint fatigue failure analysis will be studied in a future paper.
Acknowledgments
This research has been supported by Samsung Electronics, and
Y. Cinar thanks the Korean National Institute for International Education (NIIED) for a scholarship supporting his Ph.D work.
Fig. 15. Comparison of stress variation for N-1 and N-6 solder balls on package 5.
References
Fig. 16. Stress distribution around N-6 solder joint of package 5.
the high-stress concentration solder joints under harmonic excitation. Modal damping ratios are also used in the forced vibration
analysis. It showed that the failure occurs due to the relative dis-
[1] Steinberg DS. Vibration analysis for electronic equipment. 3rd ed. New
York: Wiley; 2000.
[2] Pidaparti RMV, Song X. Fatigue crack propagation life analysis of solder joints
under thermal cyclic loading. Theor Appl Fract Mech 1996;24:157–64.
[3] Che FX, Pang HLJ. Thermal fatigue reliability analysis for PBGA with Sn–3.8Ag–
0.7Cu solder joints. In: Proc 6th electronics packaging technology conference,
Singapore; December 8–10, 2004. p. 787–92.
[4] Che FX, Pang HLJ, Zhu WH, Sun Wei, Sun Anthony YS, Wang CK, et al.
Development and assessment of global–local modeling technique used in
advanced microelectronic packaging, EuroSime2007, London, UK; April 15–18,
2007. p. 375–81.
[5] Basaran C, Chandaroy R. Mechanics of Pb40/Sn60 near eutectic solder alloy
subjected to vibration. Appl Math Model 1998;22:601–27.
[6] Kim YB, Noguchi H, Amagai M. Vibration fatigue reliability of BGA-IC package
with Pb-free solder and Pb–Sn solder. Microelectron Reliab 2006;46:459–66.
[7] Wu ML. Vibration induced fatigue life estimation of ball grid array packaging. J
Micromech Microeng 2009;19:065005.
[8] Che FX, Pang John HL. Vibration reliability test and ﬁnite element analysis for
ﬂip chip solder joints. Microelectron Reliab 2009;49:754–60.
[9] Zhou Y, Al-Bassyiouni M, Dasgupta A. Vibration durability assessment of
Sn3.0Ag0.5Cu and Sn37Pb solders under harmonic excitation. J Electron Pack
2009;131:011016-1–6-9.
[10] Zhou Y, Al-Bassyiouni M, Dasgupta A. Harmonic and random vibration
durability of SAC305 and Sn37Pb solder alloys. IEEE Trans Compon Pack
Technol 2010;33(2):319–28.
[11] JEDEC standard for vibration: JESD22-B103B, JEDEC Solid State Technology
Association; 2002.
[12] Bathe KJ. Finite element procedures. Prentice-Hall; 1996.
[13] de Silva CW. Vibration fundamentals and practice. CRC; 1999.
[14] Gloth G, Sinapius M. Analysis of swept-sine runs during modal identiﬁcation.
Mech Sys Signal Process 2004;18:1421–41.