International Journal of Fatigue 88 (2016) 42–48

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International Journal of Fatigue

journal homepage: www.elsevier .com/locate / i j fa t igue

Fatigue life estimations of solid-state drives with dummy solder ballsunder vibration

http://dx.doi.org/10.1016/j.ijfatigue.2016.03.0160142-1123/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: ghjang@hanyang.ac.kr (G. Jang).

Jinwoo Jang, Gunhee Jang ⇑, Juyub Lee, Yeungjung Cho, Yusuf CinarDepartment of Mechanical Convergence Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, Republic of Korea

a r t i c l e i n f o

Article history:Received 16 December 2015Received in revised form 18 February 2016Accepted 11 March 2016Available online 12 March 2016

Keywords:Vibration analysisDummy solder ballGlobal–local analysisBasquin equationLead free solder ballSolid-state drive (SSD)

a b s t r a c t

An investigation of the effect of dummy solder balls on the fatigue life of a solid-state drive (SSD) undervibration was studied. Finite element analysis and forced vibration experiments of an SSD were con-ducted to evaluate the fatigue life of an SSD. Global–local analysis techniques were adopted in the finiteelement analysis to calculate the stress of the solder balls in the SSD. In the vibration experiments, theSSD with dummy solder balls was excited via a sinusoidal sweep vibration around the first resonant fre-quency until the SSD failed. Using the stress results from global–local analysis and the cycle to failureresults from the experiment, an S–N curve was derived for the SSD. This study showed that the solderjoints at the corners of the controller package were the most vulnerable components, and that applyingthe dummy solder balls to those areas decreased the stress of the solder balls and increased the fatiguelife of the SSD.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

A solid-state drive (SSD) is an electronic product that uses flashmemory to permanently store data, and is a next-generation infor-mation storage device that replaces hard disk drives (HDD). SSDshave no moving mechanical components, so they are characteristi-cally light weight, low in noise, low in power consumption, andhave fast data processing speeds as compared to HDDs. Theseadvantages have increased the demand of SSDs. However, portabledevices such as notebooks and tablet PCs are continuously exposedto vibrations and shock under various conditions, so an evaluationof the reliability and life of an SSD under vibration and shock hasbecome important during the developmental process. Steinbergannounced that 20% of electronic products are destroyed due tovibration [1], and the joint electron device engineering council(JEDEC), which is an independent semiconductor engineering tradeorganization and standardization body, set a standard for thevibration life test of electronic devices [2].

SSDs are an electronic product in which packages are connectedto the printed circuit board (PCB) through the surface mounting ofsolder balls, and solder balls are the most critical components todetermine fatigue-based failure in the SSD. Lead-containing soldermaterial has been conventionally used for centuries, but applyinglead-free solder materials for electronic devices has become obli-

gatory due to environmental issues [3]. In particular, the Sn–Ag–Cu (SAC) series of lead-free solder is the most commonly used sol-der material because its mechanical properties are more robustthan conventional solder materials [4–6]. SAC solder balls exhibitrobust performance against static loads and thermal loads, butexhibit poor fatigue characteristics for dynamic loads such as dropsand vibration [7].

Lee classified fourteen solder joint fatigue models into five cat-egories: stress-based, plastic strain-based, creep strain-based,energy-based, and damage-based [8,9]. Vibration load conditionsare one form of high cycle fatigue conditions, so the Basquin equa-tion based on stress was a proper model to predict the fatigue lifeof solder joints [10]. Therefore, many researchers have conductedstudies to predict the fatigue life of solder balls under vibrationusing the Basquin equation. Perkins and Wong proposed a vibra-tion test method for solder balls of a ceramic column grid arrayand a plastic ball grid array, and showed that the Basquin equationwas suitable for the vibration fatigue model [11,12]. Chen and Chepredicted the fatigue life of flip chip solder balls under various loadconditions using the cumulative damage index of Miner’s rule[13,14]. Cinar estimated the fatigue life change of Dynamic Ran-dom Access Memory (DRAM) modules according to the solderpad size change via vibration testing [15]. Methods to improvethe fatigue life of solder balls have also been developed. Typicalways to improve the fatigue life of solder balls are the dummy sol-der ball method and the underfill filling method. The underfill fill-ing method is a method used to fill epoxy in the empty space

Fig. 1. Layout of an mSATA SSD: (a) top view, and (b) side view.

J. Jang et al. / International Journal of Fatigue 88 (2016) 42–48 43

between the PCB and package to decrease the thermal stresscaused by the thermal expansion coefficient difference betweenthe PCB and package material. Noh compared the fatigue life ofelectronic devices according to types of underfill, and found thatapplying the underfill filling method increased the fatigue life ofdevices by 250% [16]. Solder balls in the outermost corners are usu-ally the most vulnerable to environmental conditions such asvibration, thermal cycling, shock, and bending. The dummy solderball method involves replacing vulnerable function solder balls atthe corners of a ball grid array with dummy solder balls whichdo not function electrically. Dummy solder balls do not affect theoperation of the product, and stresses on the function balls nearthe outermost corners can be decreased by exchanging them withdummy solder balls. However, the effect of dummy solder balls onthe fatigue life of electronic products such as SSDs has not beeninvestigated and mechanical reliability improvements in the vibra-tion fatigue life of SSDs has not been proposed.

In this report, the vibration fatigue life of a real SSD withdummy solder balls was estimated, and the effect of dummy solderballs on the fatigue life of SSDs was evaluated. Since the first nat-ural frequency has a major influence on fatigue fractures causedby vibration, forced vibration analysis and experiments were con-ducted around the first natural frequency. Locations of vulnerablesolder balls under vibration were determined via finite elementanalysis and experimentation. Local finite element analysis wasperformed to calculate accurate stress on the solder balls. Thestress of solder joints was calculated via finite element analysisand the measured fatigue lifetimes of SSDs in vibration experi-ments were used to obtain the Basquin equation. Using theobtained Basquin equation, the number of cycles to failure wasestimated for SSDs with and without dummy solder balls.

Fig. 2. Global finite element model of an SSD.

2. Global–local finite element analysis of SSDs

2.1. Development and verification of a finite element model for SSDs

We investigated an SSD with a mini serial advanced technologyattachment (mSATA) model as shown in Fig. 1. NAND, DRAM, andcontroller packages were mounted on the PCB with SAC 305 solderballs whose yield strength is 36 MPa. Generating an appropriatefinite element model of the solder balls was difficult because therewere a large quantity of solder balls which were too small com-pared to the overall SSD. Therefore, a global–local finite elementanalysis method was used to effectively analyze the behavior of asolder ball [17,18]. Fig. 2 shows a global finite element model ofthe entire SSD with 48,052 solid elements with 8 nodes. The globalfinite element model was composed of three different parts: a PCB,solder ball, and package. Each solder ball was modeled with onesolid element to minimize the number of element. The global finiteelement model was used to analyze the vibrational response ofoverall SSD and identify the position of the most vulnerable solderjoint among all solder balls. Fig. 3 is a local finite element model ofone solder joint which has 54,894 solid elements with 8 nodes. It iscomposed of a solder ball, upper and lower solder pads and soldermasks, and parts of package and PCB. And the solder ball in thelocal finite element model was modeled with 10,224 solid ele-ments. The displacement calculated from the global finite elementmodel was substituted into all nodes on the cut boundary of thelocal finite element model to analyze the detailed behavior of themost vulnerable solder joint. In this research, all of the materialbehaviors were assumed to be linear elastic under vibration load,because all of the components were expected to be under yieldstrength. The material properties of the global and local finite ele-ment models are represented in Table 1.

In order to verify the developed finite element model of the SSD,modal analysis and modal testing were performed. Fixed boundaryconditions were applied to the connector and two screw holes ofthe SSD in the analysis and experiment to describe real attachedsituations to the electronic device. The experimental setup to mea-sure the natural frequency of the SSD is shown in Fig. 4. The SSDwas excited by an impact hammer and the response of the SSDwas measured with a laser Doppler vibrometer (LDV). Fig. 5 showsthe frequency response function of the SSD mounted on a jig. Thefirst natural frequency of the SSD was 1443 Hz, and the response ofthe SSD was dominant at the first natural frequency in the fre-quency range between 20 Hz and 2000 Hz as described in theJEDEC standard. In Fig. 6, the simulated natural mode at the firstnatural frequency was compared to the measured one. In the anal-ysis and experiment, the maximum displacement occurred nearthe center of the SSD and the frequency difference was 0.649%.

2.2. Global finite element analysis

In global finite element analysis, the overall response of the SSDwas analyzed. According to the JEDEC standard, a sweeping sine

(a) Overall view

(b) Sectional view

Fig. 3. Local finite element model of a solder joint.

Table 1Material properties of an SSD.

Component Material Density(kg/m3)

Young’s modulus(MPa)

Poisson’sratio

PCB FR4 2752 26,000 0.40NAND, DRAM,

controller2138.6 13,000 0.402114.2 13,0002454.4 13,000

Solder ball SAC305 7094 44,113.2 0.36Solder pad Cu 8960 117,000 0.34Solder mask Epoxy 1150 5000 0.30

Fig. 4. Modal testing setup for an SSD.

Fig. 5. Frequency response function for an SSD mounted on a jig.

(a) Analysis result (b) Experimental result

Fig. 6. First mode shape of a mounted SSD at the first natural frequency.

44 J. Jang et al. / International Journal of Fatigue 88 (2016) 42–48

signal with 20 G amplitude was used for forced vibration analysis.The frequency function for a 1 dec/min sweep rate could be repre-sented as follows:

f ðtÞ ¼ f s10t60 ð1Þ

where f s was the starting frequency. The sweeping sine function forthe excitation force is shown below:

pðtÞ ¼ Mna0g sin60� 2pf slnð10Þ ð10 t

60 � 1Þ� �

ð2Þ

where Mn, a0, and g were the mass of the SSD, vibration amplitude,and gravitational acceleration, respectively.

The first natural frequency of the SSD was 1433.7 Hz, which wasthe only natural frequency in the frequency range between 20 Hzand 2000 Hz as described in the JEDEC standard. To determinethe damping effect of the structure, the damping ratio of the firstnatural frequency was calculated from the frequency responsefunction in Fig. 5 via the half power bandwidth method andapplied in a forced vibration analysis [19]:

n ¼ Dx2xn

¼ x2 �x1

2xnð3Þ

where Dx was the half power bandwidth between x1 and x2, andxn was the natural frequency. The damping ratio nwas measured as0.04.

Since the first natural frequency had a major influence on thevibration-induced fatigue fracture, global finite element analysiswas conducted around the first natural frequency [20]. A modesuperposition method using 40 natural modes was applied in thetransient analysis of the global finite element model after confirm-ing the convergence of the proposed global finite element model.The z-directional force as shown in Eq. (2) excited the SSD as a baseexcitation. An integration time step of 10 ls was set to accuratelyanalyze the behavior of an SSD in its first natural frequency of1433.7 Hz. Fig. 7 shows the time–displacement result at the centerof the SSD during the forced vibration analysis. It showed that themaximum displacement occurred when the sweeping sine fre-quency passed through the first natural frequency [21,22].

While the SSD was deformed, von Mises stress was calculated atthe solder balls under multiaxial stress and strain. Fig. 8 shows themaximum solder ball stress under NAND, DRAM, and controllerpackages according to frequency increase under 20 G vibrationamplitude, and the positions of the maximum solder ball stressunder NAND, DRAM, and controller packages are a, b and c in

Fig. 7. Time–displacement result at the maximum response point of an SSD aroundthe first natural frequency.

Fig. 9. Stress distribution of solder balls for a global model at 1435 Hz.

J. Jang et al. / International Journal of Fatigue 88 (2016) 42–48 45

Fig. 9. The maximum stress was calculated at 1435 Hz, which wasafter the first natural frequency. The stress distribution of ball gridarray on the top side of the SSD when the force excited at 1435 Hz,can be seen in Fig. 9. The solder ball under the controller packagewhere the maximum displacement occurred also yielded the max-imum stress. Large stress value was calculated at the solder ballnear the corner of a package and it was calculated in order of thesolder balls c, d, and e. The stress values of solder ball c and e werecalculated as 16.89 MPa and 11.74 MPa under 20 G vibrationamplitude. Thus, it was expected that solder balls would fail inthe order of the solder balls c, d, and e. In the real SSD, solder ballsc and d were dummy solder balls, and solder ball e was a functionsolder ball, so the SSD works until solder ball e fails. Even if thehighest stress occurred at dummy solder ball c in the SSD, functionsolder ball e which was the most vulnerable among all functionsolder balls determined the fatigue life of the SSD.

2.3. Local finite element analysis

To identify the precise position and stress value for a vulnerablesolder ball, a local finite element model of the SSD was analyzedunder forced vibrations. For the local finite element analysis, a fullmatrix method was applied and the integration time step was setto 10 ls, which was identical to the value used for the global finiteelement analysis. Calculated time–displacement results aroundfunction solder ball e and dummy solder ball c from the global

1430 1433 1436 1439 14420

5

10

15

20

25

Frequency [Hz]

Stre

ss [M

Pa]

Under Controller packageUnder DRAM packageUnder NAND package

1435 Hz

Fig. 8. A comparison of the maximum solder ball stress for each package area.

finite element model were applied to the cut boundary of the localfinite element model as shown in Fig. 3(a).

Fig. 10 shows the stress distribution of dummy solder ball c ofthe controller package under forced vibration with an amplitudeof 20 G. The results showed that the maximum stress occurred atthe interconnections between the upper solder pad and solder balland that the solder joint crack would occur at the interconnectionsbetween the upper solder pad and solder ball. Using the samemethod, a local finite element model was analyzed repeatedly forthe function solder ball. Fig. 11 shows the maximum stress valueat the interconnections of function solder ball e and dummy solderball c according to vibration. Similar to the result of the globalfinite element analysis, the maximum stress of the solder ball inthe local finite element analysis also occurred around the first nat-ural frequency. For a vibration amplitude of 20 G, 6.26 MPa ofstress occurred in dummy solder ball c, and 4.66 MPa of stressoccurred in function solder ball e. Therefore, stress on a functionsolder ball within an SSD could be reduced by 26% by applyingdummy solder balls.

3. Forced vibration experiments to estimate the fatigue life ofSSDs

3.1. Forced vibration experiments of SSDs

Forced vibration experiments of SSDs were conducted to verifythe position of the most stress concentration in global–local finiteelement analysis and to measure the number of cycles to failure forthe SSD under various vibration amplitude. The SSD with dummy

(a) Isometric view (b) Side view

Fig. 10. Local finite element model stress distribution of a solder ball at 1435 Hz.

1430 1433 1436 1439 14420

3

6

9

12

15

Frequency [Hz]

Stre

ss[M

Pa]

20G excitation with dummy ball25G excitation with dummy ball30G excitation with dummy ball

(a) Function solder ball e.

1430 1433 1436 1439 14420

3

6

9

12

15

Frequency[Hz]

Stre

ss[M

Pa]

20G excitation without dummy ball25G excitation without dummy ball30G excitation without dummy ball

(b) Dummy solder ball c.

Fig. 11. Comparison of the maximum function solder ball stress due to theexcitation amplitude.

(a) Overall setup

(b) Jig to mount a SSD on the shaker

Fig. 12. Forced vibration experimental setup for a mounted SSD.

46 J. Jang et al. / International Journal of Fatigue 88 (2016) 42–48

solder balls was excited by a LDS V450 magnet shaker with asweeping sine signal. The sweep range was set between 1400 Hzand 1500 Hz to measure the response of the SSD around the firstnatural frequency. Vibration amplitudes of 20 G, 25 G, and 30 Gwere applied to determine the various fatigue lifetimes of theSSD according to the stress of the solder balls. The experimentalsetup is shown in Fig. 12. A signal analyzer and power amplifierwere set to generate the sweeping sine signal and excite the SSD.The jig was used to mount an SSD on the shaker and to depictthe real attached situation of the SSD to the electronic device. Asshown in Fig. 12(b), the left side of the SSD was tightened on thebase by two screws and the right side was closed by the coverand fastened by two screws to match the real joint condition ofthe SSD as well as the boundary condition of the global finite ele-ment analysis. The SSD was connected to a computer via a univer-sal serial bus (USB) port, and detection of the SSD by the computerwas simultaneously checked to measure the number of cycles tofailure for the SSD. In the sweeping sine test, the total number ofcycles to failure was calculated as follows:

N ¼ tfatiguetloop

Z tloop

0f s10

t60dt ð4Þ

where tloop was the time required to increase the excitation fre-quency from 1400 Hz to 1500 Hz, and was the time difference cal-culated by substituting the starting and ending frequency to Eq.(1). tfatigue was the total time to failure for the SSD.

In the experiment, it was confirmed that solder joint cracksoccurred only in dummy solder balls c and d, and function solderball e under the controller package. The experimental resultsshowed that concentrated stress cracked dummy solder ball c first,propagating to dummy solder ball d, and finally to function solderball e. The SSD malfunctioned after the stress cracks propagated tofunction solder ball e, and the cross-sectional images of crackedsolder balls are shown in Fig. 13. The images showed that the crackoccurred at the interconnection between the solder ball and uppersolder pad. The position of the crack was same as with the concen-trated stress in the local finite element analysis.

3.2. Derivation of the S–N curve for SSDs

Fatigue failure occurred while a material was under repeatedtensile and compression loading with damage accumulating. Thenumber of cycles to failure for the material decreased as the exter-nal force and stress increased. The relationship between theamount of stress on the material and the number of cycles to fail-ure could be represented by an S–N curve [23]. In this study, thenumbers of cycles to failure for the SSD under various vibrationamplitudes were measured in forced vibration experiments, withthe maximum stress at the most vulnerable solder balls being cal-culated via global–local finite element analysis. Two number ofcycles to failure and one maximum stress for each vibrationalamplitude were used to derive the SSD S–N curve shown inFig. 14. A stress-based S–N curve for high cycle fatigue under vibra-tion could be determined by the Basquin equation as follows:

ra ¼ r0f ð2Nf Þb ð5Þ

where ra was the stress amplitude and 2Nf was the number of fail-ure reversals. The material constants r0

f and b were the fatiguestrength coefficient and fatigue strength exponent, respectively.From Fig. 14, the material constants of the SSD with dummy solderballs were determined to be 112.7 MPa and �0.198, respectively.Fig. 14 shows that the fatigue lifetimes of an SSD under vibrational

(a) Solder ball layout (b) Function solder ball e

(c)Dummy solder ball c (d) Dummy solder ball d

Fig. 13. Cross-sectional views of a cracked solder joint.

Fig. 14. S–N curve of an SSD with dummy solder balls.

Fig. 15. Fatigue life comparison due to dummy solder balls in an S–N curve.

J. Jang et al. / International Journal of Fatigue 88 (2016) 42–48 47

amplitudes of 20 G, 25 G, and 30 G were estimated to be 9.09, 2.96,and 1.18 million cycles, respectively.

3.3. Fatigue life improvement due to dummy solder balls

The fatigue life improvement of an SSD due to dummy solderballs was estimated by assuming that dummy solder balls c andd were function solder balls. If dummy solder balls c and d werereplaced with function solder balls and 20 G of vibration wereapplied to the SSD, 6.26 MPa stress would result, which was thestress on dummy solder ball c (the maximum stress value for allfunction solder balls). Using the derived S–N curve, the fatigue life-time could be estimated for an SSD without dummy solder balls. InFig. 15, the derived S–N curve showed that 6.26 MPa of stressresulted in 2.07 million cycles, which was 4.5 times lower thanfor a stress of 4.66 MPa, which was the stress on function solderball e. Therefore, it could be concluded that applying dummy sol-der balls in the SSD decreased the concentrated stress in the func-tion solder balls by 26% and increased the fatigue lifetime by 4.5times for the given SSD.

4. Conclusion

In this study, the fatigue life of SSDs under vibration was eval-uated with real modules, not daisy chains. The effect of dummysolder balls on the fatigue life of SSDs was also estimated via glo-bal–local finite element analysis and forced vibration experiments.Modal testing was conducted with an SSD attached to a jig, andfinite element models were developed within 1% error of the SSDnatural frequency. It was confirmed that the first natural frequencyof an SSD had a dominant effect on fatigue failure. Therefore, asweeping sine excitation around the first natural frequency wasused to perform the analysis and experiment. The stress distribu-tion for the global finite element analysis showed that the positionof the most vulnerable solder ball was at the corner of the SSD con-troller package. Local finite element analysis was performed foreach dummy solder ball and function solder ball. The resultsshowed that the maximum stress of the function solder ballsdecreased by 26%, when dummy solder balls were applied at thecorners of the packages. The number of cycles to failure were mea-sured in forced vibration experiments and confirmed that the sol-der balls cracked at the same position of maximum stress as solderballs in the global–local finite element analysis. Based on theresults of the forced vibration analysis and experiments, materialconstants of the Basquin equation were calculated, and the S–Ncurve was derived. Comparing the maximum stress of function sol-der balls in SSDs with and without dummy solder balls, the S–Ncurve showed that dummy solder balls increased the fatigue life-time of SSDs by 4.5 times. This research will contribute to estimat-ing and improving the fatigue life of SSDs.

Acknowledgement

This research was supported by a Semiconductor Industry Col-laborative Project between Hanyang University and Samsung Elec-tronics Co. Ltd.

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