Damage mechanics of The Author(s) 2013 electromigration and · 2014-09-22 · electromigration and...

Article

Damage mechanics ofelectromigration andthermomigration in lead-freesolder alloys under alternatingcurrent: An experimental study

Wei Yao and Cemal Basaran

Abstract

Electromigration and thermomigration reliability of Sn96.5%Ag3.0%Cu0.5 (SAC305 by weight) solder

joints under alternating current is studied experimentally with the maximum current density from

2.1� 105 A/cm2 to 1.76� 106 A/cm2, and frequency from 100 kHz to 4 MHz. During the experiment,

hot spots are observed at current crowding corners and the skin layer of solder joints. As a result,

highly localized current density and joule heating exist. The combined effect of electron wind force and

thermal gradient drives mass to diffuse toward the center of solder joints. Resistance change due to

temperature change and current crowding was carefully recorded. Ten percent resistance change after

thermal steady state was defined as failure. Scanning electron microscopic images show void formation in

current crowding corners and in the skin layer of solder joints. Damage of solder joints under alternating

current stressing is observed a combined process of both electromigration and thermomigration, and to

be proportional to the loading frequency and current density. Owing to the reversed electron wind force,

material healing is observed in most of our test vehicles. A statistical mean time to failure equation is

proposed for lead-free solder joints under alternating current stressing.

Keywords

Alternating current electromigration, alternating current thermomigration, scanning electron microscope,

solder joint, mean time to failure, skin effect, electronic packaging

International Journal of Damage

Mechanics

2014, Vol. 23(2) 203–221

! The Author(s) 2013

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DOI: 10.1177/1056789513488396

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Electronic Packaging Laboratory, Department of Civil, Structural and Environmental Engineering, University at Buffalo, The State

University of New York, Buffalo, NY, USA

Corresponding author:

Cemal Basaran, Electronic Packaging Laboratory, Department of Civil, Structural and Environmental Engineering, University of

Buffalo, The State University of New York, Buffalo 14260, NY, USA.

Email: [email protected]

Introduction

The insatiate demand for smaller electronic packaging, higher performance and larger input/output(I/O) count has made flip-chip ball grid array (BGA) the only practical connection in very large scaleintegration (VLSI) device packaging. It is estimated that the solder bump diameter will reach 10 mmranges in the near future (Tu, 2007). Consequently, the nominal current density carried by solderjoints will jump to 105A/cm2. Electromigration (EM) and thermomigration (TM) in electronicdevices have become the major reliability concerns in the electronic packaging industry. EM is anelectron wind force driving mass diffusion process. Conducting electrons scatter with ions andtransfer part of their momentum to ions. As a result, some of the ions diffuse in the same directionas the electrons. It causes mass hillock at the anode side of solders and depletion at the cathode side.Two types of failure relate to the EM damage mechanism: short-circuit failure on the anode side,and open-circuit failure on the cathode side. The anode side is less of a failure concern because theminimum clearance specified in design and polymer fill-in between solders, which effectively preventwhisker-induced short-circuit failure. It makes mass depletion at the cathode side the major concern.

Increased resistance, highly localized joule heating and signal distortion are attributed to EMdamage mechanism. Another important reliability issue comes from TMwhich is caused by unevenlydistributed joule heating in solder joints. Temperature at current crowding corners is several degreeshigher than region at the center of solder joints. This difference in temperature creates a thermalgradient large enough to transport atoms from hot to cold regions. Ye (2004) and Ye et al. (2004a)showed that 1000�C/cm temperature gradient is critical gradient to initiate TM in solder alloys. Themass diffusion process during direct current (DC) loading is driven by four forces: (1) momentumexchange between scattering electrons and atoms, or ‘electron wind force’; (2) thermal gradient drivenmass diffusion, or TM; (3) chemical potential induced material redistribution; (4) stress gradientdriven mass diffusion. Both EM and TM failure mechanisms of solder joints subjected to DC stressinghave been studied extensively in several literatures (Abdulhamid and Basaran, 2009; Abdulhamidet al., 2008; Basaran and Jiang, 2002; Basaran and Lin, 2007, 2008; Basaran and Wen, 2003; BasaranandYan, 1998; Basaran et al., 2003, 2005a, 2005b, 2005c, 2007, 2008; Bastawros andKin, 2001; Chengand Siewert, 2003; Chuang and Lin, 2003; Lee et al., 2001; Li and Basaran, 2009; Li et al., 2008a,2008b; Lin and Basaran, 2005; Ye et al., 2004b, 2006, 2008). However, alternating current (AC)-induced EM and TM degradation in literature is very scarce, especially for lead-free solder joints.

The driving forces in AC differ substantially from those in DC loading. Electron wind forcereverses its direction during negative current loading period, which partially heals the mass diffusionfrom the previous positive loading period, at least theoretically. This is called material healing effect(Amiri et al., 2011; Yao and Basaran, 2012a, 2012b, 2013a, 2013b; You et al., 2009). Due to jouleheating, the highest temperature happens at current crowding corners, and drives atoms into thecenter of the cross section. Since the current density distribution is independent of the currentflowing profile as far as TM concerned, there is no difference whether AC or DC is applied. Bothchemical potential and stress gradient terms depend on how the vacancy concentration developsduring the current loading history (Basaran et al., 2012; English et al., 1972; Jiang et al., 1994;Shingubara et al., 2004; Tang and Basaran, 2001). In experiments, we observed that mass accumu-lation happened first at one side of the solder joint, inducing compressive stress locally; withincreased loading time, mass hillock transferred to the exact opposite side, which reversed thedirection of chemical potential and stress gradient driving forces. The different degradation mech-anisms between AC and DC lead to substantial different estimation in the reliability concern, e.g.lifetime under AC stress can be an order of magnitude longer than that under DC with otherwise thesame conditions (Aronstein, 1996a; Hatanaka et al., 1989; Liew et al., 1989; Tao et al., 1998;Ting et al., 1993; Wu et al., 2009; Zhang et al., 2002). Tao et al. (1993a, 1993b, 1996, 1997) studied

204 International Journal of Damage Mechanics 23(2)

AC EM reliability of aluminum and copper thin films in a wide frequency range, from 1MHz to200MHz. The authors claimed that pure AC lifetime depends on TM instead of EM at highfrequencies, and current loading contributes only to material healing, thus proposing an effectivecurrent density based mean time to failure (MTTF) equation. Tao’s MTTF model has limitations,due to the fact that it is based on empirical data from Al and Cu thin films, as such, it only works formetal thin film interconnects. Solder joints have an asymmetric current conducting path, e.g. inter-connect to solder joint connection makes current density in corners of solder joints much higher thantheir neighboring areas. Thus, diffusion from positive loading cannot be healed fully during thefollowing negative loading period as observed in pure metal thin films. Aronstein (1996b) didexperiments on aluminum thin films subjected to AC loading at a current density of 106 A=cm2.In his study, thin film conductors failed from AC EM. However, lifetime was found to be less thanthose subjected to DC stressing, which has never been confirmed by any other researcher. Byassuming perfect material healing effect in thin film conductors under AC, Tu (2007) indicated inhis book that thin film conductors subjected to AC loading fails due to TM instead of EM. However,this is not true in solder joints because: (1) solder joints are alloy with intermetallic compounds(IMCs); (2) mass diffusion from the positive loading period cannot be restored fully during thenegative one, because their microstructure is not symmetric; (3) lattice structure is not perfect,defects in lattice, IMCs and microcracks contribute to EM damage unevenly; (4) Al/Cu race inter-connection with solder joint makes current crowding and joule heating highly localized. ThereforeEM/TM in solder joints is not perfectly symmetric, such that it can be healed just partially byreversing current direction. These factors do not exist in metal thin film conductors. Finally, theskin effect during high frequency AC stressing results in a higher than usual current density in the‘skin layer’ of a solder joint, which induces more mass diffusion than the theoretical estimation.We believe that both TM and EM contribute to failure of solder joints under AC.

With wide-spread application of AC signals and BGAs in microelectronic devices, AC-inducedfailure mechanisms of lead-free solder joints need to be studied in order to provide a better lifetimeestimation of microelectronic devices. In this study, we report the influence of skin effect, frequencyand current density on MTTF of lead-free solder joints subjected to AC stressing experimentally.

Experiment setup

Test vehicles

The test vehicle in Figure 1 is a specially designed flip-chip package. Lead-free Sn96.5%Ag3.0%Cu0.5 (SAC305 by weight) BGA connects the chip to the printed circuit (PC) board. Pitchbetween adjacent solder bumps is 270 mm with polymer fill-in. The solder bump has a diameter of112 mm and stand-off height of 105 mm. Cu pad of the substrate is surface finished with electrolessplated Ni/Au. Diameter of tri-layer Ti/Cu/Ni under bump metallurgy (UBM) is 112 mm with athickness of 3 mm. The aluminum trace is 65 mm wide and 1 mm thick on the silicon die side, con-necting to the top of solder bumps; while copper trace of 65 mm wide and 15 mm thick on the PCboard contacts to the bottom. The substrate solder mask opening is 110 mm. Dimension and materialfinish information of the test vehicle is listed in Table 1.

Experimental procedure

Experimental setup is shown in Figure 2. An AC power supply outputs the designed signals: voltage,frequency and duty cycle. Two multimeters are programmed to collect resistance reading of R1 and

Yao and Basaran 205

R2 every 5 s with a four-wire connection setup as shown in Figure 3. Principle of four-wire scheme is:(1) a parallel connected voltmeter measures voltage on the solder joint; (2) a series connected ampmeter measures current of circuitry; (3) the multimeter automatically divides voltage by the currentreading, and gives the in situ resistance. Figure 4 shows the current flowing profile in the test vehicle.It can be seen that current goes through two solder joints and one aluminum trace in R1, but onlyone solder joint and one aluminum trace in R2. Thus, we can obtain the exact resistance change ofone solder bump by R1–R2. One thermometer with two leads is programmed to measure

Figure 1. Test vehicle used in the AC electromigration/thermomigration experiments.

AC: alternating current.

Table 1. Dimension of the flip chip test vehicle package (Su and Li, 2009).

Features Dimension

Package size 27.3� 27.3� 1.14 mm3

Die size 7.62� 7.62� 0.74 mm3

UBM Ti0.1 mm/Cu0.5mm/Ni2 mm

UBM diameter 112 mm

Passivation opening 90 mm

Al trace on silicon 65 mm� 1 mm

Bump size 112 mm in diameter 105mm in standoff

Bump pitch 270 mm

Substrate pad finish Electroless Ni/Au on Cu Ni5 mm/Au0.05 mm/Cu5 mm

Substrate pre-solder Sn3%Ag0.5%Cu

Substrate Cu trace 65 mm� 15 mm

Substrate solder mask opening 110 mm

UBM: under bump metallurgy.


Figure 2. Experimental design of lead-free solder joints subjected to sine waveform AC stressing.


Figure 3. Four-wire connection scheme to measure effective resistance of solder joints subjected to AC loading.


Figure 4. Current flow scheme of the test vehicle.

Yao and Basaran 207

temperatures on the silicon chip side and PC board side every 30 s. The test vehicle is put in athermal chamber at 70�C, which is the normal operating temperature for most consumer electronicdevices. Ten percent resistance change in the solder joint is used to define failure of the solder joints.Sine waveform AC is applied onto the test vehicle, with frequencies varying from 100 kHz to 4MHz,and maximum current density varying from 2.1� 105A/cm2 to 1.76� 106A/cm2.

Three sets of the same test vehicles are also used to test for skin effect in solder joints. Data fromthe three sets of test vehicles are averaged to obtain conclusive results.

Results and discussion

Lifetime of solder joints under AC is longer compared to that of solder joints under DC. Figure 5shows scanning electron microscopic (SEM) images of solder joints under various AC loadings withone under pulsed direct current (PDC) for comparison. Figure 5(a) is the initial profile of solderjoints before any electric loading. Figure 5(b) shows a solder joint subjected to 500 kHz PDC loadingat a maximum current density of 1.76� 106A/cm2, while in test (c) we change the current signal toAC but keep other parameters the same. Under current loadings, both PDC and AC loading resultin observable vacancy formation as shown in Figure 5(b) and (c). However, void formation is onlyobserved in the skin layer and at the current crowding corner rather than across the entire crosssection commonly found in DC cases. In Figure 5(d) and (e), we increase the AC signal to 2MHzand 4MHz, respectively, while keeping other parameters unchanged. Voids growth is againobserved simply in the skin layer. The asymmetric vacancy distribution in AC results from theasymmetric current conducting path and microstructure defects. In Figure 5(f), the AC signal isincreased to 10MHz. Voids are observed to collapse at current crowding corners, which will even-tually result in open-circuit failure. In lead-free solder joints, another important reliability issuecomes from tin and copper reaction, which forms Cu6Sn5 whiskers/IMCs in the SAC305 and Cutrace interfaces (Dariavach et al., 2006; Yoon et al., 2003). It introduces cross talk between neigh-boring conductors and causes circuitry failure. From Figure 5, it can be seen that IMC grows intothe center of solder joints during PDC loadings, which indicates diffusion of substrate material intolead-free solder joints. However, in AC loadings, reactions between copper and tin are effectivelyminimized by the reversing electromagnetic field.

Skin effect

Skin effect is the current redistribution mechanism of conductors placed in time-varying electro-magnetic field. Under time-varying current loadings, eddy current is produced that repel currentflow in center cross section but intensify it in the skin layer. Current travels practically in skin layerinstead of the entire cross section. Increasing frequency thins the skin depth, and results in a highereffective resistance.

Figure 6 shows resistance of solder joints as a function of frequency of AC at an ambient tem-perature of 70�C. X-axis is plotted in logarithmic scale while the Y-axis is linear. Resistance is stablefrom 1kHz to 1MHz, with 10% measured difference between the maximum and minimum value,whereas it starts to grow at higher frequency. Larger current density results in a bigger resistancegrowth rate. Current density dependence of resistance was also reported by Basaran et al. (2009a)and Yao and Basaran (2012c). Classical physics assumes that the electric field is spatially constant inthe calculation of current flowing through conductors. This assumption is valid only when theelectric field does not vary appreciably over a distance of free conducting electron path. At lowfrequency, the skin depth is much larger than the mean free electron path, therefore classic theory


is valid. At high frequency, however, electric field penetration depth is in order of electron mean freepath, and the spatial variation of the electric field must be taken into account. From our experi-mental results, 1MHz is observed as the critical frequency above which the skin effect becomesinfluential. The critical frequency (usually inMHz range) only depends on conducting material andshape of the conductor. It should be pointed out that for current density above 1.41� 106A/cm2 andfrequency of 15MHz (Figure 6), it was observed that resistance stops growing so much that itactually decreases about to 15%.

Figure 5. SEM profiles of solder joints under time-varying current loadings: (a) initial profile; (b) under 500 kHz

PDC; (c) under 500 kHz AC; (d) under 2 MHz AC; (e) under 4 MHz AC; (f) under 10 MHz AC.SEM: scanning electron

microscope; AC: alternating current; PDC: pulsed direct current.

Yao and Basaran 209

The measured resistance has an exponential dependence on AC frequency with the curve fittingconfident value r-square being 96%

R0 ¼ �� e�f ð1Þ

where R’ is the effective resistance of a solder ball in Ohm, � and � are parameters depending on thecurrent density and AC waveform and f is the frequency in megahertz. It is found that a¼ 0.84 �and �¼ 0.01361/MHz for sine AC at a current density of 1.1� 106A/cm2. � is found to be between0.021 and 0.0075 for current density from 2.64� 105A/cm2 to 2.11� 106A/cm2. Higher currentdensity has a smaller � and larger �.

Figure 7 shows the current density dependence of the effective impedance of solder joints underAC with varied frequencies at 70�C. It can be seen that the measured resistance grows linearly withcurrent density. The growth rate does not vary appreciably with frequency. High frequency inducesa larger resistance value owing to the skin effect discussed above. The following linear equation isobtained with r-square of 93%

R ¼ �1j ð2Þ

where j is the current density (A/cm2), and �1 is a material constant that depends on conductors,0.5� cm2/A for SAC305 solder joints. Combing equations (1) and (2), we obtain the effective resist-ance of lead-free solder joint under AC as

R ¼ R0 �� e�f þ �j� �

ð3Þ

where R0 is the initial resistance; � and � are parameters depending on the current density and ACcurrent waveforms; � is a parameter only depending on conducting materials, which is 0.5 � cm2/Afor SAC305 solders.

Figure 6. Frequency dependence of skin effect in solder joints under AC stressing at 70�C.



Current density dependence of failure mechanism

In this study, 10% resistance increase after thermal equilibrium (steady state) is used to define thefailure of a solder joint (Basaran et al., 2009b; Li et al., 2008). Thermal equilibrium is defined astemperature increasing initially due to joule heating and reaching the steady state. MTTF of solderjoints is a function of current density, frequency and ambient temperature. On account of the skineffect discussed above, initial resistance varies under different testing conditions. For comparisonpurpose, resistance in all figures is set to start at 1. The detailed testing data are presented in Table 2.

In this section, we set the frequencies for all tests at 4MHz, temperature at 70�C, duty cycle at50%, and vary the current density from 2.1� 105A/cm2 to 1.76� 106A/cm2. Current density spe-cified above is the maximum value at current crowding corners as shown in Figure 8. Electricpotential gradient (indication of current density) at Al/Cu trace and solder joint connection areais 2.72� 103V/m, around 20 times of the value in the center cross section, 1.183� 102V/m.

Figure 7. Current density dependence of resistance of solder joints under AC stressing at 70�C.


Table 2. Frequencies and current densities dependence of mean time to failure of lead-free solder joint subjected to

sine waveform AC at an ambient temperature of 70�C.

Sine AC test at 70�C Frequency Initial R (�) Failure R (�) Current density (A/cm2) Time to failure (h)

Frequency

dependence

100 kHz 0.521 0.672 1.76� 106 217.8

500 kHz 0.207 0.224 1.76� 106 163.7

2 MHz 0.353 0.381 1.76� 106 27.5

4MHz 0.397 0.441 1.76� 106 3.9

Current density

dependence

4 MHz 0.292 0.351 2.1� 105 169.5

4 MHz 0.383 0.424 6.5� 105 112

4 MHz 0.416 0.458 1.4� 106 66.5

4 MHz 0.397 0.441 1.76� 106 3.9


Yao and Basaran 211

Moreover, with AC frequency being above 1MHz, the skin depth of solders cannot be ignored.Thus, effective maximum current density in solder joints can reach an even higher value. The highlylocalized current distribution also induces an unevenly distributed joule heating. Figure 9 shows thattemperature in the aluminum trace of the silicon die side is 6�K higher than the bottom copper trace.The silicon die serves as major heat sinks, with a heat conductivity coefficient of 149 W/m�K. Wedefine thermal gradient as the difference between the average temperatures in the copper trace nearthe substrate TCu and the aluminum trace near the chip TAl, divided by the bump height, h: (TAl–TCu)/h. Thermal gradient is calculated to be 600�K/cm. This thermal gradient is not large enough toinduce TM (Hsiao and Chen, 2009; Ye et al., 2003), so we can conclude that the damage mechanismof solders under AC is mainly due to EM.

Figure 10 shows temperature and resistance evolution of a solder joint subjected to AC densitybetween 2.1� 105A/cm2 and 1.76� 106A/cm2, frequency of 4MHz and an ambient temperature of70�C. Figure 10(a) shows the temperature profile for the solder joint under a current density of2.1� 105A/cm2. Temperature in Al at silicon chip side increases from 70�C to 73�C during the firsthour, then reaches its thermal equilibrium and fluctuates between 72.5�C and 73.5�C with a periodof 200 s. Figure 10(b) shows the corresponding resistance change. Comparing Figure 10(a) and (b),we conclude that resistance change during the first hour is due to joule heating, as the test vehicle’stemperature increases from 70�C to 73�C. EM/TM induced mass diffusion is responsible for thefollowing resistance change. Similar temperature distribution is observed in other tests; hence thetemperature profile is not plotted for all tests. From Figure 10(b), it can be seen that the solder jointresistance fluctuates forming a band during the loading history, with the average value growingcontinually. Since the thermal gradient does not change during AC loading, the resistance dropreflects simply material healing from the reversed electron wind force. Failure happens after 169 h ofcurrent loading at 0.35 � as shown in Table 2. In Figure 10(c) we increase the current density to8.75� 105A/cm2 while keeping other parameters unchanged. The initial load-on resistance is 0.38 �.Eight percent resistance increase is observed in the first 60 h of current loading. Then it reaches a

Figure 8. Electric potential gradient of the solder bump subjected to AC loadings at 70�C from FEA.

AC: alternating current; FEA: finite element analysis.


quasi-stable state. The test vehicle fails after another 50 h of current loadings. The post-failureresistance drop comes from vacancy collapse at the current crowding corner, which forces thecurrent to conduct through inner layer of the damaged solder bump. In Figure 10(d), we furtherincrease current density to 1.4� 106A/cm2. This time resistance grows continuously after reaching73�C with healing barely observed. The solder joint fails after 66 h of current stressing. InFigure 10(e), the current density is further increased to 1.76� 106A/cm2. The thermal steady-statetemperature was increased to 76�C with a thermal gradient as high as 600�K/cm. Lifetime reducesconsiderably to 3.9 h with very limited material healing observed during the loading history. Itshould be pointed out that during the whole loadings history we do not observe a temperaturerise large enough to induce this amount of resistance change. We conclude that tested solder jointsubjected to high current density fails EM/TM even under AC stressing.

The current density dependence of MTTF is plotted in Figure 11. Increasing current densityresults in a shorter lifetime. Non-linear regression gives the following relationship between MTTFand electric potentials with r-square value of 83%

MTTF ¼ 64:9� j�0:64 ð4Þ

where MTTF is mean time to failure of solder joints in hours, and j is the current density in A/mm2.

Frequency dependence of failure under AC

In this section, we set the nominal current density at 1.76� 106A/cm2, temperature at 70�C, dutycycle at 50%, and vary the frequency from 100 kHz to 4MHz.

Figure 9. Temperature profile of the test vehicle subjected to AC loading with current density of 7.0� 105 A/cm2

and ambient temperature of 70�C from FEA.

AC: alternating current; FEA: finite element analysis.

Yao and Basaran 213

Figure 10. Resistance of lead-free solder joint subjected to 4 MHz sine waveform AC loadings at an ambient

temperature of 70�C: (a) temperature profile; (b) resistance profile at current density of 2.1� 105 A/cm2; (c) resist-

ance profile at current density of 8.75� 105 A/cm2; (d) resistance profile at current density of 1.4� 106 A/cm2;

(e) resistance profile at current density of 1.76� 106 A/cm2.



Figure 10. Continued.

Figure 11. Current density dependence of MTTF of solder joints subjected to 4 MHz AC stressing at 70�C.

MTTF: mean time to failure; AC: alternating current.

Yao and Basaran 215

In Figure 12(a), 100 kHz AC loading is applied to the test vehicle. The initial resistance fluctu-ation is due to joule heating as discussed in the previous sections. It reaches the steady value after21 h of current loadings, then it stays stable for another 24 h. An abrupt 6% resistance surge isobserved in another 1 h, which is followed by material healing. Resistance slowly heals back to theinitial value in about 5 h. The solder joint survives 217.8 h of AC loading, with resistance surgingfrom 0.52� to 0.67�. The failure point is circled in Figure 12(a). The frequency is increased to500 kHz in Figure 12(b). Material healing is observed continuously during the loading history, withmaximum 80% healing resistance observed. Failure happens after 163.7 h of current stressing. Evenafter the failure, resistance still heals back a noticeable amount. However, since 10% resistancechange is defined as the failure, the test vehicle is considered to be failed. In Figure 12(c), we increasethe frequency to 2MHz. Resistance rises just 3% in the first 22 h. The resistance growth rate thenpicks up and fails the solder joint in another 5 h. Resistance growth during the test comes from thevoid formation at the current crowding corner and skin layer of solder joints. During the initialloading period, negative electron wind force partially heals material damage from previous positiveloading period. However, the damage and healing are not symmetric, due to asymmetric micro-structure and package geometry. With increased loading time, chemical potential and stress gradientalso start to build up. As a result, the resistance of the solder joints increases to about 10% in a shorttime. In Figure 12(d) we further increase the AC frequency to 4MHz. At this high frequency, nomaterial healing is observed. Resistance increases directly from 0.395� to 0.441� in around 4 h ofcurrent loadings, and fails the solder joint.

Frequency dependence of MTTF of lead-free solder joints is plotted in Figure 13. It can be seenthat increasing frequency shortens the lifetime of a solder joint, which follows a power relationship.The following nonlinear regression equation gives a relationship between frequency and MTTF with86% confidence value

MTTF ¼ 76:5� f �0:48 ð5Þ

where MTTF is the mean time to failure of solder joints in hours and f is the frequency inMHz.

Mean time to failure of solder joint under AC stressing

The detailed testing data are shown in Table 2. To obtain a statistical meaningful formulation, eachresult averages from several identical tests. The frequency and current density dependence of MTTFof solder joints under AC stressing follows a lognormal distribution. By combining equations (4)and (5), the following equation is obtained

MTTF ¼’

f 0:48 � j 0:64ð6Þ

After incorporating Arrhenius temperature dependency term, we propose MTTF for lead-freesolder joints under AC stressing as follows

MTTF ¼’

f 0:48:j 0:64eE=kT ð7Þ

where ’ is a parameter depending on material properties, f is the frequency inMHz, j is the currentdensity inA/cm2, E is the vacancy activation energy in eV, and k is the Boltzmann’s constant.


Figure 12. Solder joints subjected to sine AC wave form current loadings at 70�C with current density

1.76� 106 A/cm2: (a) resistance profile under 100 kHz AC; (b) resistance profile under 500 kHz AC; (c) resistance

profile under 2 MHz AC; (d) resistance profile under 4 MHz AC.


Yao and Basaran 217

The current density has an exponent of 0.64, which is much smaller than the exponent of 2commonly found in DC loading cases. The lifetime is also inversely proportional to frequencywith an exponent of 0.48.

Conclusions

In this study, EM/TM failure of lead-free solder joints subjected to AC loadings is studiedexperimentally for the first time in reported literature. A specially designed test vehicle is usedto investigate damage of solder joints under sine waveform AC stressing. The material degrad-ation mechanism is observed as a combined process of EM and TM. SEM images of solderjoints show that mass diffusion happens only in current crowding corners and the skin layer.MTTF of solder joints is found to be inversely proportional to frequency f 0.48 and currentdensity j 0.64.

Skin effect is studied as well. The measured resistance of solder joints is exponentially related tofrequency and linearly to current density j. The critical frequency above which skin effect of lead-freesolder joints become influential is 1MHz.

Acknowledgment

The authors would like to express their sincere appreciation to Dr Yi-Shao Lai, director of ASE (Taiwan), forproviding his support of the test vehicles for this program.

Conflict of interest

None declared.

Funding

This research project has been sponsored by the US Navy, Office of Naval Research, Advanced ElectricalPower Program under the direction of Peter Cho.

Figure 13. Frequency dependence of mean time to failure (MTTF) of solder joints at 70�C.


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