Effect of Al-trace dimension on Joule heating and current crowding in flip-chip solder joints under accelerated electromigration

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Effect of Al-trace dimension on Joule heating and current crowding in flip-chip solder

joints under accelerated electromigration

S. W. Liang, Y. W. Chang, and Chih Chen

Citation: Applied Physics Letters 88, 172108 (2006); doi: 10.1063/1.2198809

View online: http://dx.doi.org/10.1063/1.2198809

View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/88/17?ver=pdfcov Published by the AIP Publishing

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Effect of Al-trace dimension on Joule heating and current crowding

in flip-chip solder joints under accelerated electromigration

S. W. Liang, Y. W. Chang, and Chih Chena兲

Department of Material Science and Engineering, National Chiao Tung University, Hsin-chu, Taiwan 30050, Republic of China

共Received 31 January 2006; accepted 27 March 2006; published online 25 April 2006兲

Three-dimensional thermoelectrical simulation was conducted to investigate the influence of Al-trace dimension on Joule heating and current crowding in flip-chip solder joints. It is found that the dimension of the Al-trace effects significantly on the Joule heating, and thus directly determines the mean time to failure共MTTF兲. Simulated at a stressing current of 0.6 A at 70 °C, we estimate that the MTTF of the joints with Al traces in 100␮m width was 6.1 times longer than that of joints with Al traces in 34␮m width. Lower current crowding effect and reduced hot-spot temperature are responsible for the improved MTTF. © 2006 American Institute of Physics.

关DOI:10.1063/1.2198809兴

To meet the relentless drive for miniaturization of por-table devices, flip-chip technology has been adopted for high-density packaging due to its excellent electrical charac-teristic and superior heat dissipation capability. As the re-quired performance in microelectronics devices becomes higher, the design rule indicates that in each bump the opera-tion current is expected to attain a value of 0.2 A, with fur-ther increase to 0.4 A likely in the near future.1Loading with such a high current at the confined space of the solder bump, electromigration inevitably becomes a critical reliability issue.2 In addition, during accelerated electromigration test, the applied current may reach 2.0 A,3 rendering substantial Joule heating in the solder bumps.4The total length of the Al trace is typically few hundreds to few thousands microme-ters, which corresponds to a resistance of approximately few hundreds milliohms or few ohms. In contrast, the resistances of the solder bumps and the Cu trace in the substrate are relatively low, typically in the order of few or tens of millio-hms. Therefore, the primary contributor for Joule heating in the solder joints is the Al trace.4As a result, the temperature in the bumps during accelerated testing is likely to be much higher than that of the ambient because of the Joule heating. The other critical issue is the current crowding effect in the solder bumps. The line-to-bump geometry is believed to ren-der undesirable current crowding behavior, resulting in el-evated current density in the solder regime than the average current density.5 These two issues play substantial roles in the mean-time-to-failure共MTTF兲 analysis, as delineated by Black’s equation,6

MTTF = A1

jnexp

冉

Q

kT

冊

, 共1兲

where A is a constant, j is the current density, n is a model parameter for current density, Q is the activation energy, k is the Boltzmann constant, and T is the average bump tempera-ture. It follows that the MTTF decreases exponentially with increasing bump temperature. Wu et al.7 conducted a series of electromigration tests for SnPb solder bumps, and ob-served that the MTTF decreased from 711 to 84 h as the

testing temperature was raised from 125 to 150 ° C at a cur-rent density of 5.0⫻103 _{A / cm}2_{. In addition, the MTTF} de-creased from 277 to 84 h as the current density was doubled from 2.5⫻103_{to 5.0}_⫻103_{A / cm}2 _{at 150 ° C. Predicted by} Black’s equation and validated experimentally by Wu et al., the stressing temperature and the current density both play substantial role in determining the observed MTTF.

Several intrinsic material characteristics contribute to the Joule heating and current crowding effects. They include the dimension of Al trace, the thickness of under bump metalli-zation共UBM兲, the UBM materials, the solder materials, as well as the dimension of passivation.8Among them, the di-mension of Al trace is believed to be the critical one. How-ever, no systematic studies have been initiated to elucidate the effect of Al-trace dimension in Joule heating and current crowding of the solder joints during electromigration. This is because the solder joints are completely encapsulated by Si die, underfill, and underlying substrate. Hence, it is some-what difficult to analyze the temperature fluctuation and the current density inside the solder joints. To overcome this problem, in this study we used a three-dimensional thermo-electrical simulation to identify the temperature and the cur-rent density inside the solder bumps. This study offers a bet-ter insight on the effect of Al-trace dimension in the Joule heating and current crowding during accelerated electromi-gration of solder joints.

To proceed our simulation, four models with identical structure of solder bumps and Cu lines but with different dimensions of Al trace were constructed. Shown in Fig. 1共a兲 is a standard model, which includes two SnPb solder bumps connected by an Al trace of 1840␮m in length, 34␮m in width, and 1.5␮m in thickness. For the second model, as shown in Fig. 1共b兲, the width of the Al trace was increased to 100␮m with the remaining structure unchanged. Figure 1共c兲 exhibits the third model, in which the thickness of the Al trace was adjusted to 4.4␮m with the remaining dimension identical to those of the first model. It is noted that the sec-ond and the third model had the same cross-sectional area of Al trace. For the fourth model, as depicted in Fig. 1共d兲, a shorter Al trace which is 670␮m less than the standard model was used while the remaining features identical to those in the first model. The dimension of the Si chip was

a兲_{Author to whom correspondence should be addressed; electronic mail:}

[email protected]

APPLIED PHYSICS LETTERS 88, 172108共2006兲

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7.0⫻4.8 mm2 _{with its thickness of 290}_␮_{m. The dimension} of the bismaleimide triazine 共BT兲 substrate was 5.4 mm in width, 9.0 mm in length, and 480␮m in thickness. The bot-tom of the BT substrate was maintained at 70 ° C and the convection coefficient was set to be 10 W / m2° C in a 25 ° C ambient temperature. The intrinsic parameters of materials used in this simulation can be found in our previous publication.9 Constant currents, ranging from 0.1 to 0.6 A, were applied through the two Cu lines on the BT substrate.

The current crowding effect can be relieved to some ex-tent by increasing the width or the thickness of the Al trace. In this letter, we designate the crowding ratio to be the maxi-mum current density inside the solder bump divided by the average current density in the UBM opening, which was ob-tained assuming the current spreads uniformly on the UBM opening. The crowding ratio indicates the degree of nonbal-ance in the current distribution in the solder bump. It is re-alized that the current crowding would accelerate the damage caused by electromigration because of the enhanced wind force in the current crowding region. Figures 2共a兲–2共d兲 dem-onstrate the cross-sectional views for the current density dis-tribution of the four models as they were stressed at 0.6 A. As shown, the local current density inside the solder bump near the entrance of the Al trace was reduced substantially in the second and the third model. The crowding ratio for the first model reached a value of 19.8. When the cross section of the Al trace was increased by 2.9 times, the crowding ratios were reduced down to 12.0 and 11.7 for the second and the third model, respectively. Since the geometry of the Al trace near the solder bump was not varied for the fourth model, the distribution of current remained the same as the first model. From our simulation, we conclude that increas-ing the cross section of the Al trace directly reduced the crowding ratio.

Furthermore, the dimension of the Al trace exerts signifi-cant effect on Joule heating of the solder bumps. Figures 3共a兲–3共d兲 illustrate the temperature distributions in the center cross sections for the four models when they experience a stress current of 0.6 A at 70 ° C. A hot spot inside the solder bump was observed near the entrance point of the Al trace into the solder bump just beneath the passivation opening. The mean temperature was obtained by averaging the node temperatures in a 70⫻70␮m2 _{area, as shown in Fig. 3共a兲.} The temperatures in the hot spot were 102.8, 81.7, 83.6, and 90.3 ° C for the four models, respectively, whereas the aver-age temperatures were 97.9, 80.6, 82.0, and 86.1 ° C, respec-tively. It can be seen that the Joule heating effect was greatly reduced when the cross section of the Al trace was increased. Figures 4共a兲 and 4共b兲 show the hot-spot and average tem-peratures as a function of the applied current up to 0.6 A. Also, the trend for lower stressing current behaves the same with smaller magnitude in temperature difference as that stressed by 0.6 A. Due to the hot spot, a thermal gradient was built up across the solder bump. The thermal gradient was derived from the temperature difference between the hot-spot and the average temperature of the solder close to the BT side, divided by the bump height. It can be observed that the second model exhibits the lowest thermal gradient among the four models.

In general, the Al trace is considered to be the primary Joule heating source during accelerated electromigration test as its cross-section area is typically one to two orders of magnitude less than that of the solder bump and the Cu line. Under the same applied current, the Joule heating power is proportional to the total resistance of the stressing circuit. The resistance of the Al trace for the first model was 1331 m⍀, whereas it decreased to 530, 551, 532 m⍀ for the rest of the three models, respectively. Therefore, the Joule heating effect was less significant for the stressing circuit configuration with smaller total resistance. In addition, for the third and fourth models, the total resistance and the cross section for heat dissipation were almost identical, yet there is still 6.7 ° C difference in hot-spot temperature. Since the av-erage current density in the Al trace for the fourth model was about three times larger than that for the third model, the local Joule heat power, which is proportional to the square of the local current density, is likely to be responsible for the temperature difference in these two models.

Furthermore, the effect of Al-trace dimension on the MTTF could be estimated using Eq.共1兲. For the same solder joint with different dimensions of the Al traces under the FIG. 1. The four models constructed in this study.共a兲 The first model with

a 34-␮m-wide, 1.5-␮m-thick, and 1848-␮m-long Al trace.共b兲 The second model with a wider Al trace of 100␮m.共c兲 The third model with a thick Al trace of 4.4␮m.共d兲 The fourth model with a shorter Al trace of 1178␮m.

FIG. 2. The cross-sectional views for the current-density distribution in the solder bump when they were stressed by 0.6 A.共a兲 The first model. 共b兲 The second model.共c兲 The third model. 共d兲 The fourth model.

FIG. 3. The cross-sectional views for the temperature distribution in the solder bumps when they were applied by 0.6 A at 70 ° C. 共a兲 The first model.共b兲 The second model. 共c兲 The third model. 共d兲 The fourth model.

172108-2 Liang, Chang, and Chen Appl. Phys. Lett. 88, 172108共2006兲

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same stressing conditions, the activation energy Q and the constant A are kept identical for the four models. Choi et al. proposed that the term j−n_{in the equation needs to be revised} to共cj兲−n_{in order to include the high current crowding effect} in the solder joints. In addition, the temperature factor is modified to共T+⌬T兲 to account for considerable Joule heat-ing effect durheat-ing the accelerated electromigration test. Bran-denburg and Yeh found that n is equal to 1.8 for the eutectic solder joints when the average current density is employed, and the activation energy they measured was 0.5 eV for the SnPb solder with Al/ Ni共V兲/Cu UBM.10

Since voids

typi-cally form near the entrance point of the Al trace where the solder experiences the maximum current density and the hot-spot temperature, we propose that the共cj兲 term to be taken as the maximum current density and the hot-spot temperature should be adopted for the共T+⌬T兲 term. For the solder joint in the standard model, the maximum current density reached 1.05⫻105_{A / cm}2 _and _the _hot-spot _temperature _was 102.8 ° C. For the solder joint with Al trace in 100␮m width, the maximum current density was 6.39⫻104_{A / cm}2 and the hot-spot temperature was reduced down to 81.7 ° C. The MTTF would be 6.1 times longer than that of the stan-dard model under 0.6 A at 70 ° C, in which the relief of current crowding contributed about 2.5 times, and the de-crease in Joule heating contributed approximately 2.5 times on the lifetime increase. For the joint with Al trace in 4.4␮m thickness, the maximum current density decreased to 6.20⫻104_{A / cm}2_{and the hot-spot temperature was reduced} to 83.6 ° C. The estimated MTTF would be 5.9 times longer than that of the standard. For the fourth model, the MTTF is about 1.7 times longer than that of the standard model, mainly due to lower Joule heating effect. It is noteworthy that the Joule heating effect could be further reduced if the length of the Al trace is further decreased, but the current crowding effect remains the same when only the length is changed. The above estimation demonstrates that the solder joints with wider or thicker Al traces could significantly crease the electromigration resistance. In addition, it also in-dicates that the Joule heating effect needs to be taken into account during the accelerated electromigration test. Other-wise, the MTTF may be underestimated.

In conclusion, the dimension of the Al trace plays a cru-cial role in the Joule heating effect during accelerated elec-tromigration test since the Al trace is the dominant heating source. The solder joints with wider or thicker Al trace would render reduced current crowding and Joule heating effects. Therefore, the electromigration lifetime would be ex-tended significantly for the solder joints with wider or thicker Al traces under the same stressing conditions.

The authors would like to thank the National Science Council of Taiwan for the financial support through Grant No. 94-2216-E-009-021. In addition, the assistance on simulation facility from the National Center for High-Performance Computing共NCHC兲 in Taiwan is appreciated.

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FIG. 4.共a兲 The hot-spot temperature. 共b兲 The average temperature. 共c兲 The thermal gradient in the solder bump as a function of applied current up to 0.6 A at 70 ° C for the four models.

172108-3 Liang, Chang, and Chen Appl. Phys. Lett. 88, 172108共2006兲