Al-trace design

To investigate the effect of Al-trace dimension on Joule heating and current crowding, four models with identical structure of solder bumps and Cu lines but with different dimensions of Al-trace were constructed. The first one is the standard model, which includes two SnPb solder bumps connected by an about 1840-μm-long Al trace of 34 μm wide and 1.5 μm thick, as shown in the Figure 5-8 (a). For the second model, as shown in Figure 5-8 (b), the width of Al trace was increased to 100 μm with the rest of the structure remained the same. Figure 5-8 (c) shows the third model, in which the thickness of Al trace was increased to 4.4 μm while the rest of the features remained the same as the standard model. The second and the third models had the same cross-section area of Al trace. For the fourth model, as depicted in Figure 5-8 (d), shorter the Al trace with 670 μm less than the standard model was adopted with the rest of the features remained the same as those in the first model.

The current crowding effect can be relieved to some extent by increasing the width or the thickness of Al trace. In this letter, we denote the crowding ratio to be the maximum current density inside the solder bump divided by the average current density in UBM opening, which was obtained by assuming the current spreads uniformly on UBM opening. The crowding ratio means the non-balanced degree of the current distribution in the solder bumps, and the current crowding would accelerate the

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EM damage due to larger wind force in the current-crowding region. Figures 5-9 (a) through (d) show the cross-sectional views for the current density distribution of the four models when they were stressed by 0.6 A. The local current density inside the solder bumps near the entrance of Al trace was reduced in the second and the third models. The crowding ratio for the first model 1 was as high as 19.8. When the cross-section of 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 bumps did not change for the fourth model, the distribution of current remained the same as the first model. Therefore, enlarging the cross-section of Al trace may reduce the crowding ratio.

Furthermore, the dimension of Al trace had significant effect on Joule heating of the solder bumps. Figures 5-10 (a) to (d) illustrate the temperature distributions in the center cross-sections for the four models when they were applied by 0.6 A at 70°C. A hot spot inside solder bumps occurred near the entrance point of Al trace into solder bumps below the passivation opening. The average temperature was obtained by averaging the node temperatures in 70 μm × 70 μm area, as shown in Figure 5-10 (a).

The temperature in the hot spot was 102.8 °C, 81.7 °C, 83.6 °C and 90.3 °C for the four models, respectively, whereas the average temperature was 97.9 °C, 80.6 °C, 82.0

°C, and 86.1 °C for the four models, respectively. It is obvious that the Joule heating

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effect was greatly reduced when the cross-section of Al trace was increased. Figures 5-11 (a) and (b) show the hot-spot and average temperatures as a function of applied current up to 0.6 A. The trend for lower stressing current behaves the same as that stressed by 0.6 A. Due to the hot spot, a thermal gradient was built up across the solder bumps. The thermal gradient in this section was calculated 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 had the lowest thermal gradient among the four models. In Figure 5-11 (c), the gradient in the fourth model was almost the same as than in the first model, which implies that the hot spot was mainly induced by current crowding effect.

In general, Al trace is the major Joule heat source during accelerated EM test, since its cross-section area is typically one to two orders in magnitude less than that of the solder bumps and Cu line. Under the same applied current, Joule heating power is proportional to the total resistance of the stressing circuit. The resistance of Al trace for the first model was 1331 mΩ, whereas it decreased to 530 mΩ, 551 mΩ and 532 mΩ for the rest of the three models, respectively. Therefore, the Joule heating effect was less significant for the stressing circuit with smaller resistance.

Furthermore, the effect of Al trace dimension on MTTF could be estimated by using Equation 1.6. For the same solder joint with different dimension of Al traces

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under the same stressing condition, the activation energy Q and the constant A are the same for the four models. For the solder joint in the standard model, the maximum current density reached to 1.05 × 10⁵ A/cm² and the hot-spot temperature was 102.8 °C.

For the solder joint with 100-μm-wide Al trace, the maximum current density was 6.39

× 10⁴ A/cm² and the hot-spot temperature was reduced down to 81.7 °C. The MTTF would be 6.1 times longer than that of the standard model under 0.6 A at 70 °C, in which the relief of current crowding contributed about 2.5 times, and the decrease in Joule heating contributed approximately 2.5 times on the increasing of the lifetime increase. For the joint with 4.4-μm-thick Al trace, the maximum current density decreased to 6.20 × 10⁴ A/cm² 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. It is noteworthy that the Joule heating effect could be further reduced if the length of 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 increase the EM resistance.

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Figure 5-8: The four models constructed in this study. (a) The first model with a 34-μm-wide, 1.5-μm-thick and about 1000-μm-long Al trace. (b) The second model with a wider Al trace of 100 μm. (c) The third model with a thick Al trace of 4.4 μm.

(d) The fourth model with a shorter Al trace of about 400 μm.

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Figure 5-9: The cross-sectional views for the current-density distribution in the solder bumps when they were stressed by 0.6 A. (a) The first model. (b) The second model.

(c) The third model. (d) The fourth model.

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Figure 5-10: The cross-sectional views for the temperature distribution in the solder bumps when they were applied by 0.6 A at 70°C. (a) The first model. (b) The second model. (c) The third model. (d) The fourth model.

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Figure 5-11: (a) The hot-spot temperature. (b) The average temperature. (c) The thermal gradient in the solder bumps as a function of applied current up to 0.6 A at 70

°C for the four models.

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