Distribution of current density and temperature in flip chip solder joints

Figure 18(a) shows the simulated temperature distribution in the Al trace and in the solder joints when stressed by 0.59 A. The simulation results fit the experimental results very well.

The temperature distribution inside the solder in one of the cross sections near the entrance of the Al trace is shown in Figure 18(b). As for the temperature distribution in the solder bump, Figure 18(a) shows the distribution in the solder bump only, in which the Al pad, UBM, IMC layer, and the BT substrate were excluded. It is clear that there is a hot spot near the entrance point of the Al trace, as indicated by the arrow in the Figure. Figure 18(b) shows the

distribution in the center cross-section of the bump, in which the temperature distribution across the solder bump can be clearly seen. The average value was obtained by averaging the values in the area of 70×70 μm², as labeled in the Figure. The occurrence of the hot spot may be mainly attributed to the local Joule heating effect, since there is serious current crowding effect in the hot-spot region.[16] This gradient play important role in the thermomigration in the solder joints.[18, 24]

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Figure 18 (a) The temperature distribution of a bump. A hot spot exist at the entrance points of the Al trace into the solder at the passivation opening.

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Figure 18 (b) The temperature distribution in the solder bump. the average temperature in the solder bump was obtained by averaging the temperatures in a square of 70 μm × 70 μm in the center of the solder.

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Figure 19(a) shows the simulated temperature distribution in the Al trace and in the solder joints when stressed by 0.59 A. The simulation results fit the experimental results very well.

The temperature distribution inside the solder in one of the cross sections near the entrance of the Al trace is shown in Fig. 19(b). A hot spot existed in the solder adjacent to the entrance points of the Al trace into the solder at the passivation opening. The temperature at the spot was 95.6 °C, which was 4.5 °C higher than the average value in the solder. The temperature on the chip side was higher than that on the substrate side. In addition, the vertical thermal gradient was measured to be 276 °C/cm, whereas the horizontal thermal gradient was

calculated to be 634 °C/cm at this stressing condition. The thermal gradient is denoted in this letter as the subtraction of the temperature in the hot spot by the temperature at the opposite end of the solder, then divided by the distance between the two locations. Under this stressing condition, the current density in the Al trace was 1.1 x 10⁶ A/cm². The average current density in the joint was 5.2 x 10³ A/cm² based on the UBM opening. In the hot spot, the maximum current density was 1.7 x 10⁵ A/cm2, whereas the average current density involved in a volume of 5 μm x 5 μm x 5 μm was estimated to be 1.4 x 10⁵ A/cm².

The Joule heating effect was also inspected at various applied currents. Figure 20(a) depicts the temperature in the hot spot and the average temperature in the solder as a function of applied current up to 0.8 A. Both of them increased rapidly with the increase of applied current. The difference in these two temperatures increases as the applied current increases,

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and it may be as high as 9.4 °C when stressed by 0.8 A. Figure 20(b) shows the vertical and horizontal thermal gradients as functions of the applied current. They also increase with the increase in stressing current. Moreover, the horizontal thermal gradient rose more quickly than the vertical one, reaching 1320 °C/cm under the stressing of 0.8 A.

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Figure 19 (a) Simulated temperature distribution in the stressing circuit when powered by 0.59 A. The distribution matched the experimental data in Figure 18(a).

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Figure 19 (b) Temperature distribution inside the solder bump. A hot spot was found in the entrance point of the Al traces.

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Figure 20 (a) Depicts the temperature in the hot spot and the average temperature in the solder as a function of applied current up to 0.8 A.

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Figure 20 (b) Vertical and horizontal thermal gradients as functions of the applied current.

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3.2.1 Joule heating effect in flip chip solder joints 3.2.1.1 Hot spot in solder joint during electromigration

The existence of the hot spot may be attributed to two reasons. First, it may be due to the local Joule heating inside the solder itself. The heating power can be expressed as (2.1).

In our simulation model, the total resistance of the Al trace was about 900 mΩ, and the resistance of the solder bump was about 10 mΩ. Therefore, the Al trace generated most of the heat. Due to the serious current crowding in the solder joint, the current density in the vicinity of the Al entrance into the solder joint is typically one to two orders higher than the average value,[9, 18, 19] causing local Joule heating there. Second, the Al trace has higher Joule heating effect, and the hot spot was close to the Al trace. At lower stressing current, the hot spot is not obvious because there is less heat generation. However, it became more

pronounced as the applied current increased due to large heat generation and difficulty in heat dissipation. The solder in the hot spot was the most vulnerable part in the solder joint during electromigration testing, since it may experience much larger electron wind force due to the higher current density and the higher diffusivity owing to the higher temperature as well as it’s low melting point. Hence, voids start to form at this spot.

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