When electrons flowed from the cathode side to the anode side, Sn atoms migrated gradually in the same direction. Figures 4.1 (a) to 4.1 (f) show the depletion at the cathode side of the Sn stripes under different current densities at room temperature. We can clearly see that as the current density goes up, shorter time is required to form the depletion at the cathode side. We also found that the faster drift velocity (defined by depletion length divided by stressing time) we would get upon increasing the current density. The drift velocities for the current densities of 2.5 × 104, 5 × 104, 7.5 × 104, 1 × 105, 1.25 × 105, 1.5 × 105 A/cm2 are 0.013, 0.031, 0.070, 0.100, 0.136, 0.146 nm/s, respectively. (The depletion area was calculated by a commercial computer software “Inspector”) It is reasonable to explain that when more electrons were supplied from the cathode side of the Sn stripes under higher current density, more Sn atoms received momentum transferred form the electrons. At this time,
more
FIG. 4.1. Plan-view SEM images of the cathode side stressed at R.T. (a) 2.5 × 104 A/cm2 for 166 h; (b) 5 × 104 A/cm2 for 92 h; (c) 7.5 × 104 A/cm2 for 63.5 h; (d) 1 × 105 A/cm2 for 54 h; (e) 1.25 × 105 A/cm2 for 37 h; (f) 1.5 × 105 A/cm2 for 18 h.
more Sn atoms were pushed by the electrons and migrated from the cathode side of the stripe to the anode side.
At 50℃, as shown in figures 4.2 (a) to 4.2 (f), same phenomenon was found. At higher current density, shorter time is required to form the depletion and the drift velocity increases gradually. The drift velocities for the current densities of 2.5 × 104, 5 × 104, 7.5 × 104, 1 × 105, 1.25 ×
We have to mention that the depletion area in figure 4.3 (d) seems larger than the area shown in figures 4.3 (e) and 4.3 (f), but the time required for figure 4.3 (e) and 4.3 (f) was shorter than that for figure 4.3 (d). After calculation, the drift velocities for figures 4.3 (e) and 4.3 (f) are faster than that in figure 4.3 (d). Besides, the reason why we didn’t show the data of 1.5 × 105 A/cm2 at 100℃ is because the high current density might generate sufficient Joule heat at 100℃ that thermal migration starts to contribute to deplete the atoms at the cathode side. Since it is another issue, we discuss it elsewhere.
FIG. 4.2. Plan-view SEM images of the cathode side stressed at 50℃ (a) 2.5 × 104 A/cm2 for 91.5 h; (b) 5 × 104 A/cm2 for 63 h; (c) 7.5 × 104 A/cm2 for 40 h; (d) 1 × 105 A/cm2 for 28 h; (e) 1.25 × 105 A/cm2 for 24h; (f) 1.5 × 105 A/cm2 for 20 h.
FIG. 4.3. Plan-view SEM images of the cathode side stressed at 75℃ (a) 2.5 × 104 A/cm2 for 43 h; (b) 5 × 104 A/cm2 for 25.5 h; (c) 7.5 × 104 A/cm2 for 21 h; (d) 1 × 105 A/cm2 for 19 h; (e) 1.25 × 105 A/cm2 for 15h; (f) 1.5 × 105 A/cm2 for 12 h.
FIG. 4.4. Plan-view SEM images of the cathode side stressed at 100℃ (a) 2.5 × 104 A/cm2 for 25 h; (b) 5 × 104 A/cm2 for 12 h; (c) 7.5 × 104 A/cm2 for 12 h; (d) 1.25 × 105 A/cm2 for 6h.
Comparing the cathode of the Sn stripes stressed under the same current density but at different testing temperatures, we found that as the testing temperature goes up, faster drift velocity was obtain, as shown in figures 4.5 (a) to 4.5 (d). Figure 4.5 shows that the depletion of the cathode side of Sn stripes stressed under the current density of 1.25 × 105 A/cm2 at R.T., 50℃, 75℃, and 100℃. The stressing time for figures 4.5 (a) to 4.5 (d ) are 37 h, 25 h, 15 h, 6 h, respectively. It was found that the higher the stressing temperature, the faster the drift velocity. This phenomenon is reasonable and easy to explain. When we increased the testing temperature, Sn atoms had higher thermal fluctuation that they could overcome the barrier and move to the anode side than they were under lower testing temperatures. So, we can easily find that the drift velocities were faster, when Sn atoms were stressed under higher temperatures. The plot of the drift velocity against the applied current density at different temperatures is shown in figure 4.6. The drift velocity increased linearly with the increase of applied current density.
On the anode side, two types of whiskers, the hillock-type and needle-type ones, were observed. Figures 4.7 (a) to 4.7 (d) show the morphology on the anode side stressed under the current density of 5 × 104 A/cm2. It was found that the hillock-type whiskers could be grown at room temperature up to 100 ℃. However, the needle-type whisker can be only observed frequently on the Sn stripes stressed at room temperature, as shown in figure 4.7 (a). Only one needle-type whiskers was found on the samples stressed at 50 ℃, and no needle-type whiskers were observed on the samples stressed at 75 ℃ and at 100 ℃ As mentioned in . introduction, the needle-type whiskers grew when the Sn stripes were
stressed at room temperature
FIG. 4.5. Plan-view SEM images of the cathode side after the current stressing by 1.25 × 105 A/cm2 (a) ar RT for 37 h with a depletion area of 800 µm2. (b) at 50℃ for 28 h with a depletion area of 1164 µm2. (c) at 75℃ for 15 h with a depletion area of 15700 µm2. and (d) at 100℃ for 6 h with a depletion area of 960 µm2.
FIG. 4.6. Plan-view SEM images of the cathode side after the current stressing by 1.25 × 105 A/cm2 Threshold current densities can be obtained by extrapolating from the fitting curves to the zero drift velocity.
FIG. 4.7. Plan-view SEM images of the anode side after the current stressing by 5 × 104 A/cm2 (a) at R.T. for 37 h, both hillock-type and needle-type whiskers are formed; (b) at 50 ℃ for 28 h, hillock-type whiskers are formed (needle-type whiskers may be observed when the film was stressed longer);
(c) at 75 ℃ for 15 h, only hillock-type whiskers are formed.
(d) at 100 ℃ for 12 h, only hillock-type whiskers are formed.
stressed at room temperature. However, in our previous study, we found that the growth rate of whiskers was faster when the stripes were stressed at 50 ℃.16 The discrepancy may be owing to different stressing times.
The stressing times in our previous study were longer than 90 h. However, in this study, the stressing times were shorter than 91 h. Pure Sn stripes with longer stressing time may accumulate higher stress for breaking the surface oxide of Sn, and then start to grow whiskers. Moreover, when stressed at 75 ℃ and 100 ℃ no needle-type whiskers were observed , even when the stripes were stressed at 1.5 A/cm2 for 150 hours. The reason for that is not clear at this moment. This may be attributed to the softer surface oxide, resulting in the formation of the hillock-type whiskers at higher temperatures.32, 33