136
GI, it can be deduced that the crack may propagate preferably along a local mode II. But again this is not sure as no values of fracture toughness are known for this case.
Figure 6.14: Evolution of GII the shearing mode during 6 PTC cycles in the top IMC
137
Figure 6.16: Evolution of GI the opening mode during 3 APC cycles at the interface chip/IMC
For the shearing mode, GII is always positive and thus represents a displacement to the right for the layer above the crack compared to the layer underneath. At low temperatures the layer above the crack moves to the right side and comes back more or less closer to the layer underneath the crack at high temperatures. Here GII
varies continuously during heating and cooling phases, thus the crack is always evolving. This means that long pulse width can be more critical than short pulse width in terms of shearing crack growth. Regarding the evolution of GII, minima and maxima are slightly decreasing cycle after cycle. Thus the system may not be stable after 3 cycles, but as the amplitude of GII remains constant, it was sufficient for our analysis to simulate only 3 cycles.
Figure 6.17: Evolution of GII the shearing mode during 3 APC cycles at the interface chip/IMC
As this kind of crack was never observed, it can be concluded that the maximal value of GI and GII are not critical for crack growth under APC, even if no fracture toughness are known. The maximal values of GI and GII reached under APC are similar to the ones reached under PTC, and more generally the crack behavior is similar. Then, as the G values reached for the mode II are higher than for the mode I, it can be deduced that the crack may propagate preferably along a local mode II. But again this is not sure as no values of fracture toughness are known for this case.
138
6.3.2 Crack growth in the Al metallization
Here again, due to the plastic properties of the Al metallization, the crack zone shows a large scale yielding (Figure 6.18). The evolution of the CTOD criterion is plotted for both opening mode (Figure 6.19) and shearing mode (Figure 6.20). For the opening mode, a negative displacement represents a crack closing and a positive displacement represents a crack opening. At high temperatures the crack is closed while at low temperatures the crack is open.
Figure 6.18: Plastic strain at the crack tip in the Al metallization (areas in grey have a plastic strain superior to 0,259517 m/m)
The absolute maximum value of displacement is reached quite at the beginning of heating or cooling phases, and then a slight decrease occurs until the end of the phase. This relaxation behavior may be explained by the rate dependent properties of the top solder located above the Al metallization. The crack opening remains narrow as the maximum displacement observed is under 0,01 µm. This may be explained by the fact that the Cu clip soldered on top of the Al metallization and the mold are restricting out-of-plane displacements and thus crack opening. A slight shift in the maximum and minimum displacement values is noticeable with an increasing number of cycles for both opening and shearing modes. This shift comes from the rate dependent properties of the top solder. The CTODI needs a few more cycles to stabilize, but its amplitude stays constant, thus calculating 3 cycles was sufficient for our analysis.
Figure 6.19: Evolution of CTODI the opening mode during 3 APC cycles in the Al metallization
For the shearing mode, the negative CTODII represents a displacement to the left for the layer above the crack compared to the layer underneath. At low temperatures, the layer above the crack is moving further to the left, and at high temperatures, the layer above the crack is coming back to the right. Here also the minimum and
139
maximum values of displacement are reached quite at the beginning of heating or cooling phases, and then a slight increase or decrease occurs depending on the case, until the end of the phase. Shear displacements are quite important as the maximal CTODII value reached is about 0,4 µm. This means that the maximum shearing component CTODII is 40 times higher than the maximum opening component CTODI. So the absolute maximum value of CTOD component at the new crack tip is obtained by the shearing component, and thus crack growth will occur along a local mode II direction. But it is not possible to determine if CTODs have reached critical values as no fracture toughness values are known.
The crack behavior under PTC and APC is very similar, and the same order of values is reached for both CTODs. There is only slightly bigger amplitude observed for shearing mode under APC than under PTC.
Figure 6.20: Evolution of CTODII the shearing mode during 3 APC cycles in the Al metallization
6.3.3 Crack growth at the top IMC
Figure 6.21: von Mises stress at the crack tip in the top IMC (areas in grey have a von Mises stress superior to 500MPa)
After the 3 APC cycles, the crack in the top IMC is open (Figure 6.21). The evolution of the energy release rate for opening and shearing modes is plotted respectively Figure 6.22 and Figure 6.23 for more details. For the mode I, the positive values of GI are traducing a crack opening. At high temperature the crack is almost closed and at low temperature the crack is open. During heating phases, GI stays constant thus meaning that the crack remains closed and does not further move. On the other hand, GI reached its maximum value right at the beginning of the cooling phase and directly after, it severely decreases until the end of the cooling operation. The maximal value of GI increases cycle after cycle, thus the system may not be stable after 3 cycles. But as the values reached are quite small, there is no significant difference in the amplitude of variations of GI, thus simulating 3 cycles was sufficient for our analysis. The maximal values reached by GI
are really low compared to the absolute maximal values reached by GII the shearing component. Indeed the absolute value GII is about 100 times higher than GI.
140
Figure 6.22: Evolution of GI the opening mode during 3 APC cycles in the top IMC
For the shearing mode, negative values of GII are representing a displacement to the left for the layer above the crack compared to the layer underneath. At low temperatures the layer above the crack moves to the left side and comes back to its original closed position at high temperatures. Right at the beginning of the heating phase the crack joins its original closed position and then some small shearing displacements are occurring.
The absolute maximum of GII is also reached right at the beginning of the cooling phase and then a decrease occurs until the end of the phase. Regarding the evolution of GII, it can be seen that the system seems to be already stable after the first cycle.
As no fracture toughness are known for this crack in the IMC, it cannot be determined if the values of G reached are critical for crack growth under APC. But as the absolute values reached by GII are 100 times higher than values reached by GI, it can be deduced that the crack may propagate preferably along a local mode II. But again this is not sure as no values of fracture toughness are known for this case.
Finally the crack behavior under PTC and APC is very similar and the values reached for both G components are comparable.
Figure 6.23: Evolution of GII the shearing mode during 3 APC cycles in the top IMC
141