Home    Introduction    Theory    Numerical    Results    Conclusions

Results

In the groove structure, depending on the magnitude of the surface migration and the surface diffusion mobility, micro structure is formed differently. If surface migration mobility is dominant, the groove will become flat surface which is a self-healing process. On the other hand, in case where the diffusion mobility is high, the structure is expected to form the void inside. This difference of evolution is also depending on the aspect ratio of the initial geometry. If deep groove exists on the surface, due to the lack of time to fill up the structure in order to minimize its overall surface, it will change into void structure. However, when the depth is small compared to the width of the groove, the surface will be flat.  

Result #1. Surface migration factor

From the simulations in MATLAB, we have obtained results in two different groups. The first category is prediction of structure evolution by changing ratio between the surface migration factor (L) and the diffusion factor (M). If there is only surface migration factor, we could achieve self-healing structure. Otherwise, if there have surface migration and diffusion factor at the same time, we are able to get a void structure finally. We assumed that all structure have same dimension: a=10 (height), b=2 (diameter) and c=4 (pitch between each rod).

Result #1-1. Surface migration factor 2D plot

All structure have same dimension: a=10 (height), b=2(diameter), c=4

Result #1-2. Surface migration factor 3D plot

All structure have same dimension: a=10 (height), b=2(diameter), c=4

• Void Formation occurs when the groove is deep enough (L = 0.1) to allow the sides to come together and for a void to break away from the rest of the top surface. We can get a void structure eventually. This is because surface diffusion is much larger than surface migration factor.

• Modified void shape (looks like a knob-stick) is formed, when L value is 0.5.

• If L is larger than (0.8), we always are unable to make a void structure. Instead of making hollow structure, two of each side contact together before making a void structure.

• If L is larger than (1.0), we always are unable to make a void structure. Instead of making hollow structure, two of each side contact together much faster than in case of L =0.8 due to the migration factor is dominant.

Result #2. Aspect ratio

The second category is observing structure evolution depending on the initial geometry values. In this case we fixed the migration and diffusion factor. Depending on the valley depth, we can get either void or self-healing structure.

Result #2-1. Aspect ratio 2D plot

Result #2-2. Aspect ratio 3D plot

• a=4 (height), b=2 (diameter), c=4 (pitch between each rod) and aspect ratio = 2:1. As predicted from the model section, the groove heals itself and will revert back to a straight line on the surface after time. As time goes on, we can finally get a self-healing structure.

• a=6 (height), b=2 (diameter), c=4 (pitch between each rod) and aspect ratio = 3:1. As time goes on, we can get a void structure.

• a=10 (height), b=2 (diameter), c=4 (pitch between each rod) and aspect ratio = 5:1. As time goes on, we can get the largest void structure. In light of the fact that as the valley depth increases, it is much easier to observe the void structure.