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Theory

 In the surface groove evolution, there are two competing factors which need to be considered. First is the surface migration term which has something to do with the phase change of the small structure. Through surface migration phenomena, structure keeps decreasing the surface which leads to the reduced Gibb’s free energy. Secondly, the surface diffusion term affects its structural morphology change by rearranging the atoms composing the structure. The surface diffusion is defined through setting mass conservation within the boundary on the surface where the net influx of atoms is same as the net atom increase inside the boundary. For instance, when material is added on the surface through chemical vapor deposition process, physically phase change of the material can be explained through surface migration. On the other hand, after the material deposited on the substrate and when thin film is formed across the board, the configuration of the atoms will change which can be explained through diffusion.

 For forming the void inside the structure starting from the groove, surface migration, diffusion, and the aspect ratio of the groove must be taken into consideration at the same time. Depending on the three parameters, not only can we observe the self-healing process of the micro structure, we possibly fabricate different size and shape of the void inside the structure. If surface migration mobility is much larger than diffusion mobility, the groove will be filled up rapidly due to its higher tendency for growth and reducing the surface. On the contrary, if diffusion is more governing the evolution, void will be formed inside. And in case of high aspect ratio structure, since diffusion effect is larger, it forms the void inside. However, when the initial geometry is set as the low aspect ratio, migration effect is relatively larger thus, groove is filled up.

 The following is the governing equation including diffusion and migration. Both equations represent the Gibb’s free energy in the system. By letting equation (1) and (2) to be equal, we can check the nodal velocities for each time step and update their positions. In two equations, J is the mass flux, δI is the mass displacement, M is the surface diffusion mobility. In addition, j is the volume of matter added to the unit area of the solid surface per unit time, δi is the volume of the matter added to the unit area of the surface, L represents the surface migration mobility.