13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- 7740 glass and silicon. The higher the bonding temperature was, the larger the difference of thermal expansion coefficient between the glass and silicon, that is, the larger the residual stress was. The residual stress results in these fractures. (a) Bonding temperature at 350 °C (b) Bonding temperature at 375 °C Figure 5. The typical fractures in the samples with Al film of 950 Å 3.2. Fractal patterns and dendritic nanostructures 3.2.1. Fractal patterns With the optical microscope, many fractal patterns were found in the intermediate aluminum film, as shown in Figure 6. The size of the patterns decreases with the thickness of Al film and increases with the bonding temperature. The fractal patterns in the aluminum film have the characteristics of two-dimensional Diffusion-Limited Aggregation (DLA) model [14, 15]. The fractal dimensions of the typical fractal patterns are calculated by sand-box method [16, 17]. (a) 350 °C (b) 375 °C Figure 6. Fractal patterns distribution in 500 Å thick Al film at different bonding temperatures The fractal patterns in the intermediate aluminum film have the typical dimension of 2-D DLA process, and their fractal dimension is around 1.7, as listed in Some fractal patterns were analyzed with the EDX and EBSD systems of INCA. The microanalyses show that the fractal patterns contain the crystalline grains of Aluminum and Silicon. These fractal patterns were formed in the process of anodic bonding due to the limited diffusion and aggregation of Si atoms in the Al film.
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