Fractal fracture of single crystal silicon

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Abstract
The quantitative description of surfaces that are created during the fracture process is one of the fundamental issues in materials science. In this study, single crystal silicon was selected as a model material in which to study the correlation of fracture surface features as characterized by their fractal dimension for two different orientations of fracture with the fracture toughness of the material as measured using the strength-indentation and fracture surface analysis techniques. The fracture toughness on the {110} fracture plane of single crystal silicon was determined to be 1.19 MPa m1/2for the {100} tensile surface and 1.05 MPa m1/2for the {110} tensile surface using the indentation-strength three-point bending method. The fracture surface features of these two orientations are correspondingly different. Within our limitations of measurements (1–100 μm), the fractal dimension appeared different in different regions of the fracture surface. It has a higher value in the branching region and a lower value in the pre-branching and post-branching regions. The fractal dimensions are about the same in the pre-branching regions and post-branching region for these two orientations (D= 1.01 ± 0.01), i.e., nearly Euclidean (smooth); but the fractal dimensions are higher in the branching region for these two orientations. The fractal dimension is 1.10 ±0.4 for the {100} tensile surface and is 1.04 ±0.3 for the {110} tensile surface. If we select the highest dimension on a surface to represent the dimensionality of the surface, then a material with a higher fracture toughness has a higher fractal dimension in the branching region.

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