Macroscopic measure of the cohesive length scale: Fracture of notched single-crystal silicon

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We study atomistically the fracture of single-crystal silicon at atomically sharp notches with opening angles of $0\ifmmode^\circ\else\textdegree\fi{}$ (a crack), $70.53\ifmmode^\circ\else\textdegree\fi{},$ $90\ifmmode^\circ\else\textdegree\fi{}$ and $125.3\ifmmode^\circ\else\textdegree\fi{}.$ Such notches occur in silicon that has been formed by etching into microelectromechanical structures and tend to be the initiation sites for failure by fracture of these structures. Analogous to the stress intensity factor of traditional linear elastic fracture mechanics which characterizes the stress state in the limiting case of a crack, there exists a similar parameter K for the case of the notch. In the case of silicon, a brittle material, this characterization appears to be particularly valid. We use three interatomic potentials; that which gives critical K values closest to experiment is the modified embedded atom method (MEAM). Because the units of K depend on the notch angle, the shape of the K versus angle plot depends on the units used. In particular when an atomic length unit is used the plot is almost flat, showing---in principle, from macroscopic observations alone---the association of an atomic length scale to the fracture process. Moreover the normal stress on the actual fracture plane at this distance from the notch tip turns out to be even flatter and emerges as a possible fracture criterion, namely 33 MPa at a distance of one \AA{} (for MEAM silicon).