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In a microelectronic device, the strain field may be intensified at a sharp feature, such as an edge or a corner, injecting dislocations into silicon and ultimately failing the device. The strain field at an edge is singular and is often a linear superposition of two modes of different exponents. We characterize the relative contribution of the two modes by a mode angle, and determine the critical slip systems as the amplitude of the load increases. We calculate the critical residual stress in a thin-film stripe bonded on a silicon substrate.