The control of crack arrays in thin films

Thin-film fracture can be used as a nano-fabrication technique but, generally, it is a stochastic process that results in non-uniform patterns. Crack spacings depend on the interaction between intrinsic flaw populations and the fracture mechanics of crack channeling. Geometrical features can be used to trigger cracks at specific locations to generate controlled crack patterns. However, while this basic idea is intuitive, it is not so obvious how to realize the concept in practice, nor what the limitations are. The control of crack arrays depends on the nature of the intrinsic flaw population. If there is a relatively large density of long flaws, as commonly assumed in fracture-mechanics analyses, reliable crack patterns can be obtained fairly robustly using relatively blunt geometrical features to initiate cracks, provided the applied strain is carefully matched to the properties of the system and the desired crack spacing. This process is analyzed both for cracks confined to the thickness of a film and for cracks growing into a substrate. The latter analysis is complicated by the fact that increases in strain can either drive cracks deeper into the substrate or generate new cracks at shallower depths. If the intrinsic flaws are all very short, the geometrical features need to be very sharp to achieve the desired patterns. While careful control of the applied strain is not required, the strain needs to be relatively large compared to that which would be required to propagate a large flaw across the film. This results in an approach that is not robust against the introduction of accidental damage or a few large flaws.