Crack patterns in brittle thin films

The physical system studied is a brittle elastic film bonded to an elastic substrate with different elastic properties; a residual tensile stress is p resumed to exist in the film. The focus of the study is the influence of th e mismatch in elastic properties on patterns of crack formation in the film . The stress intensity factor and crack driving force for growth of a perio dic array of cracks in the direction normal to the interface under two-dime nsional conditions are determined for any crack depth and any mismatch in e lastic parameters. It is found that, even for a relatively stiff film mater ial, the stress intensity factor of each crack as a function of crack depth exhibits a local maximum. The driving force for crack extension in the dir ection parallel to the interface is then determined on the basis of these t wo-dimensional results, and the equilibrium spacing of crack arrays is esti mated for given residual stress. The results of the calculations are used a s a basis for qualitative arguments to explain the crack patterns which hav e been observed in GaN films on Si substrates.