The mechanics of a free-standing strained film/compliant substrate system

The deformation of film/substrate systems due to a through-the-thickness distribution of mismatch strain is discussed for cases when the layers are thin, compliant and freestanding. The connection between substrate curvature and mismatch strain is reviewed within the framework of small strains and small deflections. These results are applied to determine the second-order correction to the Stoney formula and to note the connection between mismatch strain distribution and curvature history. Then, for small strains but large deflections, it is observed that a symmetric system with equi-biaxial mismatch strain can undergo a bifurcation in deformation mode. It is also shown that the bifurcation response is sensitive to system imperfections. Finally, the critical condition for introduction of an interface misfit dislocation in an epitaxial system is established, thereby extending the Matthews-Blakeslee criterion to the case of free-standing compliant systems.