The ratcheting of compressed thermally grown thin films on ductile substrates

An analysis of the displacements experienced by undulating thermally grown thin films upon thermal cycling has been presented. The film has been assigned a thermal expansion coefficient that causes it to be compressed upon cooling. It has also been allowed to thicken at high temperature by oxidation of the substrate. It is shown that, in some circumstances, ratcheting occurs, wherein the undulation amplitude, a, increases with each thermal cycle. When such a response happens, undesirable cyclic failure modes are induced. The analysis reveals that there is a critical undulation amplitude, a c, below which ratcheting does not occur. This critical size is related to the expansion misfit, the substrate yield strength and the growth strain in the film per cycle. Connections between these variables and a c are derived.