Mathematical model for strain relaxation in multilayer metamorphic epitaxial structures

A class of models of plastic relaxation is identified, in which relaxation is due to a function of state of strained layers which can be summed over a multilayer heterostructure. It is shown that in these models relaxation occurs at a single plane which can move upwards (away from the substrate) but not downwards through the structure. These results permit a simple algorithm to predict strain relaxation in heterostructures, and also demonstrate that there are conditions under which a relaxed buffer layer may be made stable with respect to the growth of further strained layers or device structures on top.