The present invention relates to a heterostructure, in particular, a piezoelectric structure, comprising a cover layer, in particular, a layer of piezoelectric material, the material of the cover layer having a first coefficient of thermal expansion, assembled to a support substrate, the support substrate having a second coefficient of thermal expansion substantially different from the first coefficient of thermal expansion, at an interface wherein the cover layer comprises at least a recess extending from the interface into the cover layer, and its method of fabrication.