Misfit dislocations in epitaxial heterostructures with different elastic constants of the substrate and epitaxial layer

We calculate the elastic energy of a heterostructure consisting of material s with different elastic moduli. In the framework of the continuous theory of elasticity we obtain an analytical solution for the elastic field of a p eriodic arrangement of screw misfit dislocations. This solution allows to c alculate the critical thickness of the epitaxial layer (epilayer) and to an alyse its dependence on the elastic contrast between the substrate and the epilayer. Analysis of the total elastic energy of the heterostructure shows that a transition from a pseudomorphic state to a state with misfit disloc ations occurs similarly to either a first-order or a second-order phase tra nsition. The type of transition that the system follows depends on the rela tion between the elastic moduli of the substrate and the epilayer.