Critical thickness for interface misfit dislocation formation in two-dimensional materials

In-plane heterostructures of two-dimensional (2D) materials form interface misfit dislocations to relieve lattice mismatch strain, much like heterostructures of 3D materials. Here, using graphene-hexagonal boron nitride (h-BN) as a model system, we consider interface misfit dislocations in 2D lateral heterostructures resting on a flat support layer that prevents out-of-plane deformation. Using an accurate empirical interatomic potential, we carry out a rigorous energetic analysis of the graphene/h-BN interface with 5-7 or 8-6 dislocation cores. We define and extract critical thicknesses for the formation of an interface misfit dislocation in the heterostructure, for the limiting cases when the h-BN or graphene domains are significantly different in size (equivalent to the classic 3D thin film critical thickness problem), and the intermediate case, where the h-BN and graphene domains are of comparable size (equivalent to the classic 3D compliant substrate problem). This makes it possible to compare the alternative dislocation core structures and to determine the resulting dislocation core energy in a continuum analysis. It also reveals a design space where defect-free heterostructures can be grown.