On the applicability of elastic model to very thin crystalline layers

Elastic model of continuum material is often used to simulate the relaxation of crystalline heterostructures. There are many reports on the successful application of the theory of elasticity to nano-sized crystalline heterostructures, even if the continuum condition for them is hardly fulfilled. On the other hand, progress in epitaxial growth allows for the preparation of stable ultra-thin layers with thickness of few monolayers. For such ultra-thin layers, results provided by continuum model and molecular statics/dynamics calculations become diverging. The key problem seems to be located at the modelling of the interface between layers, which is problematic in the continuum approach. By applying a step-wise substitutive compositional interfacial function, it is possible to obtain good agreement with molecular dynamics calculations, even for a single monolayer heterostructure. We propose another approach that uses composition as an extra parameter during finite element calculations, along with classical nodal displacements. Such an approach creates a chemo-elastic coupling that allows to interpolate the composition much like in the case of atomistic calculations. (paper)