Energy scaling and asymptotic properties of step bunching in epitaxial growth with elasticity effects

In epitaxial growth on vicinal surfaces, elasticity effects give rise to step bunching instability and some self-organization phenomena, which are widely believed to be important in the fabrication of nanostructures. It is challenging to model and analyze these phenomena due to the nonlocal effects and interactions between different length scales. In this paper, we study a discrete model for epitaxial growth with elasticity. We rigorously identify the minimum energy scaling law and prove the formation and appearance of one bunch structure. We also provide sharp bounds for the bunch size and the slope of the optimal step bunch profile. Both periodic and Neumann boundary conditions are considered.