A new approach to the continuum modeling of epitaxial growth: slope selection, coarsening, and the role of the uphill current

We develop a new approach to the macroscopic modeling of epitaxial growth, focusing on the slope selection and coarsening observed in spiral-mode growth. Our model distinguishes between the surface height and the surface adatom density. These quantities evolve by a coupled pair of partial differential equations: a Hamilton–Jacobi equation for the height, coupled to a nonlinear diffusion equation for the adatom density. The influence of the Ehrlich–Schwoebel barrier is included through an “uphill current” in the equation for adatom density. Our model predicts slope selection and coarsening—thus it offers a possible mechanism for these effects. The model predicts, in particular, that the coarsening rate depends mainly on the strength of the Ehrlich–Schwoebel barrier.