On the shape of wedding cakes

The large-scale morphology of a growing surface is characterized for a simple model of crystal growth in which interlayer transport is completely suppressed due to the Ehrlich-Schwoebel effect. In the limit where the ratio of the surface diffusion coefficient to the deposition rate D/F --> infinity the surface consists of wedding-cake-like structures whose shape is given by the inverse of an error Function. The shape can be viewed as a separable solution of the singular diffusion equation u(t) = [u(-2)u(x)](x). As an application, expressions For the number of exposed layers as a function of coverage and diffusion length are derived.