Abstract
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 rateD/F→∞ 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 equationu 1=[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.
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Krug, J. On the shape of wedding cakes. J Stat Phys 87, 505–518 (1997). https://doi.org/10.1007/BF02181234
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DOI: https://doi.org/10.1007/BF02181234