Journal of Statistical Physics

, Volume 87, Issue 3–4, pp 505–518 | Cite as

On the shape of wedding cakes

  • Joachim Krug
Articles

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 equationu1=[u−2u x ] x . As an application, expressions for the number of exposed layers as a function of coverage and diffusion length are derived.

Key Words

Crystal growth growth instability surface diffusion singular diffusion equations hydrodynamic limit 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Joachim Krug
    • 1
  1. 1.Fachbereich PhysikUniversität GH EssenEssenGermany

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