Continuum models for surface growth

Abstract

As an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations (PDEs). Their {\em heuristic derivation} makes use of inherent symmetries in the physical process (mass conservation, crystal symmetry, ...) which determines their {\em structure}. Two examples of applications are given, one for large scale properties, one including crystal lattice discreteness. These are: (i) a simplified model for {\em mound coarsening} and (ii) for the transition from {\em layer-by-layer} to {\em rough growth}. Virtues and shortcomings of this approach is discussed in a concluding section.