We examine a class of step ow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. ur goal is to derive a consistent contin uummodel for the ev olutionof the lm surface. Away from peaks and valleys, the surface height solves a Hamilton- acobi equation (H E). he peaks are free boundaries for this H E. heir evolution must be speci ed by boundary conditions re ecting the microscopic physics of nucleation. e investigate this boundary condition by numerical simulation of the step ow dynamics using a simple n ucleationlaw. ur results rev ealthe presence of sp ecial structures in the pro le near a peak; we discuss the relationship between these structures and the contin uumequation. e further address the importance of ev aporationfor matching the local behavior near the peak to the solution of the contin uum equation.

We examine a class of step ow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. Our goal is to derive a consistent contin uummodel for the evolutionof the film surface. Away from peaks and valleys, the surface height solves a Hamilton-Jacobi equation (HJE). The peaks are free boundaries for this HJE. Their evolution must be specified by boundary conditions reecting the micro- scopic physics of nucleation. We inv estigate this boundary condition by numerical simulation of the step ow dynamics using a simple nucleation law. Our results rev ealthe presence of special structures in the profile near a peak; we discuss the relationship between these structures and the contin uumequation. We further address the importance of evaporation for matching the local behavior near the peak to the solution of the contin uum equation.