Growth with surface diffusion in d = 1 + 1

A restricted solid-on-solid model where surface relaxation occurs by atom desorption and by surface diffusion is introduced and studied in 1+1 dimensions. The interface profile is mapped onto a four-vertex model and the kinetic equation describing the moving surface is solved exactly for small samples. In the presence of desorption we classify different growth regimes using the Wilson-Frenkel law. In the presence of surface diffusion with step edge barriers we find evidence for a sharp transition from stable to unstable growth which occurs with increasing diffusion length. Growth modes during the thermal evaporation of the crystal are also discussed.