MORPHOLOGICAL INSTABILITY IN EPITAXIALLY STRAINED DISLOCATION-FREE SOLID FILMS - LINEAR-STABILITY THEORY

The morphological instability of a growing epitaxially strained disloc ation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface d iffusion driven by a stress-dependent chemical potential. From the tim e-dependent linear stability problem the conditions for which a growin g film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; ho wever, low temperatures as well as elastically stiff substrates are st abilizing influences. The results also reveal that the critical film t hickness for instability depends on the growth rate of the film itself . Detailed comparison with experimental observations indicates that th e instability described exhibits many of the observed features of the onset of the ''island instability.''