Instabilities in crystal growth by atomic or molecular beams

Abstract When growing a crystal, a planar front is desired for most of the applications. This plane shape is often destroyed by instabilities of various types. In the case of growth from a condensed phase, the most frequent instabilities are diffusion instabilities , which have been studied in detail by many authors but will be briefly discussed in simple terms in Section 2. The present review is mainly devoted to instabilities which arise in ballistic growth, especially molecular beam epitaxy (MBE). The reasons of the instabilities can be geometric, but they are mostly kinetic (when the desired state cannot be reached because of a lack of time) or thermodynamic (when the desired state is unstable). The kinetic instabilities which will be studied in detail in Sections 4 and 5 result from the fact that adatoms diffusing on a surface do not easily cross steps (Ehrlich–Schwoebel or ES effect). When the growth front is a high symmetry surface, the ES effect produces mounds which often coarsen in time according to power laws. When the growth front is a stepped surface, the ES effect initially produces a meandering of the steps, which eventually may also give rise to mounds. Kinetic instabilities can usually be avoided by raising the temperature, but this favours thermodynamic instabilities of the thermodynamically unstable materials (quantum wells, multilayers …) which are usually prepared by MBE or similar techniques. The attention will be focussed on thermodynamic instabilities which result from slightly different lattice constants a and a +δ a of the substrate and the adsorbate. They can take the following forms. (i) Formation of misfit dislocations, whose geometry, mechanics and kinetics are analysed in detail in Section 8. (ii) Formation of isolated epitaxial clusters which, at least in their earliest form, are ‘coherent’ with the substrate, i.e. dislocation-free (Section 10). (iii) Wavy deformation of the surface, which is presumably the incipient stage of (ii) (Section 9). The theories and the experiments are critically reviewed and their comparison is qualitatively satisfactory although some important questions have not yet received a complete answer. Short chapters are devoted to shadowing instabilities, twinning and stacking faults, as well as the effect of surfactants.