Morphological instabilities

Instabilities in mechanics are ubiquitous and often generate interesting patterns. A typical example is the Raylaigh-Taylor instability observed in both fluids and soft elastic solids.

Departing from purely mechanical problems, we consider the morphological instabilities observed on crystal surfaces during crystal growth. More specifically, as atoms are deposited on top of a crystal, the latter grows through the propagation of atomic steps. These are subject to the bunching and meandering instabilities that lead to the pattering of the surface. This problem involves a coupling between the elastic field generated by the atomic steps within the bulk and the diffusion of atoms on top of the surface.

Through a linear stability analysis of the step-flow problem, we show [Guin et al., 2020] that step bunching can develop under conditions where the propagation of steps was supposedly stable, furnishing a possible explanations for bunching observed on Si(111) and GaAs(001) .