Theory of controllable shape of quantum structures upon droplet epitaxy

• We develop a model to control the shape of quantum structures upon droplet epitaxy.
• The diffusion of III-column element atoms governs the shape of final nanostructures.
• A shape phase diagram in the space of temperature and As flux density is yielded.
• The shape can be well controlled through regulating temperature and flux intensity.

During droplet epitaxy, the shape of final crystalline quantum structures is determined by the growth temperature and As flux density. Here we develop a theoretical model with which we elucidate that the diffusion of III-column element atoms away from the droplet and the trapping of As atoms critically govern the shape of final quantum structures, yielding a shape phase diagram in the space of growth temperature and As flux density. Theoretical investigation suggests that we not only control the basic shape of quantum structures but also design the heights of ring-shaped quantum structures through regulating growth temperature and As flux intensity.