Theoretical prediction of GaN nanostructure equilibrium and nonequilibrium shapes

A wide variety of nanostructure shapes have been observed for GaN under different growth conditions. These shapes include but are not limited to hexagonal pyramid, prismatic, triangular cross-section nanowires, and arrow-headed shapes. Using Wulff’s plot and kinetic Wulff’s plot for GaN under thermodynamic equilibrium and under various kinetic conditions, we present a model to theoretically predict and explain these faceted nanostructure shapes. Legendre transformation on Wulff’s plot and kinetic Wulff’s plot has been extensively utilized to obtain the faceted equilibrium shapes in equilibrium. In addition, equilibrium and nonequilibrium faceted geometry of nanostructures have also been predicted by numerical simulations using level set methods and the proposed kinetic Wulff’s plot.