Growth thermodynamics of nanowires and its application to polytypism of zinc blende III-V nanowires

Theoretical model for the growth thermodynamics of nanowires in different epitaxial techniques is presented, which enables one to determine morphological and structural configurations of the nanowire ensemble with minimum formation energy. It is demonstrated that nanowire ensembles are metastable and controlled entirely by the growth kinetics. The model is applied to studying the polytypism of zinc blende III-V nanowires. It is shown that structural transition should occur within a certain domain of radii and vapor supersaturations. Different polytypes between wurtzite and zinc blende structures with periodicity up to 18 layers are analyzed. It is demonstrated that $4H$ polytype has the lowest formation energy and the largest critical radius of transition amongst all polytypes. Numerical estimates predict the critical radius of structural phase transition of $17–25\mathrm{nm}$ for GaAs nanowires growing on the $\mathrm{Ga}\mathrm{As}\left(111\right)B$ substrate.