Theoretical model for the growth of semiconductor nanowires is developed, which enables one to determine the growth conditions under which the formation of nanowires is possible. General expression for the nanowire growth rate as function of its radius and the growth conditions is obtained and analyzed. The model also describes the transformation from cubic to hexagonal crystal phase of nanowires. It is shown that the observed crystal structure is controlled mainly by the growth kinetics. Structural diagrams and probabilities of cubic and hexagonal phase formation are calculated as functions of supersaturation and nanowire radius within the plausible range of material parameters. Numerical estimates for the domains of phase mixing and phase purity are presented and analyzed.

Mechanisms of nanowhisker formation during molecular beam epitaxy (MBE) are studied theoretically within the frame of a kinetic model that accounts for the adatom diffusion from the surface to the top of nanowhiskers. It is shown that the adatom diffusion flux may considerably increase the vertical growth rate of nanowhiskers. The decreasing length/diameter dependence of the MBE grown nanowhiskers is obtained that explains a number of experimentally observed facts. The results of experimental investigations of GaAs nanowhiskers grown by MBE on the GaAs(111)B surface activated by Au at different conditions are presented and analyzed. It is shown that the length of thin GaAs nanowhiskers is several times larger than the effective thickness of deposited GaAs. Theoretical and experimental length/diameter curves are compared to each other and a good correlation between them is demonstrated.

We present a general model for the vapor-liquid-solid nanowire (NW) growth rates which accounts for adatom diffusion from the substrate and sidewalls into the Au catalyst drop as well as the Gibbs-Thomson effect of elevated chemical potential in the drop with a curved surface. The growth model is compared with the experimental length-diameter dependences for InP and Si NWs grown via metal organic chemical vapor deposition (MOCVD) and GaAs nanowires grown via molecular beam epitaxy (MBE). We show that MBE growth is affected mainly by adatom diffusion from the substrate, whereas MOCVD growth is affected mainly by direct Au drop impingement and sidewall diffusion. The Gibbs-Thomson effect is shown to limit growth for smaller diameter nanowires. Fits for diffusion lengths and the Gibbs-Thomson radii are determined which explain the experimental length-diameter dependence observed.

A theoretical model of nanowire formation by the vapor-liquid-solid mechanism during molecular beam epitaxy and related growth techniques is presented. The model unifies the conventional adsorption-induced model, the diffusion-induced model, and the model of nucleation-mediated growth on the liquid-solid interface. The concentration of deposit atoms in the liquid alloy, the nanowire diameter, and all other characteristics of the growth process are treated dynamically as functions of the growth time. The model provides theoretical length-diameter dependences of nanowires and the dependence of the nanowire length on the technologically controlled growth conditions, such as the surface temperature and the deposition thickness. In particular, it is shown that the length-diameter curves of nanowires might convert from decreasing to increasing at a certain critical diameter and that the nanowires taper when their length becomes comparable with the adatom diffusion length on the sidewalls. The theoretical dependence of the nanowire morphology on its lateral size and length and on the surface temperature are compared to the available experimental data obtained recently for Si and $\mathrm{GaAs}$ 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.