We propose a model that explains the phenomenon of polytypism in metal particle-seeded III-V semiconductor nanowires. The model is based on classical nucleation theory, utilizing the axial next-nearest-neighbor Ising (ANNNI) model to account for interlayer interaction up to the third nearest-neighboring layer. We investigate the limits of polytypism by varying the ANNNI interaction parameters. These calculations lead to attainability diagrams, which show the regions in interaction energy space where certain polytypes can be attained given that the supersaturation is precisely tuned. We calculate the values of the ANNNI interaction parameters for six common III- V materials from first principles by means of the projector-augmented wave method. We discuss our calculated values in view of previous results. Using these calculated values in our nucleation model, our analysis suggests that besides the commonly observed 3C (zinc blende) and 2H (wurtzite) polytypes the higher order polytypes 4H and 6H can also be attained, in agreement with experimental observations.
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