The incubation time preceding nucleation and growth of surface nanostructures is interesting from a fundamental viewpoint but also of practical relevance as it determines statistical properties of nanostructure ensembles such as size homogeneity. Using in situ reflection high-energy electron diffraction, we accurately deduce the incubation times for Ga-assisted GaAs nanowires grown on unpatterned Si(111) substrates by molecular beam epitaxy under different conditions. We develop a nucleation model that explains and fits very well the data. We find that, for a given temperature and Ga flux, the incubation time always increases with decreasing As flux and becomes infinite at a certain minimum flux, which is larger for higher temperature. For given As and Ga fluxes, the incubation time always increases with temperature and rapidly tends to infinity above 640 {deg}C under typical conditions. The strong temperature dependence of the incubation time is reflected in a similar variation of the nanowire number density with temperature. Our analysis provides understanding and guidance for choosing appropriate growth conditions that avoid unnecessary material consumption, long nucleation delays, and highly inhomogeneous ensembles of nanowires. On a more general ground, the existence of a minimum flux and maximum temperature for growing surface nanostructures should be a general phenomenon pertaining for a wide range of material-substrate combinations.
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