Kinetic narrowing of size distribution

We present a model that reveals an interesting possibility for narrowing the size distribution of nanostructures when the deterministic growth rate changes its sign from positive to negative at a certain stationary size. Such a behavior occurs in self-catalyzed one-dimensional III-V nanowires and more generally whenever a negative "adsorption-desorption" term in the growth rate is compensated by a positive "diffusion flux." By asymptotically solving the Fokker-Planck equation, we derive an explicit representation for the size distribution that describes either Poissonian broadening or self-regulated narrowing depending on the parameters. We show how the fluctuation-induced spreading of the size distribution can be completely suppressed in systems with size self-stabilization. These results can be used for obtaining size-uniform ensembles of different nanostructures.