Diffusion-induced growth of nanowires: Generalized boundary conditions and self-consistent kinetic equation

• Diffusion-induced nanowire growth is analyzed theoretically with a model based on the diffusion equations with generalized boundary conditions.
• Discontinuity of the adatom chemical potential at the nanowire base is taken into account.
• A new growth equation coupling the diffusion transport with the kinetics of 2D nucleation under the droplet is derived.
• This equation describes the depression of the growth rate of narrow nanowires much better than the Gibbs–Thomson correction.
• Overall, our equation describes very well the length–radius correlations of nanowires obtained by different epitaxy techniques.

In this work, we present a theoretical analysis of the diffusion-induced growth of “vapor–liquid–solid” nanowires, based on the stationary equations with generalized boundary conditions. We discuss why and how the earlier results are modified when the adatom chemical potential is discontinuous at the nanowire base. Several simplified models for the adatom diffusion flux are discussed, yielding the 1/pR1/Rp radius dependence of the length, with pp ranging from 0.5 to 2. The self-consistent approach is used to couple the diffusion transport with the kinetics of 2D nucleation under the droplet. This leads to a new growth equation that contains only two dimensional parameters and the power exponents pp and qq, where qq=1 or 2 depends on the nucleus position. We show that this equation describes the size-dependent depression of the growth rate of narrow nanowires much better than the Gibbs–Thomson correction in several important cases. Overall, our equation fits very well the experimental data on the length–radius correlations of III–V and group IV nanowires obtained by different epitaxy techniques.

Experimental length–radius dependence of the MOCVD-growth InP nanowires (symbols) and theoretical fits obtained from our model (solid line) and with the Gibbs–Thomson curve (dashed line).Figure optionsDownload as PowerPoint slide