Controlling the shape of a tapered nanowire: lessons from the Burton-Cabrera-Frank model

Abstract

The propagation of sidewall steps during the growth of nanowires is calculated in the frame of the Burton-Cabrera-Frank model. The stable shape of the nanowire comprises a cylinder section on top of a cone section: their characteristics are obtained as a function of the radius of the catalystnanowire area, the desorption-limited diffusion length of adatoms on the terraces, and the sticking of adatoms at step edges. The comparison with experimental data allows us to evaluate these last two parameters for InP and ZnTe nanowires; it reveals a different behavior for the two materials, related to a difference by an order of magnitude of the desorption-limited diffusion length.

The onset of tapering in the early stage of growth of a nanowire

“…1a) may be preferable for a better light collection in photovoltaic devices 6,7 . Similar shapes and sizes have been demonstrated for different systems in spite of large differences in the material parameters, for instance ZnTe and InP with orders of magnitudes difference in the diffusion length along the nanowire 8 . However, the growth strategy has to be adapted to each material and the range of available values of length and radius has to be determined.…”

“…The value of λ means that the desorption of adatoms from the ZnSe sidewalls is strong. It is even stronger than for ZnTe nanowires with the zinc-blende structure, where λ =90 nm 8 . Much larger values of the diffusion length are commonly reported for III-V nanowires, for instance λ ≃ 1 µm for InP nanowires 8 .…”

“…It is even stronger than for ZnTe nanowires with the zinc-blende structure, where λ =90 nm 8 . Much larger values of the diffusion length are commonly reported for III-V nanowires, for instance λ ≃ 1 µm for InP nanowires 8 . We observe nevertheless a significant radial growth, and tapered nanowires can be grown.…”

“…1a) 15 , and then develop a cone shape 16 while keeping the cylinder segment on top of the cone ("CC" in Fig. 1a), as the sidewall steps do not reach the seed 8 .…”

“…These profiles will be discussed later on. (b) Same as (a), taking into account the incorporation at step edges (Burton-Cabrera-Frank model 8,13,14 ).…”