Figure 3: The growth tip and VLS processes in it.

(a–c) TEM images of the spherical particle at the tip of the nanostructure. Angle θ is defined in (a), in which R and r are, respectively, the radii of the spherical particle and the nanowire. It should be pointed out that θ defined here is the supplementary angle of the traditionally defined one such as in ref. 23. We used the present definition because it leads to much simpler mathematical express in following derivation processes. (d) The growth model of VLS: a nanosize droplet sits on a solid surface surrounded by vapour. Here, the surface tension between the solid and the liquid phase is drawn along the radial direction. It is because oscillation of the wire diameter is controlled by the surface tension and thus movement of the vapour–solid contact point in the radial direction is concerned.