The role of surface diffusion of adatoms in the formation of nanowire crystals

A model of the formation of nanowire crystals on surfaces activated by droplets of the catalyst of growth is developed. In the model, the diffusion of adatoms from the surface of the substrate to the lateral surface of the crystals is taken into account. The exact solution of the diffusion problem for the flow of adatoms from the surface to the nanowire crystals is obtained, and the particular cases of the solution for the short and long diffusion lengths of adatoms, lambda(s), are analyzed. A general expression for the length of the nanowire crystals, L, in relation to their radius R and to the conditions of growth is derived. The expression is applicable to a large variety of technologies of growth. The theoretical results are compared with the experimental dependences L(R) in the range of R = 20-250 nm for GaAs nanowire crystals grown by molecular-beam epitaxy on the GaAs (I 11) V Ga surface activated by Au. It is shown that, in some range of the parameters, the dependence L(R) follows the function 1/(RIn)-In-2(lambda(s)/R), which is radically different from the classical diffusion dependence 1/R.