Prediction of Formation of Cubic Boron Nitride Nanowires inside Silicon Nanotubes

Abstract

A model that predicts the formation of cBN nanowires inside Si nanotubes was developed by taking the effect of surface tension induced by the nanosize curvature of critical nuclei and the Si nanotubes into account. The radius and formation energy of the critical nuclei of cBN, the phase transition probability, and the growth velocity of the cBN nuclei were calculated with the proposed model, and the effect of the radii of Si nanotubes on the nuclei was also investigated. The results show that the temperature and supersaturation limited to a range of 1300-1500 K and 2-5, respectively, and radii of Si nanotubes of less than 5 nm are favorable for the formation of cBN nanowires inside Si nanotubes.

Theoretical analysis of the formation of face-centered cubic Si nanocrystals by magnetron sputtering

“…On the concave surface with radius R 0 , however, the change in Gibbs free energy by the formation of a spherical nucleus with a radius r in the low-pressure gas phase can be given by [11][12][13][14] …”

“…c sc , c sa , and c ca are the interface energies of the substrate-nucleus, the substrate-vapor, and the nucleus-vapor, respectively, and S sc and S ca are the corresponding interface areas, respectively. Moreover, Dg is the Gibbs free energy difference per unit volume and can be generally given by Dg ¼ ðÀRT=V m ÞlnðP=P e Þ, 11 where R, T, P, and P e are the gas constant, temperature, pressure, and equilibrium-vapor pressure of fcc-Si, respectively. Taking the effect of the nanosize-induced additional pressure on the nucleation energy of critical nuclei into account by the Laplace-Young equation and Kelvin equation, Dg can be expressed by 11,12 Dg ¼ À 1 2 The above equation can be applied to the nucleation of both on the flat surface and concave surface.…”

“…On the basis of the above thermodynamic theory, the probability f of the formation of fcc-Si is also measured by the following expression 11,15 :…”