The shape of epitaxially grown silicon nanowires and the influence of line tension

Silicon nanowires grown epitaxially via the vapor-liquid-solid mechanism show a larger diameter at the base of the nanowire, which cannot be explained by an overgrowth of the nanowire alone. By considering the equilibrium condition for the contact angle of the droplet, the Neumann quadrilateral relation, a quasi-static model of epitaxial nanowire growth is derived. It is found that a change of the contact angle of the droplet is responsible for the larger diameter of the nanowire base, so that the expansion has to be considered a fundamental aspect of epitaxial vapor-liquid-solid growth. By comparison of experimental results with theoretical calculations, an estimate for the line tension is obtained. In addition, the growth model predicts the existence of two different growth modes. Only within a certain range of line-tension values is the mode corresponding to ordinary nanowire growth realized, whereas nanowire growth stops at a relatively small height if the line tension exceeds an upper boundary. An approximate analytic expression for the upper boundary as a function of the surface tensions is given.