Katharine F. Gurski, Geoffrey B. McFadden
Mathematical and Computational Science Division, National Institute for Standards and Technology, Gaithersburg, MD 20899-8910
Quantum wires (alternatively called nanowires) are "one-dimensional" crystals that are grown epitaxially on a heterogeneous substrate. The wires are typically less than than one nanometer high, a few nanometers wide, and can be as long as a micron. A linear stability analysis suggests that quantum wires with an isotropic surface energy would tend to bead up rather than persist as wires ("Rayleigh instability"). However, there are also several sources of anisotropy in the system, including surface tension anisotropy and elastic anisotropy associated with an elastic misfit between the wire and substrate crystal structures. To address the effects of surface tension anisotropy on the Rayleigh instability, we compute the second variation of the surface free energy of an isolated wire whose cross section is given by the associated two-dimensional equilibrium shape. We consider the case of a cubic material, and compute the stability of the wire to general perturbations when the axis of the wire is in high symmetry orientations such as , , and . For small levels of anisotropy, the stability can be computed approximately via perturbation theory. For larger amplitudes of anisotropy, we have computed the stability numerically by solving an associated Sturm-Liouville eigenvalue problem. We find that surface tension anisotropy can either promote or suppress the Rayleigh instability, depending on the orientation of the wire and the magnitude and sign of the anisotropy.