Stability of heteroepitaxial coherent growth modes on nanowire radial surfaces

Abstract

The thermodynamic stability of the coherent shell and Stranski-Krastanov heteroepitaxial growth modes on cylindrical nanowires is analyzed theoretically. In contrast to previous studies, the exact geometrical shape of pyramidal Stranski-Krastanov islands is considered for the calculation of surface- and elastic-energy contributions. In particular, the impact of the pyramid base angle on the relaxation energy is included. Moreover, the dependence of island facet surface-energy density on the distance of the surface to the nanowire substrate is taken into account. Maps of the growth-mode stability are derived for the Si-core/Ge-shell structure, which display the favored mode as a function of deposited volume, wetting-layer thickness, and nanowire radius. We show that for nanowire radii in the range between 15 and 100 nm, the Stranski-Krastanov mode becomes stable only for larger pyramid angles. In addition, it is found that the exact value of the surface-energy density significantly influences the transition between the two growth modes, leading to a stabilization of islands bound by low-energy crystal facets, as observed in experiments.