Stabilizing the hexagonal diamond metastable phase in silicon nanowires

At the nanoscale, the proportion of atoms at the surface of solids becomes significant, which may change the equilibrium of atomic edifices. In the case of silicon, experimental observations have evidenced indeed the presence of the hexagonal diamond (HD) metastable structure in as-grown nanowires of a few nm in diameter, as if that phase could become the stable one in such small objects. We present ab initio calculations that demonstrate the existence of stable domain for the HD structure in silicon nanowires. Surfaces of HD Si are first studied without and with hydrogen, including possible relaxations, and compared to CD Si surfaces, with a globally favourable energy ratio for HD surfaces. The energies of several plausible HD and CD Si NWs of different thicknesses are then calculated and compared to estimate their relative phase stabilities, again in favour of HD NWs, without and with hydrogen at surfaces. Analytically extrapolating the ab initio results as functions of bulk, surface and edge energy contributions, the main result is that HD Si NWs are intrinsically stable with respect to CD Si NWs for effective diameters up to only about 15 nm, for pure Si NWs as well as for surface hydrogenated NWs. Thicker HD NWs can thus only be metastable. This may explain why Si HD NWs are so difficult to grow. The diameter size limit for germanium, silicon's big brother, is three times smaller, making HD Ge NWs much less likely, in agreement with recent experimental attempts to grow Ge NWs.