Theoretical Metastability of Semiconductor Crystallites in High-Pressure Phases, with Application to β-Tin Structure Silicon

We examine prospects for metastability of six-coordinate high-pressure semiconductor phases at ambient temperature and pressure (STP). We investigate a simple “thermodynamic”, coherent transformation model for nanocrystals of size >2 nm and, as a quantitative example, apply it to the silicon β-tin to diamond structural phase transition. The unit cell transformation path is taken from a calculation by Mizushima et al. (Mizushima, K.; Yip, S.; Kaxiras, E. Phys. Rev. 1994, B50, 14952). Surface energies and the initial crystallite shape are included in an absolute rate model. The model assumes that the crystallite shape substantially changes to accommodate the unit cell c/a variation from 1.414 (diamond) to 0.55 (β-tin). The model predicts that the β-tin nanocrystal lifetime increases rapidly with increasing size. Near-round β-tin nanocrystals are more stable and have slower transformation rates than oblate spheroid nanocrystals with larger surface energy. For size >2 nm, both near-round and oblate β-tin nanocrystals are metastable with half-lives of years or more. An alternate, classical nucleation model is considered for surface nucleation in larger microcrystals. In this model the β-tin nanocrystal lifetime decreases with increasing size. Yet micron-size and smaller crystallites are metastable as well. Defect and strain-free β-tin microcrystals appear to be metastable at STP. More generally, stabilization of high-pressure semiconductor phases at STP should be more widespread in nanocrystals than in bulk crystals, because of (1) the relative ease in annealing out defects, strain, and impurities in nanocrystals and (2) the use of surface passivation in lowering the surface energy of the high-pressure phase.