| We perform atomistic simulations to better understand solid phase epitaxy in silicon, the process by which the amorphous phase transforms into the diamond structure crystal phase at an amorphous-crystal interface. We begin by developing a quantum-mechanical nonorthogonal tight-binding (TB) model to describe the energetics of silicon atoms in bulk phases including the diamond and {dollar}beta{dollar}-Sn structures, point defects, and activation energies. These structures are chosen to represent the range of geometries present in defective crystalline and amorphous silicon, including coordination from 4 to 6, point defects, and strained bond angles. We compare the results of this model Hamiltonian to other nonorthogonal TB models and to density functional theory calculations for several bulk crystal phases, relaxed and unrelaxed point defects, and surface energies. Using a combination of this TB model and the Stillinger-Weber empirical interatomic potential we simulate the melting and quenching of a silicon sample to create a system that is part crystal and part amorphous, with an interface between the two phases. We develop several localized measures of order to characterize the interface, and plot pictures of the atomic configurations at the interface to gain an understanding of its atomistic features. Using the environment dependent interatomic potential (EDIP), which is more reliable than the Stillinger-Weber potential, we create additional interface samples and simulate their annealing at various temperatures and pressures. We see thermally activated growth with Arrhenius behavior (log of growth rate is proportional to one over temperature) with an activation energy of 0.1-0.4 eV at low temperatures and 0.8-1.7 eV at high temperatures. In experiment only one activation energy of 2.7 eV is seen over a wide range of temperatures. We also observe an exponential dependence of the interface speed with pressure, corresponding to an activation volume for growth of about -0.7 {dollar}Omega{dollar}Si, compared with -0.28 {dollar}Omegasb{lcub}Si{rcub}{dollar} in experiment. |
