Molecular dynamics determination of Two-dimensional nucleation kinetic coefficient for modeling the faceted growth of Si (1 1 1) from an undercooled melt

• Si (1 1 1) facet nucleation and growth are investigated from MD simulations. • Mechanisms for the birth and spreading of two-dimensional facets are described. • A nucleation rate-undercooling relationship is proposed. • The MD-derived nucleation model is fitted to a facet growth rate model. • The solidification front is qualitatively compared to that of the HRG process. The discrepancies between kinetic model predictions and experimental observations of two-dimensional (2D) nucleation-mediated growth of silicon limits modeling reliability for existing and new crystal growth processes. Molecular dynamics (MD) simulations were performed to identify the mechanism of evolution of crystallites on a Si (1 1 1) facet and semi-quantitatively describe 2D nucleation kinetics using the forced-velocity solidification (FVS) and free-solidification (FS) MD simulations techniques. Both MD models predicted similar nucleation expressions but gave lesser nucleation energy barriers than predicted from Monte Carlo (MC) nucleation model. The estimated nucleation rate from MD was fitted to a polynuclear growth model to estimate a 2D kinetic model and compared to available experimentally reported growth rates. The Si (1 1 1) facet velocity model derived from the kinetic coefficient given in this work generally provided more conservative estimates of undercooling and the minimum undercooling that may result in kinetic roughening transition. In addition, the FVS model implemented in this work provided a unique opportunity for qualitatively describing the behavior of a crystal-melt interface and gave a molecular-level perspective on the interface stability criterion for the growth of single-crystal silicon during the horizontal ribbon growth (HRG) process.