Velocity versus temperature relation for solidification and melting of silicon: A molecular-dynamics study.

Abstract

We report on molecular-dynamics simulations to determine the steady-state velocity versus temperature relation for (001) solidification and melting of silicon using the Stillinger-Weber potential to model the interactions between the silicon atoms. Down to 250 K of undercooling, the simulation values show good agreement with experimental results. The slope of the temperature velocity relation near the melting point is reported as (-15\ifmmode\pm\else\textpm\fi{}5 K)/(m/s) whereas we find the slope of the transition-state curve that we fitted to the simulation values has a slope (-9.8 K)/(m/s) at the melting point.However, since Stillinger-Weber amorphous silicon is not formed easily by cooling the melt our simulations do not show the growth into amorphous silicon at the critical velocity of \ensuremath{\approxeq}15 m/s (undercooling below \ensuremath{\approxeq}250 K) that is observed experimentally. Instead in our simulations the velocity of growth into crystalline silicon increases to a maximum of 19.4 m/s at 1350 K and then decreases to at least 1050 K. At 1000 K, the system grows a few incomplete planes, which we suggest may be associated with the growth of amorphous silicon. At 950 K, we did not detect any growth during the 115 ps of the simulation. We also did not observe growth at 1600 or 1700 K over the 115 ps of these simulations. The simulation velocity versus temperature relation shows asymmetry in the solidification and melting portions of the curve with no discontinuity in slope at the melting point. We fitted our simulation velocity versus temperature relation by using the transition-state theory parametrized to Stillinger-Weber silicon. The transition-state theory gives a good qualitative description of the simulation values at all temperatures.It is interesting that the transition-state theory also fits the experimental values for crystallization even though it is parametrized for Stillinger-Weber silicon. The results of these epitaxial-growth studies of silicon are important for studies attempting to model the growth of layered structures by atom deposition with use of molecular dynamics with the Stillinger-Weber potential. Our results show that, even if the deposited atoms have kinetic energies 60% below the melting temperature, the growth of the crystal may be caused by liquid epitaxial growth with one (001) plane grown every 10 ps.