Advanced numerical methods have been used to model the growth of crystalline silicon from the amorphous phase in the presence of stress. This involved, for the first time, the coupling of the boundary integral method for stress evaluation with the Level Set method for front tracking. The crystal was modeled as an elastic solid and the amorphous phase as a viscous fluid with a time dependent viscosity. The simulations yielded a very good match with experiments, and provide conclusive proof that the experimentally observed instability is a consequence of the stress effect on atom mobility.
The experiments show a growth instability at the crystal/amorphous interface wherein the amplitude of the interface ripple increases in the presence of compressive non-hydrostatic stress. It is well known that, in equilibrium, a non-hydrostatic stress provides a driving force that creates a rippling instability of a flat surface. However, growth and morphology of a solid are also determined by the "non-equilibrium" mobilities of the interface atoms. The effect of stress on mobility and its subsequent effect on growth morphology is generally ignored. These results support our earlier work and definitively show that the observed growth instability is driven by the stress dependence of the atom mobilities at the interface.
These advanced numerical techniques provide an important capability for studying phase transformations and chemical reactions in solids. Future applications include the study of silicon oxidation during semiconductor device fabrication and the investigation of chemical reactions in multiphase condensed matter as a method for synthesizing self-constructing nanostructures.