Fluid–solid interaction finite element modeling of a kinetically driven growth instability in stressed solids

The kinetically driven growth instability in stressed solids has been a subject of recent investigation as there is an increasing interest in the effects of non-hydrostatic stresses on crystal growth processes. Recent experimental and modeling work using advanced numerical methods such as boundary element and level set methods have demonstrated that the effect of stress on the solid phase epitaxy (SPE) growth of crystalline silicon from the amorphous phase is responsible for the roughening of its amorphous–crystalline interface. Although our previous model (Phan et al., in Model Simul Mater Sci Eng, 9:309–325, 2001) has been able to explain the observed interfacial instability during the crystal growth of intrinsic silicon, it has not been very successful when extended to the SPE growth process of doped silicon. In an effort to identify the sources that may improve the accuracy and robustness of the previously proposed model, we present in this paper a new approach for modeling the crystal growth in stressed Si layers. The technique is based upon the coupling of a transition-state-theory-based model, a finite element model of the sequentially weak coupling analysis for fluid-solid interaction, and the marker particle method.