Modeling a Growth Instability in Stressed Boron Doped Silicon

Abstract

The effects of rate-enhancing dopants and externally applied stress on interfacial growth during silicon crystallization are modeled using advanced numerical methods. The boron doped crystalline Si is modeled as an isotropic linear elastic solid, and the amorphous as a viscous fluid with a time dependent viscosity to reflect structural relaxation. The e ffect of the dopant is included through its position dependent effect on the rate of crystallization at the interface. Appropriate coupling conditions across the boundary are defined, and both problems are solved using advanced boundary integral methods. The interface is advanced in time using the level set technique. The simulation results match well with experiments and support the fact that both stress and dopant-gradient e ffects, along with interface orientation e ffects, must be accounted for to explain the observed behavior. These new effects are of general relevance to the growth of all non-hydrostatically stressed solids, and are therefore important in film synthesis, with potentially significant applications in electronic devices and thin film coatings.