On Kinetically vs. Energetically Driven Growth Instabilities in Solid and Vapor Phase Epitaxy

A stress-induced kinetically-driven morphological instability is of general applicability to driven systems. The effect of stress on the reaction mobility for incorporation into the growing solid couples to stress variations along a perturbed planar growth front, resulting in amplification or decay of the perturbation depending on the sign of the stress. Experimentally we studied a model system in which stress is applied externally to a chemically pure substance, permitting us to isolate the effect of strain from any possible effects of composition, and found that the new kinetically-driven effect dominates the behavior for solid phase epitaxial growth (SPEG) of Si(001). A linear stability analysis of a sinusoidally perturbed planar growth front, incorporating both the kinetically and the energetically driven effects, has been performed. Stability maps are developed, indicating parameter ranges under which the morphological evolution is dominated by the energetically-driven instability, the kinetically-driven instability, and the kineticallydriven stabilization. Numerical values of the key dimensionless parameters for SPEG and for SiGe/Si(001) Molecular Beam Epitaxy (MBE) are very similar in cases where they are known, indicating that the kinetically-driven effect may be important in determining morphological evolution related to quantum dot formation in MBE as well.