Abstract
ABSTRACTA 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 kinetically-driven 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
Highlights
The morphological stability of surfaces and interfaces in elastically stressed solids is of great current interest
Atoms tend to spontaneously move from the troughs to the peaks, thereby amplifying the perturbation. Opposing this process is the effect of capillarity, but for perturbation wavenumbers below a critical value the elastic strain energy decrease is sufficient to "pay" for the increased surface energy, and the perturbation spontaneously grows
The mass transport pathway does not alter the critical wavenumber of the instability; it alters only the dependence of the amplification rate on wavenumber
Summary
The morphological stability of surfaces and interfaces in elastically stressed solids is of great current interest. SPEG is analogous to growth from the vapor by evaporation-condensation: the chemical potential in the fluid phase is spatially uniform, and the magnitude of the discontinuity at the interface varies from peak to trough The organizers of this symposium invited this paper in order to engender a discussion of whether the BC instability may be important for quantum dot formation in growth from the vapor. The linear stability of a sinusoidally perturbed interface growing with elastic strain contributions to both the energetics and a mobility has been analyzed only recently [5,6,7, 11, 12] These analyses are for stressed bulk solids rather than strained films on unstrained substrates and they neglect any anisotropy in the mobility, interfacial tension, and elastic constants (Yu and Suo [11] included elastic anisotropy in 2+1 dimensions). Any differences between so-called "type A" and "type B" steps, as well as asymmetries in ∆μincorp at up-steps and down-steps, are beyond the scope of this discussion
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