| We consider single-crystal semiconductor functional materials just typical of Ge/Si and GaAs/Si. Strained semiconductor epitaxial nanostructures made from this kind of materials are widespreadly applied in civil and military high-tech fields such as electronic, optical and optoelectronic devices, quantum computing, and information storage.Here we concentrate our attention on the solid surface stability under the condition of the pre-strained epitaxial film/substrate system, in which the surface diffusion is assumed to be a dominant mass transport mechanism. Our model incorporates the effect of strain energy, capillary pressure and long-range forces like wetting potential, van der Waals interaction, electrostatic energy on the perturbed morpology of the surface. In our model, strain energy, van der Waals interaction and electrostatic energy destabilize the solid surface while capillary pressure and wetting potential stabilize the solid surface. The energy competition among them can lead to the stable ordered surface morphology and at this moment the total energy of the system is minimized. By a linear perturbation analysis, we study how the pre-strain affects the surface morphology of the elastic solid and discuss the regulating of the pattern. We have developed the phase microelasticity model as well, by means of which, the shape-dependent composition profile of strained epitaxial alloy quantum dots is simulated and the composition segregation driven by inhomogeneous stress fields is predicted.First of all, we study the morphological stability of a pre-strained epitaxial system subjected to long-range forces which include wetting potential and van der Waals interaction between the surface of the film and the interface of the film/substrate, the film surface stress and wetting potential. By a linear stability analysis, we reveal the dependence of the critical instability thickness and wavenumber of Ge/Si and GaAs/Si thin films on the pre-strain. Moreover, the larger the magnitude of the equi-biaxial pre-tension, the thicker the critical film and the smaller the critical wavenumber; the uni-axial pre-tension inhibits the film instability in the direction parallel to pre-tension but promotes the one in the perpendicular direction; if the uni-axial pre-compression works, the conclusion is reverse. When the surface stress of the film is tensile, it stabilizes the film; when the surface stress of the film is compressive, it destabilizes the film. The surface instability morphology of the elastic thin film can be regulated by equi-axial pre-strain or uni-axial pre-strain.Then, we develop the phase microelasticity model and investigate the composition segregation of strained epitaxial alloy quantum dots. Our model incorporates the lattice mismatch energy, the gradient energy and the mixing chemical energy of prepyramidal and dome-like quantum dots. When the minimization of the energy of the total system is reached, the composition profile and the stress profile of the quantum dots, whose evolution is driven by inhomogeneous stress fields, are obtained.Finally, we perform a linear stability analysis towards the surface morphology of the elastic conducting half-space subjected to an electromechanical coupling interaction. The elastic energy, the electrostatic energy and the surface energy are involved in our model and the electric stress coupling boundary condition is taken into account. The dispersion relation is derived. We find that adjusting the electric field and pre-stress can regulating the surface instability morphology.The surface diffusion is the dominant mass transport mechanism for the instability and evolution of microstructures discussed in this article. The energy considered consists of the strain energy, the interface(surface) energy, the mixing chemical energy and the potential energy from long-range forces. Regulating pre-strain and thus evolving the surface chemical potential can create the ordered the pattern of microstructures.
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