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Unified theory of linear instability of anisotropic surfaces and interfaces under capillary, electrostatic, and elastostatic forces: The regrowth of epitaxial amorphous silicon

Ogurtani, Tarik Omer
The first-order unified linear instability analysis (LISA) of the governing equation for the evolution of surfaces and interfaces under capillary, electromigration (EM), and elastostatic forces is developed. A formal treatment of the thermomigration (Soret effect) driven by the nonuniform temperature distribution caused by exothermic phase transformation (growth) at the surface and interfacial layers is presented and its apparent influence on the capillary force in connection with the stability is also established in a concise analytical form. This unified approach, which relies on a rigorous theory of irreversible thermodynamics of surfaces and interfaces, seriously considers the anisotropies associated with the generalized growth mobility, the interfacial specific Gibbs free energy (i.e., the surface stiffness), and the surface diffusivity in thin solid films. The singularity in the surface stiffness at the cusp regions of the Wulff construction of the surface Gibbs free energy is fully elaborated by using a modified cycloid-curtate function as a basis for generating the Dirac delta distribution, which shows an unusually strong anomalous effect on the surface morphological instability even in the absence of EM forces, as illustrated clearly by the graphical representation of the EM-induced instability threshold level as a function of tilt angle and wave number, in a three-dimensional plot for various intrinsic and normalized system parameters. In the development of LISA theory special attention is paid to the origin of the elastostatic forces, which include not only the elastic strain energy density, but also the elastic dipole tensor interaction between mobile atomic species and the applied stress field. The profound influence of the anomalous surface stiffness anisotropy on the surface morphological evolution under the applied stress system is demonstrated by three-dimensional computer graphics applied for copper and silicon thin single-crystal solid films having, respectively, sixfold {111}- and fourfold {100}-symmetric singular (vicinal) planes as the top surfaces, which reveal the fine features of the theory and give insight into some controversial issues related to LISA in the literature. This unified approach also considers the stress dependence of the generalized growth mobility and its profound influence on the stability of the interface displacement and roughening in thin solid films. As a special application of the theory, the effects of uniaxial and biaxial applied stresses on the recrystallization and the interfacial morphological evolution of amorphous Si deposited on silicon substrates are thoroughly analyzed and excellent quantitative agreement is found with the published experimental data in the literature.