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

Thermal grain-boundary grooving in bicrystal thin solid films having strong anisotropic surface Gibbs free energy represented by the modified cycloid-curtate function

“…In the present study for the strong surface stiffness anisotropy, a more realistic and mathematically more sound basic function such as the modified cycloid-curtate function developed by the author is utilized [18] to see not only the secondary features of the theory but also the effects of the temperature on the root topography above and below the roughening temperature, clearly. To present our findings in a systematic fashion, the simulation experiments are collected under two different subsections after a short presentation of the surface stiffness function used in the present studies.…”

“…Then one writes C Thres: ¼ l s 1 þ a cosðBÞ n sinðBÞ (18) This expression in connection with Eqs. (14) and (15) shows that the threshold level of the anisotropy constant for the ridge formation (or inversion) depends upon the wetting parameter l s , Wulff surface topography index number a explicitly, and the tilt angle f implicitly.…”

Generic role of the anisotropic surface free energy on the morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate

“…The anisotropic surface Helmholtz free energy, and the surface stiffness are all represented by the well accepted trigonometric functions. 41 While various tilt angles and anisotropy constants are considered during simulation experiments, the main emphasis were given on the two-fold, four-fold and six-fold rotational symmetries iii. In general for a given anisotropy constant, the tilt angle may have profound effects on the morphology of the SK islanding.…”

Morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate: Dynamical simulations

“…(1), in Ref. [27] by taking any possible diffusivity and surface free energy anisotropies into account. 27 However, in that theory, we did not consider the wetting effect, which we are going to launch now in this paper.…”

“…[27] by taking any possible diffusivity and surface free energy anisotropies into account. 27 However, in that theory, we did not consider the wetting effect, which we are going to launch now in this paper. The wetting effect may be included by linearizing the wetting potential at the position of the original flat film surface denoted as o h (i.e., defined as the integrated thickness of the droplet of any shape) by using the local tangent line for the linear extrapolation.…”