Browsing by Author "Mauk, M.G."
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Item A Model for Anisotropic Epitaxial Lateral Overgrowth(Department of Mathematical Sciences, 2001) Khenner, M.; Braun, Richard J.; Mauk, M.G.The model for anisotropic crystal growth on a substrate covered by a mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase if developed. The model assumes that surface diffusion and deposition flux are the main mechanisms of the growth, and that the three key surface quantities (energy, mobility and adatom diffusivity) are anisotropic with either four- or six-fold symmetry. A geometrical approach to the motion of crystal surface in two dimensions is adopted and nonlinear evolution equations are solved by a finite-difference method. The model allows the direct computation of the crystal surface shape and the study of effects due to finite mask thickmness. As in experiments, lateral overgrowth of crystal onto the mask if found, as well as comparable crystal shapes; the anisotropy of the surface mobility is found to play the dominant role in the shape selection. The amount of the overgrowth and the shapes can be effectively controlled by orienting the fast and slow growth directions with respect to the substrate.Item A Model for Isotropic Crystal Growth from Vapor on a Patterned Substrate(Department of Mathematical Sciences, 2001) Khenner, M.; Braun, Richard J.; Mauk, M.G.We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface diffusion and the flux of particles from vapor are assumed to be the main mechanisms of growth. A geometrical approach to the motion of crystal surface in two dimensions is adopted and nonlinear evolution equations are solved by finite-difference method. The model allows the direct computation of the crystal surface shape, as well as the study of the effects due to mask regions of effectively nonzero thickness. As in experiments, lateral overgrowth of crystal onto the mask and enhanced growth in the region near the contact of the crystal and the mask is found, as well as the comparable crystal shapes. The growth rates inveritcal and lateral directions are investigated.