Tailoring of crystal surface morphology by induced spatiotemporal oscillations of temperature.
This paper presents the model for pattern formation in the course of stable (unfaceted) and unstable (faceted) crystal growth from the vapor phase, which is influenced by the rapid spatiotemporal variations of the substrate and film temperature. In the model, such variations result from the interference heating of a substrate by weak pulsed laser beams. The ensuing form of the temperature field perturbation from the ground state is fairly generic and simple, and thus it may as well serve to model other situations. In the stable case the surface relaxational dynamics is influenced by surface diffusion transport of adatoms from the hot to the cold regions of a substrate; this leads to the accumulation of mass in the cold regions and depletion in the hot regions. In the unstable case the underlying faceting instability coupled to the directed diffusion transport leads to the formation of the stationary hill-and-valley structure, where the hills may terminate sharply or have the rough tops. The characteristic lateral scale of this structure increases as the wavelength of the temperature nonuniformity decreases, but the coarsening rate of the transients decreases. By effectively redistributing adatoms through the enhanced, spatially inhomogeneous diffusion the mechanism also delays the onset of the spatiotemporal chaos as the growth rate increases. These scenarios are modeled using the framework of the classical continuum theory of the morphological evolution, enriched with the recently developed regularization method for the ill-posed, unstable evolution partial differential equation (PDE), and coupled to the concept of the spatiotemporal oscillatory surface temperature as the "tailoring force" for the evolution dynamics. A mass-conserving finite volume method is developed that is capable of the accurate computation of the large-slope solutions of the unstable, strongly nonlinear, sixth order evolution PDE for the surface height.
Khenner
M
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Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA.