Dynamics of ultrathin metal films on amorphous substrates under fast thermal processing

摘要

A mathematical model is developed to analyze the growth/decay rate of surface perturbations of an ultrathin metal film on an amorphous substrate (SiO_2). The formulation combines the approach of Mullins [W. W. Mullins, J. Appl. Phys. 30, 77 (1959)] for bulk surfaces, in which curvature-driven mass transport and surface deformation can occur by surface/volume diffusion and evaporation-condensation processes, with that of Spencer et al. [B. J. Spencer, P. W. Voorhees, and S. H. Davis, Phys. Rev. Lett. 67, 26 (1991)] to describe solid-state transport in thin films under epitaxial strain. Modifications of the Mullins model to account for thin-film boundary conditions result in qualitatively different dispersion relationships especially in the limit as kh_o 1, where k is the wavenumber of the perturbation and h_o is the unperturbed film height. The model is applied to study the relative rate of solid-state mass transport as compared to that of liquid phase dewetting in a thin film subjected to a fast thermal pulse. Specifically, we have recently shown that multiple cycles of nanosecond (ns) pulsed laser melting and resolidification of ultrathin metal films on amorphous substrates can lead to the formation of various types of spatially ordered nanostructures [J. Trice, D. Thomas, C. Favazza, R. Sureshkumar, and R. Kalyanaraman, Phys. Rev. B 75, 235439 (2007)]. The pattern formation has been attributed to the dewetting of the thin film by a hydrodynamic instability. In such experiments the film is in the solid state during a substantial fraction of each thermal cycle. However, results of a linear stability analysis based on the aforementioned model suggest that solid-state mass transport has a negligible effect on morphological changes of the surface. Further, a qualitative analysis of the effect of thermoelastic stress, induced by the rapid temperature changes in the film-substrate bilayer, suggests that stress relaxation does not appreciably contribute to surface deformation. Hence, surface deformation caused by liquid phase instabilities is rapidly quenched-in during the cooling phase. This deformed state is further evolved by subsequent laser pulses. These results have implications to developing accurate computer simulations of thin-film dewetting by energetic beams aimed at the manufacturing of optically active nanoscale materials for applications including information processing, optical devices, and solar energy harvesting.