  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 [J. Appl. Phys. v30, 77, 1959]
for bulk substrates, 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. [Phys. Rev. Lett. v67, 26, 1991] to
describe solid state transport in thin films under epitaxial strain. 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 fast a 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 [Phys. Rev. B, v75, 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. Results of a linear
stability analysis based on the aforementioned model suggest that solid state
mass transport has negligible effect on morphology changes of the surface.
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.
