Surface-diffusion-driven decay of high-aspect-ratio gratings: existence of morphologically related classes

We present numerical and theoretical results concerning the technologically important process of evolution of high-aspect-ratio profiles due to surface diffusion under thermal treatment. We show how a broad class of initial gratings adopt, after a short transient stage, a typical shape that can be accurately described as a curve whose curvature has only two single Fourier modes as a function of the arc-length parameter. Moreover, we introduce a set of evolution equations for the relevant parameters that accounts very accurately for both morphological and kinetic aspects of the transformation processes for these curves in a wide region in parameter space. Regarding the decay of rectangular gratings, our numerical results show the existence of geometrically related classes that asymptotically approach to the same trajectory in parameter space. Gratings belonging to the same class pass through the same sequence of morphologies before reaching the final equilibrium state.