Generalized Fourier analysis for nanopatterns with overhangs

Abstract

We present a new approach to the classic problem of surface-diffusion?driven pattern decay, relevant in nanoscale applications. By means of a generalized Fourier expansion of the pattern shape, considered as a quasiperiodic function, we can very accurately describe the pattern shape during the whole decay process. The approach is especially suitable for those cases in which patterns cannot be described by single-valued functions, i.e. patterns with overhangs. Symmetry considerations on the initial interface can be used to obtain relationships involving the expansion coefficients. Finally, by using a low-order expansion in the case of an initially sinusoidal interface, we obtained the time dependence of the amplitude decay, improving the linear-theory approximation.