A theoretical framework to obtain interface’s shapes during the high-temperature annealing of high-aspect-ratio gratings

High-temperature annealing applied to solid samples produces important morphological modifications on their surfaces, particularly in high-aspect-ratio gratings. We show, how by means of a framework based in a nonlinear analysis of the Mullins’ equation [J. Appl. Phys. 28, 333 (1957)], we can mathematically reproduce surface’s shapes just by measuring a few characteristic features of the interfaces (essentially pattern’s amplitudes and wavelengths). We compared our results with experimental data on silicon samples, finding a close agreement between experimental shapes and those theoretically predicted. The introduced framework could be particularly useful in those situations where no cross-sectional information were available.