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Surface-diffusion-driven decay of patterns: beyond the small slopes approximation

By combining analytical results and computer simulations, we studied the continuous theory of surface diffusion applied to the decay of periodic high-aspect-ratio patterned substrates. Our results show that, after a transient stage, and for a broad class of initial conditions, patterns adopt a ‘universal’ mathematically well-specified shape that depends on two coefficients. Moreover, we were able to determine the time-dependence of such coefficients, which enabled us to mathematically reconstruct the pattern’s shape at any subsequent time. So, our analysis can be a useful predictive theoretical tool for the design and interpretation of experiments on thermal treatments of high-aspect-ratio patterns.