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Abstract: In this work, a study of epitaxial growth was carried out by means ofwavelets formalism. We showed the existence of a dynamic scaling form inwavelet discriminated linear MBE equation where diffusion and noise are thedominant effects. We determined simple and exact scaling functions involvingthe scale of the wavelets when the system size is set to infinity. Exponentswere determined for both, correlated and uncorrelated noise. The waveletmethodology was applied to a computer model simulating the linear epitaxialgrowth; the results showed a very good agreement with analytical formulation.We also considered epitaxial growth with the additional Ehrlich$-$Schwoebeleffect. We characterized the coarsening of mounds formed on the surface duringthe nonlinear phase using the wavelet power spectrum. The latter have anadvantage over other methods in the sense that one can track the coarsening inboth frequency or scale space and real space simultaneously. We showed thatthe averaged wavelet power spectrum also called scalegram over all thepositions on the surface profile, identified the existence of a dominant scale$a^*$, which increases with time following a power law relation of the form$a^* \sim t^n$, where $n\simeq 1-3$.



Author: Z. Moktadir

Source: https://arxiv.org/







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