Morphology of ion-sputtered surfaces

Maxim A. Makeev, Rodolfo Cuerno, Albert László Barabási

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427 Scopus citations


We derive a stochastic nonlinear continuum equation to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter erosion, we calculate the coefficients appearing in the continuum equation in terms of the physical parameters characterizing the sputtering process. We analyze the morphological features predicted by the continuum theory, comparing them with the experimentally reported morphologies. We show that for short time scales, where the effect of nonlinear terms is negligible, the continuum theory predicts ripple formation. We demonstrate that in addition to relaxation by thermal surface diffusion, the sputtering process can also contribute to the smoothing mechanisms shaping the surface morphology. We explicitly calculate an effective surface diffusion constant characterizing this smoothing effect and show that it is responsible for the low temperature ripple formation observed in various experiments. At long time scales the nonlinear terms dominate the evolution of the surface morphology. The nonlinear terms lead to the stabilization of the ripple wavelength and we show that, depending on the experimental parameters, such as angle of incidence and ion energy, different morphologies can be observed: asymptotically, sputter eroded surfaces could undergo kinetic roughening, or can display novel ordered structures with rotated ripples. Finally, we discuss in detail the existing experimental support for the proposed theory and uncover novel features of the surface morphology and evolution, that could be directly tested experimentally.

Original languageEnglish (US)
Pages (from-to)185-227
Number of pages43
JournalNuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms
Issue number3-4
StatePublished - Dec 2002

Bibliographical note

Funding Information:
We would like to acknowledge discussions with E. Chason, B. Kahng, H. Jeong, F. Ojeda and L. Vázquez. This research was supported by NSF-DMR CAREER and ONR-YI awards (A.-L.B. and M.M.) and DGES (Spain) grants PB96-0119 and BFM 2000-0006 (R.C.).


  • Ion irradiation
  • Ripples
  • Roughening
  • Sputtering
  • Surface morphology

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