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Continuum modeling of particle redeposition during ion-beam erosion

One-dimensional case

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Abstract

We present a detailed analysis of a laterally one-dimensional continuum model for target particle redeposition during ion-beam erosion under normal incidence. We show that the redeposition mechanism can be approximated by a Taylor expansion around the mean surface height and clarify the impact of redeposition on nano-scale patterning. Most importantly, we show that stable well-ordered periodic patterns can result in a common Kuramoto-Sivashinsky-like continuum model for ion-beam erosion in cooperation with the model for particle redeposition and identify parameter ranges where they appear.

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References

  1. G. Carter, J. Phys. D 34, R1 (2001)

    Article  ADS  Google Scholar 

  2. W.L. Chan, E. Chason, J. Appl. Phys. 101, 121301 (2007)

    Article  ADS  Google Scholar 

  3. J. Muñoz-García, L. Vázquez, R. Cuerno, J.A. Sánchez-García, M. Castro, R. Gago, in Toward Functional Nanomaterials, edited by Z.M. Wang (Springer, Heidelberg, 2009)

  4. R. Cuerno, A.L. Barabási, Phys. Rev. Lett. 74, 4746 (1995)

    Article  ADS  Google Scholar 

  5. A.K. Hartmann, R. Kree, U. Geyer, M. Kölbel, Phys. Rev. B 65, 193403 (2002)

    Article  ADS  Google Scholar 

  6. S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, H.L. Hartnagel, Science 285, 1551 (1999)

    Article  Google Scholar 

  7. F. Frost, A. Schindler, F. Bigl, Phys. Rev. Lett. 85, 4116 (2000)

    Article  ADS  Google Scholar 

  8. F. Frost, B. Rauschenbach, Appl. Phys. A 77, 1 (2003)

    Article  ADS  Google Scholar 

  9. F. Frost, B. Ziberi, T. Höche, B. Rauschenbach, Nucl. Instr. Meth. B 216, 9 (2004)

    Article  ADS  Google Scholar 

  10. F. Frost, B. Ziberi, A. Schindler, B. Rauschenbach, Appl. Phys. A 91, 551 (2008)

    Article  ADS  Google Scholar 

  11. B. Ziberi, F. Frost, M. Tartz, H. Neumann, B. Rauschenbach, Appl. Phys. Lett. 92, 063102 (2008)

    Article  ADS  Google Scholar 

  12. S. Facsko, T. Bobek, A. Stahl, H. Kurz, T. Dekorsy, Phys. Rev. B 69, 153412 (2004)

    Article  ADS  Google Scholar 

  13. W.W. Mullins, J. Appl. Phys. 28, 333 (1957)

    Article  ADS  Google Scholar 

  14. M.A. Makeev, R. Cuerno, A.L. Barabási, Nucl. Instr. Meth. B 197, 185 (2002)

    Article  ADS  Google Scholar 

  15. R.M. Bradley, J.M.E. Harper, J. Vac. Sci. Tech. A 6, 2390 (1988)

    Article  ADS  Google Scholar 

  16. S.A. Norris, J. Samela, M. Vestberg, K. Nordlund, M.J. Aziz, arXiv:1303.2674 (2013)

    Google Scholar 

  17. S.A. Norris, arXiv:1205.6834 (2012)

  18. G. Ozaydin, A.S. Ozcan, Y. Wang, K.F. Ludwig, H. Zhou, R.L. Headrick, D.P. Siddons, Appl. Phys. Lett. 87, 163104 (2005)

    Article  ADS  Google Scholar 

  19. G. Ozaydin, K.F. Ludwig, H. Zhou, R.L. Headrick, J. Vac. Sci. Tech. B 26, 551 (2008)

    Article  Google Scholar 

  20. J. Zhou, S. Facsko, M. Lu, W. Möller, J. Appl. Phys. 109, 104315 (2011)

    Article  ADS  Google Scholar 

  21. M. Raible, S. Linz, P. Hänggi, Eur. Phys. J. B 27, 435 (2002)

    Article  ADS  Google Scholar 

  22. M. Raible, S.J. Linz, P. Hänggi, Phys. Rev. E 62, 1691 (2000)

    Article  ADS  Google Scholar 

  23. L. Bischoff, K.H. Heinig, B. Schmidt, S. Facsko, W. Pilz, Nucl. Instr. Meth. Phys. Res. B 272, 198 (2012)

    Article  ADS  Google Scholar 

  24. J.M. Hyman, B. Nicolaenko, S. Zaleski, Physica D 23, 265 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. M. Castro, R. Cuerno, L. Vázquez, R. Gago, Phys. Rev. Lett. 94, 016102 (2005)

    Article  ADS  Google Scholar 

  26. C.S. Madi, B. Davidovitch, H.B. George, S.A. Norris, M.P. Brenner, M.J. Aziz, Phys. Rev. Lett. 101, 246102 (2008)

    Article  ADS  Google Scholar 

  27. R.M. Bradley, P.D. Shipman, Phys. Rev. Lett. 105, 145501 (2010)

    Article  ADS  Google Scholar 

  28. P.D. Shipman, R.M. Bradley, Phys. Rev. B 84, 085420 (2011)

    Article  ADS  Google Scholar 

  29. S. Vogel, S.J. Linz, Phys. Rev. B 72, 035416 (2005)

    Article  ADS  Google Scholar 

  30. S. Vogel, S.J. Linz, Eur. Phys. Lett. 76, 884 (2006)

    Article  ADS  Google Scholar 

  31. S. Vogel, S.J. Linz, Phys. Rev. B 75, 085425 (2007)

    Article  ADS  Google Scholar 

  32. S. Vogel, S.J. Linz, Phys. Rev. B 75, 155417 (2007)

    Article  ADS  Google Scholar 

  33. K. Dreimann, S.J. Linz, Chem. Phys. 375, 606 (2010)

    Article  ADS  Google Scholar 

  34. N. Anspach, S.J. Linz, J. Stat. Mech. 2010, P06023 (2010)

    Article  Google Scholar 

  35. N. Anspach, S.J. Linz, J. Stat. Mech. 2012, P06012 (2012)

    Article  Google Scholar 

  36. R.M. Bradley, Phys. Rev. B 83, 075404 (2011)

    Article  ADS  Google Scholar 

  37. C. Diddens, S.J. Linz, in preparation (2013)

  38. C. Diddens, S.J. Linz, submitted for publication (2013)

  39. R. Smith, S.S. Makh, J.M. Walls, Philos. Mag. B 47, 453 (1983)

    Article  ADS  Google Scholar 

  40. R. Smith, M.A. Tagg, J.M. Walls, Vacuum 34, 175 (1984)

    Article  Google Scholar 

  41. Q. Wei, K.D. Li, J. Lian, L. Wang, J. Phys. D 41, 172002 (2008)

    Article  ADS  Google Scholar 

  42. T.J. Whitaker, P.L. Jones, A. Li, R.O. Watts, Rev. Sci. Instrum. 64, 452 (1993)

    Article  ADS  Google Scholar 

  43. G.A. Gottwald, I. Melbourne, Proc. Roy. Soc. A 460, 603 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str.9, 48149, Münster, Germany

    Christian Diddens & Stefan J. Linz

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  1. Christian Diddens
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  2. Stefan J. Linz
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Correspondence to Christian Diddens or Stefan J. Linz.

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Diddens, C., Linz, S. Continuum modeling of particle redeposition during ion-beam erosion. Eur. Phys. J. B 86, 397 (2013). https://doi.org/10.1140/epjb/e2013-40555-7

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  • DOI: https://doi.org/10.1140/epjb/e2013-40555-7

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