Abstract
We thoroughly investigate the impact of redeposition on the self-organized pattern formation during ion-beam erosion within the framework of a spatially two-dimensional continuum model. An analysis on prestructured patterns allows the extraction of general properties of this mechanism, the typical distribution of redepositing particles and approximations in terms of the surface height in particular. By combining the redeposition model with erosion models, we present detailed results about the impact of redeposition on spatio-temporal surface evolutions. It is shown that redeposition can play a decisive role for pattern formation under ion-beam erosion within an extended range in the parameter space.
Article PDF
Similar content being viewed by others
References
J. Muñoz-García, L. Vázquez, R. Cuerno, J. Sánchez-García, M. Castro, R. Gago, in Toward Functional Nanomaterials, Lecture Notes in Nanoscale Science and Technology, edited by Z.M. Wang (Springer-Verlag New York, 2009), Vol. 5, pp. 323–398
G. Carter, J. Phys. D 34, R1 (2001)
W.L. Chan, E. Chason, J. Appl. Phys. 101, 121301 (2007)
J. Muñoz-García, L. Vázquez, M. Castro, R. Gago, A. Redondo-Cubero, A. Moreno-Barrado, R. Cuerno, Mater. Sci. Eng. R 86, 1 (2014)
M. Navez, C. Sella, D. Chaperot, C.R. Hebd. Acad. Sci. 254, 240 (1962)
S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, H.L. Hartnagel, Science 285, 1551 (1999)
F. Frost, A. Schindler, F. Bigl, Phys. Rev. Lett. 85, 4116 (2000)
S. Facsko, T. Bobek, T. Dekorsy, H. Kurz, Phys. Stat. Sol. B 224, 537 (2001)
S. Facsko, H. Kurz, T. Dekorsy, Phys. Rev. B 63, 165329 (2001)
F. Frost, B. Rauschenbach, Appl. Phys. A 77, 1 (2003)
F. Frost, B. Ziberi, T. Höche, B. Rauschenbach, Nucl. Instrum. Meth. B 216, 9 (2004)
L. Bischoff, W. Pilz, B. Schmidt, Appl. Phys. A 104, 1153 (2011)
L. Bischoff, K.H. Heinig, B. Schmidt, S. Facsko, W. Pilz, Nucl. Instrum. Meth. B 272, 198 (2012)
R. Böttger, L. Bischoff, S. Facsko, B. Schmidt, Europhys. Lett. 98, 16009 (2012)
R. Böttger, L. Bischoff, K.H. Heinig, W. Pilz, B. Schmidt, J. Vac. Sci. Technol. B 30, 06FF12 (2012)
R. Böttger, K.H. Heinig, L. Bischoff, B. Liedke, S. Facsko, Appl. Phys. A 113, 53 (2013)
R. Böttger, K.H. Heinig, L. Bischoff, B. Liedke, R. Hübner, W. Pilz, Phys. Stat. Sol. RRL 7, 501 (2013)
G. Ozaydin, A.S. Özcan, Y. Wang, K.F. Ludwig, H. Zhou, R.L. Headrick, D.P. Siddons, Appl. Phys. Lett. 87, 163104 (2005)
G. Ozaydin, K.F. Ludwig, H. Zhou, R.L. Headrick, J. Vac. Sci. Technol. B 26, 551 (2008)
J.A. Sánchez-García, L. Vázquez, R. Gago, A. Redondo-Cubero, J.M. Albella, Z. Czigány, Nanotechnology 19, 355306 (2008)
J. Zhou, S. Facsko, M. Lu, W. Möller, J. Appl. Phys. 109, 104315 (2011)
R. Cuerno, A.L. Barabási, Phys. Rev. Lett. 74, 4746 (1995)
W.W. Mullins, J. Appl. Phys. 28, 333 (1957)
G. Carter, V. Vishnyakov, Phys. Rev. B 54, 17647 (1996)
R.M. Bradley, J.M.E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988)
S.A. Norris, J. Appl. Phys. 114, 204303 (2013)
M. Raible, S. Linz, P. Hänggi, Eur. Phys. J. B 27, 435 (2002)
M. Raible, S.J. Linz, P. Hänggi, Phys. Rev. E 64, 031506 (2001)
M. Raible, S.J. Linz, P. Hänggi, Phys. Rev. E 62, 1691 (2000)
J.M. Hyman, B. Nicolaenko, S. Zaleski, Physica D 23, 265 (1986)
B.M. Boghosian, C.C. Chow, T. Hwa, Phys. Rev. Lett. 83, 5262 (1999)
T. Bobek, S. Facsko, H. Kurz, T. Dekorsy, M. Xu, C. Teichert, Phys. Rev. B 68, 085324 (2003)
S. Facsko, T. Bobek, A. Stahl, H. Kurz, T. Dekorsy, Phys. Rev. B 69, 153412 (2004)
M. Castro, R. Cuerno, L. Vázquez, R. Gago, Phys. Rev. Lett. 94, 016102 (2005)
C.S. Madi, B. Davidovitch, H.B. George, S.A. Norris, M.P. Brenner, M.J. Aziz, Phys. Rev. Lett. 101, 246102 (2008)
R.M. Bradley, P.D. Shipman, Phys. Rev. Lett. 105, 145501 (2010)
P.D. Shipman, R.M. Bradley, Phys. Rev. B 84, 085420 (2011)
S. Vogel, S.J. Linz, Phys. Rev. B 72, 035416 (2005)
S. Vogel, S.J. Linz, Europhys. Lett. 76, 884 (2006)
S. Vogel, S.J. Linz, Phys. Rev. B 75, 085425 (2007)
S. Vogel, S.J. Linz, Phys. Rev. B 75, 155417 (2007)
K. Dreimann, S.J. Linz, Chem. Phys. 375, 606 (2010)
M. Osthues, C. Diddens, S.J. Linz, in preparation
R. Smith, S.S. Makh, J.M. Walls, Philos. Mag. B 47, 453 (1983)
R. Smith, M. Tagg, J. Walls, Vacuum 34, 175 (1984)
H.B. Kim, G. Hobler, A. Steiger, A. Lugstein, E. Bertagnolli, Nanotechnology 18, 265307 (2007)
J. Saussac, J. Margot, L. Stafford, M. Chaker, J. Appl. Phys. 107, 063306 (2010)
S. Lindsey, G. Hobler, Nucl. Instrum. Meth. B 282, 12 (2012)
N. Anspach, S.J. Linz, J. Stat. Mech. 2010, P06023 (2010)
N. Anspach, S.J. Linz, J. Stat. Mech. 2012, P06012 (2012)
R.M. Bradley, Phys. Rev. B 83, 075404 (2011)
C. Diddens, S.J. Linz, Eur. Phys. J. B 86, 397 (2013)
C. Diddens, S.J. Linz, Europhys. Lett. 104, 17010 (2013)
Q. Wei, K.D. Li, J. Lian, L. Wang, J. Phys. D 41, 172002 (2008)
T. Chini, S. Bhattacharyya, D. Ghose, D. Basu, Nucl. Instrum. Meth. B 72, 355 (1992)
H. Gnaser, Low-energy Ion Irradiation of Solid Surfaces (Springer, Berlin, 1999)
T. Chini, M. Tanemura, F. Okuyama, Nucl. Instrum. Meth. B 119, 387 (1996)
T.J. Whitaker, P.L. Jones, A. Li, R.O. Watts, Rev. Sci. Instrum. 64, 452 (1993)
M.A. Makeev, R. Cuerno, A.L. Barabási, Nucl. Instrum. Meth. B 197, 185 (2002)
G.A. Gottwald, I. Melbourne, Proc. R. Soc. London A 460, 603 (2004)
R.M. Bradley, P.D. Shipman, Appl. Surf. Sci. 258, 4161 (2012)
I. Beresnev, V. Nikolaevskiy, Physica D 66, 1 (1993)
H.W. Xi, R. Toral, J.D. Gunton, M.I. Tribelsky, Phys. Rev. E 62, R17 (2000)
B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge Monographs on Applied and Computational Mathematics (Cambridge University Press, 1996)
G. Beylkin, J.M. Keiser, L. Vozovoi, J. Comput. Phys. 147, 362 (1998)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Diddens, C., Linz, S. Continuum modeling of particle redeposition during ion-beam erosion. Eur. Phys. J. B 88, 190 (2015). https://doi.org/10.1140/epjb/e2015-60468-7
Received:
Published:
DOI: https://doi.org/10.1140/epjb/e2015-60468-7