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A Model for Ion-Sputtering: from Pattern Formation to Rough Surfaces

Published online by Cambridge University Press:  10 February 2011

R. Cuerno ,
H. A. Makse ,
S. Tomassone ,
S. T. Harrington  and
H. E. Tanley
R. Cuerno
Affiliation:
Center for Polymer Studies and Dept. of Physics, Boston University, Boston, MA 02215
H. A. Makse
Affiliation:
Center for Polymer Studies and Dept. of Physics, Boston University, Boston, MA 02215
S. Tomassone
Affiliation:
Department of Physics, Northeastern University, Boston, MA 02115
S. T. Harrington
Affiliation:
Center for Polymer Studies and Dept. of Physics, Boston University, Boston, MA 02215
H. E. Tanley
Affiliation:
Center for Polymer Studies and Dept. of Physics, Boston University, Boston, MA 02215
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Abstract

Many surfaces eroded by ion-sputtering have been observed to develop morphologies which are either periodic, or rough and non-periodic. We have introduced a discrete stochastic model that allows to interpret these experimental observations within a unified framework. A simple periodic pattern characterizes the initial stages of the surface evolution, whereas the later time regime is consistent with self-affine scaling. The continuum equation describing the surface height is a noisy version of the Kuramoto-Sivashinsky equation.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 407: Symposium M – Disordered Materials and Interfaces-Fractals, structure and Dynamics , 1995 , 307
Copyright
Copyright © Materials Research Society 1996

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References

REFERENCES

[1] Carter, G. et al., Navinšek, B. and Whitton, J. L. in Sputtering by Particle Bombardment, Vol. II, edited by Behrisch, R., (Springer-Verlag, Heidelberg 1983), p. 231.Google Scholar
[2] Cross, M. C. and Hohenberg, P. C., Rev. Mod. Phys. 65, 851 (1993).Google Scholar
[3] Meakin, P., Phys. Rep. 235, 189 (1993); T. Halpin-Healey and Y.-C. Zhang, ibid. 254, 215 (1995); A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge 1995).Google Scholar
[4] Chason, E. et al., Phys. Rev. Lett. 72, 3040 (1994); T. M. Mayer et al., J. Appl. Phys. 76, 1633 (1994).Google Scholar
[5] Eklund, E. A. et al., Phys. Rev. Lett. 67, 1759 (1991); E. A. Eklund et al., E. J. Snyder and R. S. Williams, Surf. Sci. 285, 157 (1993); J. Krim et al., Phys. Rev. Lett. 70, 57 (1993); H.-N. Yang, G.-C. Wang, and T.-M. Lu, Phys. Rev. B 50, 7635 (1994).Google Scholar
[6] Cuerno, R., Makse, H. A., Tomassone, S., Harrington, S. T., and Stanley, H. E., Phys. Rev. Lett. in press.Google Scholar
[7] Kuramoto, Y. and Tsuzuki, T., Prog. Theor. Phys. 55, 356 (1977); G. I. Sivashinsky, Acta Astronaut. 6, 569 (1979).Google Scholar
[8] Kardar, M., Parisi, G. and Zhang, Y.-C., Phys. Rev. Lett. 56, 889 (1986).Google Scholar
[9] Cuerno, R. and Lauritsen, K. B., Phys. Rev. E 52, 4853 (1995). For d > 2, L. Golubović and R. Bruinsma, Phys. Rev. Lett. 66, 321 (1991); ibid. 67, 2747 (E) (1991).+2,+L.+Golubović+and+R.+Bruinsma,+Phys.+Rev.+Lett.+66,+321+(1991);+ibid.+67,+2747+(E)+(1991).>Google Scholar
[10] Zaleski, S., Physica D 34, 427 (1989); K. Sneppen et al. Phys. Rev. A 46, R7351 (1992); F. Hayot et al., Phys. Rev. E 47, 911 (1993).Google Scholar
[11] Sigmund, P., Phys. Rev. 184, 383 (1969).Google Scholar
[12] Sigmund, P., J. Mat. Sci. 8, 1545 (1973); R. M. Bradley and J. M. E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988).Google Scholar
[13] Herring, C., J. Appl. Phys. 21, 301 (1950); W. W. Mullins, J. Appl. Phys. 28, 333 (1957); in the context of surface roughening, see D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990); S. Das Sarma and P. I. Tamborenea, Phys. Rev. Lett. 66, 325 (1991).Google Scholar
[14] Siegert, M. and Plischke, M., Phys. Rev. E 50, 917 (1994).Google Scholar
[15] Carter, G. et al., Surf. Interface Anal. 20, 90 (1993); A. N. Protsenko, Nucl. Instr. And Meth. 82, 417 (1993).Google Scholar
[16] This argument can be made more precise, see [20].Google Scholar
[17] An initial random erosion regime (β0 = 0.5) is also observed before correlations build up in the system.Google Scholar
[18] Edwards, S. F. and Wilkinson, D. R., Proc. R. Soc. Lond. A 381, 17 (1982).Google Scholar
[19] Krug, J. and Spohn, H., Phys. Rev. Lett. 64, 2332 (1990).Google Scholar
[20] Lauritsen, K. B., Cuerno, R., and Makse, H. A., preprint.Google Scholar