Skip to main content

Formation of the wave nanorelief at surface erosion by ion bombardment within the Bradley-Harper model

Abstract

The formation of wave nanorelief at surface erosion by ion bombardment is investigated within the Bradley-Harper model. It is shown that such a relief can result from ion bombardment when the stability of a plane profile is lost due to the smallness of the diffusivity or the large fluence. When a number of conditions are met, the family of spatially inhomogeneous solutions describing the dissipative structures of the type of periodically traveling waves bifurcates from the equilibrium state. For this problem, the conditions of existence of the dissipative structures are obtained that correspond to the micro- and nanoripples observed experimentally.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Sigmund, P., Sputtering by Ion Bombardment. Theoretical Concepts. Sputtering by Particle Bombardment, Behrisch R., Ed., Berlin: Springer-Verlag, 1981.

  2. 2.

    Elst, K. and Vandervorst, W., Influence of the Composition of the Altered Layer on the Ripple Formation, J. Vac. Sci. Technol. A, 1994, no. 12, p. 3205.

    Google Scholar 

  3. 3.

    Bradley, R.M. and Harper, J.M.E., Theory of Ripple Topography Induced by Ion Bombardment, J. Vac. Sci. Technol., 1988, vol. 6, no. 6, pp. 2390–2395.

    Google Scholar 

  4. 4.

    Kudryashov, N.A., Ryabov, P.N., and Strikhanov, M.N., Numerical Simulation of the Nanostructure Formation on the Plate Substrate Surface during Ion Bombardment, Yad. Fiz. Inzhiniring, 2010, vol. 1, no. 2, pp. 151–158.

    Google Scholar 

  5. 5.

    Rudy, A.S. and Bachurin, V.I., Spatially Nonlocal Model of Surface Erosion by Ion Bombardment, Izv. Akad. Nauk. Ser. Fiz., 2008, vol. 72, no. 5, pp. 624–629.

    Google Scholar 

  6. 6.

    Carter, G., The Physics and Applications of Ion Beam Erosion, J. Phys. D: Appl. Phys., 2001, vol. 34, pp. R1–R22.

    Article  Google Scholar 

  7. 7.

    Bolotin, V.V., Nonconsevative Problems of the Theory of Elastic Stability, Moscow: GIFML, 1961, p. 337.

    Google Scholar 

  8. 8.

    Sobolev, S.L., Some Applications of the Functional Analysis in Mathematical Physics, Leningrad: Izd. Leningrad. Gos. Univ., 1950.

    Google Scholar 

  9. 9.

    Sobolevskii, P.E., On Parabolic Equations in the Banch Space, Trudy Moskovskogo Matematicheskogo Obshchestva, 1961, vol. 10, pp. 297–350.

    MathSciNet  Google Scholar 

  10. 10.

    Kulikov, A.N., Kulikov, D.A., Metlitskaya, A.V., and Rudyi, A.S., Surface Topography Evolution under the Ion Bombardment, Proc. ENOC, 2011, Leon, pp. 126–131.

    Google Scholar 

  11. 11.

    Neimark, M.A., Linear Differential Operators, Moscow: Nauka, 1969.

    Google Scholar 

  12. 12.

    Functional Analysis. Reference Mathematical Library, Moscow: Nauka, 1972.

  13. 13.

    Mishchenko, E.F., Sadovnichii, V.A., Kolesov, A.Yu., and Rozov, N.Kh., Autowave Processes in Nonlinear Media with Diffusion, Moscow: Fizmatlit, 2005.

    Google Scholar 

  14. 14.

    Kolesov, A.Yu. and Kulikov, A.N., Invariant Tores of Nonlinear Evolution Equations, Yaroslavl: Izd., 2003.

    Google Scholar 

  15. 15.

    Kulikov, A.N. and Kulikov, D.A., Local Bifurcations of Traveling Waves of the Generalized Cubic Schrödinger Equation, Differential Equations, 2010, vol. 40, no. 9, pp. 1290–1299.

    MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. V. Metlitskaya.

Additional information

Original Russian Text © A.V. Metlitskaya, A.N. Kulikov, A.S. Rudy, 2013, published in Mikroelektronika, 2013, Vol. 42, No. 4, pp. 298–305.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Metlitskaya, A.V., Kulikov, A.N. & Rudy, A.S. Formation of the wave nanorelief at surface erosion by ion bombardment within the Bradley-Harper model. Russ Microelectron 42, 238–245 (2013). https://doi.org/10.1134/S1063739713030050

Download citation

Keywords

  • Boundary Problem
  • Surface Erosion
  • RUSSIAN Microelectronics
  • Dissipative Structure
  • Linear Differential Operator