Russian Microelectronics

, Volume 42, Issue 4, pp 238–245 | Cite as

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

  • A. V. MetlitskayaEmail author
  • A. N. Kulikov
  • A. S. Rudy


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.


Boundary Problem Surface Erosion RUSSIAN Microelectronics Dissipative Structure Linear Differential Operator 
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  1. 1.
    Sigmund, P., Sputtering by Ion Bombardment. Theoretical Concepts. Sputtering by Particle Bombardment, Behrisch R., Ed., Berlin: Springer-Verlag, 1981.Google Scholar
  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.CrossRefGoogle 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.MathSciNetGoogle 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.Google Scholar
  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.MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • A. V. Metlitskaya
    • 1
    Email author
  • A. N. Kulikov
    • 1
  • A. S. Rudy
    • 1
  1. 1.Yaroslavl State UniversityYaroslavlRussia

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