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.
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Sigmund, P., Sputtering by Ion Bombardment. Theoretical Concepts. Sputtering by Particle Bombardment, Behrisch R., Ed., Berlin: Springer-Verlag, 1981.
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.
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.
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.
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.
Carter, G., The Physics and Applications of Ion Beam Erosion, J. Phys. D: Appl. Phys., 2001, vol. 34, pp. R1–R22.
Bolotin, V.V., Nonconsevative Problems of the Theory of Elastic Stability, Moscow: GIFML, 1961, p. 337.
Sobolev, S.L., Some Applications of the Functional Analysis in Mathematical Physics, Leningrad: Izd. Leningrad. Gos. Univ., 1950.
Sobolevskii, P.E., On Parabolic Equations in the Banch Space, Trudy Moskovskogo Matematicheskogo Obshchestva, 1961, vol. 10, pp. 297–350.
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.
Neimark, M.A., Linear Differential Operators, Moscow: Nauka, 1969.
Functional Analysis. Reference Mathematical Library, Moscow: Nauka, 1972.
Mishchenko, E.F., Sadovnichii, V.A., Kolesov, A.Yu., and Rozov, N.Kh., Autowave Processes in Nonlinear Media with Diffusion, Moscow: Fizmatlit, 2005.
Kolesov, A.Yu. and Kulikov, A.N., Invariant Tores of Nonlinear Evolution Equations, Yaroslavl: Izd., 2003.
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.
Original Russian Text © A.V. Metlitskaya, A.N. Kulikov, A.S. Rudy, 2013, published in Mikroelektronika, 2013, Vol. 42, No. 4, pp. 298–305.
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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
- Boundary Problem
- Surface Erosion
- RUSSIAN Microelectronics
- Dissipative Structure
- Linear Differential Operator