Skip to main content
SpringerLink
Log in

Three-Dimensional Simulation of an Ion Charge Exchange with Metal Surfaces

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

Ion beams are used to diagnose and modify the surface of solids. Simulation of an ion charge exchange with the surface is necessary not only for understanding its fundamental laws but also for quantitative diagnostics since charged particles (ions) are recorded in most experimental setups. Due to the inevitable substantial numerical complexity in the direct simulation of the charge exchange, until recently only approximate one- and two-dimensional methods had been used. A few years ago, the authors created a program code that implements a direct three-dimensional simulation for graphical processing units. This article presents some examples of the calculations and studies the correct setting of the initial conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

Notes

  1. The energy position (level) of an atomic particle is the potential energy of an electron located on an atomic particle. For an isolated neutral atom, its energy position is equal to the ionization energy.

REFERENCES

  1. Yu. V. Martynenko, “On the theory of sputtering of single crystals,” Sov. Phys. Solid State 6, 1581 (1964).

    Google Scholar 

  2. V. E. Yurasova, V. S. Chernysh, M. V. Kuvakin, and L. B. Shelyakin, “Change in the sputtering of single-crystal nickel on going through the Curie point,” JETP Lett. 21, 79–92 (1975).

    Google Scholar 

  3. J. Los and J. J. C. Geerlings, “Charge exchange in atom-surface collisions,” Phys. Rep. 190, 133–190 (1990).

    Article  Google Scholar 

  4. J. P. Gauyacq, A. G. Borisov, and D. Teillet-Billy, in Formation/Destruction of Negative Ions in Heavy Particle-Surface Collisions, Ed. by V. A. Esaulov (Cambridge Univ. Press, Cambridge, 1996).

    Google Scholar 

  5. H. Chakraborty, T. Niederhausen, and U. Thumm, “Resonant neutralization of H- near Cu surfaces: effects of the surface symmetry and ion trajectory,” Phys. Rev. A 70, 052903 (2004).

    Article  Google Scholar 

  6. E. Marenkov, V. Kurnaev, A. Lasa, and K. Nordlund, “On the molecular effect in hydrogen molecular ions penetration through thin films,” Nucl. Instrum. Methods Phys. Res., Sect. B 269, 876–880 (2012).

    Google Scholar 

  7. P. A. Karaseov, K. V. Karabeshkin, A. I. Titov, V. B. Shilov, G. M. Ermolaeva, V. G. Maslov, and A. O. Orlova, “Nonlinear optical effect upon the irradiation of GaN with cluster ions,” Semiconductors 48, 446–450 (2014).

    Article  Google Scholar 

  8. N. N. Andrianova, A. M. Borisov, E. S. Mashkova, and V. I. Shulga, “Influence of surface corrugation on the sputtering of carbon materials under high-fluence ion bombardment,” J. Clin. Invest. 10, 412 (2016).

    Google Scholar 

  9. V. V. Evstifeev and I. V. Ivanov, “Computer simulation of Cs+ ion scattering from a W (100) surface,” Surf. Sci. 217, L373–L376 (1989).

    Article  Google Scholar 

  10. A. Tolstogouzov, S. Daolio, and C. Pagura, “Hyperthermal and low-energy Ne+ scattering from Au and Pt surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 183, 116–127 (2001).

    Google Scholar 

  11. A. Tolstogouzov, S. Daolio, and C. Pagura, “Evaluation of inelastic energy losses for low-energy Ne+ ions scattered from aluminum and silicon surfaces,” Surf. Sci. 441, 213–222 (1999).

    Article  Google Scholar 

  12. I. K. Gainullin, “Slow ion scattering by crystal surfaces and nanostructures,” J. Surf. Invest.: X-Ray, Synchrotr. Neutron Tech. 6, 122–126 (2012).

    Article  Google Scholar 

  13. I. K. Gainullin, E. Yu. Usman, Y. W. Song, and I. F. Urazgil’din, “Electron-exchange processes between hydrogen negative ion and thin aluminum films,” Vacuum 72, 263–268 (2003).

    Article  Google Scholar 

  14. A. R. Canario et al., “Nonadiabatic effects in atom-surface charge transfer,” Phys. Rev. B 71, 121401 (2005).

    Article  Google Scholar 

  15. I. K. Gainullin, E. Y. Usman, and I. F. Urazgil’din, “Electron exchange between hydrogen ion and thin disk: quantum-size effect observation,” Nucl. Instrum. Methods Phys. Res., Sect. B 232, 22–26 (2005).

    Google Scholar 

  16. A. A. Magunov, D. K. Shestakov, I. K. Gainullin, and I. F. Urazgildin, “Quantum size effect during the electron exchange between a negative hydrogen ion and a cluster of aluminum atoms,” J. Surf. Invest.: X-Ray, Synchrotr. Neutron Tech. 2, 764–767 (2008).

    Article  Google Scholar 

  17. I. K. Gainullin, “Three-dimensional modeling of resonant charge transfer between ion beams and metallic surfaces,” Phys. Rev. A 95, 052705 (2017).

    Article  Google Scholar 

  18. I. K. Gainullin and V. A. Khodyrev, “Quantum-hydrodynamic approach to the problem of electron exchange between atomic particles and nanosystems,” J. Surf. Invest.: X-Ray, Synchrotr. Neutron Tech., No. 6, 1126–1129 (2011).

  19. I. K. Gainullin and A. L. Klavsyuk, “Electron capture in the collision of a proton with a hydrogen atom,” Bull. Russ. Acad. Sci.: Phys. 76, 542–545 (2012).

    Article  Google Scholar 

  20. P. J. Jennings, R. O. Jones, and M. Weinert, “Surface barrier for electrons in metals,” Phys. Rev. B 37, 6113 (1988).

    Article  Google Scholar 

  21. E. V. Chulkov, V. M. Silkin, and P. M. Echenique, “Image potential states on metal surfaces: binding energies and wave functions,” Surf. Sci. 437, 330–352 (1999).

    Article  Google Scholar 

  22. J. N. Bardsley, “Pseudopotentials in atomic and molecular physics,” Case Stud. At. Phys. 4, 299–368 (1974).

    Google Scholar 

  23. J. S. Cohen and G. Fiorentini, “Stripping of H- in low-energy collisions with antiprotons: classical-trajectory Monte Carlo calculation,” Phys. Rev. A 33, 1590 (1986).

    Article  Google Scholar 

  24. A. G. Borisov, D. Teillet-Billy, J. P. Gauyacq, H. Winter, and G. Dierkcs, Phys. Rev. B 54 (17), 166 (1996).

    Article  Google Scholar 

  25. B. Bahrim, B. Makarenko, and J. W. Rabalais, “Band gap effect on H- ion survival near Cu surfaces,” Surf. Sci. 594, 62–69 (2005).

    Article  Google Scholar 

  26. L. Y. Ming and N. D. Lang, “Direct evidence of electron tunneling in the ionization of sputtered atoms,” Phys. Rev. Lett. 50, 127 (1983).

    Article  Google Scholar 

  27. A. Henriet and F. Masnou-Seeuws, “Model potential calculations for the ground, excited and Rydberg 2Σ states of Li2+, Na2+ and K2+: Core polarization effects,” Chem. Phys. Lett. 101, 535–540 (1983).

    Article  Google Scholar 

  28. H. Chakraborty, T. Niederhausen, and U. Thumm, “Effects of the surface Miller index on the resonant neutralization of hydrogen anions near Ag surfaces,” Phys. Rev. A 69, 052901 (2004).

    Article  Google Scholar 

  29. J. N. M. van Wunnik et al., “Effect of parallel velocity on charge fraction in ion-surface scattering,” Surf. Sci. 126, 618–623 (1983).

    Article  Google Scholar 

  30. A. G. Borisov, D. Teillet-Billy, and J. P. Gauyacq, “Dynamical resonant electron capture in atom surface collisions: H- formation in H-Al (111) collisions,” Phys. Rev. Lett. 68, 2842 (1992).

    Article  Google Scholar 

  31. V. A. Ermoshin and A. K. Kazansky, “Wave packet study of H- decay in front of a metal surface,” Phys. Lett. A 218, 99–104 (1996).

    Article  Google Scholar 

  32. H. Winter, “Collisions of atoms and ions with surfaces under grazing incidence,” Phys. Rep. 367, 387–582 (2002).

    Article  Google Scholar 

  33. A. G. Borisov, A. K. Kazansky, and J. P. Gauyacq, “Finite time effect in the charge transfer process during an ion-metal surface collision,” Phys. Rev. Lett. 80, 1996 (1998).

    Article  Google Scholar 

  34. J. P. Gauyacq and A. G. Borissov, “Dynamics of resonant electron transfer in the interaction between an atom and a metallic surface,” Springer Ser. Chem. Phys. 83, 87–109 (2007). https://doi.org/10.1007/978-3-540-34460-5_4

    Article  Google Scholar 

  35. I. K. Gainullin, “Towards quantitative LEIS with alkali metal ions,” Surf. Sci. 677, 324–332 (2018).

    Article  Google Scholar 

  36. C. Leforestier et al., “A comparison of different propagation schemes for the time dependent Schrodinger equation,” J. Comput. Phys. 94, 59–80 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  37. I. K. Gainullin and M. A. Sonkin, “High-performance parallel solver for 3D time-dependent Schrödinger equation for large-scale nanosystems,” Comput. Phys. Commun. 188, 68–75 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  38. T. Iitaka, “Solving the time-dependent Schrödinger equation numerically,” Phys. Rev. E 49, 4684 (1994).

    Article  Google Scholar 

  39. I. K. Gainullin, “High-performance GPU parallel solver for 3D modeling of electron transfer during ion-surface interaction,” Comput. Phys. Commun. 210, 72–78 (2017).

    Article  MATH  Google Scholar 

  40. I. Foster, Designing and Building Parallel Programs (Addison Wesley, Boston, 1995), Vol. 78.

    MATH  Google Scholar 

  41. P. Micikevicius, “3D finite difference computation on GPUs using CUDA,” in Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units (ACM, 2009), pp. 79–84.

  42. E. R. Amanbaev, I. K. Gainullin, E. Y. Zykova, and I. F. Urazgildin, “Electron exchange between atomic particle and thin metal island films,” Thin Solid Films 519, 4737–4741 (2011).

    Article  Google Scholar 

  43. I. K. Gainullin and M. A. Sonkin, “Three-dimensional effects in resonant charge transfer between atomic particles and nanosystems,” Phys. Rev. A 92, 022710 (2015).

    Article  Google Scholar 

  44. D. K. Shestakov, I. K. Gainullin, and I. F. Urazgil’din, “Features of the electron exchange under grazing scattering of H- ions from a thin aluminum disk,” J. Surf. Invest.: X-ray, Synchrotr. Neutron Tech. 3, 33–37 (2009).

    Article  Google Scholar 

  45. D. K. Shestakov, T. Yu. Polivnikova, I. K. Gainullin, and I. F. Urazgildin, “Electron exchange between an H- ion and a spherical cluster of aluminum atoms,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 2596–2600 (2009).

    Google Scholar 

  46. E. R. Amanbaev, D. K. Shestakov, and I. K. Gainullin, “Features of electron exchange under grazing scattering of negative hydrogen ions by a spherical cluster of aluminum atoms,” J. Surf. Invest.: X-ray, Synchrotr. Neutron Tech. 3, 865 (2009).

    Article  Google Scholar 

  47. I. K. Gainullin and I. F. Urazgildin, “Quantum size effect in the electron exchange between a H– ion and a thin metal disk,” Phys. Rev. B 74, 205403 (2006).

    Article  Google Scholar 

  48. E. Yu. Zykova, A. A. Khaidarov, I. P. Ivanenko, and I. K. Gainullin, “Formation of aluminum island films under electron irradiation of a sapphire surface,” J. Surf. Invest.: X-ray, Synchrotr. Neutron Tech. 6, 877–881 (2012).

    Article  Google Scholar 

  49. J. H. Macek et al., “Origin, evolution, and imaging of vortices in atomic processes,” Phys. Rev. Lett. 102, 143201 (2009).

    Article  Google Scholar 

  50. L. Guillemot and V. A. Esaulov, “Interaction time dependence of electron tunneling processes between an atom and a surface,” Phys. Rev. Lett. 82, 4552 (1999).

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

I.K. Gainullin thanks Profs. A.F. Aleksandrov and M.V. Kuzelev for their helpful comments in discussing the work.

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 16-02-00478)

Author information

Authors and Affiliations

  1. Moscow State University, 119991, Moscow, Russia

    I. K. Gainullin

  2. Tomsk Polytechnic University, 634050, Tomsk, Russia

    M. A. Sonkin

Authors
  1. I. K. Gainullin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Sonkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. K. Gainullin.

Ethics declarations

The authors declare that they have no conflict of interest.

Additional information

Translated by I. Pertsovskaya

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gainullin, I.K., Sonkin, M.A. Three-Dimensional Simulation of an Ion Charge Exchange with Metal Surfaces. Math Models Comput Simul 11, 964–972 (2019). https://doi.org/10.1134/S2070048219060048

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048219060048

Keywords:

Search

Navigation