MEAN NUMBER OF ATOMS, CHARGE AND ENERGY OF CLUSTERS UNDER ION SPUTTERING OF A METAL 

Kochkin Sergey Alekseevich, Candidate of physical and mathematical sciences, associate professor, subdepartment of mathematical analysis, algebra and geometry, Northern (Arctic) Federal University named after M. V. Lomonosov (17 Severnaya Dvina embankment, Arkhangelsk, Russia), E-mail: s.kochkin@narfu.ru 

532.533 

10.21685/2072-3040-2019-2-8 

Background. A theoretical description of metal ion sputtering in the form of polyatomic systems (clusters) of various electric charges has until recently been the subject of theoretical discussions. Zygmund's well-known cascade theory of sputtering is able to explain sputtering only in the form of single atoms, other theoretical approaches, unfortunately, did not explain most of the results of ion sputtering in the form of clusters, and numerical calculations using molecular dynamics methods were complex due to the many-particle nature of the phenomenon. The purpose of this work is the further development of the theory of elastic ion sputtering of a solid surface in the form of polyatomic particles and, in particular, the calculation of the average values of their main characteristics: the number of atoms, charge and energy.
Materials and methods. The model representation in describing the phenomenon under consideration is based on simple principles of quantum mechanics and statistical physics, while calculating the mean values of the main characteristics of polyatomic sputtering products, a statistical approach was used based on the obtained sputtering probabilities and the energy distribution of the sputtered clusters.
Results. Expressions for the numerical calculation mean values of atoms’ number and cluster charge depending on the metal surface temperature are obtained, an accurate analytical expression for the mean energy of the sputtered clusters is obtained. As an example, the mean values of atoms’ number, charge and energy for the sputtered clusters of niobium, tantalum, silver and iron were calculated, and the obtained results were compared with the available experimental data.
Conclusions. A good agreement of the obtained results with the experiment once again confirmed the correctness of the theoretical approach developed by us to the description of the ion sputtering of a metal in the form of clusters. In addition to fundamental and theoretical significance, the results can be used for comparison with new experimental data. 

ion sputtering, solid, clusters, mean number of atoms, mean charge, mean energy 

1. Sigmund P. Phys. Rev. 1969, vol. 184, p. 383.
2. Ziegler J. F., Biersack J. P., Littmark U. Stopping Powers and Ranges of ions in Matter. Pergamon, New Yok, 1985, vol. 1, 321 p.
3. Urbassek H. M., Hofer W. O. K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 1993, vol. 43, pp. 97–126.
4. Baranov I. A., Martynenko Yu. V., Tsepelevich S. O. et al. Uspekhi fizicheskikh nauk [Progress of physical science]. 1988, vol. 156, p. 478. [In Russian]
5. Wucher A., Wahl W. Nucl. Instr. Meth. B. 1996, vol. 115, pp. 581–589.
6. Belykh S. F., Habets B., Rasulev U. Kh. et al. Nucl. Instr. Meth. B. 2000, vol. 164–165, pp. 809–819.
7. Staudt C., Heinrich R., Mazarov P. et al. Nucl. Instr. Meth. B. 2000, vol. 164–165, pp. 715–719.
8. Wucher A. Izvestiya Akademii nauk. Seriya fizicheskaya [Proceedings of the Academy of Sciences. Series: physics]. 2002, vol. 66, no. 4, pp. 499–508. [In Russian]
9. Staudt C., Heinrich R., Wucher A. Nucl. Instr. Meth. B. 2000, vol. 164–165, pp. 677–686.
10. Belykh S. F., Veryovkin I. V. et al. International Journal of Mass Spectrometry. 2004, vol. 237 (1), pp. 55–63.
11. Morozov S. N., Rasulev U. Kh. Nucl. Instr. Meth. B. 2003, vol. 203, pp. 192–197.
12. Bekkerman A. D., Dzhemilev N. Kh., Verkhoturov S. V. et al. Mikrochim. Acta [Suppl.]. 1998, vol. 15, pp. 371–377.
13. Matveev V. I., Kochkin S. A. Zhurnal tekhnicheskoy fiziki [Journal of applied physics]. 2004, vol. 74, no. 3, pp. 65–71. [In Russian]
14. Matveev V. I., Kochkin S. A. Zhurnal eksperimental'noy i teoreticheskoy fiziki [Journal of experimental and theoretical physics]. 2010, vol. 137, no. 4, pp. 820–828. [In Russian]
15. Abramovits M., Stigan I. Spravochnik po spetsial'nym funktsiyam [Special functions handbook]. Moscow: Nauka, 1979, 832 p. [In Russian]