Simulation of cathode surface sputtering by ions and fast atoms in Townsend discharge in argon-mercury mixture with temperature-dependent composition

The mixture of argon and mercury vapor is used as the background gas in different types of gas discharge illuminating lamps. The aim of this work was development of a model, describing transport of electrons, ions and fast atoms in the one-dimensional low-current gas discharge in argon-mercury mixture, and determination of the dependence of their contributions to the cathode sputtering, limiting the device service time, on the temperature.

For simulation of motion of electrons we used the Monte Carlo method of statistical modeling, whereas the ion and metastable excited atom motion, in order to reduce the calculation time, we described on the basis of their macroscopic transport equations, which allowed to obtain their flow densities at the cathode surface. Then, using the Monte Carlo method, we found the energy spectra of ions and fast atoms, generated in collisions of ions with mixture atoms, at the cathode surface and also the effective coefficients of the cathode sputtering by each type of particles.

Calculations showed that the flow densities of argon ions and fast argon atoms, produced in collisions of argon ions with slow argon atoms, do not depend on the temperature, while the flow densities of mercury ions and fast argon atoms generated by them grow rapidly with the temperature due to an increase of mercury content in the mixture.

There are represented results of modeling of the energy spectra of ions and fast atoms at the cathode surface. They demonstrate that at low mercury content in the mixture of the order of 10–3 the energies of mercury ions exceed that of the other types of particles, so that the cathode is sputtered mainly by mercury ions, and their contribution to sputtering is reduced at a mixture temperature decrease.

1. Samukawa S., Hori M., Rauf S., Tachibana K., Bruggeman P., Kroesen G., Whitehead J.C., Murphy A.B., Gutsol A.F., Starikovskaia S., Kortshagen U., Boeuf J.-P., Sommerer T.J., Kushner M.J., Czarnetzki U., Mason N. The 2012 plasma roadmap. J. Phys. D: Appl. Phys., 2012, vol. 45, no. 25, pp. 253001. doi: 10.1088/0022-3727/45/25/253001

2. Schwieger J., Baumann B., Wolff M., Manders F., Suijker J. Backcoupling of acoustic streaming on the temperature field inside high-intensity discharge lamps. J. Phys.: Conf. Ser., 2015, vol. 655, pp. 012045. doi: 10.1088/1742-6596/655/1/012045

3. Hadrath S., Beck M., Garner R.C., Lieder G., Ehlbeck J. Determination of absolute Ba densities during dimming operation of fluorescent lamps by laser-induced fluorescence measurements. J. Phys. D: Appl. Phys., 2007, vol. 40, no. 1, pp. 163–167. doi: 10.1088/0022-3727/40/1/009

4. Kristya V.I., Fisher M.R. Monte Carlo simulation of gas ionization in the interelectrode gap of a lowcurrent discharge in an argon-mercury mixture. Bull. Russ. Acad. Sci.: Phys., 2010, vol. 74, no. 2, pp. 277–280. doi: 10.3103/S106287381002036X

5. Sobota A., van den Bos R.A.J.M., Kroesen G., Manders F. Transition between breakdown regimes in a temperature-dependent mixture of argon and mercury using 100 kHz excitation. J. Appl. Phys., 2013, vol. 113, no. 4, pp. 043308. doi: 10.1063/1.4789598

6. Bondarenko G.G., Fisher M.R., Kristya V.I. Modeling of the effect of temperature and field-induced electron emission from the cathode with a thin insulating film on the Townsend discharge ignition voltage in argon-mercury mixture. Vacuum, 2016, vol. 129, pp. 188–191. doi: 10.1016/j.vacuum.2016.01.008

7. Bogaerts A. Comprehensive modelling network for dc glow discharges in argon. Plasma Sources Sci. Technol., 1999, vol. 8, no. 2, pp. 210–229. doi: 10.1088/0963-0252/8/2/003

8. Hagelaar G.J.M., Kroesen G.M.W., Klein M.H. Energy distribution of ions and fast neutrals in microdischarges for display technology. J. Appl. Phys., 2000, vol. 88, no. 5, pp. 2240–2245. doi: 10.1063/1.1287758

9. Capdeville H., Pedoussat C., Pitchford L.C. Ion and neutral energy flux distributions to the cathode in glow discharges in Ar/Ne and Xe/Ne mixtures. J. Appl. Phys., 2002, vol. 91, no. 3, pp. 1026–1030. doi: 10.1063/1.1430891

10. Liu C., Wang D. Monte Carlo simulation of ions inside a cylindrical bore for plasma source ion implantation. J. Appl. Phys., 2002, vol. 91, no. 1, pp. 32– 35. doi: 10.1063/1.1421239

11. Yoon S.J., Lee I. Theory of the lifetime of the MgO protecting layer in ac plasma display panels. J. Appl. Phys., 2002, vol. 91, no. 4, pp. 2487–2492. doi: 10.1063/1.1433928

12. Ito T., Cappelli M.A. Ion energy distribution and gas heating in the cathode fall of a direct-current microdischarge. Phys. Rev. E, 2006, vol. 73, no. 4, pp. 046401. doi: 10.1103/PhysRevE.73.046401

13. Ito T., Cappelli M.A. On the production of ener- getic neutrals in the cathode sheath of direct-current discharges. Appl. Phys. Lett., 2007, vol. 90, no. 10, pp. 101503. doi: 10.1063/1.2711416

14. Wang H., Sukhomlinov V.S., Kaganovich I.D., Mustafaev A.S. Simulations of ion velocity distribution functions taking into account both elastic and charge exchange collisions. Plasma Sources Sci. Technol., 2017, vol. 26, no. 2, pp. 024001. doi: 10.1088/1361-6595/26/2/024001

15. Sukhomlinov V.S., Mustafaev A.S., Murillo O. Ion energy distribution function in the wall layer at a negative wall potential with respect to the plasma. Phys. Plasmas, 2018, vol. 25, no. 1, pp. 013513. doi: 10.1063/1.5017309

16. Kristya V.I., Savichkin D.O., Fisher M.R. Modeling of cathode sputtering in a low-current gas discharge in a mixture of argon with mercury vapor. J. Surf. Investig., 2016, vol. 10, no. 2, рp. 441–444. doi: 10.1134/S1027451016020300

17. Bondarenko G.G., Fisher M. R., Kristya V.I. Simulation of charged and excited particle transport in the low-current discharge in argon-mercury mixture. J. Phys.: Conf. Ser., 2012, vol. 406, pp. 012031. doi: 10.1088/1742-6596/406/1/012031

18. Bondarenko G.G., Fisher M.R., Kristya V.I. Influence of temperature on the ionization coefficient and ignition voltage of the Townsend discharge in an argon– mercury vapor mixture. Technical Physics, 2017, vol. 6, no. 2, pp. 223–229. doi: 10.1134/S1063784217020050

19. Phelps A.V. The application of scattering cross sections to ion flux models in discharge sheaths. J. Appl. Phys., 1994, vol. 76, no. 2, pp. 747–753. doi: 10.1063/1.357820

20. Andersen H.H., Bay H.L. Sputtering by Particle Bombardment I. Physical Sputtering of Single-Element Solids, ed. R. Behrisch. Berlin–Heidelberg, Springer, 1981, p. 145.