Global Model of Micro-Hollow Cathode Discharges

1. Global Model ofMicro-Hollow Cathode Discharges Pascal CHABERT Laboratoire de Physique des Plasmas, Ecole Polytechnique, Palaiseau FRANCE • Claudia LAZZARONI • Laboratoire des Sciences des Procédés et des Matériaux, Université Paris 13, Villetaneuse FRANCE

2. Acknowledgments • Micro-Hollow Cathode Discharges (MHCD’s): • Antoine Rousseau • Nader Sadeghi

3. 100µm Microdischarges • History of microplasmas : plasma displays (since 60s..) • Microhollow cathode type (Schoenbach 1996) • DC source • Microarray (Eden 2001) • AC source • Microneedle (Stoffels 2002) • rf source • Micro APPJ (Schulz-von der Gathen 2008) • rf source • Applications in variousfields: • Surface treatment/ Light sources (excimer)/ Biomedicine

4. Global models • Volume-averaged (0D) model: densities and temperatures are uniform in space • Particle balance: • Electron power balance:

5. Particle balance: low pressure • Particle losses at the walls. The term Pa contains volume and wall losses. For the electron particle balance at low pressure, wall losses dominate and in one dimension: • A plasma transport theory is required to relate the space-averaged electron density to the flux at the wall

6. Particle balance: issues in µdischarges • In microdischarges, ionization is often non uniform. Classical low-pressure transport theories do not apply • Fortunately in some instances volume losses dominate (recombination) • However, evaluation of wall losses is a critical point for high-pressure discharges modeling

7. Other issues • Properly evaluate the reaction rates: • Electron energy distribution function is unknown • In microdischarges, Te is often strongly non uniform in space, and may vary in time… • Properly evaluate the electron power absorption: • Distinguish between electron and ion power (and other power losses in the system) • Equivalent circuit analysis is often useful. I-V characteristic of a device is a good starting point

8. So why one would use global models? • They are easily solved, sometimes analytically. Therefore they provide scaling laws and general understanding of the physics involved • They can be coupled to electrical engineering models to give a full description of a specific design • They allow very complex chemistries to be studied extensively. Numerical solutions of global models with complex chemistries only take seconds

9. Micro Hollow cathode Discharges (MHCD’s) • Gas : Argon • Pressure : 30-200 Torr • Excitation : DC DC

10. confined inside the micro-hole normal: cathode expansion self-pulsing I-V Characteristics: mode jumps Aubert et al., PSST 16 (2007) 23–32

11. Equivalent electrical circuit Hsu and Graves, J. Phys.D36 (2003) 2898 Aubert et al., PSST 16 (2007) 23 P. Chabert, C. Lazzaroni and A. Rousseau, J. Appl. Phys. 108 (2010) 113307 C. Lazzaroni and P. Chabert, Plasma Sources Sci. Technol. (2011) 20055004

12. abnormal: confined in the hole normal: cathode expansion Non-linear plasma resistance Rp = switch A3=0 Rpcontrols the physics of the transition between the two stable regimes

13. Stable regimes Stable and unstableregimes 3 1 2 dV/dt=0 equilibrium dId/dt=0 equilibrium Abnormal regime 1 Normal regime 3 Self-pulsing regime 2

14. Electricalsignals/ Phase-spacediagram

15. Electrical model of the MHCD • Total absorbed power simply: • Whatis the physicalorigin of Rp? What fraction of the total power goesintoelectrons?

16. Decomposition in two main regions Makashevaet al, 28th ICPIG(2007) 10 The resistance of the positive columnissmall

17. Structure in the cathodicregion

18. sheath d R Cathode r 0 bulk Sheath Calculation of sheaththickness (d) • One-dimensionalcylindricalgeometry: • Ions/electrons fluxes:

19. Sheaththickness vs pressure -decrease of the sheath size with the increase of pressure -maxima of bothemissionlineslocatedafter the sheathedge -same trends for the evolution of d thanthat of the maxima of the emission line -the sheathedgecoincidewith the maxima of the ionic line C. Lazzaroni, P. Chabert, A. Rousseau and N. Sadeghi, J. Phys. D: Appl. Phys. 43(2010) 124008

20. Abnormal and self-pulsingregime P and V highenough

21. Power absorbed in the cathode sheath • Electrons: • Same for ions with:

22. Power absorbed by electrons • Fraction of power absorbed by electrons: • Power absorbed in the volume underconsideration:

23. Power balance Power lossat the wallisnegligible

24. Particle balance

25. Results in the self-pulsingregime P=150 T Global model - withexcitedspecies/2 - withoutexcitedspecies*3 Experiments • -ne(withexc states) ≈ 6 ne(withoutexc states) •  Importance of multi-stepionization • ne(withoutexc states) = ne(exp)/3.7 • ne(withexc states) = 1.7 ne(exp) Model withexcited states in better agreement withexperiment

26. Results in the self-pulsing regime P=150 Torr Multi-step ionization Recombination Strong and short Tepeak  e-impact This has been observed experimentally: Aubert et al., Proceedings of ESCAMPIG, Lecce, Ed. M. Cacciatore, S. D. Benedictis, P. F. Ambrico, M. Rutigliano, ISBN 2-914771-38-X, Vol. 30G (2006).

27. Electron temperaturedynamics C. Lazzaroni and P. Chabert J. Appl. Phys. 111 (2012) 053305

28. Conclusions (1) • Global models are very useful to understand the general behavior of plasma discharges • They provide analytic solutions and scaling laws and allow fast numerical solutions of complex chemistry • However, they rely on many assumptions and therefore need to be benchmarked by experiments or more sophisticated numerical simulations

29. Conclusions (2) • The need for many simplifications and assumptions forces one to propose physical explanations, sometimes at the expense of being “rigorous” • Global models do not explain the detailed and microscopic phenomena taking place in plasma discharges. they offer a representation of reality that becomes more accurate when more realistic fundamental assumptions are made