Control of ion and electron distribution functions by the Electrical Asymmetry Effect. U. Czarnetzki

Transcription

1 Control of ion and electron distribution functions by the Electrical Asymmetry Effect U. Czarnetzki 64t h GEC, Salt Lake City, November 2011 Institute for Plasma and Atomic Physics 1

2 Ion energy: Ion flux: Process Requirements - deposition or etching/sputtering - quality and selectivity - process speed, substrate heating Ideal concept: Independent control of ion energy and flux. This can be achieved by the Electrical Asymmetry Effect. 2

3 Voltage Balance Model of CCP Discharges RF C RF sheath p bulk sheath g φ = φ + φ + φ + φ C sp sg b Balance of all voltages. One-dimensional model (plane-parallel, cylinder, sphere). Unequal electrode areas included in non-planar geometries. All voltages φ are expressed as functions of q(t), the positive space charge in the sheath at the powered electrode. 3

4 φ RF + η = q Simplified System 1 ε The total positive space charge q t in both sheaths is approximately constant. Sheaths are well characterized by a quadratic 2 charge-voltage relation: φ = The bulk voltage is negligible in most cases. The time varying part of the capacitor voltage is also negligible. A single parameter characterizes the symmetry of the system by the ratio of areas and mean sheath ion densities: ε = ε qt = sp q A 2 p A g n n + sp sg ε q ( 1 ε )( φ ( ϕ) + η) t RF + ε ( qt q) q( ϕ) 4

5 Self-bias and total charge Assuming for flux balance approximately a full collapse of the sheaths at times of the applied voltage extremes determines the total charge q t and the self-bias η : q t = φm φm 1+ ε and φm 1 + ε φ η = 1+ ε 1 2 m2 η ε η = 1 + ε ε In a single-frequency discharge the self-bias is: determined by the area ratio A p / A g. vanishes in a geometrically symmetric discharge (ε = 1). Heil B G, Czarnetzki U, Brinkmann R P and Mussenbrock T, 2008 J. Phys. D: Appl. Phys

6 The Electrical Asymmetry Effect (EAE) Unequal voltage extremes lead to a self-bias for any value of the symmetry parameter ε. This can be realized by a two successive harmonics: ( ϕ, θ ) = ( cos( ϕ + θ ) + cos( 2ϕ )) φ ~ ~ φm 1( θ ) + φm2( θ ) 0 η 0 / 2 The phase θ is the control parameter! Η Ε Θ 1.5 6

7 Bias Variation by the Phase high potential at ground, low potential at the electrode low potential at ground, high potential at the electrode The bias varies almost linearly with the phase. The bias can be varied over a large range. The role of the two electrodes can interchanged. Z. Donkó, J. Schulze, B.G. Heil and U. Czarnetzki, Journal of Physics D: Applied Physics 42, (2009) 7

8 PIC-MC: Ion Energy Distribution (Argon, 2.7 Pa, d = 6.7 cm, φ 0 = 315 V ) powered electrode grounded electrode Ion energy distribution can be well controlled by the phase. The role of the two electrodes can be reversed. Donkò Z, Schulze J, Heil B G, Czarnetzki U 2009 J. Phys. D: Appl. Phys

9 Experimental Ion Energy Distributions E [ev] 4 Pa θ [Degree] Ion flux [a.u.] 10 Pa E [ev] θ [Degree] Ion flux [a.u.] The experiment very well confirms theory and simulation. Schulze J, Schüngel E, Czarnetzki U 2009 J. Phys. D: Appl. Phys

10 Mean Sheath Potentials The massive ions react only on the mean sheath potential. Therefore, the mean sheath potential controls the ion energy. φ sp = q η φ sg = φ sp + η η φ sp + φ sg const. The mean sheath potentials are approximately linear functions of the self bias. The sum of the absolute values is approximately constant. Ion energies can be varied complimentary at the electrodes. E. Schüngel, J. Schulze, Z. Donkó, and U. Czarnetzki Physics of Plasmas 18, (2011) 10

11 PIC Simulation of the Mean Sheath Potentials 0.8 I<φ s >I powered sum ground Argon p = 100 Pa φ 0 = 100 V d = 1 cm η Linear variation of the mean sheath potential. Sum is approximately constant. Good agreement with the model. This explains the linear variation of the mean ion energy. E. Schüngel, J. Schulze, Z. Donkó, and U. Czarnetzki Physics of Plasmas 18, (2011) 11

12 Mean Ion Energies PIC (100 Pa) Experiment Pa, 2.5 cm 10 Pa, 2.5 cm 20 Pa, 1 cm <ε i > [ev] θ [Degree] Linear variation of the mean ion energy by the phase angle. Good agreement with the mean sheath potential. J. Schulze, E. Schüngel and U Czarnetzki Journal of Physics D: Applied Physics 42, (2009) 12

13 Mean Ion and Total Power P i i Γ n φ sp P i P ( ) φ + φ e + = sp φ P sg e P P e e sg Γ const. + P i i P e Abs o rbed power density [ kw m -3 ] Electrons Ions Total Θ [Degrees] The mean sheath voltages vary linearly with the bias. The power dissipated by the ions is proportional to the power dissipated by the electrons. Then the same applies also to the total power. E. Schüngel, J. Schulze, Z. Donkó, and U. Czarnetzki Physics of Plasmas 18, (2011) 13

14 Electron velocity distribution functions Ionization rate: V 0 = 200 V, f = MHz, Theta = 0 deg, L = 2.5 cm, p = 3 Pa (argon), T = 400 K The powered electrode is at x=0, time covers one period of the MHz cycle. The grey lines indicate equipotential contours (spacing = 20 V). The applied voltage waveform leads apparently to complicate sheath dynamics and electron distribution functions. Z. Donkó, Plasma Sources Sci. Technol. 20, (2011) 14

15 Simulated and measured Excitaiton As expected, the complex time-space structure of the sheath voltage waveforms leads to similar complexity in excitation. Positions and strengths of the various maxima are varying with the phase, i.e. with the form of the waveform. J. Schulze, E. Schüngel, Z. Donko, and U Czarnetzki Plasma Sources Sci. Technol. 19, (2010) 15

16 Non-local contribution to the distribution function The distribution function in the bulk has a local, basically constant part and a non-local part caused by ballistic electrons from the sheath. The relative contribution is scaled by the ratio of the sheath to the bulk density α z. The part originating from the sheath is expanded in the time varying drift velocity u z. J. Schulze, E. Schüngel, Z. Donko, and U Czarnetzki Plasma Sources Sci. Technol. 19, (2010) 16

17 Excitation Rates The excitation rate E in the bulk can be split into a constant and a time varying part. Of particular interest is the ration between peak values at both sheaths. A similar argument could be made for ionization, although more difficult to measure. The velocity u can be related to the derivative of q and so to the derivative of the applied voltage φ. J. Schulze, E. Schüngel, Z. Donko, and U Czarnetzki Plasma Sources Sci. Technol. 19, (2010) 17

18 Ratio of the absolute maxima at both sheaths Experiment, simulation, and model agree very well. Excitation is clearly related to the beam electrons from the sheaths. The excitation can be well described by the calculated q(t). J. Schulze, E. Schüngel, Z. Donko, and U Czarnetzki Plasma Sources Sci. Technol. 19, (2010) 18

19 Phase dependence of the absolute maximum Again, very good agreement is found, supporting the rather simple model description, i.e. the physical picture related to the model. J. Schulze, E. Schüngel, Z. Donko, and U Czarnetzki Plasma Sources Sci. Technol. 19, (2010) 19

20 Power Dissipated by the Electrons a) Experiment (I 2 ) b) PIC simulation c) 2 Analytical Model I q& Identical results throughout! Variations by θ cancel out almost entirely in the integral over ϕ. 2 E. Schüngel, J. Schulze, Z. Donkó, and U. Czarnetzki Physics of Plasmas 18, (2011) 20

21 Mean Electron Power Not more than 10 % variation of the mean power! E. Schüngel, J. Schulze, Z. Donkó, and U. Czarnetzki Physics of Plasmas 18, (2011) 21

22 PIC (2.7 Pa) Ion Flux Experiment (4 Pa) Grounded electrode Ion flux [a.u.] θ [Degree] The ion flux is nearly independent of the phase angle. Ion energy and flux can be controlled separately. Z. Donkó, J. Schulze, B.G. Heil and U. Czarnetzki, Journal of Physics D: Applied Physics 42, (2009) 22

23 Summary The electrical asymmetry effect allows a convenient control of ion energy distribution functions. Increasing the ion energy at one electrode reduces correspondingly the ion energy at the counter electrode, allowing even for a full reversal. The control parameter is the phase between the two RF frequencies. Electron energy distribution functions and correspondingly excitation and ionization show a complicate spatial-temporal behavior. The temporal and spatial average is, however, approximately constant leading to a constant density and ion flow. Support by the DFG in the frame of SFB 591, GK 1051, the RUB Research School, the Federal Ministry for Environment and the Hungarian Fund for Scientific Research is gratefully acknowledged. Commercialization and licensing is via RUBITEC. 23

24 More about the EAE on this meeting Shinya Iwashita, Tuesday ET4 4 Edmund Schüngel, Thursday QRP1 45 Julian Schulze, Thursday QRP1 46 Sebastian Mohr, Thursday QRP1 47 Julian Schulze, Friday SF1 2 24