1. Voltage, current and electron density measurements in an air radio-frequency plasma I. INTRODUCTION Various RF discharges are widely used in different kinds of production technologies. Still, questions of quality improvement often arise. That leads companies to look for a way of improving and optimising production processes. This cannot be done without appropriate diagnostic techniques. Power input control is really alluring because of its simplicity in implementation. In most experiments the main characteristic for the RF discharge is its consumed power. Nevertheless, in most theoretical works, the rf voltage is taken to be constant, which makes comparisons between experimental and theoretical difficult. Using the technique mentioned above it is possible to get the desired results. Microwave methods to measure electron density are advantageous due to its time resolution possibilities. Moreover, it is also a non-intrusive in situ measurement technique. II EXPERIMENT The experiment has been carried out with a 13.56 MHz capacitively coupled air plasma, confined in an aluminium cylinder cavity with two symmetrical slits. A schematic drawing of the plasma chamber is shown on Fig. 1. The dimensions are: diameter – 120mm, height – 37mm, slit width – 10mm, distance between antennas – 90mm, the lower power electrode diameter – 107mm. Fig. 1 Cylindrical microwave cavity Fig. 2 Experimental setup III. DIAGNOSTICS A schematic drawing of the measurements is shown on Fig. 2. Fig 3 – Schematic of IV Sensor (reproduced from [1]) Power input measurements Using a Plasma Impedance Monitor (PIM) device by Scientific Systems we obtain information on the amplitudes of voltage and current for the driving frequency and first four harmonics, as well as on the value of phase shift between them. Along with that, power and impedance are calculated. Fig. 3 shows the principle of the PIM IV Sensor. These graphs strongly resemble those that one would expect to see in case of simple electrical circuit with direct current and constant resistance. Though, it is seen that the curves do not trend to zero, as it would be for a simple resistor. Microwave technique The resonance frequency of the cavity, which depends on the number of free electrons within, is determined by tuning the microwave generator to maximum transmission. From the shift  f = f – f 0 of the resonant frequency f with respect to its value in vacuum (f 0 ) the microwave field averaged electron density (n eo ) is deduced [2]: ( 1) This method does not provide any spatial resolution as n e0 is merely a space averaged density weight with the square of the field strength (E 2 ), (2) However, by combining results from several modes some spatial information can bee obtained. Fig. 6 Represents spectrum of the cavity. Fig. 6. Cavity spectrum Fig. 7. Preliminary results IV RESULTS Two measurement series have been carried out: the 1 st - Power variation, with keeping the pressure constant (0.10 ± 0.005 Torr), and the 2 nd - Pressure variation with constant amplitude of fundamental voltage harmonic (100 Volts). On Fig. 13 and 14 calculated electron density values are presented. Fig. 13 Electron Density in air discharge. Fixed pressure O.10 Torr. Fig. 14 Electron Density in air discharge. Fixed Voltage (100 Volts) It was noticed that by changing the discharge pressure from 0.6 to 0.8 Torr the discharged seemed to come to another state. Also, it was clearly seen from the graphs for the phase difference between harmonics of current and voltage (Fig.15), that in mentioned above pressure range the value for the first and, especially, for the third harmonics experiences dramatic changes. The idea of monitoring certain processes through the study of the phase behaviour is not a new one [1] and can be very promising in commercial production environment. Fig. 15 Phase shift between harmonics of Voltage and Current in air discharge. Fixed Voltage (100 Volts) Fig. 17 Real Power RMS. Fixed Voltage[0] (100Volts). V ACKNOWLEDGEMENT This work is supported by the European Commission under contract No. NNE5-1999-0004 H-alpha solar. The research of W.W. Stoffels has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences (KNAW). ------------------------------------------------- [1] Kieran Dobbyn, M.Sc. thesis, “Design and Application of a Plasma Monitor for RF Plasma Diagnostics.” Dublin City University, 2000. [2] E. Stoffels, W.W. Stoffels, D. Vender, M. Kando, G.M.W. Kroesen, and F.J. de Hoog. Phys. Rev. 51, 2425- 2435 (1995) [3] J.D. Jackson, “Classical Electrodynamics” Second Edition, Wiley, p.335 Fig. 18. Impedance. Fixed Voltage[0] (100Volts). M. Sorokine, D. Hayashi, W.W. Stoffels, G.M.W. Kroesen Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Frequencies of the cavity modes were calculated beforehand. As it was expected, the two series (3036900 kHz and 3924600 kHz – the two upper lines), that were believed to correspond to Transverse Magnetic Waves (TM) - TM 110 and TM 210 modes, showed the best agreement between each other. They were also the best distinguishable in the cavity spectrum observed and had the most appropriate frequency for the calculated modes. So, these two modes were chosen for the experiments, presented in this work. Fig.8 and 9 show the spatial electric field distribution for TM 110 and TM 210 [3] within the cylindrical cavity with dimensions mentioned above. It has been noticed that the behaviour of the first harmonics of current, voltage and power (Fig.16, 17, 18) is pretty much the same as the behaviour of the electron density. Fig. 16. Current RMS. Fixed Voltage[0] (100 Volts). Fig. 16. Voltage RMS. Fixed Voltage[0] (100 Volts). Fig. 18 presents impedance changes. Imp[i]=Voltage[i]RMS/Current[i]RMS Since the current in the odd harmonics (3f, 5f etc) is low (Fig. 16), no accurate Impedance can be calculated for those frequencies. It can be noticed that the Impedance for the third harmonics (imp[3]) experiences dramatic change with pressure goes higher then 4 Torr. Fig. 4 Fig.5 Fig. 4 and 5 show Current/Power and Voltage/Power graphs for 0.10 Torr Air discharge. Fig.8. TM 110 mode electric field spatial profile. No z dependence. Only E z is present. Fig.9. TM 210 mode electric field spatial profile. No z dependence. Only E z is present. En experimental study of the electric field in the cavity has also been carried out. If a piece of plastic is placed within the cavity, then, according to formula (1), the resonant frequency will change its magnitude. And, the bigger the field at the position of the probe, the bigger the frequency shift. Hence, the space profile of the microwave electric field within the chamber cavity can be examined. Measurements have been made in two vertical planes, perpendicular to each other: the plane with slits (slits’ plane), and the antennas’ plane. A plastic probe was placed at different places in the cavity. Dimensions of the probe are: 15mm x 15mm x 10mm. For each probe position a resonance frequencies for the modes have been found and then used in further calculations. has been calculated. As there is E 2 under the integral in the equation (2), obtained behavior of the value F E needs to be compared to the one of the E 2 obtained from the theory. Taking into account finite size of a plastic probe (10mm) a following value has been calculated: (3) For the estimation of electric field value F E Fig.10. Electric field spatial profile experiment. (4) Fig.11 and 12 show both F E and F Et [see equations (3) and (4)] for the two different planes in cavity. Fig.11. TM 110 and TM 210 modes in a plane of the antennas.Fig.12. TM 110 and TM 210 modes in a plane of the slits. A good agreement is seen from the graphs, though for the middle of the cavity the experimental electric field is higher than that obtained from the theory. Probably this can be explained by other harmonics contributing to the field in the middle. Also, analysis of the mode structure up to 5 GHz shows that the TM 110 and TM 210 modes are the only ones that can fit the experimental curve. Fig.10. Gives a schematic drawing of the experiment. Several spectrum peaks were examined during preliminary experiments. Fig. 7 shows results for 4 of total 7 observed modes. Those that are not presented showed no change in frequency within the error of the measurements. The lines with dots are the experimental curves, and the thin solid lines are obtained from the theory.