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The determination of the real power consumed in RF gas discharges and of the discharge impedance has been a subject of intense investigations for the last 15 years. The reason for spending this effort is that the electrical properties of such discharges can give an insight in both understanding and controlling the processes. The use of an RF (SWR) powermeter in the RF transmittance line for measuring the power dissipation in the discharge is nowadays not acceptable as it is very well known that a The power consumption on this - the frequency of plasma excitation and - the elements that are used in the electrical circuit: - matching network - shunt circuit - RF electrode shield - RF electrode length - .... Thus, the power dissipation in this On the other hand, the - frequency - pressure - gas composition - power - flow - .... Therefore,
It consists of an RF oscillator providing purely sinusoidal waves in the range of 25 KHz to 250 MHz, a linear RF amplifier, a conventional wattmeter and, depending on the excitation frequency, a π- or L- type matching network. The Faraday cub hosts a shunt circuit, a passive (typically 1:100 or 1:1000 voltage probe) and an inductive current probe. The digital two channel oscilloscope and the personal computer that are also shown in the figure are necessary for power and impedance calculation. The method is based on recording This The
The - the L-C circuit represents the cell parasitics, - the L - the R V The electrical analysis of the circuit shows that that the n
V-jω_{n}_{n}LI_{n}
_{n}^{2}LC)I-jω_{n}_{n}CV_{n}For the actual cell parameters, the parasitic currents are large and the equivalent magnitudes are very sensitive even to small errors in the measured values. In fact, the electrode current I The Measurements of this residual current have lead to the inclusion of this Finally, taking into account the shunt elements and the resistance RL the equations used for converting the measured values to the equivalent values at the electrode are given by the relations:
_{n}^{2}LC)I-jω_{Ln}_{n}CV_{n}
_{L}-jω_{n}C_{s}V-ω_{n}/(1_{n}^{2}L_{s}C_{s})
The determination of the exact values of the electrical components that are involved in the equivalent circuit combined to the measured values V The experimental measurements and the fitting with the RLC model used for the calculation of voltage and current waveforms on the RF electrode are shown in the figure above. The excellent agreement between the experimental and the RLC model results, confirms the applicability of the equivalent circuit. These results are applied to derive the following electrical characteristics for the chamber used in this example: inductance L=40nH, capacitance C=285pF, resistance R=0.8Ω and a resonance reactor frequency of 43MHz. Furthermore, the resistance RL that has been introduced to the equivalent circuit to counterbalance the remaining residual current can be calculated by using the following procedure. The shunt circuit is connected to the circuit, is tuned and the cell is excited at different driving voltages. The values of voltage and current are recorded and plotted in the figure presented above. The slope of the curve result to the calculation of the resistance RL=1700 Ω. In addition the values of the shunt circuit elements C
- The real power consumed on the discharge as: - The ohmic part of the discharge impedance: - The reactive part of the discharge impedance: A complete description of the method as well as the extension to frequencies higher than 13.56 MHz are given in the following 1. "Power dissipation and impedance measurements in radio frequency discharges" 2. "Frequency variation under constant power conditions in hydrogen radio frequency discharges" Applications of the method are presented in a number of publications as well.
The usefulness of the method is shown in the above figure. The black curves in figures a, b represent the voltage and current waveforms as measured. The measurements are in an Argon discharge at a gas pressure of 100 mTorr, frequency of 13.56 MHz and excitation peak to peak voltage of 100 Volts. The red curves represent the voltage and current waveforms transformed by applying the equivalent circuit for the RF electrode. The measured and the calculated waveforms of the voltage differs only in phase, the amplitude being almost the same. In addition the contribution of higher harmonics is almost negligible being less than 2% of the fundamental frequency. On the other hand, there is a significant difference between the current waveform at the point of measurement and at the RF electrode. The current waveform at the RF electrode that represents the real discharge current differs in phase, amplitude and distribution of harmonics compared to the measured current. The difference in phase is the result of the delay that is introduced by the current probe. The difference in amplitude is the result of the current flow though the shunt circuit and the flow from the RF electrode to the ground. The strong hanarmonicity (about 20 % of the fundamental frequency, figure d) is the result of the non-linear response (non-linear impedance) of the discharge.
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