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Measurement of electron density with the phase-resolved cut-off probe method
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View: Figures


Image of FIG. 1.
FIG. 1.

(Color online) Schematics of the experimental setup (a) and the quadrupole antenna (b).

Image of FIG. 2.
FIG. 2.

(Color online) Schematics of the cut-off probe structure (a), and the CST simulation chamber and probe setup (b).

Image of FIG. 3.
FIG. 3.

(Color online) Schematics of the two EM simulation models. One has a sheath between the two tips (a) and the other does not (b).

Image of FIG. 4.
FIG. 4.

(Color online) Simulation results based on models as shown in Fig. 3 . (a) Transmitted signal and (b) phase signal.

Image of FIG. 5.
FIG. 5.

The FFT spectrum measured on the power feeding part of the Q-antenna with a high voltage probe and a oscilloscope at 50 mTorr, 350 W.

Image of FIG. 6.
FIG. 6.

(Color online) The phase differences around cut-off probe measured in the repeated measurements with different sweeping speed in the same conditions of Fig. 5 . (a) A high speed sweeping ∼ 1.1 G/s: a condition of 6 GHz frequency spectrum sweeping with 1600 data points in 5.4 s. (b) A low speed sweeping ∼ 0.037 G/s: a condition of 200 MHz frequency spectrum sweeping with 1600 data points in 5.4 s.

Image of FIG. 7.
FIG. 7.

(Color online) The various spectrums in the same conditions of Fig. 5 . (a) A phase difference spectrum between two antennas [cut-off frequency (∼ 1.35 GHz)]. (b) A group delay spectrum which is derivative of spectrum (a) with the frequency . (c) A transmittance spectrum. (d) A spectrum I of Eq. (2) calculated from Eq. (2) and the data in Fig. 9 .

Image of FIG. 8.
FIG. 8.

The examples of phase delay spectrum measured in the repeated measurement.

Image of FIG. 9.
FIG. 9.

The calculated spectrum of I in Eq. (2) with different power factors (a) 2, (b) 6.

Image of FIG. 10.
FIG. 10.

(Color online) The dependence of rf power (150 ∼ 500 W) in a measurement of cut-off frequency with two different methods (transmittance and phase delay) at the condition of (a) 100 mTorr, (b) 300 mTorr.

Image of FIG. 11.
FIG. 11.

(Color online) The summary of remarkable results of the cut-off probe using a phase delay: the cut-off frequencies are clearly obtained by the group delay method even (a) at high power (300 mTorr, 500 W), (b) at high pressure (1 Torr, 400 W), (c) at small discharge volume, cavity mode (20 mTorr, 300 W, a tripod inserted).

Image of FIG. 12.
FIG. 12.

The measured plasma frequencies which are obtained from 13 times repeated measurements at the fixed experimental condition (50 mTorr, 350 W).

Image of FIG. 13.
FIG. 13.

(Color online) (a) The transmittance and phase delay spectrums measured in the dc filament discharge with various filament bias voltage in conditions of 25 mTorr and 6 A. (b) The FFT spectrum measured on biased filament with a high voltage probe and a oscilloscope in the same condition of bias voltage 50 V.

Image of FIG. 14.
FIG. 14.

(Color online) The simulation result of CST M/W studio for the transmittance and phase difference spectrums under the condition of the density ripples which are artificially made in the simulation.

Image of FIG. 15.
FIG. 15.

(Color online) The magnified simulation result for important frequency points regimes where the density ripple effect can be reflected similar to the cut-off and the cavity resonance frequency points: the magnified phase difference result of (a) α in Fig. 14 , (b) β in Fig. 14 , (c) χ in Fig. 14 , (c-1) χ in Fig. 14 with refined phase arrangement, (d) δ in Fig. 14 .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Measurement of electron density with the phase-resolved cut-off probe method