Journal of the Korean Physical Society, Vol. 55, No. 5, November 2009, pp. 1841∼1848
Effect of Bias Frequency on the Accuracy of Floating Probe Measurements Myung-Sun Choi, Seok-Hwan Lee and Gon-Ho Kim∗ Division of Energy Systems Engineering, Seoul National University, Seoul 151-744 (Received 2 September 2008, in final form 28 March 2009) The particle contamination and the plasma perturbation caused by probe, such as an electrical Langmuir probe, invasion in the plasma should be minimized in plasma processing. Since the floating probe method can minimize probe contact with the plasma, it has become attractive for monitoring the plasma properties. For the floating probe method, the plasma properties are analyzed from the AC coupled current signals in the system of the probe circuit. The main current consists of a displacement current through the stray capacitance of the probe system and a conduction current through the probe sheath. Thus, the current signal is sensitive to the capacitance of the probe system and the driving frequency. The accuracy of the measurement can be improved by minimizing the displacement component in the current signal. Here, we show that the accuracy of measurement can be obtained from the conduction sheath current obtained from an extrapolation of the harmonics of the current signals taken at the several different bias frequencies. In addition, the driving frequency of the probe can be optimized by considering the sensing resistance, the sheath resistance, and the stray capacitance. The improved accuracy of the plasma density and temperature measurements was demonstrated for various operating pressures and powers. PACS numbers: 52.70.-m Keywords: Plasma diagnostic, Floating probe, Harmonic method, Displacement current on probe DOI: 10.3938/jkps.55.1841
I. INTRODUCTION
Monitoring of the plasma property becomes important in plasma-assisted manufacturing of devices such as nano-scaled semiconductor devices, which can be manufactured through precise etching and deposition processes. Recently, in-situ plasma monitoring tools have been developed to reduce the probe contamination to the plasma. Many plasma monitoring tools have been developed by means of the optical emission spectrum [1], the wave propagation in plasma [2], the reactance of plasma [3], and the sheath resistance [4]. Especially, the electrical probe method has become more attractive due to its structural simplicity and wide range of measured plasma properties. The traditional electrical probe is known as the Langmuir probe (LP) [5] and collects the plasma current by varying the applied voltage, so it perturbs the local plasma and may cause contamination. As for the modification of this method, non-invasive electrical probe techniques, such as the floating probe method [6], have been developed and applied to monitoring plasmas [7–10]. Because the probe signal is obtained at the float condition of probe and the circuit is isolated by the coupling capacitor and/or by using the insulated tip, the perturbation of plasma can be minimized in plasma mon∗ E-mail:
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itoring. The application of probe has been developed to monitor the deposition rate of the process [11]. As mentioned earlier, the floating probe current is obtained from the biasing AC signal through the isolation capacitor. Since the current is coupled to the displacement current flowing in the stray capacitance of the probing system and the conduction current through the sheath, it is often distorted by the high impedance of probing system. In addition, it induces harmonics in the biasing signal, resulting in reduction of the measurement accuracy. Amemiya et al. observed that the electron energy distribution function (EEDF) depended on the driving frequency in the Langmuir probe measurement [12, 13]. Olson et al. found that the stray capacitance between the cable and the system had a considerable effective on the distortion of probe current signal when the driving frequency was above 10 kHz [14]. This study is focused on improving the accuracy of the floating probe measurement by reducing the biasingfrequency effect. The conduction current through the probe sheath (hereafter the conduction sheath current) can be separated from the current signal, thus obtaining the current signals to analysis the plasma properties which are insensitive to the stray capacitance of the probing system and the driving frequency. The effect of the stray capacitance on the current can be properly eliminated by using the correction method introduced in the following sensation. The conduction current data can be
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Journal of the Korean Physical Society, Vol. 55, No. 5, November 2009
determined from the extrapolation method, which is applied to the probe data taken at several different frequencies. These corrections provide current data less sensitive to the driving frequency and to the system structure. The proposed method was evaluated from a comparison of the analyzed plasma data and the RF-compensated LP data taken in a capacitively-coupled plasma at various operating pressures and powers.
II. PRINCIPLES When a floating probe is in contact with plasma, plasma sheath is formed on the probe tip. A conduction sheath current flows with satisfaction of the flux of impinging ions equal to that of electrons and it varies with the applied bias voltage. For a low pressure and cold plasma, the sheath current can be estimated under the following assumptions: (i) The electron distribution is Maxwellian, and the ions are very cold. (ii) Collision effects are not serious enough to change the sheath current, and the Bohm condition is satisfied at the sheath edge [15]. (iii) When applying an oscillating bias on the probe, no additional plasma is generated in the sheath region. (iv) When the driving frequency is much higher than the ion frequency and less than the electron frequency (fpe >> f >> fpi ), a rectified electron current flows in the probe with the driving frequency. While the driving frequency is lower than the ion and electron frequency (f
