## 3 The Method of Electron Density and Temperature by Langmuir Probes
Combining the voltage curve and the current curve, the I-V curve of the Langmuir probes containing ion saturation region and transition region can be obtained. From the I-V curve of the Langmuir probes, the (In I-Vp) curve slope in the transition region is 0.736, namely _Tev.probe_ = 1.3578 eV. In addition, the average current in the ion saturation current region is 0.0613 mA, namely _Isat_ = 0.0613 mA. Inserting the parameters in Table 1 into Equation (1), it can be found that the density of the plasma is \(n=1.3569\times 10^{-16}\) m\({}^{-3}\). The Langmuir probe is a feasible method to measure the plasma. However, as the plasma reaction progresses, there is gradually some phase difference between the voltage curve and the current curve, and the current is decreased compared with the beginning, as shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Symbol** & **Value** & **Units** \\ \hline Ion species & Ar+ & & \\ Ion mass & mi & \(6.7\times 10^{-26}\) & kg \\ Microwave power & Mpower & 800 & W \\ Pressure & Pa & 80 & Pa \\ Probe diameter & dprobe & 1 & mm \\ Probe length & lprobe & 8 & mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the coaxial microwave driven plasma and Langmuir probes used to measure electron temperature and density. Figure 4: The I-V curve of the clean Langmuir probe (**a**) the voltage and current curve, (**b**) I-V curve. Figure 5: The voltage and current curve of the Langmuir probe with contamination. It is generally considered that hysteresis and current decrease are caused by surface contamination. These two features are well explained by the equivalent circuit model, reported by [PERSON] and [PERSON] (1972), as shown in Figure 6 [13]. Figure 6 shows that the contamination layer on the probe surface might cause the capacitor Cc and the resister Rc. The Cc and Rc make the hysteresis and current decreased. Therefore, if the power supply of the Langmuir probe is changed from AC to DC, the effect of the capacitor Cc can be counteracted. Loading DC supply on the Langmuir probe and sweeping the voltage from \(-60\) V to \(+60\) V, the I-V curve can be obtained, as shown in Figure 7.  
Although the effect of capacitance is eliminated, resistance will still cause erroneous information. It is well known that the contamination attached to the probe surface leads to a higher incorrect electron temperature. From Figure 7, it can be seen that there is no significant change in ion saturation current. Other studies on probes also show that the contamination on the probe has little effect on ion saturation current [7; 8; 13]. When the voltage is less than \(-48\) V, the ion current of the probe with contaminations  
Figure 6: Equivalent circuit of the electrode contamination. Figure 7: The I–V curve of the clean Langmuir probe and the probe with contaminations driven by DC supply. enters the ion-electron saturation region. The average current in this region is 0.0601 mA and is close to the ion saturation of the clean Langmuir probe. The probe surface cleaning can be done in several ways, such as ion bombardment, warm probe, and emissive probe [17; 18; 19]. However, most of these methods need to interrupt the plasma reaction. Even the probe has been cleaned, the probe also would be contaminated. In the chemical reaction process such as PECVD, the contamination would be in several minutes. From the above presentation, the Isat can also be measured by the probe with contamination. The electron density \(n\) in Equation (4) can be calculated from the I-V curve of the probe with contamination, if the electron temperature _Tev_ is measured by optical emission spectrometry (OES).