The Effect of a Multihollow Cathode on the Self-Bias Voltage of Methane RF Discharge Used for a-C : H Deposition

In this work we report the measurement of the self-bias voltage of radiofrequency (RF) capacitevely coupled plasma, with a multihollow cathode and methane precursor, used for amorphous hydrogenated carbon (aC:H) thin film deposition. The plasma is produced in the incident power and pressure ranges between 20 300 W and 10 100 mTorr, respectively. It was found that the self-bias voltage Vdc is a linear function of the square root of the incident power WRF. The relationship between the self-bias voltage and gas pressure P is established; this gives an empirical relation for  0 P P   . From this result, the pressure corresponding to the transition from hollow cathode effect to hollow cathode arc effect is determined. 0 P


Introduction
The amorphous hydrogenated carbon films (a-C:H) that are typically dense, hard and transparent are of great interest in different areas of sciences and technology; such as in microelectronics, IR spectroscopy; instrumental and medical industries [1][2][3][4][5][6].Various deposition methods are used such as arc [7], sputtering [8,9] and plasma enhanced chemical vapor deposition (PECVD) [10,11].However, changing the system operation parameters, in particular gas pressure and incident power can strongly affect the deposited film structure and properties [11,12].The geometry of the cathode plays also a crucial role on the plasma parameters, such as the energy and flux of ions that strike the film surface, which can affect the deposition parameters like growth rate of the deposited film [13].This is why it is so important to make coupling between the plasma parameters, the system operation parameters and the geometry of the cathode for controlling and understanding the basic mechanisms and also to improve the film deposition.Frequently, the capacitevely radio frequency (RF) discharge with parallel-plate electrode is widely used for the deposition of a-C:H because the apparatus system is very simple.But they present a disadvantage, the electron density and deposition rate are lower regarding other configuration.Consequently, the other alternative geometry can be used such as hollow cathode, which is widely used as a light source [14], and active media for gas lasers [15], these discharges are recognized to produce denser plasma [16].Recently, there are interests to use the hollow cathode discharge for the deposition of thin films, because they gives the possibility to produce plasma with higher electron density and lower electron temperature, that reduces the damage caused to the film deposition [17].For this purpose, Ohtsu et al. [18] have used multihollow cathode discharges for deposition of diamondlike-carbon (DLC) thin film at 13.56 MHz in methane gas, and they prove that they achieved a high deposition rate of DLC film.Their investigation concerns a cathode with 35 small holes.In the present study we focus on using multihollow cathode with seven (07) holes and each hole has 40 mm of diameters used for the deposition of amorphous hydrogenated carbon films (a-C:H) with CH 4 gas precursor at 13.56 MHz frequency.We are interested in the influence of the system operation parameters on the self-bias voltage.The latter has been subject of many researches carried out in the fields of electric diagnostics of the RF (13.56 MHz) discharges [19,20].The self-bias voltage is macroscopic parameters is known to have a major influ-ence on the film deposition, the impact of ions energies on the substrate are to be taken only as approximate values; as often reported, where only the self-bias voltage (V dc ) is given, as pointed out by Catherine et al. [20] in the study of the electric behaviour of 13.56 MHz discharge in CH 4 used for a-C:H film deposition.
This paper is organized as follows: In Section 2 a description of the experimental setup will be given.Results and discussion will follow in Section 3, and in Section 4 the conclusions are summarized.

Experimental Setup
The experimental setup used in the present study is shown in Figure 1.The ionization chamber consisted of a stainless steel cylindrical vessel of 230 mm diameter and 260 mm height.The electrode creator of plasma is a multihollow cathode, of 126 mm diameter and 50 mm height, with seven holes.Each hole has 40 mm inner diameter and 50 mm height.The wafer holder (bottom electrode) of 150 mm diameter is situated at 50 mm from the upper electrode, which is capacitively coupled to the RF (13.56 MHz) generator through a matching network.The ionization chamber walls were grounded (asymmetrical diode-type reactor), and a base vacuum of less than 10 -5 mbar is achieved by the pumping system.The range of variation of the incident power and pressure are 20 -300 W and 10 -100 mTorr respectively.A self-bias voltage is measured with a voltmeter through a low pass filter, and the saturation ion current density is collected at the wafer holder that is a dc polarized.

Results and Discussions
The knowledge of the electric parameters of the dis The knowledge of the electric parameters of the discharge such as the self-bias voltage (V dc ) is of crucial importance for understanding the electric behaviour of the discharge.Thus, we have studied the evolution of this electric parameter as a function of incident power and pressure.
The self-bias voltage V dc .The self-bias voltage was modeled by different authors in various plasma discharges.Using the capacitive sheath model, Y. Catherin [20] gives the dependence of the self-bias voltage on incident power and pressure in the case of RF parallel plate electrode discharge by the following equation: where W RF is the incident power and P is the pressure Another expression of the self-bias voltage can be obtained from the cathode layer model in the case of discharge with RF antenna [21]: where a is constant depend on the plasma parameters, W RF is the incident power and P is the pressure.It can be seen from both Equations ( 1) and ( 2), that the self-bias voltage has the same dependence on incident power and differ with pressure; because the variation of the self-bias voltage with pressure is related to the sheath thickness which depends on the cathode geometry.Figure 2 represents the variation of the self-bias voltage V dc versus the square root of the incident power W RF 0.5 at different gas pressure; the self-bias voltage is proportional to the square root of the incident power, this can be attributed to plasma volume with resistive behaviour [20].The same evolution was observed in the cases of parallel plate and antenna cathode [20][21][22].This result confirms that the evolution of the self-bias voltage with  incident power is independent of the cathode geometry.
The variation of the self-bias voltage with the pressure is shown in Figure 3.We can split these curves on two parts: at low pressure (10 -40 mTorr) we notice a fast decrease of the self-bias voltage.This can be attributed to the hollow cathode effect, which is manifested by an abrupt decrease in the operating voltage [23,24].
For the pressure ranging in the domain 40 -100 mTorr, the self-bias voltage became constant, this behaviour may be due to the transition of the discharge to the hollow cathode arc discharge [24].
The fitting corresponding to our experimental results can be expressed by the following empirical relation: where α, β and γ are constants that depend on the system operation parameters.P 0 is the pressure corresponding to the inflection point.The result of fitting procedures showed a very good agreement with our experimental results.In Table 1 we summarized the parameter of Equation ( 3) which are depend on the incident power.
The key fit parameter P 0 represents the transition of the discharge from an regime to an other.At this values of pressure, the self-bias voltage change his behaviour.
From the variation of the self-bias voltage versus pressure, we can establish the transition pressure of the discharge regime, which represents the passage from

Conclusions
In this work we studied the electrical parameters of 13.56 MHz capacitive discharge used for the deposition of a-C:H film, with multihollow cathode.It was shown that, the self-bias voltage is linear function of W RF 0.5 independent of the geometry of the cathode.From the dependence of the self-bias voltage on pressure an empirical relation is deduced: V dc ~ (P/P 0 ) γ .From this result, the transition pressure 0 from hollow cathode to hollow cathode arc effect was determined.

Figure 2 .
Figure 2. Influence of the square root of incident power on the Self-bias voltage.

Figure 3 .
Figure 3. Influence of the pressure on the Self-bias voltage.

Table 1 . Empirical function fit parameters.
hollow cathode to hollow cathode arc discharge.