Electrical characteristics of a RF-GD-OES cell

Abstract

The purpose of this work is to describe, using a self-consistent two dimensional hybrid fluid-particle model, the electrical characteristics of a discharge operating in a RF-GD-OES cell. We show that, for typical operating conditions at 13.56 MHz, the discharge has a capacitive electrical behavior and that the main current component at the powered electrode is the displacement current. These results are not in agreement with previously published calculations and this point is discussed.

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Introduction

Glow discharge optical emission spectroscopy (GD-OES) is an analytical technique widely used for elemental analysis. ¹ Radiofrequency excitation (rf-GD-OES) of the glow discharge for GD-OES is now being developed for analysis of nonconducting samples. The main reason for the interest in using radiofrequency discharges for GD applications is because it is possible, depending on the operating conditions, to produce a discharge almost continuously with an insulating surface covering one or both electrodes. Recently it has been shown that this technique, using radiofrequency excitation, is very promising for the analysis of polymeric materials. ²

Radiofrequency discharges operating at 13.56 MHz have been studied extensively over the past decade in the context of plasma processing for surface treatment in the microelectronics industry and thus these discharges are fairly well understood. The cell geometry and operating conditions used in rf-GD-OES are, however, different from those generally used in plasma processing; the pressure, voltage, and the dc self-bias are higher in rf-GD-OES. It is therefore useful to analyse the behavior of rf discharges for conditions typical of those used in rf-GD-OES analysis.

Physical and numerical model

Numerous models have been developed to study radiofrequency discharges and their associated plasmas. ³ These models together with plasma diagnostic techniques have proven to be very useful for developing an understanding of the basic mechanisms occurring in these discharges. In particular, the mechanisms by which rf discharges are sustained have been clarified by detailed modeling and comparison with experiment. A discussion of these mechanisms and additional information can be found in ref. 4.

For the study described here we have used a self-consistent, two-dimensional hybrid fluid-particle model. This model has been used previously for dc glow discharges ⁵ and has been adapted here to rf excitation. In this model, fluid equations are used to describe the ions and electrons which contribute to the space charge and these equations are solved self-consistently with Poisson's equation for the electric field. Results from this model are the charged particle densities and the electric field as functions of space and time. Cylindrical symmetry is assumed and the results thus depend on distances in the radial and axial directions. The distinguishing feature of our hybrid fluid-particle model is that the ionization source terms appearing in the continuity equations for the charged particles are determined from a particle (Monte Carlo) approach. Such a particle treatment of the ionization source term is necessary because the ionization source term in the rapidly varying electric field in the cathode fall of a glow discharge is very nonlocal. ⁶

This model was adapted to rf excitation in the following way. In a dc discharge, electrons emitted from the cathode and accelerated in the cathode sheath deposit their energy in excitation and ionization and then diffuse to the anode or side walls. When their total energy (kinetic plus potential) drops below the ionization potential of the neutral gas, the electrons are no longer capable of producing ionization and they can be dropped from the Monte Carlo simulation. In contrast, in rf discharges, since the opposite electrode acts as the cathode for part of the cycle, electrons diffusing to the instantaneous anode can be accelerated in the advancing sheath as the electrodes change polarity. Electrons accelerated in this way are called `wave-riding' electrons. In order to include the ionization produced by these electrons in our Monte Carlo calculation, electrons are included in the simulation until they reach an electrode (they are not dropped from the simulation when their total energy decreases below the ionization potential).

Our model is similar in most respects to that developed more recently by Bogaerts et al.⁷ One important difference between our rf model and that of Bogaerts et al. is in the treatment of the ionization source terms. In the model of ref. 7, a Monte Carlo simulation of the cathode emitted electrons is used to determine the ionization of the electrons emitted from the cathode which are followed until their energy drops below a certain threshold value. Ionization produced when these cool (fluid) electrons are reheated on the opposite half cycle of the applied voltage is calculated separately. Thus, the electron energy balance equation is solved to yield the mean energy of the fluid electrons as a function of position, and the ionization rate coefficient is supposed to be a known function of this mean energy. (It is not clear how the collisional energy losses are taken into account in the energy balance equation in ref. 7.) The total ionization is then the sum of two components, the ionization due to cathode emitted electrons as determined from the Monte Carlo simulation plus the ionization due to the fluid electrons which depends on their mean energy.

Results

1. Cell geometry and operating conditions

The cell geometry we have considered here is presented in Fig. 1. The grounded electrode is a cylinder (4.8 cm length and 3 cm diameter); this electrode reduces to a smaller cylinder (5.6 mm diameter, 6 mm length) separated from the rf powered electrode by a dielectric (2 mm thick). The rf voltage is applied through a capacitor.

Fig. 1 Schematic of the discharge cell used for the calculations.

Although this geometry is slightly different from the standard Grimm source, the differences are outside the active region of the discharge and do not influence the results much. The gas considered is argon at a constant density of 3.54 × 10 ¹⁶ atoms per cm ⁻³. Note that the gas density enters into the model equations rather than the gas pressure and temperature. Using the ideal gas law, this density corresponds to 1.5 Torr at 300 K or to 4.5 Torr at 900 K. The applied voltage is V = V_rfcos( ωt) with V_rf = −800 V, and the frequency of the applied voltage is 13.56 MHz.

2. Electrical characteristics

Fig. 2 shows the potential and total discharge current at the powered electrode as a function of time for one rf cycle.

Fig. 2 Time variation of the applied potential (full circles) and total discharge current (open circles) at the powered electrode for an rf cycle. The time is normalized to one cycle of the applied voltage.

Due to the difference in surface area of the two electrodes, a large dc bias is established. Thus, the potential at the powered electrode is V = V_rfcos( ωt) + V_bias, and the model yields a value of V_bias of −700 V.

The calculated discharge current at the powered electrode is sinusoidal with a peak value slightly above 0.05 A. It is interesting to note the capacitive behavior of the discharge; the phase shift between the current and voltage is close to π/2. This behavior is typical of rf discharges at 13.56 MHz used in the microelectronics industry (provided negative ions are not present in large quantities which leads to a more resistive behavior). It is also interesting to note that the powered electrode acts as an anode for only a small fraction of the cycle.

Fig. 3 shows the different components of the total current at the powered electrode, the electron and ion conduction currents and the displacement current.

Fig. 3 Time variation of the total discharge current (full line), ion current (squares), electron current (triangle) and displacement current (open circle), during an rf cycle, same conditions as Fig. 2.

We find that the major current component of the powered electrode is the displacement current. This displacement current is directly proportional to the temporal variation of the electric field on the electrode. The electron current to the powered electrode is essentially zero for most of the cycle, but it is important during the anodic part of the cycle for the powered electrode. This is the moment that the electric field on the powered electrode reaches its minimum and allows the electrons to flow out of the discharge. An ion conduction current to the powered electrode is present during the cathodic part of the cycle because of the electric field accelerating ions to the electrode.

Far from the electrodes in the plasma itself, displacement current is negligible and the total current is almost uniquely an electron conduction current.

Summary and discussion

Using a self-consistent two dimensional hybrid fluid-particle model, we have calculated the electric field and charge particle densities for one set of conditions appropriate to rf-GD-OES. The main results reported here are: (1) the discharge has a capacitive behavior, i.e., the current–voltage phase-shift is close to π/2; (2) on the powered electrode, the main current component is the displacement current.

Thus we find that the electrical properties of discharges in rf-GD-OES conditions are similar to capacitively coupled discharges operating at 13.56 MHz and used for plasma processing of microelectronics. This is encouraging because we would expect that the understanding developed in that context is applicable to rf-GD-OES conditions.

It is important to note that our results are not in agreement with previously published calculations. ⁷ The main difference concerns the relative magnitudes of the displacement current and the particle conduction currents at the powered electrode. In ref. 7 it is found that the displacement current is negligible. The consequence of this is that the phase shift between the current and the voltage is very small, i.e., the discharge has a resistive behavior. On the other hand, these authors find, on the powered electrode, a very high varying electric field, and this should be related to a large displacement current. There are several differences between the physical model we use and that of ref. 7: (a) we do not include electron reflection or emission from the anode and (b) we do not include ionization due to heavy particles (ions or fast neutrals). Although these phenomena could certainly affect the magnitude of the calculated currents, neither changes the fundamental capacitive nature of the discharge. There are also differences between ref. 7 and our work in numerical aspects. In our model, all ionization is calculated with the Monte Carlo simulation whereas in ref. 7, ionization due to wave-riding electrons is treated separately.

This distinction between capacitive and resistive discharges is important because the differences between the two are related to the spatial distribution of the potential and hence the gas excitation and light emitted in GD-OES. In a capacitive rf discharge, the potential drop occurs mainly in a thin sheath region immediately in front of the electrodes. For conditions typical of rf-GD-OES, the positive charges are immobile on the time scale of the rf cycle. The lighter electrons, however, are pushed away from the instanteous cathode on each half cycle, exposing the immobile background of positive space charge. This excess positive charge in front of the cathode leads to a large potential drop in that region. The electric field in the quasi-neutral plasma region is small (very little potential drop in the plasma). In contrast, a resistive discharge is one in which most of the potential drop is in the plasma.

Measured electrical characteristics ⁸ show that, depending on the applied parameters, the discharge exhibits a capacitive behavior. More measurements are needed to clearly understand the electrical behavior of the discharge operating in a radio frequency GD-OES cell.

ack

The authors would like to acknowledge useful discussions with members of the European Community Network on Glow Discharge Spectroscopy. Ph. Belenguer wants to thank J. P. Bœuf for numerous discussions on radiofrequency discharges and L. Wilken and V. Hoffmann for discussing their results on electrical characteristics measurements. This work has been partly supported by CEA/VALDUC.

References

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