Gaseous Electronics Conference Reference Reactor Research Articles

A generalized electron energy probability function for inductively coupled plasmas under conditions of nonlocal electron kinetics

A generalized equation for the electron energy probability function (EEPF) of inductively coupled Ar plasmas is proposed under conditions of nonlocal electron kinetics and diffusive cooling. The proposed equation describes the local EEPF in a discharge and the independent variable is the kinetic energy of electrons. The EEPF consists of a bulk and a depleted tail part and incorporates the effect of the plasma potential, Vp, and pressure. Due to diffusive cooling, the break point of the EEPF is eVp. The pressure alters the shape of the bulk and the slope of the tail part. The parameters of the proposed EEPF are extracted by fitting to measure EEPFs (at one point in the reactor) at different pressures. By coupling the proposed EEPF with a hybrid plasma model, measurements in the gaseous electronics conference reference reactor concerning (a) the electron density and temperature and the plasma potential, either spatially resolved or at different pressure (10–50 mTorr) and power, and (b) the ion current density of the electrode, are well reproduced. The effect of the choice of the EEPF on the results is investigated by a comparison to an EEPF coming from the Boltzmann equation (local electron kinetics approach) and to a Maxwellian EEPF. The accuracy of the results and the fact that the proposed EEPF is predefined renders its use a reliable alternative with a low computational cost compared to stochastic electron kinetic models at low pressure conditions, which can be extended to other gases and/or different electron heating mechanisms.

Numerical analysis of the non-equilibrium plasma flow in the gaseous electronics conference reference reactor**Project supported by the National Natural Science Foundation of China (Nos. 11372325, 11475239).

The capacitively coupled plasma in the gaseous electronics conference reference reactor is numerically investigated for argon flow using a non-equilibrium plasma fluid model. The finite rate chemistry is adopted for the chemical non-equilibrium among species including neutral metastable, whereas a two-temperature model is employed to resolve the thermal non-equilibrium between electrons and heavy species. The predicted plasma density agrees very well with experimental data for the validation case. A strong thermal non-equilibrium is observed between heavy particles and electrons due to its low collision frequency, where the heavy species remains near ambient temperature for low pressure and low voltage conditions (0.1 Torr, 100 V). The effects of the operating parameters on the ion flux are also investigated, including the electrode voltage, chamber pressure, and gas flow rate. It is found that the ion flux can be increased by either elevating the electrode voltage or lowering the gas pressure.

Effect of metastable atom reactions on the electron energy probability functions in afterglows

Time resolved electron densities, temperatures and energy probability functions (EEPFs) of modulated-power glow discharges through argon and helium in the Gaseous Electronics Conference reference reactor have been measured using an RF compensated Langmuir probe and a microwave interferometer. RF power was capacitively coupled to the glow and square wave amplitude modulated with a 50% duty cycle and 100% modulation depth. We found that a metastable-metastable ionization reaction can produce energetic electrons during the afterglow. This reaction can also cause the electron density to increase during the afterglow despite the RF excitation being off. The electron density as a function of time can be modelled and the result is an estimated metastable atom density as a function of time. The hot electrons in the EEPF can also be modelled, but the modelling result does not fit the experimental EEPF until the smoothing of the EEPF caused by the experimental method is taken into account. This smoothing of the EEPF can be accounted for using the Druyvesteyn method formula and indicates that accurate measurements of the EEPF in very low electron temperature plasmas can become difficult. In effect, one should have some knowledge of the shape of the EEPF before the experiment in order to obtain an accurate measurement. The electron density and EEPF results become self-consistent once the smoothing is taken into account. By moving the Langmuir probe along the diameter of the chamber it was determined that the electron density decreases more quickly between the electrodes than outside the electrode edges. This causes the plasma density profile in argon to becomes doughnut shaped during the afterglow and causes the glow to re-ignite from the edges into the centre. The electron temperature at re-ignition in helium discharges can become larger than that at steady state in the active glow. It quickly relaxes to the steady state value. This last effect is not nearly as pronounced in argon.

Two-dimensional laser-induced fluorescence imaging of metastable density in low-pressure radio frequency argon plasmas with added O2, Cl2, and CF4

The effect of minor additions of O2, Cl2, and CF4 on the argon metastable relative density and spatial distribution in low-pressure, radio-frequency argon plasmas, generated within a parallel-plate Gaseous Electronics Conference reference reactor, has been investigated using planar laser-induced fluorescence imaging. For the conditions examined (33.3 Pa, 75–300 V, <10 W), the addition of only a few percent of these electron attaching gases was found to decrease the metastable density by as much as an order of magnitude, despite the fact that the excited-state argon emission indicated an increase in the metastable production rate. In the dilute O2/Ar discharges examined here, the spatial distribution of metastables was similar to that of the electropositive, pure argon cases, exhibiting a strong axial peak near the interface between the plasma bulk and the sheath at the powered electrode. In contrast, the addition of either Cl2 or CF4 was found to significantly modify the spatial distribution of the emission intensity and metastable density, resulting in a more symmetric and uniform axial metastable distribution. This change in metastable distribution for these mixtures was particularly apparent at lower powers and/or higher Cl2/CF4 concentrations, and suggests a transition from an electropositive to a somewhat electronegative discharge.

Time-resolved power and impedance measurements of pulsed radiofrequency discharges

The power to a pulsed RF discharge in the Gaseous Electronics Conference reference reactor has been measured with sub-microsecond time resolution. There are large swings in the power delivered to the cell as a function of time during the first 5-10 mu s of the transient turn-on and turn-off. These power oscillations are in large part caused by the passive circuitry between the current-voltage sensors and the electrode assembly of the cell and have been modelled using an equivalent network with reasonable accuracy. They make it difficult to determine the plasma impedance at very early times during the discharge turn-on. This passive circuitry can also store RF energy and release it both to the plasma and to the RF generator at plasma turn-off. The power delivered to a 500 mTorr argon discharge does not reach steady state until approximately 500 mu s after the discharge turn-on even though the initial power oscillations end within the first 10 mu s. This longer term power variation appears to be related to a contraction of the electrode sheaths as well as to an electron density increase and electron temperature decrease during this time. As the sheath contracts, less of the RF field penetrates to the body of the glow and the electron atom collision frequency, which is related to the electron average energy, decreases by a factor of two.

Two-dimensional model of a capacitively coupled rf discharge and comparisons with experiments in the Gaseous Electronics Conference reference reactor.

We present results from a two-dimensional (2D) numerical fluid model of rf discharges in conditions close to recently published measurements of the spatial distribution of plasma density in the Gaseous Electronic Conference reference cell. The discharge is in pure argon at pressures in the 100 mtorr range, frequency 13.56 MHz, and rf voltage amplitudes on the order of 100 V. The model is based on solutions of the continuity, momentum (drift-diffusion), and energy equations for the electrons, continuity, and drift-diffusion equation for positive ions, coupled with the Poisson equation. The results of the model are qualitatively and quantitatively in good agreement with the experiments. The model predicts a maximum of plasma density off axis, as in the experiment. The ion current density on the electrode is also nonuniform, and increases radially in the conditions of the experiments. The effects of the rf voltage, pressure, and reactor geometry (electrode dimensions, gap length, guard rings, etc.) on the plasma properties and on the uniformity of the ion current on the powered electrode are also discussed. It is shown that the existence of a maximum of plasma density in the radial direction, in the conditions of the experiment, is due to the small value of the electrode spacing. The results show that the harmonic content of the discharge current is also geometry dependent. The comparisons show that 2D, three-moment fluid models can accurately describe the discharge and the effects of the chamber geometry on the plasma properties for pressure above the limit where collisionless electron heating does not play a significant role.

Spatial variations in the charge density of argon discharges in the Gaseous Electronics Conference reference reactor

The spatially dependent ion and electron concentrations of argon discharges in the gaseous electronics conference reference reactor reach a saddle point maximum in the center of the glow. The concentrations were measured using a Langmuir probe. The charge density decreases in the axial direction from the glow center to the electrode sheath edges as expected. In contrast, the charge density increases in the radial direction from the glow center to the radial electrode edge. The maximum occurs approximately 1 cm inside of the actual electrode edge. The most plausible explanation for this increase is enhanced ionization at the electrode edges due to field enhancement there. The electric field is enhanced by the close proximity of the ground shield and driven electrode at the radial edge of the electrode. We estimate that the ionization rate in the plasma near the electrode edge must be almost double of that in the glow center.

Comparison of electron-density measurements made using a Langmuir probe and microwave interferometer in the Gaseous Electronics Conference reference reactor

A Langmuir probe and a microwave interferometer have been combined to measure the electron density of argon glow discharges in the Gaseous Electronics Conference reference reactor [Bull. Am. Phys. Soc. 36, 207 (1991)]. The two techniques indicate the same charge density at 100 mTorr to within 30%. This 30% difference is easily explained by the experimental peculiarities. While the predicted charge densities obtained from the two techniques track one another as the applied rf voltage is varied at constant pressure, they do not track one another as the pressure is varied at constant rf voltage. In fact, the charge densities predicted from the Langmuir probe using Laframboise’s theory (Tech. Rep. 100, Univ. Toronto Inst. Aerospace Study, 1966) are factors of 2 and 4 times lower than those from the interferometer at 250 and 500 mTorr, respectively. It appears that the probe alters the charge density in its vicinity when the probe radius becomes greater than the ion mean free path. The interferometer has also been used to investigate the macroscopic perturbation of the plasma electron density caused by the Langmuir probe. It was found that presence of the probe in a radio-frequency discharge does not appreciably alter the electron density measured by the interferometer at a set rf voltage irrespective of the potential placed upon it. This was not the case for dc discharges in the same apparatus where the volume-averaged electron density could be depleted by as much as 70% when the probe was biased even a few volts above plasma potential.