F A Haas

Floating potential in a bi-Maxwellian RF plasma

The floating potential is investigated for a planar probe/electrode in a DC/RF plasma with a bi-Maxwellian electron distribution. A form of Bohm velocity is adopted appropriate to a two-temperature (T1, T2) plasma with corresponding electron densities n1, n2. Taking hydrogen as an example, a numerical study shows that for given values of T1/T2, n1/n2 and RF amplitude (normalized to T1), the floating potential (normalized to T1) is unique. On the other hand, using the same normalizations for prescribed values of floating potential and RF amplitude, and given n1/n2, there are two values of T1/T2. Conversely for given values of floating potential, RF amplitude and T1/T2, n1/n2 may be single or double valued. Under conditions of sheath inversion RF plasmas again show uniqueness or two valuedness, according to the prescription.

Tailoring of electron energy distributions in low temperature plasmas

Assuming a background Maxwellian electron distribution we investigate the effects of tailoring the tail of the distribution upon the plasma density and electron temperature in a capacitive discharge. Taking the latter to be in the intermediate pressure regime the main effect of the tail is to modify the rate coefficients for ionization and excitation, and hence to alter the collisional energy loss per electron-ion pair created. We demonstrate that the background temperature can be suppressed and the electron density increased by enhancing the tail population. The model is applied to a typical set of low temperature conditions in argon and the changes in temperature and density calculated. Injecting 100 eV electrons into an argon plasma under very similar conditions to those of the application of our model, the corresponding densities and temperatures are measured. Good qualitative agreement is found.

Electron and ion sheath effects on a microwave “hairpin” probe

A microwave measurement of electron density in low-pressure plasmas can be based on a hairpin probe. The hairpin forms a transmission line that supports a quarter-wavelength standing wave. The resonance is related to the relative permittivity of the surroundings, and hence, in a plasma, electron density can be evaluated. For improved fidelity, a general model is developed to include the effects of positive and negative space-charge sheaths formed around the hairpin wires. The former tends to lower the resonance, whereas the latter tends to raise it initially. This is qualitatively in agreement with experiments in dc argon plasmas.

A simple model of an asymmetric capacitive plasma with dual frequency

Recently, simulations have been carried out to investigate a dual frequency capacitive plasma in a system consisting of a pair of coaxial cylindrical electrodes. Considering the same asymmetric configuration, it is shown here that a sharp plasma?boundary model may be used to capture the essential dynamical features of the simulations.

Modelling the effects of an electron beam on the potential distribution in a low pressure parallel electrode discharge

The effect of an electron beam on the potential distribution in a one-dimensional model of a steady parallel electrode discharge is investigated theoretically. Taking the electrodes to be well separated, it is shown that the potential across the sheath of the emitting electrode is decreased by the electron beam. At the absorbing electrode the potential across the sheath is increased. For the latter electrode the potential must be less than a certain maximum value if the beam electrons are to traverse the discharge. Coupling the electrodes by an external current Iext , a characteristic is derived relating Iext and the applied voltage Va . Assuming the beam current at the absorber is some fraction of the beam current at the emitter, then the maximum slope of the characteristic can be used to determine the electron temperature, or . Finally, the properties of the special case of coupled electrodes with Iext = 0, one electrode being earthed, is discussed.

Tailoring of electron energy distributions in low-pressure inductive discharges

Assuming a background Maxwellian electron distribution, the effects of adding an energetic tail upon the electron temperature and density in an inductive low-pressure argon discharge are investigated theoretically. The principal effect of the tail is to modify the rate constants for ionization, excitation, and momentum transfer. Using particle and energy conservation, the possibility of suppressing the electron temperature and increasing the electron density is demonstrated. It is found that under typical conditions of operation the electron temperature can be decreased from 2.5 to 1.5 eV, and the electron density increased by at least a factor of 2.4.

Some aspects of collisionless heating in inductive discharges

Considering a simple model of a spiral antenna inductive discharge in the collisionless heating regime, the basis of the equivalence of the stochastic and surface impedance methods is demonstrated. Formulae for the power per unit area, for each approach, are obtained in the regime of small normalized RF frequency, w, and shown to have the same functional dependence on w; the numerical coefficients agree to within a factor of 0.6. A study of the azimuthal electric field, Eθ, appropriate to the surface impedance method shows that although generally nonmonotonic, within the vicinity of the coil Eθ falls exponentially. The decay length δc very closely matches the skin depth of the stochastic method for a range of electron densities and RF frequencies. Thus the assumption that an exponential decay for Eθ in the stochastic method is a very good approximation for the purpose of calculating the collisionless heating is confirmed.

Simple analysis of a capacitive discharge with a bi-Maxwellian electron distribution

Considering the situation where the ion mean free path is less than or of order the plasma thickness, the particle and energy conservation equations are used to establish a simple analysis of a capacitive discharge in which the electrons have a bi-Maxwellian distribution. Prescribing the density of the cold group of electrons and analysing the data taken from a 100 mTorr argon plasma, the hot electron temperature and density are found to be in satisfactory agreement with the measured values for a range of discharge currents (100-500 mA), while the cold electron temperatures agree to within a factor two of the measurements.

Energetics of secondary electrons in a simple model of an RF sheath

A simple current-regulated model of an RF sheath (angular frequency ω) is used to investigate the energetics of secondary electrons emitted from an electrode. The sheath potential is spatially quadratic and consists of a steady potential together with two harmonics. An equation is derived for the motion of a secondary electron in this potential. The energy of emission at the electrode is prescribed. It is necessary to take account of the phase difference between the electron motion and the sheath current. A relation between the phase and the transit time tf is obtained by matching the instantaneous sheath–plasma boundary position to the electrons position at the instant of arrival at this boundary. An analytic solution is derived in terms of the small parameter ω/ωpe where ωpe is the electron plasma frequency. Expressions for the electron transit time tf are derived and it is shown that ω/ωpe1 is equivalent to tf/T1, where T is the RF period. Under these conditions the electron energy is conserved, the energy at the plasma–sheath boundary being the potential energy at the electrode upon emission. The resulting secondary electron distribution in the bulk plasma is derived.

The electron distribution function at an RF planar probe due to an incident electron beam

Experiments with a planar probe embedded in the grounded electrode of the GEC cell run in the capacitive mode suggest the presence of extra-energetic electrons. In particular, under a wide range of filling pressure and power the I–V characteristic rises linearly towards the ion saturation current. To model this analytically, an electron beam is taken to be incident at the plasma–sheath boundary of the planar probe. The beam electrons are retarded, as they approach the probe surface, by a combination of a steady component of potential and that fraction of applied RF which is distributed between the plasma and ground; the electron transit time is assumed short compared to the RF period. The electron distribution function received at the probe is expressed in terms of a convolution integral. The distribution received at the probe is used to calculate the resulting component of beam current at the probe surface for the special case that the incident beam distribution has a top hat form. Combining this current with the ion sound and electron thermal currents leads to the I–V characteristic. Given a specified range of energies for the incident beam it is shown that the characteristic rises linearly towards the ion saturation current. It is concluded that this feature of the characteristic can be plausibly interpreted as due to extra-energetic electrons.