Work done at UCLA BPPL and University of Innsbruck, Austria - Research on sheath ionization effects

Transient phenomena and instabilities in electron-rich sheaths have been studied in weakly ionized plasmas where ionization occurs near positively biased electrodes. A dominant instability of electron-rich sheaths is the high frequency sheath-plasma instability. It is a transit-time or inertial instability of electrons. The electron transit time through the sheath is of order of the electron plasma period. An oscillating electric field at this frequency is amplified since bunched electrons feed back in phase when delayed by one period. The same principle is used in diode oscillators where the electron transit time is matched to a resonant cavity oscillation to produce a "monotron" oscillator. In the case of the plasma the sheath-plasma resonance is excited.

The sheath-plasma instability provides useful diagnostic information about the properties of electron-rich sheaths. It yields information about plasma potentials and electron densities near the sheath edge which would be difficult to obtain with probes. It is non-perturbing and time resolved to within plasma periods. When a positive pulsed voltage is applied to a floating electrode one can obtain the transition from an ion-rich sheath into an electron-rich sheath and vice-versa. New transient phenomena have been observed and explained.

Ionization can occur in sheaths when the electron energy exceeds the ionization energy in a partially ionized plasma. The formation of ions inside an electron-rich sheath changes the sheath potential profile. A reduction of the electron space charge widens the sheath which changes the frequency and amplitude of the sheath-plasma instability. The electron transit time through a widened sheath does not match the oscillation period of the sheath-plasma resonance the instability is quenched.

Depending upon the degree of ionization the sheath can evolve into different states. Weak ionization produces a transient behavior: Ions are expelled by the sheath electric field and the electron-rich sheath reforms. Then the process repeats. This results in transient currents similar to those seen for pulsed electrode voltages. However, ionization transients arise at a constant electrode voltage due to fluctuations in the plasma potential near the electrode.

For strong ionization the sheath keeps expanding. The ionization rate increases with sheath thickness. This leads to an avalanche-like sheath expansion which ends with the formation of a "fireball". It is a local discharge near the positive electrode, sometimes called an anode discharge. It has been studied for a long time by many authors, starting perhaps by Langmuir.

A fireball plasma is a localized discharge. The electrode forms the anode, the ambient plasma can be considered a cathode which injects electrons. At the fireball boundary the electrons are energized to somewhat above the ionization energy so as to excite and ionize some neutrals inside the fireball. The potential drop at the fireball boundary forms a double layer. It satisfies the Langmuir condition, i.e., electrons are injected from the background plasma at the electron saturation current and ions from the fireball plasma are ejected at the Bohm current. Since electrons and ions are accelerated to the same energy at the double layer the pressure balance is maintained, which explains the spherical symmetry of stable fireballs. In steady-state the fireball size and potential are coupled so as to balance ion production and ion losses. If the balance is not achieved a fireball grows and collapses, which results in the frequently observed pulsating fireballs.

The electron-rich sheath of the electrode is thoroughly modified when a fireball is formed. Prior to the fireball the sheath potential drop is large compared to the ionization energy which in turn is large compared to kTe. During the fireball the sheath potential drop becomes small or even reverses into an ion-rich sheath since the electrode becomes the anode of the fireball discharge. In a discharge plasma the potential is usually close to that of the anode. The double layer potential is usually slightly above the ionization potential, 15.8 eV in Argon. Thus, the ambient plasma potential rises to approx. the electrode voltage minus the double layer voltage. Since the ambient plasma is nearly collisionless the plasma potential is constant up to the wall where a strong ion-rich sheath is formed.

Since a fireball destroys the electron-rich sheath no sheath-plasma instability occurs. Pulsating fireballs lead to pulsating sheath-plasma oscillations, absent during the fireball, present in between. Even sheath ionization strongly modulates the sheath-plasma instability, explaining its bursty behavior.

Sheath ionization pictures

Fig. 1. Pictures of sheaths with light excitation and ionization. The electrode is a 5 cm diam plane grid. Electrode bias +100 V, Argon 10-4 Torr range, ambient plasma 109 cm-3, 3 eV, B=0 (a) Thin sheath, (b) wide sheath (note color change as electrons are accelerated at sheath edge), (c) fireball (high light intensity, no blue light indicating electron energy well below 100 eV, but above excitation levels, >15 eV). The sharp light boundary is due to the local electric field of a double layer.


Transients and relaxation instabilities due to sheath ionization.

Fig. 2. Spontaneous transient currents and instabilities observed in the presence of sheath ionization on a positively biased grid (Vgrid=200 V). The physics of these phenomena has been clarified in the present research: A probe at the grid center shows large amplitude potential fluctuations indicated by Vprobe. When the potential drops a large displacement current pulse is induced in the grid (top trace). The sheath-plasma instability is excited since a large sheath potential drop is present (middle trace shows 300 MHz oscillations in Vgrid). Sheath ionization raises the plasma potential near the grid which lowers the sheath electric field, destroys the sheath-plasma instability and subsequently stops sheath ionization. ions are ejected from the sheath, it becomes electron-rich and the sheath-plasma instability starts again. Then the process repeats. Further details are explained below.


Transient currents.

Fig. 3. Transient currents due to a step voltage applied to a gridded electrode in a discharge plasma. (a) A family of voltage steps some of which show high frequency oscillations near the electron plasma frequency when the dc voltage exceeds a threshold of approx. 30 V. (b) Measured grid currents corresponding to the voltage waveforms. Two transients are observed, one during the voltage rise which is a displacement current associated with the sheath capacitance. A second smaller current pulse is observed when the plasma potential near the probe collapses as the electron-rich sheath is formed. This occurs when the ions have been ejected from the originally ion-rich sheath which takes about an ion plasma period. Once the electron-rich sheath is established the sheath-plasma instability starts. (c) The I-V characteristics during the first current overshoot is essentially linear, governed by I=CdV/dt. (d) I-V characteristics during and after formation of the electron-rich sheath, which show the transition to a saturation current. However, the ejection of ions from the grid lowers the initial density such that the traces are not useful for plasma diagnostics. Ionization raises the density which occurs at higher voltages and longer time scales (shown later).


Transient currents.

Fig. 4. Further properties of the second current transient: (a) Transient current pulses in the grid current occurs for a constant grid voltage. It is a displacement current due to a sudden drop in plasma potential in front of the grid as the electron-rich sheath is formed. (b) The plasma potential is inferred from the ion saturation current to a probe radially movable in 5 mm steps parallel to the grid surface. The probe voltage increases when the plasma potential increases. The potential in the middle of the grid drops, outside it slightly increases. A potential well is formed as the electron-rich sheath is established. It exhibits transient oscillations. The falling potential near the sheath drives a displacement current into the plasma. The rising potential in the plasma produces a displacement current at the wall which closes the current flow through the external circuit. The same current transient is observed in relaxation oscillations caused by periodic sheath ionization.

Short fast pulse excitation.

Fig. 5. Using the sheath-plasma instability to determine the growth and decay time of an electron-rich sheath: A large amplitude, fast rise and short duration voltage pulse is applied to the gridded elecrode. The pulse is too short to produce significant ionization. The sheath-plasma instability is observed within an ion plasma period when the electron-rich sheath has been formed. The oscillations exists until the very end of the voltage pulse, indicating that the sheath still has a positive potential when Vgrid=0. The rf and dc grid voltages have comparable amplitudes. The current transients are displacement currents. The high frequency oscillations in the grid current have been smoothed.


Transient currents.

Fig. 6. Basic properties of the sheath-plasma instability: Its frequency scales with the electron plasma frequency or square root of the density which is proportional to the discharge current. The frequency is nearly independent of electrode voltage since both sheath thickness and electron velocity increase such that the transit time remains constant.


Bursty emissions.

Fig. 7. Using the sheath-plasma instability to diagnose sheath ionization: (a) Waveforms of the smoothed electrode current and sheath plasma oscillations on a probe at the sheath edge, both showing bursty behavior. (b) Time-resolved frequency spectra of the emission bursts. The frequency decreases during the bursts. It implies a density decrease which arises from the ejection of ions and a lack of ionization to replace them. The density decrease widens the sheath which triggers sheath ionization. The density increases as seen by a higher starting frequency of the next emission burst. All repeated rf bursts start and end with the same frequency, indicating that the density in front of the grid exhibits relaxation oscillations. These are controlled by density and plasma potential variations: Ionization lowers the sheath potential drop which quenches the ionization whereupon the sheath drop increases and ionization restarts, and the cycle repeats. This feedback mechanism explains the bursty current and emission of a sheath with ionization.


Bursty emissions.

Fig. 8. When sheath ionization leads to fireball formation the sheath-plasma frequency is quenched and the current-voltage (I-V) characteristics is strongly modified. (a) A set of voltage steps is applied to the electrode of sufficient amplitude and duration for the formation of fireballs. (b) Corresponding grid current waveforms. Fireball formation is indicated by a large current rise which loads the supply voltage containing a storage capcitor. (c) I-V characteristics at the growth of the fireball develops a steep current rise. (d) I-V curves develop a region of negative differential conductance, dI/dV<0. It is due to the decrease of the grid voltage as the large current discharges the storage capacitor.

References