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Figure from:Modelling of discharges and non-thermal plasmas—applications to plasma processing

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Fig. 11. Time evolution of the contours of constant potential in a transient pseudospark discharge (helium, 0.5 Torr, anode voltage 2 kV). The dots correspond to the positions of the ionization events from the particle model of high energy electrons. See ref. 23 for further details. This hybrid model can also be used to describe more complicated geometries such as the one corresponding to Fig. 11. This figure shows the temporal evolution of the spatial distribution of the potential in a transient hollow cathode discharge used for switching applications

Figure 11 Time evolution of the contours of constant potential in a transient pseudospark discharge (helium, 0.5 Torr, anode voltage 2 kV). The dots correspond to the positions of the ionization events from the particle model of high energy electrons. See ref. 23 for further details. This hybrid model can also be used to describe more complicated geometries such as the one corresponding to Fig. 11. This figure shows the temporal evolution of the spatial distribution of the potential in a transient hollow cathode discharge used for switching applications

Related Figures (15)

Fig. 1. Simplified scheme of a reactor model (after ref. 1). In this paper. we shall discuss only the submodel describing the electrical properties of the discharge. The A complete model of a plasma reactor must include three different (but coupled) submodels [1]: (1) an electri- cal model of the discharge and plasma; (2) a model describing the plasma chemistry and gas flow; (3) a model of the surface reactions. A simplified scheme of such a model is presented in Fig. 1.
Fig. 1. Simplified scheme of a reactor model (after ref. 1). In this paper. we shall discuss only the submodel describing the electrical properties of the discharge. The A complete model of a plasma reactor must include three different (but coupled) submodels [1]: (1) an electri- cal model of the discharge and plasma; (2) a model describing the plasma chemistry and gas flow; (3) a model of the surface reactions. A simplified scheme of such a model is presented in Fig. 1.
Fig. 2. Electrode geometries used in the 2D fluid model of a silane rf. discharge. Cases (a), (b) and (c) correspond to different electrode area ratios (the electrode configuration is symmetrical in case (c)). For all three cases the conditions are: silane, 0.1 Torr, 13.56 MHz, rf. voltage amplitude 100 V.
Fig. 2. Electrode geometries used in the 2D fluid model of a silane rf. discharge. Cases (a), (b) and (c) correspond to different electrode area ratios (the electrode configuration is symmetrical in case (c)). For all three cases the conditions are: silane, 0.1 Torr, 13.56 MHz, rf. voltage amplitude 100 V.
Fig. 4. Time variations of the rf. voltage and discharge voltage for the conditions of Fig. 2. Another consequence of the asymmetry of the electrode configuration is the fact that the voltage across the electrode is not purely r.f. but has a d.c. component (see e.g. ref. 26). This appears in the spatial distribution of the electric field displayed in Fig. 3 (the average sheath voltage corresponding to the small electrode is larger than the average sheath voltage of the larger electrode) and also in Fig. 4, which shows the time variations of
Fig. 4. Time variations of the rf. voltage and discharge voltage for the conditions of Fig. 2. Another consequence of the asymmetry of the electrode configuration is the fact that the voltage across the electrode is not purely r.f. but has a d.c. component (see e.g. ref. 26). This appears in the spatial distribution of the electric field displayed in Fig. 3 (the average sheath voltage corresponding to the small electrode is larger than the average sheath voltage of the larger electrode) and also in Fig. 4, which shows the time variations of
Fig. 3. Spatial distributions of electron, positive and negative ion densities and electric field on the discharge axis at four different times of the rf. cycle in the geometry of Fig. 2, case (a). Figure 3 shows the spatial distribution of the electrons, positive and negative ions and electric field on the discharge axis at four different times of an rf. cycle for case (a). The charged particle profile is not symmetrical owing to the asymmetry of the electrode configuration. Note that the ion density in the plasma is much higher than the electron density. This is due to the fact that negative ions are trapped in an rf. discharge (their mobility being much smaller than that of electrons, they
Fig. 3. Spatial distributions of electron, positive and negative ion densities and electric field on the discharge axis at four different times of the rf. cycle in the geometry of Fig. 2, case (a). Figure 3 shows the spatial distribution of the electrons, positive and negative ions and electric field on the discharge axis at four different times of an rf. cycle for case (a). The charged particle profile is not symmetrical owing to the asymmetry of the electrode configuration. Note that the ion density in the plasma is much higher than the electron density. This is due to the fact that negative ions are trapped in an rf. discharge (their mobility being much smaller than that of electrons, they
Fig. 5. Contours of constant potential at four different times of an rf. cycle (conditions of Fig. 2, case (a)). A discussion of the comparison between the model results (for 1D fluid and PIC-MC models) and experi- ments is presented in ref. 10.
Fig. 5. Contours of constant potential at four different times of an rf. cycle (conditions of Fig. 2, case (a)). A discussion of the comparison between the model results (for 1D fluid and PIC-MC models) and experi- ments is presented in ref. 10.
Fig. 6. Spatial variations of the electron density in the discharge at six different times of an r.f. cycle (conditions of Fig. 2, case (a)).
Fig. 6. Spatial variations of the electron density in the discharge at six different times of an r.f. cycle (conditions of Fig. 2, case (a)).
Fig. 8. Contours of (a) constant potential and (b) constant electron density (unit: 1.2 x 10'° cm~3) for a 1 Torr discharge in argon in the geometry of Fig. 7 for current (0.58 pA) and voltage (142.4 V) corre- sponding to a normal glow discharge. The potential increment from one equipotential contour to the next is 15 V (from the cathode) except for the contour whose value is indicated in (a).
Fig. 8. Contours of (a) constant potential and (b) constant electron density (unit: 1.2 x 10'° cm~3) for a 1 Torr discharge in argon in the geometry of Fig. 7 for current (0.58 pA) and voltage (142.4 V) corre- sponding to a normal glow discharge. The potential increment from one equipotential contour to the next is 15 V (from the cathode) except for the contour whose value is indicated in (a).
Fig. 7. Electrode geometry used in the 2D hybrid model of a dic. discharge in argon.
Fig. 7. Electrode geometry used in the 2D hybrid model of a dic. discharge in argon.
Fig. 10. Voltage vs. current characteristic curve for a 1 Torr discharge in argon in the geometry of Fig. 7. (1) and (2) correspond to the regimes of Figs. 8 and 9 respectively. J. P. Boeuf et al. {| Discharge and non-thermal plasma modelling
Fig. 10. Voltage vs. current characteristic curve for a 1 Torr discharge in argon in the geometry of Fig. 7. (1) and (2) correspond to the regimes of Figs. 8 and 9 respectively. J. P. Boeuf et al. {| Discharge and non-thermal plasma modelling
Fig. 9. Contours of (a) constant potential and (b) constant electron density (unit: 9.4 x 10'° cm~3) for a 1 Torr discharge in argon in the geometry of Fig.7 for current (3.7 pA) and voltage (163.3 V) corre- sponding to a slightly abnormal regime. The potential increment from one equipotential contour to the next is 15 V (from the cathode) except for the contour whose value is indicated in (a).
Fig. 9. Contours of (a) constant potential and (b) constant electron density (unit: 9.4 x 10'° cm~3) for a 1 Torr discharge in argon in the geometry of Fig.7 for current (3.7 pA) and voltage (163.3 V) corre- sponding to a slightly abnormal regime. The potential increment from one equipotential contour to the next is 15 V (from the cathode) except for the contour whose value is indicated in (a).
Fig. 13. (a) Ionization rate as a function of space and time during one rf. cycle for the same conditions as in Fig. 12, but without secondary electron emission (y=0), from a PIC-MC simulation. The lines correspond to contours of constant electric field (V cm ') for the same conditions. (b) Time-averaged ionization rate for the same conditions as (a).
Fig. 13. (a) Ionization rate as a function of space and time during one rf. cycle for the same conditions as in Fig. 12, but without secondary electron emission (y=0), from a PIC-MC simulation. The lines correspond to contours of constant electric field (V cm ') for the same conditions. (b) Time-averaged ionization rate for the same conditions as (a).
Fig. 12. (a) Ionization rate as a function of space and time during one rf. cycle for a discharge in helium (3 Torr, gap length 3 cm, 9.2 MHz, applied voltage amplitude 300 V, secondary electron emission coeffi- cient y=0.2) from a PIC-MC simulation. The lines correspond to contours of constant electric field (V cm™') for the same conditions. (b) Time-averaged ionization rate for the same conditions as (a).
Fig. 12. (a) Ionization rate as a function of space and time during one rf. cycle for a discharge in helium (3 Torr, gap length 3 cm, 9.2 MHz, applied voltage amplitude 300 V, secondary electron emission coeffi- cient y=0.2) from a PIC-MC simulation. The lines correspond to contours of constant electric field (V cm™') for the same conditions. (b) Time-averaged ionization rate for the same conditions as (a).
Fig. 14. (a) Electron energy distribution function integrated between the abscissa 0.12 and 0.15 cm from the left electrode as a function of energy and time during one rf. cycle for the conditions of Fig. 12; parts of the distribution corresponding to electrons whose velocity is directed forwards (towards the plasma centre) or backwards (towards the electrode) are represented separately. (b) Electron distribution function of (a) displayed at the four different times indicated by the numbers (the contributions of forward and backward electrons are added). The units are the same for all curves.
Fig. 14. (a) Electron energy distribution function integrated between the abscissa 0.12 and 0.15 cm from the left electrode as a function of energy and time during one rf. cycle for the conditions of Fig. 12; parts of the distribution corresponding to electrons whose velocity is directed forwards (towards the plasma centre) or backwards (towards the electrode) are represented separately. (b) Electron distribution function of (a) displayed at the four different times indicated by the numbers (the contributions of forward and backward electrons are added). The units are the same for all curves.
Fig. 15. (a) Electron energy distribution function integrated around the abscissa 0.25 cm from the left electrode as a function of energy and time during one rf. cycle for the conditions of Fig. 13; forward and backward electrons are represented separately. (b) Electron distri- bution function of (a) displayed at the four different times indicated by the numbers (the contributions of forward and backward electrons are added). The units are the same for all curves.
Fig. 15. (a) Electron energy distribution function integrated around the abscissa 0.25 cm from the left electrode as a function of energy and time during one rf. cycle for the conditions of Fig. 13; forward and backward electrons are represented separately. (b) Electron distri- bution function of (a) displayed at the four different times indicated by the numbers (the contributions of forward and backward electrons are added). The units are the same for all curves.