Bulk plasma

As an example, we look at tire etching of silicon in a CF plasma in more detail. Flat Si wafers are typically etched using quasi-one-dimensional homogeneous capacitively or inductively coupled RF-plasmas. The important process in tire bulk plasma is tire fonnation of fluorine atoms in collisions of CF molecules witli tire plasma electrons... 

Some workers have correlated experimental data in terms of k at the arithmetic mean temperature, and some at the temperature of the bulk plasma. Experimental validation of the true effective thermal conductivity is difficult because of the high temperatures, small particle sizes and variations in velocity and temperature in plasma jets. 

The time-averaged potential profile is shown in Figure 4b. As ions cannot follow the oscillations in the applied electric field, it is this profile that ions experience. The bulk plasma is characterized by a constant potential, Vpi. In both sheaths (regions between plasma bulk and the electrodes), the ions experience a potential difference and are accelerated towards the electrodes. This leads to energetic ion bombardment of the electrodes. Electrons are expelled from the sheaths, so all ionization and dissociation processes must occur in the plasma bulk. Plasma light, resulting from emission from excited molecules, is emitted only from the plasma bulk the sheaths are dark. 

The frequency dependence of SHG at simple metal surface has been the focus of a recent theoretical study of Liebsch [100]. Time-dependent density functional theory was used in these calculations. The results suggest that the perpendicular surface contribution to the second harmonic current is found to be significantly larger than had been assumed previously. He also concludes that for 2 a> close to the threshold for electron emission, the self-consistently screened nonlinear electronic response becomes resonantly enhanced, analogous to local field enhancement in the linear response near the bulk plasma frequency. 

The experimental results were analyzed using an integrated approach. To obtain the temporal evolution of the temperature and the density profiles of the bulk plasma, the experimental hot-electron temperature was used as an initial condition for the 1D-FP code [26]. The number of hot electrons in the distribution function were adjusted according to the assumed laser absorption. The FP code is coupled to the 1-D radiation hydrodynamic simulation ILESTA [27]. The electron (or ion) heating rate from hot electrons is first calculated by the Fokker-Planck transport model and is then added to the energy equation for the electrons (or ions) in ILESTA-1D. Results were then used to drive an atomic kinetics package [28] to obtain the temporal evolution of the Ka lines from partially ionized Cl ions. 

First, the experimental results were compared with atomic-code calculations that assume a steady state in order to derive time- and space-averaged electron temperatures of the bulk plasma. In this calculation, Thot is assumed to be 50 keV and a to be 1%. C2H3C1 plasma with an ion density of 9 x 1022 cm 3 or Al plasma with a density of 6 x 1022/cm3 was used. Results are shown in Fig. 10.4a for Cl. Due to difficulties with spectrally isolating the Cl9+ O-like Ka line from C1+ Cl8+ lines, the intensity ratios are taken with respect... 

For both processes mentioned above, the bulk plasma characteristics (electron energy distribution function and plasma potential) are varied. It is thus difficult to distinguish whether the resulting film microstructure is controlled by processes in the plasma volume (for example different fragmentation of the monomer molecules) or by surface effects. 

In this study, we control the film growth solely by substrate surface processes, by varying Ug and/or Tg, without affecting the bulk plasma parameters. This is possible when a third electrode, used as the substrate holder, is placed in the plasma system as shown in Fig. 1. A small amount of RF power delivered to this electrode results in a bias potential Vg which controls bombardment of the growing films by low energy ions. If the area of this third electrode is substantially smaller than that of the main RF electrode, its presence does not appreciably influence the plasma characteristics this has recently been confirmed by actinometric optical emission spectroscopy (8). 

The effect of formoterol 18 micrograms on histamine-induced plasma exudation into sputum has been investigated in 16 healthy subjects in a double-blind, placebo-controlled, crossover study. Plasma exudation into the airways was produced by inhalation of histamine. Sputum was induced by inhalation of hypertonic (4.5%) saline. Induced sputum was obtained at baseline and then at 30 minutes and 8 hours after histamine inhalation. Sputum concentrations of alpha2-macroglobulin were measured as a marker of microvascular-epithelial exudation of bulk plasma. Histamine-induced plasma exudation 30 minutes after placebo was considerably greater than at baseline. The median difference was 11 pg/ml (95% Cl = 0.9, 90) expressed as alpha2-macroglobulin. The... 

Figure 10. Comparison of charge distributions for different types of boundary conditions for the same bulk plasma parameters. The Debye length is rn/o = 10 for (1) and (la), and rD/a = 2 for (2) and (2a). Dashed and solid lines relate to the BC (I) and (II), respectively.

Figure 11. Relative charge distributions versus ionization rates for BC (II) at a fixed bulk plasma density. The dimensionless intensity of plasma sources, io = Ioa6/Di is (1) 1.25-10-2 (2) 2.5 10-3 (3) 5 10-4 (4) 10-4. The bold line is the linear DH theory dashed line is DD approach for BC (I). The grain radius a/ro is 0.158.

The theory of van der Waals (vdW) surface interactions is presented here in terms of correlation-self energies of the constituent parts involved in the interaction due to their mutual polarization in the electrostatic limit. In this description the van der Waals interactions are exhibited using the dynamic, nonlocal and inhomogeneous screening functions of the constituent parts. In regard to the van der Waals interaction of a single molecule and a substrate, this problem is substantially the same as that of the van der Waals interaction of an atom and a substrate, in which the atomic aspects of the problem are subsumed in a multipole expansion based on spatial localization of the atom/molecule. As we (and others) have treated this in detail in the past we will not discuss it further in this paper. Here, our attention will be focussed on the van der Waals interaction of an adsorbate layer with a substrate, with the dielectric properties of the adsorbate layer modeled as a two-dimensional plasma sheet, and those of the substrate modeled by a semi-infinite bulk plasma. This formulation can be easily adapted to an... 

Fig. 5. Establishment of a DC sheath over a wall immersed in an infinite plasma. The sheath is separated from the bulk plasma by a presheath which is of the order of an ion mean free path (Aj) long. Top shows the electron (ne) and ion (nO density profiles. Bottom shows the potential () profile. After [6].

For simphcity, consider a plane wall immersed in an otherwise infinite plasma. Also, assume a time-independent plasma so that a DC sheath develops. The transition from the bulk plasma to the wall is shown schematically in Fig. 5, which shows the charge density (top) and potential profiles (bottom) [6]. The bulk plasma is electrically quasi-neutral with almost equal densities of positive and negative charges. The presheath is also quasi-neutral but the density of the charged species decreases from the bulk value. For an electropositive plasma (no negative ions), the electron (and ion) density at the sheath/presheath interface (sheath edge) is 61% of the bulk... 

Fig. 11. Ranges of kinetic energies and densities of species typically present in glow discharge plasmas. A=secondary electrons accelerated through the sheath, B=ions backscattered from cathode (most likely neutralized), C=ions accelerated towards cathode, D=electrons in bulk plasma, E=hot ions and neutrals formed in dissociation reactions (Frank-Condon effect), F=ions in bulk plasma, and G=neutral atoms and molecules. After [39].

The excitation rate profiles are shown in Fig. 24b. Substantial modulation is observed even deep in the bulk plasma. The excitation peak moves away from the left electrode and is washed into the bulk plasma as the left electrode potential goes through the negative zero crossing (t = 0.5), to the maximum negative potential t = 0.75), to the positive zero crossing (r = 0) and finally to the maximum positive... 

In order to be consistent with the Bohm criterion for ions, the sheath edge is defined as the point where the ions have been accelerated (presumably by the presheath electric field. Fig. 5) to the Bohm velocity, i.e. the presheath is included as part of the bulk plasma. The Bohm flux also provides a boundary condition (applied at the wall because of the thinness of the sheath) for the positive ion continuity equation. The negative ion density is assumed zero at the walls. 

Electroneutrality in the bulk plasma If one is not interested in resolving length scales of the order of the Debye length, the electroneutrality constraint in the bulk plasma is applicable. 

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