A continuum model has been developed which successfully describes the concentration, movement, and energetics of charged particles within a rf discharge. This model includes continuity equations for all charged particles, Poisson’s equation to determine the local electric fields, and an electron energy balance to determine the ionization and energy-loss rates. All input parameters (diffusivity, mobility, ionization, and energy-loss rate) were defined using reported values determined in dc field experiments.
The transport of ions through rf glow-discharge sheaths was simulated with a Monte Carlo method to determine the distributions of ion-bombardment energy and angle of impact. Several sheath parameters were varied and their effects examined: (1) the type of ion-molecule scattering (hard sphere, potential field interaction, charge exchange), (2) the ratio of ion and neutral masses, (3) the ratio of the sheath width to collision mean free path, (4) spatially uniform, spatially linear, and time-dependent (rf) electric fields in the sheath, and (5) the frequency of an rf component in the sheath. The results of the Monte Carlo simulations indicate that the type of elastic scattering (hard sphere or soft sphere) does not significantly change either the impact angle distributions or the scaled ion-bombardment energy distributions. Charge-exchange scattering produces a much greater ion-bombardment directionality and a different shape of the ion-bombardment energy distribution. The fully developed distributions depend only on the ion-to-neutral mass ratio, type of ion-neutral scattering, and the dc value of the electric field-to-pressure ratio at the electrode. Fully developed distributions are reached in approximately three mean free paths in spatially uniform sheath fields and in about six mean free paths for spatially linear sheath fields. The minimum ion directionality was observed when the ion-to-molecule mass ratio was approximately unity. Time-dependent (rf) variation of the sheath field produces features in the ion energy distributions which are similar for both the collisional and collisionless sheaths.
A unit-cube geometry model is proposed to characterize the internal structure of porous carbon foam. The unit-cube model is based on interconnected sphere-centered cubes, where the interconnected spheres represent the fluid or void phase. The unit-cube model is used to derive all of the geometric parameters required to calculate the heat transfer and flow through the porous foam. An expression for the effective thermal conductivity is derived based on the unit-cube geometry. Validations show that the conductivity model gives excellent predictions of the effective conductivity as a function of porosity. When combined with existing expressions for the pore-level Nusselt number, the proposed model also yields reasonable predictions of the internal convective heat transfer, but estimates could be improved if a Nusselt number expression for a spherical void phase material were available. Estimates of the fluid pressure drop are shown to be well-described using the Darcy-Forchhiemer law, however, further exploration is required to understand how the permeability and Forchhiemer coefficients vary as a function of porosity and pore diameter.
The measurement and interpretation of ion bombardment energies in rf discharges of SF6, CF3Cl, and CF3Br from 0.2 to 1.0 Torr, are discussed. Errors in ion sampling due to disturbances of the electric field and neutral density around the sampling orifice are shown to be most important at higher pressures and with larger orifices. The dependence of the ion bombardment energy distribution on the electric-field-to-pressure ratio is reviewed. Combining this relation with a simple electrical model of a plasma gives estimates of the ion bombardment energies in collisional sheaths. The bombardment energy is proportional to (rf current)/(electrode area×frequency ×pressure) with the proportionality constant for a particular system depending on the collision cross sections and relative ion-to-netural mass ratio. The constants found for the three gases studied experimentally are close to theoretical estimates.
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