Multi-Fluid Transport/Reaction Models with Application in the Modeling of Weakly Ionized Plasma Dynamics

Abstract

The industrial use of low-ambient-temperature, weakly ionized plasmas as a reaction environment is growing rapidly. This is primarily evident in the manufacturing technologies of advanced materials, such as the ones used in micro-electronic devices [Jensen, 1987]. The advantages of the plasma environment are due primarily to the presence of high energy electrons which allow high energy chemistry to take place at low ambient temperatures. An example is the successful plasma-enhanced chemical vapor deposition of silicon nitride at temperatures as low as 250-350°C versus temperatures in the range of 700-900°C required for thermal deposition [Reif, 1984]. Thus emerges a need for modeling of the reaction chemistry and the transport phenomena within complex, multicomponent, charged-particle systems, under the influence of externally-imposed electric and magnetic fields. The present chapter addresses this need within the framework of a multi-fluid reactive continuum [Woods, 1975, ch. 9]. Multi-fluid continuum descriptions have arisen as a natural generalization of multicomponent systems in order to account for the absence of momentum and/or energy equilibria between different species populations within the same system [Enz, 1974; Woods, 1975, ch. 9]. The key underlying assumption is that of interpenetrating continua: each one of the mutually interacting, constituent subsystems is characterized as a separate continuum with its own (macroscopic) state variables. Hidden within this assumption is the local equilibrium hypothesis, not between different subsystems—that would have resulted in the more traditional multicomponent description—but within each subsystem in order for the description of each subsystem using (equilibrium) state variables to be meaningful. This is both an asset and a liability of the multi-fluid approach: an asset, because the whole framework of equilibrium thermodynamics is still applicable at the subsystem level, resulting, among other things, in a description requiring only a few well-defined macroscopic state variables; a liability, because it places very stringent requirements on the type of systems to which this theory can be applied. The multi-fluid approach is valid only for phenomena with characteristic time scales much larger than the time scale for each subsystem to reach internal (local) thermodynamic equilibrium.