Two-dimensional fluid model of high density inductively coupled plasma sources

Abstract

A two-dimensional (r,z) fluid model has been developed to study plasma transport in inductively coupled plasmas (ICP). Electron heating is treated by assuming a fixed, spatially varying power deposition profile in the electron energy balance equation. A high aspect ratio ICP reactor geometry has been studied, with two assumed power profiles: spatially uniform and localized to within several skin depths of the radial wall. The effect of neutral gas pressure on plasma uniformity is presented for an argon discharge over the range of 1–20 mTorr. Comparisons between the fluid model and predictions from a spatially averaged global model show similar scaling of plasma density, electron temperature, and plasma potential over a wide range of pressure and power.

Self-consistent kinetic modeling of low-pressure inductively coupled radio-frequency discharges

“…4 Straightforward numerical simulation using Monte Carlo treatment of electrons is a computationally very demanding task. 5 The fluid model or some hydrodynamic approach, 6,19 which treats the electron gas as a fluid characterized by density, velocity, and mean energy, can give only a rather crude description of phenomena. Comparatively fast yet effective kinetic modeling of ICP has recently been developed by Kortshagen and Tsendin.…”

A New Unconditionally Stable Algorithm for Steady-State Fluid Simulation of High Density Plasma Discharge

“…In fluid simulation of steady state, it is desirable to take a time step close to Courant time step which is larger than ω −1 p or τ d . Several methods to overcome the limitation on the simulation time step are suggested [2][3][4]. In [2,3], they used time step larger than τ d using a semiimplicit solution of Poisson's equation.…”

“…For transport modeling of high density plasma discharge, fluid simulation [2][3][4] has been extensively used to study discharge characteristics, because the global insight on the profiles of quantities such as densities, temperatures, fluxes, and potential can be obtained. But for a stable fluid simulation of high density plasma, there are severe restrictions on the time step ( t) and the grid size ( z), because the shielding time scale of an electric field perturbation is very short, and the sheath length is quite small.…”

Numerical solution of plasma fluid equations using locally refined grids

“…Solving Poisson's equation with explicitly advected electrons would force the use of an extremely small timestep due to the dielectric relaxation limit [2], [12]. A tight coupling of the electron density and potential is assured by including the drift flux with the Laplacian operator, forming a modified Poisson equation.…”