| This research develops a novel, non-dissipative discretization for the drift-diffusion expression of electron flux in capacitively-coupled, radio-frequency plasma discharges. The new discretization is more robust and accurate than commonly used numerical techniques when applied to the solution of the plasma fluid equations. On a relatively coarse grid, the method provides results within a few percent of the grid-converged solution. Low-order upwinding, a common method for discretization of the electron flux; introduces significant robustness. However, on the same coarse grid, the plasma density can differ from the grid-converged result by nearly a factor of two. Another popular discretization of the electron flux is the Scharfetter-Gummel method. Although it is accurate on coarse grids, it is more expensive computationally due to its non-linear nature, and it introduces an additional approximation. It neglects the electron temperature gradient in the flux expression; this can affect the plasma density as much as 20%.; A formal method for accelerating the solution towards the periodic, steady-state solution in one and multiple dimensions is also described. Direct integration of the governing equations in time will lead to the harmonic steady-state, but this may require tens or hundreds of thousands of radio-frequency periods when the plasma discharge contains significant neutral species that develop on a time-scale much longer than a radio-frequency period. In contrast, the acceleration scheme can reach the periodic steady-state in a few hundred to a few thousand radio-frequency periods. Previous efforts that used formal acceleration schemes were limited to one dimension.; Finally, a fluid model of an argon plasma is developed and compared to experimental data at conditions relevant to low-pressure, capacitively-coupled plasma discharges. The computed results agree reasonably well with the experiments both quantitatively and qualitatively. This model is then used to investigate the impact of an alternative method of pulsed, capacitively-coupled power deposition in the plasma discharge. Proper application of power to the plasma can result in greater ion flux uniformity and a lower average electron temperature, which are desirable characteristics in plasma processing. |
