Choosing the Number of Elements in the Extra Dimension
The Number of elements in the Extra Dimension Settings must be enough to resolve the period evolution of the electric excitation. A minimum of 30 mesh elements per period in the extra dimension is recommended. In some discharges the current and the voltage at the electrodes departs from being a sinusoidal and fine structure might appear. An example of this is a discharge where the electron current contributes significantly to the total current when the sheath collapses. This leads to a burst of electron current that needs to be resolved and consequently more mesh elements in the extra dimension are needed.
When using multiple frequencies to sustain a discharge the number of elements in the extra dimension needs to increase in order to resolve the highest frequency. For a dual frequency CCP reactor with an applied voltage of the from
(6-21)
with a low frequency fl of 2 MHz and a higher frequency fh of 60 MHz one needs 900 mesh elements in the extra dimension in order to have 30 mesh elements per period of the high frequency. Figure 6-4 and Figure 6-5 show the signal of Equation 6-21 with different resolutions. When using 100 and 300 elements in the extra dimension the high frequency signal only has 3 and 10 elements per period, respectively, leading to poorly resolved signals.
When using multiple excitation frequencies with frequencies far apart from each other, the number of elements in the extra dimension and consequently the number of degrees of freedom increases dramatically, leading to computationally expensive simulations. In these cases, it is recommended to use a 1D model to know how much resolution of the highest frequency signal is needed to capture all the necessary physics.
Figure 6-4: Dual frequency voltage for one period of the low frequency with 100 and 900 mesh elements in the extra dimension.
Figure 6-5: Zoom of Figure 6-4 with the addition of a case with 300 mesh elements in the extra dimension.