Plasma modeling for a nonsymmetric capacitive discharge driven by a nonsinusoidal radio frequency current

Abstract

An analytical solution for the sheath dynamics of an asymmetrically driven capacitively coupled plasma is obtained under the assumptions of time-independent, collisionless ion motion, inertialess electrons, and uniform current density. Modeling is performed considering that the plasma is driven by a nonsinusoidal radio frequency ͑rf͒ current which can be resolved into a finite number of harmonic components. Together with different sheath parameters the equation for the bulk plasma impedance is also obtained to calculate the overall plasma impedance and the overall rf voltage. Assuming equal plate areas the solution for a symmetric discharge is also obtainable from this model. We have found that the even harmonic components of rf voltage and impedance are always present, even in a symmetric discharge. Experimental results are shown to be in qualitative agreement with the theoretical model. The values of normalized rf voltage and impedance harmonics assume lower values as the asymmetry of the plasma chamber decreases.

Influence of electrodes area ratios and the discharge volume in RF capacitively coupled plasma

“…The distortion in the current wave comes from the nonlinearity which creates by the two sheaths near the two electrodes. When the area of the two electrodes are unequal and the ratio between the two electrodes area not equal one, this condition of CCP discharge usually called the asymmetric (nonsymmetric) discharge [2,4,15]. In the symmetry discharge the two sheaths are equal, due to equality of the areas ratio for the two electrodes are equal one, the influence of the nonlinearity which is generated by the sheath at one of the two electrodes, the other electrode will be generated the same effect but in the opposite direction [3,4,15].…”

“…Asmussen et al, [14] presented and showed the effect of the capacitor size and input pump power on the parametric interaction. Dewan et al, [15] studied the harmonics which associated with the fundamental frequency in nonsymmetry (asymmetry) discharges in current wave and confirmed the most of the CCP discharges are asymmetry. Theoretical and modeling for symmetric and asymmetric RF discharges were presented by work on the generated harmonics.…”

Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges

“…It is thus clear that on the plasma side (z < s(t)), the quasi-neutrality holds (n e ∼ n i ), while on the sheath side (z > s(t)), the electron density falls very rapidly (n e ∼ 0). Many studies dealing with the structure of cc-rf sheath therefore use this approximation known as the step model which has been extensively used in different models of cc-rf sheath [27][28][29][30][31][32][33]35]. In many of these models, the solution of the rf sheath relies on calculating the rf current through the sheaths (powered and grounded) and assuming a zero net current [27][28][29][30]33].…”

“…Many studies dealing with the structure of cc-rf sheath therefore use this approximation known as the step model which has been extensively used in different models of cc-rf sheath [27][28][29][30][31][32][33]35]. In many of these models, the solution of the rf sheath relies on calculating the rf current through the sheaths (powered and grounded) and assuming a zero net current [27][28][29][30]33]. It allows one to calculate the position of the electron sheath at all times and from there the other quantities such as the average potential drop and average electric field in the sheath can be derived.…”

“…for both symmetric [27][28][29] and asymmetric discharges [30,33]. It was nevertheless shown that, in the case of symmetric cc-rf discharges, these models were able to accurately describe the current-voltage characteristics but showed discrepancies in the potential and electric field profiles with respect to the exact solution [31].…”