Modeling of harmonic contributions to non-symmetrical RF plasmas

An analytical solution for the harmonic contributions to the 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 the effect of an arbitrary Nth harmonic sinusoidal current. The overall effect is determined by summing up the effects due to all the current harmonics. The expressions for the instantaneous and time averaged electric field within the sheath, the non-linear oscillation motion of the electron sheath boundary, the effective sheath impedance, the bulk plasma impedance and finally the overall plasma impedance are obtained. Experimental results are shown to be in good qualitative agreement with the theoretical model.