Analytic model for a dual frequency capacitive discharge

A homogeneous plasma model for dual radio-frequency (rf) discharges driven by two sinusoidal current sources has been analyzed. Under the assumptions of time-independent and collisionless ion motion and inertialess electrons, the analytic expressions for discharge parameters are obtained as a function of the effective parameters such as effective frequency, effective current, and effective voltage. Effective parameters are determined by the ratio of two currents or voltages. Two rf sources are generally coupled to each other through the plasma medium. It is also shown that the reduction of the bulk plasma length due to the sheath size has to be considered for calculating the discharge parameters since the sheath length is not always negligible compared to the bulk plasma length. Furthermore, the dependence of discharge parameters on the low frequency is presented.