Dependence of the self-bias on the plasma parameters and on the electrode areas in RF plasma reactors

From the current-voltage characteristics for the collisionless sheath the dependence of the self-bias on the plasma parameters (electron temperature, ratio of electron temperatures and electron densities at the two electrodes), on the applied external voltage, and on the ratio of the electrode areas is investigated. Sinusoidal (is well as periodic rectangular and triangular time dependences of the voltage are considered. The integral equation for the self bias voltage is solved numerically. For large external RF voltages in comparison to the floating potential, simple analytical formulas result for the dependence of the bias voltage on the plasma parameters and the dimensions of the electrodes, which can be useful in practice.