A time-dependent analytical sheath model for dual-frequency capacitively coupled plasma

The time-dependent model of the ion motion is used to study characteristics of dual-frequency (DF) capacitive sheaths. The model assumes that both the ion density and velocity vary with time, but time-derivative terms are neglected. Analytical expressions of the instantaneous electron sheath edge and the sheath potential are obtained with the assumption of a step-like electron density profile. It is shown that the present model can give monotonic spatial distributions of the sheath potential and ion density within the DF sheath. The dependence of the maximum sheath thickness and sheath voltage on the ratio of two frequencies or currents is also discussed