Dynamic sheath model at pulsed-biased insulating substrates

Characteristics of collisionless pulse-biased sheaths are studied with a one-dimensional fluid model coupled up to an equivalent circuit model. All the time-dependent terms are included in the ion fluid equations to ensure that the model can describe the sheath dynamics over a wide range of pulse frequency, especially in the intermediate pulse frequency range. The equivalent circuit model gives the instantaneous relationship between the sheath thickness and the surface potential at an insulating substrate placed on the pulse-biased electrode. The spatiotemporal variations of the potential, ion density and electron density inside the sheath are shown numerically. Additionally, the ion energy distributions arriving at insulating substrates and the charge density accumulated on insulating substrates are calculated with the model. It is shown that some parameters such as the pulse frequency, pulse duty ratio, and amplitude of the pulse voltage applied on the electrodes play an important role not only in determining the characteristics of the sheath dynamics and the ion energy distributions at insulating substrates but also in remedying the “surface charging effect.”