Research On Hydrodynamics Simulations Of Radio-frequency And Pulse-Biased Plasma Sheaths

In this paper, a self-consistent fluid model of a collisionless rf modulated sheath has been developed for studying the spatiotemporal characteristics of the sheath and predicting the energy distributions(IEDs) of ions impinging on a rf-bias electrode. The model includes all time-dependent terms in the ion fluid equations, which is valid for arbitrary frequency ratio β. Moreover, the instantaneous relationship between the voltage on the rf-bias electrode and the sheath thickness is determined by an equivalent circuit model with a time-dependent ion current on the electrode. It has been shown from the numerical results that in the low rf-frequency regime (β<<1) the ion flux on the electrode oscillates strongly with the time and its amplitude drops gradually as increasing the frequency ratio β, while the ion flux approaches the constant flux at the high-frequency limits (β>>1 ). It have been found that the instantaneous variations of the sheath thickness and the voltage wave form on the electrode are almost synchronous, the spatiotemporal variations of the potential and the electric field within the sheath are very significant in the vicinity of the electrode, and the spatial drop of the ion density in the sheath is monotonous. Finally, with obtained ion flux, we have calculated the IEDs on the electrode and found that the IEDs has a bimodal shape and the width of the IED shrinks and the two peaks of the IED approach each other with increasing the rf-frequency. Besides, the locations and heights of the two peaks in the IED are also affected by the rf-bias power. In conclusion, the frequency ratio β = ω/ωpi is a crucial parameter for determining the sheathcharacteristics, the sheath voltage waveform, and the shape of the IEDs.With an one-dimensional multiple ion dynamics model, we study characteristics of the collisionless rf sheaths in fluorocarbon plasmas and calculate the IEDs impinging on rf-biased electrodes. The numerical results show that, due to the existence of multi-ion species, the sheath structure in the present work is different from those of single ion species plasmas, and multiple peaks appear in the ion energy distributions. It is also shown that some parameters such as the bias frequency, bias power, bulk plasma density and electron temperature are crucial for determining the shape of the ion energy distribution in multicomponent plasmas. In particular, it has been found that the low- or high-energy peaks split into many small peaks due to the existence of ions with different mass. As increasing the rf-bias frequency, the energy splits in the energy peaks become indistinguishable.Characteristics of collisionless pulse-biased sheaths are studied with a one-dimensional self-consistent time-dependent fluid model coupled up to an equivalent circuit model. 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 IEDs 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 IEDs at insulating substrates but also in remedying the "surface charging effect".With the one-dimensional fluid model coupled to an equivalent circuit model built before, the characteristic parameters of the rf sheaths and pulse-biased sheaths, such as the time-dependent surface potential and sheath thickness as well as spatiotemporal variations of the potential, ion density and electron density are compared. Furthermore, the IEDs arriving at insulating substrates and the charge density accumulated on insulating substrates are also calculated with the...