Determination of the equilibrium ion sheath in the drifting plasma by numerical Simulation

A one-dimensional (1-D) particle-in-cell (PIC) numerical method is developed to determine the equilibrium steady-state sheath width established in a drifting plasma. The simulated and measured steady-state sheath widths are in approximate agreement although the measured width is slightly larger than the simulated. The probe is biased to +90 V and this greatly influences the potential structure within the sheath boundary. The simulation shows that the mean-charge state and mean-atomic-mass approach to dealing with multiple ion species with a range of charge states does not accurately predict the position of the equilibrium sheath when the difference between the charge-to-mass ratios of the ion species is large. A more robust approach is to simulate the steady sheath by a 1-D-PIC method that can handle multiple ion species. In experimental situations where the sample stage is finite in size, the assumption that the equilibrium ion sheath expands from a biased plate of infinite extent may be violated. A two-dimensional PIC numerical method expressed in r-z cylindrical coordinates has been developed to investigate the condition where the 1-D assumption becomes inaccurate. The results confirm that the 1-D-PIC method becomes inaccurate when the steady-state sheath width has dimensions comparable with the sample stage diameter.