Collapsing Behaviors of Plasma Sheath Driven by Voltage Pulse With Variable Width and Fall Time

Dynamics of an ion sheath appearing on a negatively biased electrode in plasma is a key physical issue in many plasma processes including the plasma-based ion implantation and deposition (PBIID). In this article, we have investigated the correlation of the width $t_{w}$ and the fall time $t_{f}$ of the voltage pulse with the time for the ion sheath collapse $t_{\mathrm {col}}$ and the time for the plasma recovery $t_{\mathrm {rec}}$ by changing $t_{w}$ from 5 to $40~\mu \text{s}$ and $t_{f}$ from 0.24 to 133 Ms. When the voltage pulse terminates, the sheath collapse happens by influx of neutralizing electrons and is followed by the plasma recovery driven by expansion of the adjacent plasma. It is found that the sheath collapse depends on $t_{f}$ relative to the characteristic time for plasma ions to traverse the maximum sheath thickness, $(t_{w})/u_{B} ~[s(t_{w})$ : the maximum sheath thickness and $u_{B}$ : the Bohm speed]. If $t_{pi}\ll s(t_{w})/u_{B}< t_{f}$ ( $t_{pi}$ : the period of the ion plasma oscillation), the sheath collapse and the plasma recovery advance simultaneously with a time constant of $t_{\mathrm {col}}=t_{\mathrm {rec}}=(4/3)t_{f}$ . If $t_{w}\gg t_{pi}$ and $t_{f}< t_{pi}$ , $t_{\mathrm {rec}}$ becomes much longer than $t_{\mathrm {col}}$ . As a result, a considerable time is required till the initial plasma density profile is recovered between voltage pulses that may affect the maximum repetition frequency of the PBIID system.