A Time‐Average Model of the RF Plasma Sheath

Abstract

A time‐average model of the RF plasma sheath was developed. The ion “fluid” equations were used with a frictional force to account for ion‐neutral collisions. Consideration of the collision dynamics showed that the frictional force may be taken as proportional to the square of the ion drift velocity. The sheath model was used to investigate the ion energy and flux on the electrodes of plasma reactors. The dimensionless quantity Co (collision number) was found to be important in describing the ion motion in the sheath. An analytical expression for the ion bombardment energy was derived, in terms of Co and the sheath voltage, for the range of parameter values typical of high pressure (∼1 torr) diode plasma etchers. An application of the model to an oxygen discharge in a parallel plate reactor was considered. Over the parameter range investigated, the ion bombardment energy was found to be only a few tens of eV, much lower than typical sheath voltages (∼200 V). The ion bombardment energy was found to be a function of the sheath electric‐field‐to‐pressure ratio. The model provides a framework that can be incorporated into more general plasma reactor models which consider transport and reaction phenomena along surfaces undergoing etching.