Edge-to-center density ratios in low-temperature plasmas

The ion flux leaving a plasma at a boundary can be given by: Gamma(i) = h(L)n(0)u(B), where n(0) is the maximum central plasma density, u(B) is the Bohm velocity, and h(L) is the sheath edge-to-center plasma density ratio. Such hL factors have become synonymous with global modeling of plasma discharges, where they play a vital role in the prediction of plasma losses to bounding surfaces. By performing one-dimensional (1D) particle-in-cell simulations of inductively and capacitively coupled plasmas (ICPs and CCPs) over a wide pressure range, we explicitly test the validity of standard heuristic formulae commonly used to estimate hL. The ICP simulation results are found to be in very good agreement, while a large discrepancy is present for the CCP results at high pressures. The onset of this discrepancy is found to be correlated with the bulk-to-sheath edge ionization transition that occurs in CCPs at high pressures. Consequently, global models will strongly underestimate plasma losses in this regime.