Speaker
Description
Plasma sheaths are non-neutral boundary layers that form adjacent to material surfaces
due to the higher mobility of electrons relative to ions, establishing a strong electrostatic field
normal to the boundary. Under steady-state (DC) conditions, sheath formation is governed by
the Bohm criterion, which requires ions to enter the sheath with a velocity exceeding a critical
value [1–3]. This time-independent limit provides a fundamental benchmark for more general
time-dependent sheath models.
In many practical plasma applications, electrodes are often driven by radio-frequency
(RF) sources, introducing explicit time dependence into the sheath dynamics through
oscillatory boundary conditions. In RF-driven sheaths, the sheath potential ∅s(t), sheath
width ds(t), and electric field E(x,t), vary periodically in time, leading to modulation of ion
acceleration and energy deposition at the boundary. The characteristic ion response depends
on the ratio of the RF frequency ω to the ion plasma frequency ωpi. For ω ≪ωpi ions respond
quasi-statically to the instantaneous sheath electric field, whereas for ω∼ωpi, ion motion
becomes significant and a fully time-dependent treatment is required. Many analytical RF
sheath models, therefore, rely on simplifying assumptions such as cold ions, negligible ion
inertia, or time-averaged electric fields, which restrict their validity in regimes where finite ion
temperature and pressure effects play an important role.
Motivated by these limitations, the present work develops a fully time-dependent fluid
model for collision-less RF plasma sheaths [4], incorporating ion pressure effects and driven
by a sinusoidal current source. The complete set of ion fluid equations is solved numerically
using a flux-corrected transport (FCT) algorithm to ensure stability and accuracy. An
equivalent circuit model is coupled self-consistently with the fluid equations to relate the
instantaneous sheath potential to the sheath thickness. The present model provides an enhanced
and self-consistent description of RF sheath dynamics, particularly in regimes where pressure
effects cannot be overlooked
