The boundary sheath of a low temperature plasma comprises typically only a small fraction of its volume but is responsible for many aspects of the macroscopic behavior. A thorough understanding of the sheath dynamics is therefore of theoretical and p
ractical importance. This work focusses on the so-called algebraic approach which strives to describe the electrical behavior of RF modulated boundary sheaths in closed analytical form, i.e., without the need to solve differential equations. A mathematically simple, analytical expression for the charge-voltage relation of a sheath is presented which holds for all excitation wave forms and amplitudes and covers all regimes from the collision-less motion at low gas pressure to the collision dominated motion at gas high pressure. A comparison with the results of self-consistent particle-in-cell simulations is also presented.
The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models whi
ch are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity.
The highly advanced treatment of surfaces as etching and deposition is mainly enabled by the extraordinary properties of technological plasmas. The primary factors that influence these processes are the flux and the energy of various species, particu
larly ions, that impinge the substrate surface. These features can be theoretically described using the ion energy distribution function (IEDF). The article is intended to summarize the fundamental concepts of modeling and simulation of IEDFs from simplified models to self-consistent plasma simulations. Finally, concepts for controlling the IEDF are discussed.
