An algebraic RF sheath model for all excitation waveforms and amplitudes, and all levels of collisionality

Ralf Peter Brinkmann, Abd Elfattah Elgendy, Homayoun Hatefinia, Mohammed Shihab, Torben Hemke, Alexander Wollny, Denis Eremin, Thomas Mussenbrock

66th An­nual Ga­se­ous Elec­tro­nics Con­fe­rence (GEC), Prin­ce­ton (New Jer­sey), USA, 30 Sep­tem­ber - 04 Oc­to­ber


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.Athorough understanding of the sheath dynamics is therefore of theoretical and practical 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 particlein- cell simulations is also presented.

?Deutsche Forschungsgemeinschaft DFG via SFB TR 87.