Validation of the smooth step model by particle-in-cell/Monte Carlo collisions simulations

TL;DR

This paper validates the smooth step model for plasma sheaths by comparing its analytical predictions with detailed particle-in-cell/Monte Carlo simulations, demonstrating good agreement under certain conditions.

Contribution

It provides the first validation of the smooth step model against PIC/MC simulations, confirming its accuracy in describing plasma sheaths.

Findings

Good quantitative agreement with simulations when assumptions are met

Model remains applicable under marginal assumptions

Provides a practical analytical tool for sheath analysis

Abstract

Bounded plasmas are characterized by a rapid but smooth transition from quasi-neutrality in the volume to electron depletion close to the electrodes and chamber walls. The thin non-neutral region, the boundary sheath, comprises only a small fraction of the discharge domain but controls much of its macroscopic behavior. Insights into the properties of the sheath and its relation to the plasma are of high practical and theoretical interest. The recently proposed smooth step model provides a closed analytical expression for the electric field in a planar, radio-frequency modulated sheath. It represents (i) the space charge field in the depletion zone, (ii) the generalized Ohmic and ambipolar field in the quasi-neutral zone, and (iii) a smooth interpolation for the transition in between. This investigation compares the smooth step model with the predictions of a more fundamental particle-in-cell/Monte Carlo collisions simulation and finds good quantitative agreement when the assumed length and time scale requirements are met. A second simulation case illustrates that the model remains applicable even when the assumptions are only marginally fulfilled