N 2 capacitively coupled plasma—moment analysis of particle-in-cell modeling results

Abstract A one-dimensional particle-in-cell/Monte Carlo collision simulation study of nitrogen (N₂) capacitively coupled plasma (CCP) is presented for a pressure range between 0.1 and 1.5 Torr (13.33–199.98 Pa). The primary objective is to use moment analysis of charged-particle data to systematically examine the validity of commonly employed assumptions in fluid plasma models for intermediate-pressure CCPs. The voltage and pressure range investigated include the CCP operating in the α and γ modes as well as conditions with significant electron power absorption in the bulk plasma. At RF voltage V RF = 200 V (amplitude) and ion-induced secondary electron emission coefficient γ = 0.2, the bulk plasma region broadens with increasing pressure as a result of reduced electron and ion mean free paths. Electron power absorption increases in the bulk plasma at 0.5 Torr (66.66 Pa) and higher pressures, but it does not contribute significantly to plasma production. The plasma transitions from the α to γ-mode as V RF is increased from 200 to 350 V at 0.1 Torr (13.33 Pa) with significant lowering of T e and increase of electron density ( n e ) in the bulk plasma. The collision frequencies for individual electron impact reactions as well as the total collision frequency do not exhibit a straight-forward one-on-one relationship to electron temperature ( T e ) or total electron energy ( ϵ e ). This finding contrasts with the common assumption in fluid models for CCPs. Moment analysis of the momentum conservation equations reveals that the drift-diffusion approximation is valid for electrons in the bulk plasma and the pre-sheath region under both α - and γ -mode conditions. While ion momentum transport is dominated by sheath acceleration and collisional damping, the inertia term in the ion momentum equation is important at all pressures considered. The T e conservation equation indicates that power electrons gain from the electric field does not directly increase T e , which is instead governed by collisional energy exchange. The electron heat flux exhibits complex behavior and, consistent with previous reports, the Fourier heat condition assumption in fluid plasma models is found to be invalid. A comparison of moment equations in the α and γ modes at 0.1 Torr (13.33 Pa) shows that, while the overall structure of the moment equations remains consistent, electron energy and momentum exchange shift closer to the sheath edge in the γ -mode. Overall, this study demonstrates that the primary limitations of fluid models for intermediate-pressure CCPs are the assumptions used to relate electron transport coefficients, electron heat conduction, and electron impact reaction rates to T e or ϵ e . Accurate modeling of intermediate pressure CCPs therefore require incorporation of non-local and kinetic effects for electrons.