Third-order transport coefficients for electrons in N₂ and CF₄: effects of non-conservative collisions, concurrence with diffusion coefficients and contribution to the spatial profile of the swarm

Abstract

Using a multi-term solution of the Boltzmann equation and Monte Carlo simulation technique we study behaviour of the third-order transport coefficients for electrons in model gases, including the ionisation model of Lucas and Saelee and modified Ness-Robson model of electron attachment, and in real gases, including N2 and CF4. We observe negative values in the E/n 0-profiles of the longitudinal and transverse third-order transport coefficients for electrons in CF4 (where E is the electric field and n 0 is the gas number density). While negative values of the longitudinal third-order transport coefficients are caused by the presence of rapidly increasing cross sections for vibrational excitations of CF4, the transverse third-order transport coefficient becomes negative over the E/n 0-values after the occurrence of negative differential conductivity. It is found that the accuracy of the two-term approximation for solving the Boltzmann equation is sufficient to investigate the behaviour of the third-order transport coefficients in N2, while for electrons in CF4 it produces large errors and is not even qualitatively correct . The influence of implicit and explicit effects of electron attachment and ionisation on the third-order transport tensor is investigated. In particular, we discuss the effects of attachment heating and attachment cooling on the third-order transport coefficients for electrons in the modified Ness-Robson model, while the effects of ionisation are studied for electrons in the ionisation model of Lucas and Saelee, N2 and CF4. The concurrence between the third-order transport coefficients and the components of the diffusion tensor, and the contribution of the longitudinal component of the third-order transport tensor to the spatial profile of the swarm are also investigated. For electrons in CF4 and CH4, we found that the contribution of the component of the third-order transport tensor to the spatial profile of the swarm between approximately 50 Td and 700 Td, is almost identical to the corresponding contribution for electrons in N2. This suggests that the recent measurements of third-order transport coefficients for electrons in N2 may be extended and generalized to other gases, such as CF4 and CH4.

Scanning drift tube measurements and kinetic studies of electron transport in CO

“…where n(r, t) is the electron number density, ν eff = ν i − ν a , the effective ionization frequency is the difference of the ionization (ν i ) and attachment (ν a ) frequencies, W is the bulk drift velocity, and D is a bulk diffusion tensor with two independent components, the bulk longitudinal diffusion coefficient, D L and the bulk transverse diffusion coefficient, D T . The present experimental measurements were carried out under conditions where the effects induced by higher order transport coefficients are negligible, limiting the diffusion equation to drift and diffusion only [79,80].…”

Science-based, data-driven developments in plasma processing for material synthesis and device-integration technologies

“…95,96) The third-order transport coefficients for electrons in N 2 and CF 4 were discussed. 97) To date, 2D simulations of ICPs of Ar/CF 4 /O 2 mixtures for etching applications showed the results of spatially and temporally plasma density and energy-resolved ion and radical fluxes towards surface. [98][99][100] The plasma kinetics of perfluorocyclobutane (c-C 4 F 8 ) was modeled using a selfconsistent plasma fluid simulation model.…”