Stochastic electron energy gain under sheath electric field near sidewall of chamber to drive inductively coupled magnetized plasmas

Abstract

Single-electron motions near the sidewall of a chamber to drive a type of inductively coupled magnetized plasmas are analyzed using a Monte Carlo method in a simulation model with sheath electric field (E sh ) to understand the mechanism of electron energy gain (EEG). The analysis reveals that the E × B drift caused by E sh , along the rf electric field induced in parallel to the sidewall, makes the EEG high and asymmetric between the first and second halves of an rf period. We observe spatial distributions of the EEG as a function of the distance from the wall under several sheath conditions. The EEG is higher under higher E sh and high EEG values are more concentrated in the sheath whose potential gradient is larger. Finally, observation of the phase-resolved EEG distributions demonstrates statistically that the EEG mechanism found in stochastic individual electron behaviors also works for a majority of electrons.

Analysis of electron heating due to partial resonance in an inductively coupled plasma under confronting divergent magnetic fields

“…It has been reported that a plasma sheath near the sidewall enhances the EEG. 33) Then, we adopt a simplified sheath model assuming a time-invariant sheath electric field E S with a constant sheath thickness d S and a constant voltage drop V S . This model represents the electrical neutrality of the plasma bulk and a situation that the charged particles have formed a kind of steady-state distribution.…”

“…On the high EEG near the sidewall, it has been reported that the directionality of the azimuthal electron drift caused by the electron reflection at the sidewall contributes to the EEG stochastically, 18) and the EEG is enhanced in the presence of the sheath electric field. 33) As R A increases, the amount of energy supplied to electrons in the chamber increases, the region of high EEG becomes wider, and the EEG in the resonant region tends to increase. Figure 6 shows the EEG in B(t) with B DC at 600 AT.…”

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

“…The behavior of the majority of electrons was determined by individual electrons that gained energy stochastically. 81) The azimuthal velocity of electron motion in a cylindrical chamber under an RF electric field and confronting divergent magnetic fields was simulated to evaluate the phase-resolved profiles of power deposition on electrons in a low-pressure inductively coupled magnetized plasma. 82) The average velocity of electron motion under crossed fields of alternative current (AC) electric and DC magnetic components was formulated analytically.…”

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

“…In addition, transport coefficients are required in the swarm procedure for determining the complete and consistent sets of cross-sections for collisions of charged particles with atoms and molecules of the background fluid [39][40][41][42]. These sets of cross-sections are employed as input data into the particle models of non-equilibrium plasma [43][44][45][46][47][48][49]. Due to the sensitivity of plasma models to transport coefficients and cross-section sets in the case of fluid and particle models, respectively, a great amount of attention has been dedicated to the calculation and measurement of transport coefficients of electrons and ions in numerous atomic and molecular gases.…”