Vlasov simulation of the emissive plasma sheath with energy-dependent secondary emission coefficient and improved modeling for dielectric charging effects

Abstract

A one-dimensional Vlasov–Poisson simulation code is employed to investigate the plasma sheath considering electron-induced secondary electron emission (SEE) and backscattering. The SEE coefficient is commonly treated as constant in a range of plasma simulations; here, an improved SEE model of a charged dielectric wall is constructed, which includes the wall charging effect on the SEE coefficient and the energy dependency of the SEE coefficient. Pertinent algorithms to implement the previously mentioned SEE model in plasma simulation are studied in detail. It is found that the SEE coefficient increases with the amount of negative wall charges, which in turn reduces the emissive sheath potential. With an energy-dependent SEE coefficient, the sheath potential is a nonlinear function of the plasma electron temperature, as opposed to the linear relation predicted by the classic emissive sheath theory. Simulation combining both wall-charging effect and SEE coefficient’ energy dependency suggests that the space-charged limited sheath is formed at high plasma electron temperature levels, where both sheath potential and surface charging saturate. Additionally, different algorithms to implement the backscattering in the kinetic simulation are tested and compared. Converting backscattered electrons to secondary electrons via an effective SEE coefficient barely affects the sheath properties. The simulation results are shown to be commensurate with the upgraded sheath theory predictions.

Tailoring Organic/Inorganic Interface Trap States of Metal Oxide/Polyimide toward Improved Vacuum Surface Insulation

“…Sub-surface charge migration is regulated by the trap states, which affects the above-surface process of flashover development, including SEEA, surface charging, and outgassing, and ultimately determines the surface insulation. On the one hand, the trap density and energy levels could affect the SEY by changing the trapping escape mean free path and probability of the internal SEs excited by the incident electrons (Figure d). , It has been demonstrated that the increase in trap density always yields lower SEE for a positively charged dielectric surface, which is preferable for better surface insulation. Deep trap states mainly impede surface charge emission to alleviate the surface charging and hence increase flashover voltage, which is more pronounced with higher deep trap state density and the trap energy level.…”

“…Deep trap states mainly impede surface charge emission to alleviate the surface charging and hence increase flashover voltage, which is more pronounced with higher deep trap state density and the trap energy level. The trapping mean free path of internal SEs, excited by the primary electrons, is proportional to ( n T σ T ) −1 with n T and σ T , the trap density and trapping cross-section . The deep trap energy level mainly acts on the trapping cross-section, but a quantitative relation remains elusive.…”

“…The trapping mean free path of internal SEs, excited by the primary electrons, is proportional to (n T σ T ) −1 with n T and σ T , the trap density and trapping cross-section. 67 The deep trap energy level mainly acts on the trapping cross-section, but a quantitative relation remains elusive. On the other hand, the trap states contribute to surface charging by affecting the transport of charge carriers in the dielectric surface layer, which contributes to the electric field in vacuum and thus affects the flashover voltage.…”

Surface flashover in 50 years: Theoretical models and competing mechanisms

“…In one mechanism, the emission of electrons is suppressed by the increase in energy depth and density of deep surface traps. Said et al [173] first established a relation between the SEE current density and trap level [174], and then the model was developed by Sun and Zhang et al, they indicated the SEE yield significantly decreased with the trap cross section (level) and density. Since the traps capture carriers that migrate on the surface, the surface flashover voltage increases.…”

An alternative simulation approach for surface flashover in a vacuum using a 1D2V continuum and kinetic model

“…To form the SEEA, SEE on the insulator is indispensable. The treatment of the SEE process here is different from the previously used averaged SEEY for all electrons in emissive sheath studies [55,64], instead a SEEY matrix δe of dimension dvx × dvy is constructed, with dvx and dvy the grid number in vx and vy direction. The matrix δe represents SEEY of each element (v x,i , v y,j ) in phase space.…”