Electron surface layer at the interface of a plasma and a dielectric wall

Abstract

We study the plasma-induced modifications of the potential and charge distribution across the interface of a plasma and a dielectric wall. For this purpose, the wall-bound surplus charge arising from the plasma is modelled as a quasi-stationary electron surface layer in thermal equilibrium with the wall. It satisfies Poisson's equation and minimizes the grand canonical potential of wallthermalized excess electrons. Based on an effective model for a graded interface taking into account the image potential and the offset of the conduction band to the potential just outside the dielectric, we specifically calculate the modification of the potential and the distribution of the surplus electrons for MgO, SiO2 and Al2O3 surfaces in contact with a helium discharge. Depending on the electron affinity of the surface, we find two vastly different behaviors. For negative electron affinity, electrons do not penetrate into the wall and a quasi-two-dimensional electron gas is formed in the image potential, while for positive electron affinity, electrons penetrate into the wall and a negative space charge layer develops in the interior of the dielectric. We also investigate how the non-neutral electron surface layer -which can be understood as the ultimate boundary of a bounded gas discharge -merges with the neutral bulk of the dielectric.

Wall Charge and Potential from a Microscopic Point of View

“…Multiphonon processes contribute very little to it. Since the wall charge does not affect the relative line up of the potential just outside the dielectric and the bottom of the conduction band (potential just inside the dielectric), as mistakenly assumed in [24] but corrected in [28], this conclusion also holds for a charged dielectric wall with negative electron affinity. Relaxation after initial trapping depends on the strength of transitions from the upper bound states to the lowest bound state.…”

“…The basic idea [28] is to use a graded interface potential [32] to interpolate between the sheath and the wall potential and to distribute the surplus electrons making up the wall charge in this potential under the assumption that at quasi-stationarity they are thermalized with the wall [33]. We will now discuss how the spatial profile of the electron adsorbate normal to the crystallographic interface can be determined.…”

Absorption of an Electron by a Dielectric Wall

“…It utilizes two facts noticed by Cazaux [1]: (i) low-energy electrons do not see the strongly varying short-range potentials of the surface's ion cores but a slowly varying surface potential and (ii) they penetrate deeply compared to the lattice constant into the surface. The scattering pushing the electron back to the plasma occurs thus in the bulk of the wall suggesting the probability for the electron to get absorbed by it to be the probability for transmission through the wall's surface potential times the probability to stay inside the wall despite of internal backscattering.The variation of the potential across a floating dielectric wall can be calculated self-consistently [33]. For χ > 0 it gives rise to an energy barrier for electrons whose height on the plasma side is the Coulomb energy U w an electron has to overcome to reach the wall.…”

“…For χ > 0 it gives rise to an energy barrier for electrons whose height on the plasma side is the Coulomb energy U w an electron has to overcome to reach the wall. On the solid side the height is χ since for χ > 0 electrons entering the wall and making up its charge are surplus electrons occupying the wall's conduction band [33]. For the sticking probability it is the kinetic energy of the approaching electron in the vicinity of the wall which matters.…”

Scattering of infrared light by dielectric core-shell particles

“…12,13 In our previous work 14 we analyzed the extinction efficiency of this type of core-shell particles with an eye on using it in a low-temperature plasma as an electric probe with an optical read-out. The idea, originally put forward for homogeneous dielectric particles, 15,16 is to utilize the blue-shift of the anomalous dipole resonance due to the surplus electrons collected from the plasma as a diagnostics from which the charge of the particle and thus the floating potential at the particle's position in the plasma can be determined. Whereas for homogeneous particles the charge-induced shift is most probably too small to be of practical importance, core-shell particles show a much larger blue shift.…”