Microscopic theory of electron absorption by plasma-facing surfaces

Abstract

We describe a method for calculating the probability with which the wall of a plasma absorbs an electron at low energy. The method, based on an invariant embedding principle, expresses the electron absorption probability as the probability for transmission through the wall's long-range surface potential times the probability to stay inside the wall despite of internal backscattering. To illustrate the approach we apply it to a SiO2 surface. Besides emission of optical phonons inside the wall we take elastic scattering at imperfections of the plasma-wall interface into account and obtain absorption probabilities significantly less than unity in accordance with available electron-beam scattering data but in disagreement with the widely used perfect absorber model.

The effect of realistic heavy particle induced secondary electron emission coefficients on the electron power absorption dynamics in single- and dual-frequency capacitively coupled plasmas

“…These simplifications are made mainly due to the lack of reliable data on surface processes for various combinations of the discharge gas and electrode material (with different surface properties). However, the above mentioned simplifications are commonly encountered even in computational studies of those discharges for which experimental or theoretical data on specific surface processes are available in the literature [11][12][13][14][15][16].…”

Electron kinetics at the plasma interface

“…Utilizing the electron's large penetration depth at the energies of a few electron volts [47], typical for plasma applications, we showed that the chain of events described in the previous paragraph gives rise to a sticking probability S(E, ξ) which is the product of the probability T (E, ξ) for quantum-mechanical transmission through the surface potential and the probability to stay inside the surface despite of inelastic backscattering inside it [31,32]. To make the connection between absorption by and backscattering from the dielectric surface explicit, we recast the expression for S(E, ξ) in the form…”

“…with M open the number of forward scattering events at most possible for the initial energy E, ξ the initial direction cosine, and ω 1 m = (1+m)ω. The expansion coefficients Q 1 m (E; η|η ) satisfy a linear recursion relation, to be found in [31,32], which can be solved numerically quite efficiently for given values of E, η, and η .…”

“…Lateral momentum is thus not conserved and total reflection suppressed. In [31,32] we also considered this case, based on a simple model for interfacial scattering [51] which destroys the lateral homogeneity. We then found astonishingly good agreement between calculated values for S(E, ξ = 1) and data obtained from electronbeam scattering experiments on MgO [52] and SiO 2 [53] surfaces indicating that our approach captures the essential processes responsible for low-energy electron backscattering from electro-positive dielectrics.…”

Plasma sheath material induced dependence due to secondary electron emission

“…Further works aimed to show that it should not be the case 31 , while recent works showed it may actually happen for dirty metallic surfaces 32 . New theoretical models mixing surface and plasma physics showed that this feature may also exist for insulators 33 like Al 2 O 3 34 . This SEE at low impinging energy may have an influence on the sheath potential drop and reduce it by a factor 10% 34 .…”