Absorption of an Electron by a Dielectric Wall

Abstract

We introduce a method for calculating the probability with which a low-energy electron hitting the wall of a bounded plasma gets stuck in it and apply the method to a dielectric wall with positive electron affinity smaller than the bandgap using MgO as an example. In accordance with electron beam scattering data we obtain energy-dependent sticking probabilities significantly less than unity and question thereby for electrons the perfect absorber assumption used in plasma modeling.PACS numbers: 68.49. Jk, 79.20.Hx, 52.40.Hf The interaction of electrons with surfaces plays a key role in applied science. Various methods of surface analysis [1][2][3] are based on it as well as a number of materials processing techniques [4]. In these applications the electron energy is above 100 eV and backscattering and secondary electron emission, the physical processes involved, are sufficiently well understood [5][6][7][8][9][10][11][12]. The situation is different for electron-surface interaction at energies below 100 eV, as it occurs in dielectric barrier discharges [13][14][15], dusty plasmas [16][17][18][19][20], Hall thrusters [21,22], and electric probe measurements [23]. Much less is quantitatively known about it, especially at very low energies, below 10 eV. For instance, the probability with which a low-energy electron gets stuck in the wall after hitting it from the plasma is unknown. In the modeling of bounded plasmas [24][25][26][27][28] it is assumed to be close to unity, implying for electrons the wall is a perfect absorber [29], irrespective of the material. Since electron absorption and extraction (by charge-transferring heavy particle collisions) control the wall potential, and hence the plasma sheath, which in turn affects the bulk plasma, the electron sticking probability is a crucial parameter. That its magnitude matters and should be known precisely has been recognized most clearly by Mendis [20] in connection with grain charging in dusty plasmas but the theoretical work [30,31] he refers to is based on classical mechanics not applicable to electrons.In this work we apply quantum mechanics to calculate the probability with which a low-energy electron is absorbed by a surface. We couch the presentation in a particular application: The calculation of the electron sticking probability at room temperature for a dielectric wall [32] with positive electron affinity χ smaller than the bandgap E g . But the approach is general and can be also applied to other cases. 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 desp...

Strongly Emitting Surfaces Unable to Float below Plasma Potential

“…The influx is recorded at the minimum of φ(x) so that if an emission barrier is present, the returned electrons Γ eret do not induce emission (although repeated reflections of the low energy electrons could be possible for some materials in light of Ref. [26]). …”

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…”

“…The interaction of electrons with surfaces is central for a great variety of surface diagnostics as well as materials processing techniques. It has been studied in great detail (see references in [31,32]). This knowledge however is not of immediate use for the modeling of electron-surface interaction in plasma applications, such as, dielectric barrier discharges, Hall thrusters, or the divertor region of fusion plasmas.…”

“…In [31,32] we derived the recursion relation for the function Q(Eη|E η ) under the assumption that the dielectric surface is at room temperature and the impinging electron has initially an energy E < E g , where E g is the band gap of the dielectric. The first assumption implies that the scattering occurs primarily due to emission of optical phonons while the second assumption guarantees that Coulomb-driven electron energy dissipation can be ignored.…”

Towards an integrated modeling of the plasma-solid interface

“…[210] and their stopping in the solid, as well as the electron dynamics across the interface, e.g. [20]. Here nonequlibrium quantum methods such as the quantum Boltzmann equation, density functional theory and nonequlibrium Green functions simulations, e.g.…”