Kinetics of electric double layers at dielectric plasma-facing solids

• Applicant: Privatdozent Dr. Franz Xaver Bronold
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 407495057

• Final Report Year: 2022

Final Report Abstract

The project developed first steps towards a microscopic description of the most fundamental manifestation of the interaction of a solid with a plasma: the build-up of an electric double layer in response to the net accumulation of electrons inside the solid due to electron capture and electron loss via recombination of ions. The net negative charge inside the solid triggers the electron-depleted region in front of the surface, the plasma sheath, which has been studied since the beginning of plasma physics. The physics of the wall charge, however, remains a terra incognita. Little is hence known about the plasma loss inside the surface, which for dielectrics has to occur by electron-hole recombination. To gain insights into the microscopic linking of plasma production inside a gas to plasma loss inside a dielectric, we developed a kinetic theory for charge transfer across a plasma-solid interface. It is based on two sets of Boltzmann equations, one for the electron and ion distribution functions of the plasma and one for the conduction band electron and valence band hole distribution functions of the dielectric, the Poisson equation for the electric potential energy, and matching/boundary conditions for these quantities at the interface/far away from it. Collisions inside the solid are explicitly taken into account, whereas the plasma is assumed collisionless, with plasma production modelled by selfconsistently coupling the plasma sheath to a charge-neutral, field-free bulk region. Due to limitations of computational resources, we could not incorporate the full band structure of the dielectric, nor could we treat all the scattering processes possibly taking place inside the solid. For model dielectrics, however, we could study how the electron microphysics of the solid affects the electric response of the interface. Specifically for a floating interface, we studied the interplay of plasma production in the gas and plasma loss due to nonradiative electron-hole recombination inside the dielectric. We also demonstrated thereby a viable numerical route for bringing the three selfconsistency loops, to which the kinetic modeling leads (one for the distribution functions, one for the electric potential energy, and one for the embedding parameters) to convergence. A similar calculation for a negatively biased interface demonstrated that the charge carriers responsible for the current-voltage characteristics are rather hot and thus far from thermal equilibrium. We could also show that quantum-reflection on the potential step of the interface and backscattering events inside the dielectric lead to deviations from the current-voltage characteristics of a perfectly absorbing interface. We also proposed to measure the charge accumulated at the interface by infrared reflection spectroscopy, using the dielectric as an optical internal reflection element. Calculating the response of the wall charge to an infrared light field, we constructed the correction to the Fresnel reflectivity of the dielectric-plasma interface and verified that the change of transmitivity through the optical element induced by the presence of the wall charge leads to a detectable signal from which its total amount can be deduced.

Publications

• Electron microphysics at plasma–solid interfaces. Journal of Applied Physics, 128(18).
  Bronold, F. X.; Rasek, K. & Fehske, H.
  
• Kinetic modeling of the electric double layer at a dielectric plasma-solid interface. Physical Review E, 102(2).
  Rasek, K.; Bronold, F. X. & Fehske, H.
  
• Infrared spectroscopy of surface charges in plasma-facing dielectrics. Physical Review E, 104(1).
  Rasek, K.; Bronold, F. X. & Fehske, H.
  
• Charge kinetics across a negatively biased semiconducting plasma-solid interface. Physical Review E, 105(4).
  Rasek, K.; Bronold, F. X. & Fehske, H.
  
• Kinetic modeling and infrared spectroscopy of charge carriers across the plasma-wall interface (PhD thesis, Universität Greifswald 2022)
  Kristopher Rasek