# Kinetic modeling of the electronic response of a dielectric plasma-facing solid

## TL;DR

This paper develops a self-consistent kinetic model to describe the electronic response and electric double layer formation at the interface between a plasma and a dielectric solid, incorporating quantum and semi-empirical conditions.

## Contribution

It introduces a novel kinetic theory combining Boltzmann equations, quantum matching, and hole injection models for plasma-dielectric interfaces.

## Key findings

- Model successfully predicts density and potential profiles at the interface.
- Demonstrates applicability to silicon dioxide and silicon in hydrogen plasma.
- Highlights importance of ambipolarity and double layer merging in the response.

## Abstract

We present a self-consistent kinetic theory for the electronic response of a plasma-facing dielectric solid. Based on the Poisson equation and two sets of spatially separated Boltzmann equations, one for electrons and ions in the plasma and one for conduction band electrons and valence band holes in the dielectric, the approach gives the quasi-stationary density and potential profiles of the electric double layer forming at the interface due to the permanent influx of electrons and ions from the plasma. The two sets of Boltzmann equations are connected by quantum-mechanical matching conditions for the electron distribution functions and a semi-empirical model for hole injection mimicking the neutralization of ions at the surface. Essential for the kinetic modeling is the ambipolarity inside the wall, leading to an electron-hole recombination condition, and the merging of the double layer with the quasi-neutral, field-free regions deep inside the wall and the plasma. To indicate the feasibility as well as the potential of the approach we apply it to a collisionless, perfectly absorbing interface using intrinsic and extrinsic silicon dioxide and silicon surfaces in contact with a two-temperature hydrogen plasma as an example.