Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities

Abstract

Low-pressure plasmas are nowadays widely used for technical applications of plasma-surface interactions, such as plasma etching, material deposition, sputtering, etc. For a thorough understanding of individual processes in plasma processing the electron energy distribution (EED) function in the bulk plasma is of great importance. The EED determines the rates of all electron induced reactions as ionization, excitation or dissociation of molecules. The ubiquitous assumption of a Maxwellian EED becomes progressively worse for hot and low-density plasmas. Measurements of the EED with probes penetrating the plasma result in deteriorating effects on the plasma and the probe, thus measurements without plasma contact are of great interest. A non-destructive measurement is the detection of radiation emitted by the plasma.

The form-free reconstruction of the EED from a small number of measured emission intensities results in an ill-posed inversion problem. In order to avoid spurious features due to overfitting of the data (ringing) we apply Bayesian probability theory along with the adaptive-kernel method. The Bayesian approach will be applied to emission lines of helium, since in this case the relevant atomic input quantities are best known.

Key words