The role of photon self-absorption on the H (n = 2) density determination by means of VUV emission spectroscopy and TDLAS in low pressure plasmas

The H ( n = 2) atomic density determination by means of vacuum ultra-violet (VUV) emission spectroscopy of the Lyman- α line in laboratory low pressure plasmas is strongly affected by self-absorption of emitted photons inside the plasma leading to an underestimation of this density. A correction of the densities obtained from VUV emission spectroscopy measurements is performed by using the escape factor method. The corrections applied can reach orders of magnitude even in low pressure plasmas. Assumptions on the spatial distribution of emitting and absorbing particles as well as on the corresponding line profiles have to be made. Consequently, additional measurements are performed, which raises the requirement of a benchmark of the applied correction procedure. In contrast, tunable diode laser absorption spectroscopy (TDLAS) on the Balmer- α line is a direct measurement of the H ( n = 2) density and is thus suitable for a benchmark. For the ICP under consideration, H ( n = 2) densities obtained via TDLAS are near 3 × 10 15  m −3 whereas uncorrected VUV emission spectroscopy gives values in the range of roughly 10 13  m −3 depending on pressure and applied RF power. The calculated escape factors are on the order of 2–8 × 10 −3 . An excellent agreement with TDLAS is observed by applying them to the results of the VUV emission spectroscopy.