Revisiting optical actinometry to utilize multiple argon line ratios for determination of absolute radical densities*

Determination of absolute number densities in low-temperature plasmas is critical in understanding the behaviour of reactive species. This is achievable through optical actinometry, where a small amount of a reference gas (actinometer) is added to the gas mixture, allowing calibration of unknown X densities, [X]. Actinometry often uses only a single emission line ratio (X/actinometer), which leads to relatively large uncertainties. As such, the relationship between radical species production and various input conditions may be unclear. In this work, up to 12 ratios are taken using argon as the actinometer to reduce the statistical uncertainty, with all available Ar excitation cross-sections considered. As a result, the statistical error in calculated density was <30%, and the main sources of error are uncertainties in the cross-sections of X and the electron temperature, T_e. Consequently, a single process where T_e, T_gas, and final densities were determined purely from observed optical spectra is used. The validity of this approach was verified both by modelling over the Ar partial pressure range of interest to also account for possible cascade effects and comparison to calibrated TALIF data of [O] and [H] in a RF source (1-100 Pa), with the latter giving excellent agreement. Finally, it was applied to monitor [F], [O] and [H] in an industrial grade plasma etcher leading to identification of key mechanisms during cryogenic etching.