Determination of the electron temperature in argon plasmas using collisional-radiative model without model-dependent assumptions on metastable diffusion and radiation trapping effect

Determination of the electron temperature through optical emission spectroscopy and the collision-radiation model has the advantage of a relatively simple measurement system. However, the conventional approach requires theoretical assumptions for the diffusion of metastable levels and radiation trapping effects, which introduce model-dependent parameters such as diffusion coefficients and escape factors. These parameters vary with experimental conditions and can lead to ambiguity in the diagnostics. To address this issue, we suggest a method to directly determine the metastable level densities using a linear regression method and multiple atomic spectral lines. The metastable level densities are retrieved through the inverse calculation of the photon emission coefficient matrix derived from the collisional-radiative model. This allows for the determination of the electron temperature that best reproduces the measured spectral line intensities, eliminating the need for model-dependent assumptions related to the diffusion and radiation trapping effect. In a capacitively coupled plasma at 20 mTorr and 100 W discharge power, the electron temperature was diagnosed as 3.0 eV using the suggested method with total of 12 spectral line intensities. The result obtained using a Langmuir probe was 3.3 eV, indicating a deviation of 10%. This confirms the effectiveness of the proposed method in eliminating ambiguities associated with theoretical assumptions in the conventional collisional-radiative model.