Determination of electron temperatures in plasmas by multiple rare gas optical emission, and implications for advanced actinometry

A method is described for determining the electron temperature of a low pressure plasma of the type used in microelectronics materials processing. A small amount of an equal mixture of He, Ne, Ar, Kr, and Xe is added to the process gas (in this example Cl2) and the intensities of optical emission lines from the Paschen 2p levels of the rare gases are recorded. The observed emission intensities are compared with those computed from a model that includes electron impact excitation from the ground state, as well as two-step electron impact excitation through intermediate metastable levels. This latter route is shown to be the dominant one for nearly half of the levels. Using adjusted, published electron impact excitation cross sections and assuming a Maxwellian electron energy distribution, the electron temperature (Te), the only adjustable parameter, was determined from the best match between the observed and computed intensities. For a high density, helical resonator Cl2 plasma at 10 mTorr, Te=2.2±0.5 eV w...