A study on global model with multistep ionizations in helium plasmas

Abstract

This study investigated the trends and changes of plasma parameters under various conditions using global model including multistep ionizations of the helium plasma with metastable states, and compared the results with those of the conventional argon plasma. Also, the changes and tendencies of plasma parameters in global model were studied with the change of electron energy distribution function. Studies on the global model including the metastable states have been limited to argon, and the same inert gas, helium, has consisted only of studies including simple modeling for atmospheric plasmas. In this study, particle balance equations and power balance equations were established including multistep ionizations by helium singlet and triplet states in steady state. Two metastable states and two excited states were considered, and the rate constants for each level were derived from the theoretical and experimental collision cross sectional results for each reaction, and then assigned to the equilibrium equations. According to global model results including multistep ionizations of the metastable states, the electron density was increased linearly as the power absorbed by the plasma is increased while the electron temperature was relatively constant. Also, it was confirmed that as the gas pressure was increased, the contribution of the multistep ionization reactions to the total ionization reactions does not change significantly. The electron-ion pair production energy showed very small changes with the gas pressure and the absorbed power, which is very small compared to the results in argon plasma of the same conditions. This result can be thought of as the threshold energy difference for the non-elastic collision reactions. Although the studies on global model in consideration of the existing multistep ionizations have assumed the Maxwellian electron energy distribution, the actual helium plasma may have different electron energy distribution depending on the external discharge condition, which changes the reaction constant of each energy level, internal plasma parameters and multistep ionization effects. Therefore, in this study, global model with multistep ionizations is performed including the Druyvesteyn distribution, and the results are compared with those of the Maxwellian distribution. Considering the Druyvesteyn distribution, the high energy electrons are depleted in the electron energy distribution, which results in the higher average ionization energy and lower electron density than a Maxwellian distribution. This induces relatively low metastable density in case of the Druyvesteyn distribution compared to the case of the Maxwellian distribution due to the depletion of the high energy electrons on the EEDF. At the global model including multistep ionizations including the distribution effect, the contribution of the multistep ionization was increased at the fixed power. It is because of the increase in the ionization rate constants. A little variation in the electron energy distribution function induce the change of the plasma parameters and the ratio of the multistep ionization. The results in helium plasma is different from that in argon plasma and is proportional to external discharge condition such as the absorbed power and gas pressure. These results can give the discharge parameters for discharge control to the plasma processing.