A global model study of the population dynamics of molecular hydrogen and the generation of negative hydrogen ions in low-pressure ICP discharge with an expansion region: effects of EEPF

Abstract

A global model is developed to study the effects of electron energy probability function (EEPF) on the population dynamics of molecular hydrogen and the generation of ions in low-pressure inductively coupled plasma (ICP) discharge with an expansion region. The EEPFs are measured using a commercial Langmuir probe and are found to change from bi-Maxwellian to Maxwellian type with increasing pressure. In the simulations, the measured EEPFs are employed to consider a non-Maxwellian EEPF in the low-pressure regime. The chemical reactions involving the H2(v) vibrational states are extended based on our previous study where some important reactions affecting the hydrogen vibrational population and thus the production were omitted. Compared with assuming a Maxwellian EEPF, the measured EEPF with a bi-Maxwellian distribution in the low-pressure regime produces a higher density of ions, due to a lower effective electron temperature and a higher electron density. As the pressure increases, the densities of ions under these two EEPF cases tend to be equal. The hydrogen vibrational population, together with the creation and loss mechanisms of different vibrational levels, is further investigated at different pressures under two EEPF cases, due to its key role played in the generation of ions. The dependence of the evaluated reactions contributing to the production of vibrational states on the EEPF is weakened with increasing vibrational level and pressure, whereas the evaluated reactions contributing to the destruction of vibrational states are almost independent of the EEPF. It is found that not only the indirect electron-vibration excitation (EV) and the resonant electron-vibration excitation (eV) but the vibrational-translational relaxation in collisions with molecular hydrogen (VT) are responsible for a shrinking plateau of vibrational population distribution with increasing pressure.