Modelling the discharge region of a microwave generated hydrogen plasma

A zero-dimensional steady-state model of low-pressure (2-60 Torr) microwave-generated hydrogen plasmas was developed. The electron energy distribution function (EEDF) was determined using the Boltzmann equation, coupled to species, energy and power balances. The EEDF from the Boltzmann equation permitted computation of the rate constants and average electron temperature required for simultaneous solution to the six species balances, two for neutrals (H, H-2) and four for charged (H+, H-2(+), H-3(+) and electron) species, and the energy balance. The average electron temperature and species concentrations were then employed in a power balance to check for self-consistency with the input power used to solve the Boltzmann equation. E/N values were appropriately adjusted after each iteration until self-consistency was achieved. The model provides information on the details of the transfer of power from electrons via various processes (ionization, dissociation, vibration, rotation) to the neutral species. The mechanism of energy loss from the neutrals (radiation, convection) is also computed, and thus gas temperature can be estimated. Indeed, for low-pressure (p < 15 Torr) plasmas the model yields accurate absolute gas temperatures as a function of pressure, including the fact that gas temperature rises steeply at pressures in excess of 15 Torr. This results from the fact that at low pressures a very large fraction of the input power is transmitted by the electrons to the molecular vibration modes, such that T-vib much greater than T-trans.