On the electron energy distribution function in the high power impulse magnetron sputtering discharge

Abstract

We apply the ionization region model (IRM) and the Orsay Boltzmann equation for electrons coupled with ionization and excited states kinetics (OBELIX) model to study the electron kinetics of a high power impulse magnetron sputtering (HiPIMS) discharge. In the IRM the bulk (cold) electrons are assumed to exhibit a Maxwellian energy distribution and the secondary (hot) electrons, emitted from the target surface upon ion bombardment, are treated as a high energy tail, while in the OBELIX the electron energy distribution is calculated self-consistently using an isotropic Boltzmann equation. The two models are merged in the sense that the output from the IRM is used as an input for OBELIX. The temporal evolutions of the particle densities are found to agree very well between the two models. Furthermore, a very good agreement is demonstrated between the bi-Maxwellian electron energy distribution assumed by the IRM and the electron energy distribution calculated by the OBELIX model. It can therefore be concluded that assuming a bi-Maxwellian electron energy distribution, constituting a cold bulk electron group and a hot secondary electron group, is a good approximation for modeling the HiPIMS discharge.

Modeling of high power impulse magnetron sputtering discharges with graphite target

“…Here, we use the discharge voltage and current waveforms only and determine the minimum in the least square error when the modeled discharge current resembles the experimental waveform the best. The reaction set and the rate coefficients for the argon working gas included in the IRM are mostly the same as used in our earlier work on HiPIMS discharges with a titanium target [47,48], with modifications concerning the treatment of the afterglow [49] and the rate coefficients involving the metastable argon [45]. The rate coefficients for electron impact de-excitation of the metastable levels are calculated by applying the principle of detailed balancing [50, section 8.5].…”

On the population density of the argon excited levels in a high power impulse magnetron sputtering discharge

“…The Orsay Boltzmann equation for electrons coupled with ionization and excited states kinetics (OBELIX) is a collisional-radiative model, where the Boltzmann equation is solved to determine the electron energy distribution function (EEDF). 15 It is an add-on to the ionization region model (IRM), a global plasma chemistry model developed to simulate HiPIMS discharges. The combined model is able to simulate on the one hand HiPIMS-specific effects included in the IRM.…”

“…On the other hand, OBELIX is able to calculate the electron energy distribution function, which allows us to use a much more detailed reaction set, in particular for argon, the most abundant species in a magnetron sputtering discharge. 15 Recently, we have added overall 65 individual and effective levels of the argon atom, 15 including the corresponding electron impact excitation and deexcitation reactions, and radiative transitions among these levels, as well as ionization reactions from each level to Ar þ . The merged model is thus able to calculate the population density of these excited states in a HiPIMS discharge.…”

“…Earlier, we demonstrated that there is a very good agreement between the bi-Maxwellian electron energy distribution assumed by the IRM and the EEDF that is calculated self-consistently using the OBELIX model. 15 Here, we explore the population densities, and the population and de-population mechanisms, of the excited states of the argon atom in the HiPIMS discharge as determined by the collisional-radiative model. In Sec.…”

“…II, the IRM and the OBELIX model are described. Compared to the previous version of the merged model, 15 we here add consideration of radiation trapping into the OBELIX model. This addition to the model is described in Sec.…”