Global modeling of low and high power HiPIMS discharges
Sara Gallian, Jan Trieschmann, Thomas Mussenbrock, William N. G. Hitchon, Ralf Peter Brinkmann
The 14th International Conference on Plasma Surface Engineering (PSE) 2014, Garmisch-Partenkirchen, Germany, September 15 - 19, 2014
To address the chemistry evolution and the surface interaction taking place in the ionization region of a HiPIMS discharge, a Maxwellian equilibrium (or fluid) and a kinetic volume averaged model for the electrons are developed. Both models self consistently describe the evolution of the densities of heavy particles, together with the energy and density of the electrons. The time varying Voltage-Current (V-I) characteristics are an input to both models and they represent the power coupled to the discharge. A multiplicative free parameter describes the efficiency of the power coupling and is iteratively estimated to guarantee that the power obtained from the model equates to the power imposed from the V-I characteristics. Two reference discharges are analyzed: a low (Ipeak = 1 A) and a high discharge current (Ipeak = 100 A). In the low current case, both the fluid and the kinetic model are able to reproduce the V-I characteristics, even though they yield different results: the EEDF calculated by the latter is highly non Maxwellian, therefore invalidating a fundamental hypothesis on which the fluid model relies. As for the high current simulation, the kinetic code is not able to reproduce the imposed V-I characteristic: the Ar gas suffers a strong depletion, which results in reduced production of Ar ions, and finally in an insufficient secondary electron production. To prove this point, the source rate of Ar gas is artificially enhanced, and as a result, the experimental V-I characteristics can be matched. Indeed, experimental observations of the high power regime show that the discharge reorganizes itself in brighter ionization regions that rotate in the ExB direction, referred to as spokes [see e.g. de los Arcos et al., J Phys D 46, 335201 (2013)]. It is speculated that the organization in spokes that move to regions of higher gas density supplies the additional gas influx, that was artificially enhanced in the kinetic model. In another publication, it is shown that a simple phenomenological model, relying on the balance of ionization, electron loss and neutral refilling, is able to reproduce the species density trends in steady state, in a frame co-moving with the spoke [Gallian et al., Plasma Sources Sci. Technol., 055012, (2013)].