Global modeling of the azimuthally rotating structure in HiPIMS

Sara Gallian, Ralf Peter Brinkmann, William Hitchon

Fourth International Conference on Fundamentals and Industrial Applications of HIPIMS, Braunschweig, Germany, 12 - 13 June 2013 (oral cont­ri­bu­ti­on) -> follow link to download presentation


High Power Impulse Magnetron Sputtering (HiPIMS) is a novel Ionized Physical Vapor Deposition technique, able to achieve an ultra dense plasma with a high ionization degree among the sputtered atoms. This is accomplished by applying a large bias voltage to the target in short pulses with low duty cycle. \ HiPIMS discharges are characterized by high density plasma (peak electron density $10^{18}$ - $10^{20}$ m$^{-3}$) in a strong magnetic field ($100$ mT), with highly energetic secondary electrons ($500$ - $1000$ eV). The combination of these factors results in a discharge showing a vast range of instabilities ranging from MHz (i.e. modified two stream instabilityfootnote{D. Lundin, U. Helmersson, S. Kirkpatrick, S. Rohde, and N. Brenning, emph{Plasma Sources Science and Technology} 17, 025007 (2008).}) to $10$ - $100$ kHz range.\ Here we attempt the description of ionization zones breaking the azimuthal symmetry of the set up and rotating with about $10 % $ the textbf{E} $times$ textbf{B} drift velocity in the same direction. This phenomenon has been observed by several authorsfootnote{A. Kozyrev, N. Sochugov, K. Oskomov, A. Zakharov, and A. Odivanova, emph{Plasma Physics Reports} 37, 621 (2011).}$^,$ footnote{A. Anders, P. Ni, and A. Rauch. emph{J. of Applied Physics}, 111, 5 (2012).}$^,$ footnote{A. P. Ehiasarian, A. Hecimovic, T. de los Arcos, R. New, V. S. von der Gathen, M. B"oke, and J. Winter. emph{Applied Physics Letters}, 100, 11 (2012).} in different experimental set up. It is argued that these spoke-like structures determine the overall plasma density, carry most of the discharge current and are responsible for anomalous cross field electron transport. It is therefore fundamental to understand their formation and relevance in order to characterize the system behavior. \ During the on time of the bias, the current increases until it reaches a maximum then remains constant. Experimental observationsfootnote{A. Hecimovic et al., emph{3rd HIPIMS Conference}, Sheffield UK (2012)} show the formation of a number of features rotating, that decrease in number until only one spoke remains. It is moreover observed that this spoke rotates with a constant angular velocity. We theorize that the configuration with one or more spokes depending on the power coupled to the discharge is indeed a "periodic equilibrium" configuration, to which the system relaxes to when it switches from conventional DC Magnetron Sputtering to HiPIMS mode. \ We assume there is a single structure that rotates with a constant speed, during the plateau period of the current. These condition are experimentally observed by Hecimovic et al.footnote{A. Hecimovic et al., emph{65th Gaseous Electronics Conference}, Austin TX (2012)} for a 0.17 Pa pressure Ar-Al discharge with -800 V bias and 100 A peak discharge current: the single structure shows stationary behavior after 170 $mu$s and rotates with $Omega approx$ 80 kHz.\ Since the discharge is sustained by very energetic secondaries and the electrons are far from equilibrium, we develop a global model that evolves the electron energy distribution function self-consistently with the rate equations for background gas and metal species. The volume average is performed emph{only} in the structure region and a net neutral flux term is imposed to model the spoke rotation at speed $Omegar$. Within the spoke region the species densities $n_text{e}(theta)$ and $n_text{n}(theta)$ are given a shape taken from a simple equilibrium 1D fluid model: this allows us to specify the net flux of neutrals even if the global model does not have an explicit spatial dependence.\ The system consisting of the Boltzmann equation for the electron energy distribution function and rate equations for Ar and Al species is evolved in time through a pseudo-transit using a stiff equation solver. The tracked densities $n_text{e}(t), n_text{Ar}(t)$ and $n_text{Al}(t)$ reach a steady state at physically meaningful values after only a few periods $T = 1/Omega$.\ The authors gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft within the frame of SFB-TR 87.

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