Phenomenological description of a symmetry breaking rotating instability in hppms discharges

Sara Gallian, Denis Eremin, Thomas Mussenbrock, Ralf Peter Brinkmann, Ante Hecimovic, Teresa de los Arcos, Volker Schultz-von der Gathen, Mark Böke, Jörg Winter, William N. G. Hitchon

ICOPS 2012, Edin­burgh, UK, July 8-12.


High Power Pulsed Magnetron Sputtering (HPPMS) is a recently developed Ionized Physical Vapor Deposition (IPVD) technique. A bias voltage is applied to the target for a few hundred microseconds with a frequency of a few hundreds of Hertz, delivering several kW cm$^{-2}$ of power to the target. This results in the production of an ultra dense plasma with a high ionization degree, showing some peculiar behaviors. \ Here, we focus on the phenomenological description of rotating structures recently observed during a HPPMS discharge, that break the axial symmetry of the setup.\ To address the nature of the phenomena, we present a simple 1D Advection-Diffusion-Reaction equations system, to be solved for the electron $n_text{e}(theta,t)$ and neutral $n_text{n}(theta,t)$ densities. \ The observations report the presence of a structure rotating with a constant angular velocity $Omega$, when the discharge parameters are held constant. Therefore, we look for a steady state solution in a frame moving with $Omega$. One of the equations results in an eigenvalue problem for $n_text{e}$, that we solve analytically for different profile shapes. The other equation gives the neutral density. The system solution is specified for the experimental HPPMS system at the Ruhr University of Bochum, and a comparison with experimental data is given.

Tags: breaking, HPPMS-symmetry, Instability