Gradient drift instabilities and rotating spokes in direct current and radio frequency driven magnetron discharges

Magnetron discharges, as an advanced plasma source for thin film deposition, can feature a locally enhanced ionization zone, i.e., the spoke mode. The spoke rotates azimuthally in the race track where the target is sputtered the most. The spoke mode can occur in all types of magnetron discharges (direct current, radio frequency and pulsed) and significantly affect the dynamics of electrons and ions. In spite of the decades-long study, the dynamics and formation of the spoke mode remains unclear. We have studied the spoke mode in the context of magnetron discharges under conditions of different geometries and different driven sources using a two-dimensional particle-in-cell/Monte Carlo collision approach. The linear and nonlinear evolution of the spoke instability is analyzed using the computational method and two-fluid linear theory, and also compared with numerous previous experimental observations. For cylindrical magnetrons with uniform B (magnetic field), we found that the formation of the spoke potential hump region can be explained as a result of the local collapse of the anode sheath due to the gradient drift instability (GDI), which is triggered within the anode sheath. ^{[1, 2]} For planar magnetrons with non-uniform B, the kinetic model reveals that the cathode sheath (axial) electric field triggers the GDI, deforming the local potential until the instability condition is not fulfilled and the fluctuation growth stops, at which moment the instability saturates. ^[3] The potential deformation consequently leads to the formation of the potential hump, surrounding which the azimuthal electric field E_θ is present. Further, in RF planar magnetron discharges, the saturation level of E_θ is found to be synchronized with and proportional to the time-changing voltage applied at the cathode, resulting in RF-modulation of the electron heating in the E_θ due to ▽B drift. ^[3] To conclude, our results showed that the sheath electric field is critical for the excitation and saturation level of the spoke instability. This hereby suggests a practical path to control spoke dynamics by carefully manipulating the sheath electric field via external parameters, e.g., magnetic field, cathode voltage and pressure.