A fluid model of pulsed direct current planar magnetron discharge

We simulated a pulsed direct current (DC) planar magnetron discharge using fluid model, solving for species continuity, momentum, and energy transfer equations, coupled with Poisson equation and Lorentz force for electromagnetism. Based on a validated DC magnetron model, an asymmetric bipolar potential waveform is applied at the cathode at 50-200 kHz frequency and 50-80% duty cycle. Our results show that pulsing leads to increased electron density and electron temperature, but decreased deposition rate over non-pulsed DC magnetron, trends consistent with those reported by experimental studies. Increasing pulse frequency increases electron temperature but reduces the electron density and deposition rate, whereas increasing duty cycle decreases both electron temperature and density but increases deposition rate. We found that the time-averaged electron density scales inversely with the frequency, and time-averaged discharge voltage magnitude scales with the duty cycle. Our results are readily applicable to modulated pulse power magnetron sputtering and can be extended to alternating current (AC) reactive sputtering processes.