Electron heating transition in direct current magnetron sputtering discharges

Electron heating in direct current magnetron sputtering (DCMS) discharges is investigated via fully kinetic particle-in-cell/Monte Carlo collision simulations. The similarities in DCMS of different dimension scales are observed. Under conditions of high pressure p or weak magnetic field B, the electron heating in DCMS is found mainly within the sheath. As the pressure decreases or the magnetic field increases, the electron heating shifts to the bulk plasma region, accompanied by the appearance of breathing oscillations; meanwhile, the electron mobility approaches the ion mobility, and an appreciable time-averaged potential drops outside the sheath. It is further confirmed that with the reduction of similarity invariant B/p or pd, the breathing oscillations are suppressed due to the increase in wavelength or the decrease in characteristic scale of discharge. In other words, with the onset and development of breathing oscillations, the electron heating mechanism transitions from sheath energization to Ohmic heating in the bulk plasma region. The characteristics of breathing oscillations and the transition of electron heating mechanism are scale-invariant under similar discharge conditions due to the electron kinetic invariance. The results of this study contribute to a more comprehensive understanding of the fundamentals of magnetron discharge.