Abstract
Abstract
A common feature of all types of magnetron sputtering (MS) assemblies is an effective confinement of electrons by an appropriate combination of electric and magnetic fields. Therefore, studying the motions of electrons in the fields of magnetron assemblies is of particular importance. Here, we systematically analyze the electrons motions in front of a typical DC MS cathode. We first calculate the profiles of the magnetron’s magnetic field for balanced and two types of unbalanced configurations. Then, we compute the profiles of the cathode’s electric field before the gas discharge and after the plasma formation. A semi-analytical model is utilized to compute the plasma potential. We then track the motions of electrons released from the target and electrons produced through impact ionization of the background gas in the prescribed fields. A Monte Carlo model is implemented to consider electron-gas collisions and a mixed boundary condition is employed to account for electron-wall interactions. The study analyzes the impact of field profiles on the cathode’s efficiency in trapping electron by examining electron escape from the magnetic trap and electron recapture at the target surface. It is shown that the presence of plasma in all configurations leads to a significant increase in the trapping efficiency and the ionization performance, as well as a decrease in the recapture probability. These effects are attributed to the high electric field developed in the cathode sheath. Moreover, we statistically analyze the trapping efficiency by illustrating the spatial distributions of electrons locations in both axial and radial dimensions. It is demonstrated that during their azimuthal drift motion, the electrons released from the middle region at the target surface have the smallest range of axial and radial locations, in all configurations in the absence of plasma. Finally, the impact of field profiles on the average energies of electrons is discussed.