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Closed magnetic field constructed by unbalanced magnetron sputtering (MS) cathodes has been a general means of developing  the MS coating system. However, owing to the difficulties in characterizing the complex plasma behaviors, there are still no quantitative criteria or design bases for some critical points, such as the effective object, the working mechanism, the closure condition, the layout logic and the effectivity of the closed magnetic field. Here in this work, out of the movements of charged particles in magnetic field,  the motion behaviors of electrons and ions in the vacuum chamber are studied and it is also  revealed that the closed magnetic field can affect mainly the electrons and further control the distributions of ions. A Monte-Carlo collision (MCC) model of the closed magnetic field MS coating system is established by test-electron to characterize the plasma transport characteristics, and the electron constraint and coating deposition efficiency are studied by different layouts of the magnetron cathodes and the ion sources. The simulation results show that the cathode numbers and vacuum chamber size determine the constraint effect on electrons in closed magnetic field. By 8 MS cathodes and the chamber radius of 0.5 m, the proportion of the overflow electrons can decrease to 1.77%. To increase the proportion of the electrons in the coating region, four coupled magnetic fields are introduced in the center of vacuum chamber. The studies of cathode type, rotation angle and magnetic field direction reveal that the  proportion of the overflow electrons is less than 3%. A local dense plasma distribution and a continuous uniform plasma distribution can be observed in the vacuum chamber, corresponding to the same and opposite layout in magnetic poles of the MS cathodes and the ion sources, and the  proportion of the electrons in the coating region significantly increases to 53.41% and 42.25%, respectively.

Working principle and layout logic of closed magnetic field in sputtering