Electron phase space distribution in a magnetron sputtering discharge

This study presents a comprehensive investigation of the electron phase space distribution (PSD) within a 3-in. DC magnetron sputtering (MS) discharge, analyzing its temporal evolution and time-averaged characteristics. Using a particle-tracking simulation within prescribed fields, the research systematically examines electron dynamics under balanced and unbalanced magnetic configurations, comparing pre-breakdown (plasma-off) and developed discharge (plasma-on) conditions. The methodology solves the Lorentz force equations for electrons emitted from the target and those generated via ionization, accounting for collisions with background argon gas. Temporal analysis reveals that in plasma-off conditions, electrons expand axially and decelerate due to collisions, with spatial confinement highly dependent on magnetic topology. The introduction of a plasma sheath in the plasma-on state significantly enhances the local electric field, increasing ionization rates and notably expanding the electron PSD. Over time, a general trend of outward spatial spread and velocity-range narrowing is observed. Time-averaged PSD analysis identifies the formation of sharp, stable boundaries in PSD that effectively define the electron trap. These boundaries, which vary with magnetic configuration and plasma conditions, delineate distinct regions populated by high-energy primary electrons and lower-energy impact-ionized electrons. Numerical findings are validated through comparisons with experimental observables, including the spatial extension of the ionization region, bi-Maxwellian electron energy distribution functions, and spatial electron density distributions. The study concludes that magnetic field structure and plasma sheath formation are critical factors governing electron confinement, transport, and energy distribution, offering fundamental insights for optimizing MS processes and potentially explaining phenomena such as plasma instabilities and ionization zone structuring.