Application of the Child-Langmuir law to magnetron discharge plasmas

In order to investigate the influence of magnetic field on magnetron plasmas, the dependence of discharge-current density (J_d ) on magnetic flux densities (B) perpendicular to the electric field over the whole discharge space in a magnetron apparatus with flat multi-targets has been studied. The dependencies on working gas pressures (P) and voltages (V) have been also studied in the configuration. From the experimental results, it was found that J_d was approximately proportional to B², P² and V^3/2. The sheath structure in the apparatus has been investigated as a function of B by both a probe method and a spectroscopic one. The cathode-fall thickness was roughly proportional to B^-1. From a numerical analysis on kinetics of γ electrons emitted from the cathode surface, it was found that the dependence of J_d on B could be explained by the Child-Langmuir law, in which the sheath thickness was replaced by the equivalent electron Larmor radius