Sheath model of negatively biased substrate in vacuum arcs with cathode spots

Plasma sheath near the substrate plays an important role in Vacuum Arc Deposition Technology (VADT). To analyze the sheath characteristics of the substrate in VADT, the unique ejection pattern of the cathode region must be taken into account. This paper describes a steady-state, two-dimension sheath model in which ions distribute specially according to a cosinoidal law. The model equations can be numerical soluted under specified conditions, to describe the sheath behavior of the substrate in the process of titanium film deposition using VADT. The model can be used for calculation of ion flux and heat flux flowing to the substrate in VADT, or in some other cases in which biased conductors were in vacuum arcs with cathode spots.