Improved sheath model for the biased substrate in a vacuum arc with cathode spots

This paper presents a theoretical model that describes the sheath around a negatively biased substrate in a vacuum arc deposition (VAD) plasma. The model consists of: 1) Poisson's equation for the potential distribution, 2) Boltzmann's distribution for the electrons, and 3) a cosinusoidal form for the ion spatial distribution. The simplified model equations were solved numerically for the potential distribution and sheath thickness as a function of the process parameters such as bias voltage and radial distance from the cathode. The obtained sheath thickness versus bias voltage is compared with those from the Child-Langmuir equation. The numerical results show that the sheath has a very sharp edge and that its thickness is much larger than the Debye length.