Simplified model for calculating the pressure dependence of a direct current planar magnetron discharge

A simplified model for the direct current planar magnetron discharge allowing one to simulate the pressure dependence over a wide range is presented. For sufficiently strong magnetic fields, the high energy electrons (HEE), the electrons that are responsible for the ionization, move predominantly in arch shaped regions in between interactions with the discharge gas. This allows one to model the discharge-as being built up by arches. The influence of the interactions of the HEE on their motion is modeled by calculating the probabilities for transfer of HEE among the arch shaped regions. In this way the ionization distribution of the electrons emitted at a certain position at the target surface can be calculated. The results of this approach agree well with Monte Carlo results. This modeling of the HEE motion combined with simple schemes for determining the ionization and target erosion forms the core of the simplified model. The model is made self-consistent through iteration. It appears that for a given magnet system and discharge. voltage a self-consistent solution is only possible for one particular pressure. This is the pressure for which the discharge voltage corresponds with the theoretical minimum discharge voltage needed to sustain the discharge at that pressure. The model reproduces the experimentally observed increase of the discharge voltage and widening of the erosion profile with decreasing pressure. According to the model the main cause for this pressure dependence is not the decreased confinement of electrons in the magnetic trap but the increased recapture of secondary electrons by the target. (C) 2003 American Vacuum Society.