Calculation of the effective gas interaction probabilities of the secondary electrons in a dc magnetron discharge

In sputter magnetrons the electrons emitted from the target, the so-called secondary electrons (SE), can be recaptured by the target. As a result, not all emitted SE will interact with the discharge gas. The effective gas interaction probability (EGIP) is the probability that an emitted SE interacts with the discharge gas, and thus is not recaptured by the target. To calculate the EGIP an analytical model is developed. The model is verified by comparing its results with those of a Monte Carlo model. The EGIP of an individual SE is strongly, and in a complex manner, dependent on the electric and magnetic field to which the electron is subjected and on its initial starting conditions. Therefore, it is useful to introduce the average EGIP of the discharge which is a weighted average of the individual EGIP values. The influence on the EGIP of different parameters, such as the initial energy of the SE, the electron reflection coefficient and the electric and magnetic field is discussed. For typical discharge conditions at a pressure of 0.5 Pa values for the average EGIP in the range of 0.25-0.35 are found. This means that the recapture probability lies typically between 65% and 75%, showing that it is necessary to take into account this process to accurately model and simulate the magnetron discharge.