Approximation of the erosion zone profile in planar magnetrons with a disk cathode

We have proposed a universal approximation of the normalized erosion zone profile of planar magnetrons with a disk cathode by a composite function that includes the probability density function for the minimal distribution of extremal values for the region from the center of the disk cathode to the maximum of the erosion zone and the survival Weibull distribution function (from the maximum to the outer boundary of the sputtering zone). The accuracy of the approximation has been verified for six magnetrons differing in the cathode size or in the design of the magnetic systems. In all cases, good agreement has been observed between the approximation and experimentally measured values. The results reported here can be used to analyze processes that occur on the cathode during sputtering and to refine the calculations of coating profiles.