Analytical model and measurements of the target erosion depth profile of balanced and unbalanced planar magnetron cathodes

The erosion depth profile of planar targets in balanced and unbalanced magnetron cathodes with cylindrical symmetry is measured along the target radius. The magnetic fields have rotational symmetry. The horizontal and vertical components of the magnetic field B are measured at points above the cathode target with z = 2 × 10⁻³ m. The experimental data reveal that the target erosion depth profile is a function of the angle θ made by B with a horizontal line defined by z = 2 × 10⁻³ m. To explain this dependence a simplified model of the discharge is developed. In the scope of the model, the pathway lengths of the secondary electrons in the pre-sheath region are calculated by analytical integration of the Lorentz differential equations. Weighting these lengths by using the distribution law of the mean free path of the secondary electrons, we estimate the densities of the ionizing events over the cathode and the relative flux of the sputtered atoms. The expression so deduced correlates for the first time the erosion depth profile of the target with the angle θ. The model shows reasonably good fittings to the experimental target erosion depth profiles confirming that ionization occurs mainly in the pre-sheath zone. (paper)