1. MC modelling of target erosion for round and rectangular magnetrons
Tomáš Kubart a , Jan Valter b, Rudolf Novák a
a Department of Physics, Faculty of Mechanical Engineering, Technická 4, CTU Prague
b HVM Plasma Ltd., Na Hutmance 2, , Praha 5
Introduction
Model
One of the important issues of the magnetron sputtering is related to the target erosion. Its possible non-uniformity decreases the target utilization several times and variations in the deposited layer thickness and composition may appear. In case of planar rectangular magnetron different erosion rate commonly occurs at bended ends and/or at the transition from bend to straight part of racetrack. There has been several reports of asymmetric erosion patterns at the boundary between curved section and straight part of magnetrons for transparent conductive films, called anomalous erosion. Anomalous erosion occurs when electrons passing from weaker to stronger magnetic field and as a result local erosion rate may substantially exceed values in strong field.
Although cathodes for conductive optical coatings are operated with a strong magnetic field subsequent numerical studies showed that anomalous erosion may occurs at magnetic field as low as 200/160 G in straight and uniformity of magnetic field has to be better than 10% in order to avoid this effect. While common magnetrons operate with magnetic field about 300 G, where the optimal ratio between target utilization and ionization efficiency is achieved it seems to be vital issue the possibility of occurrence of anomalous erosion at such weaker magnetic field.
Erosion of the magnetron target is simulated using single electron approach. Only the secondary electrons are traced and their collisions are simulated by Monte-Carlo method. Equation of motion of a charged particle in ExB field is solved using fourth-order Runge-Kutta method with variable time step longer in bulk plasma and shorter in sheath layer. Only elastic, excitation and single ionization collisions are taken into account. An electron is traced until its energy decreases below the ionization potential of argon, moves away of the calculation domain, or touch target surface. New electrons are emitted from the target surface according to the ion impingement density. The target erosion is determined from the ion impact density assuming constant sputtering yield when created ions fell directly to the target without any transverse motion or scattering.
The electric and magnetic fields are considered to be unaffected by the plasma. Magnetic field is calculated by FEM in software Ansys version 5.7 using reduced scalar potential approach and electric field is assumed to be constant in sheath layer and zero in bulk plasma. The sheath thickness is considered to be equal to the Larmor radius of an electron with corresponding energy.
The model is completed with recapturing of secondary electrons in order to estimate minimal voltage to sustain a discharge. The minimal voltage to sustain a discharge may be then determined from condition of steady number of secondary electrons where is mean number of ions created per one SE at applied voltage and is ion induced secondary electron yield. 1
Fig. 3. Secondary electron tracing flow chart. Each electron is traced until its energy decreases below the ionisation potential of argon or moves away of the calculation domain. After collision, the electron energy is decreased by fixed energy depending on collision kind, and particle is scattered into new direction.
Fig. 1. Eroded magnetron target. x z y
Fig. 2. Studied magnetic system is composed of SmCo (blue) and NdFeB (brown) bar magnets magnetized in vertical direction and an iron (yellow) back plate 8 mm thick. Central magnets are magnetized in +y direction. long. Target surface is 58 mm above the baseline (base of the iron plate). Magnetic system consisting of rectangular permanent magnets has been selected since it can be easily rearranged by adding and removing individual magnets and it is often used in industrial magnetrons.
Conclusion
Using Monte-Carlo method, we have simulated erosion in a rectangular magnetron sputtering system with a variable turn configuration. Simulated results were compared with sputtering experiment in order to prove reliability of used approach.
It has been shown that anomalous erosion has only second order influence in systems with field strength in range G used for hard coatings deposition and that including of recapture of secondary electrons reduce the effect of anomalous erosion.
More important is impact of deformation of electrons path in turn section resulting in higher sputtering rate in turn. Such effect has been demonstrated in second configuration of magnetic system with field equally strong in straight and end region. To get uniform erosion faster erosion in turn should be compensated by field strength adjustment or by different shape of plasma channel. The last configuration designed based on our findings has optimized target utilization with the same erosion rate throughout the target.
The agreement between simulated and measured erosion is satisfactory considering there is no resputtering included in our model. However, there is a big deviation in discharge voltage estimated from number of secondary electrons needed to sustain a discharge. Since such approach seems to be promising to get at least estimate of an operating voltage, we will continue in clarification of such discrepancy.
Results and Discussion
First experiment were aimed at verification of used approach in case of more complex magnetic field. Although there has been published many papers dealing with simulation of magnetron erosion, results are usually not directly compared with experiments or they are compared with some simple configuration like cylindrical magnetron. Therefore we performed erosion experiment with magnetic field stronger in one turn, and weaker in the second comparing with straight.. Magnetic field on the target surface is shown in Fig. 4 and resulting erosion in Fig. 6 for both simulation with and without recapturing of secondary electrons.
Fig. 4. Contour lines of parallel component of magnetic field at the target surface for experimental configuration. The red line denotes line where flux density is parallel to the target (By=0) to give information about the plasma tunnel shape. Magnetic field in straight has value of 230 G, in strong turn 280 G, and 140 G in weak turn. This correspond to ratio 1.2 resp 0.61, which should be enough to observe effects of eventual anomalous erosion.
Rectangular magnetrons are usually designed with differently strong field in straight and turn to compensate different erosion rates. To clarify this effect, we performed simulation of magnetron with equally strong field in order to observe eventual differences. Magnetic field of that configuration is shown in Fig. 7, our aim was to keep uniformity of field in range of 10%.
Fig. 8 Contour plot of normalized erosion shows clearly effect of the turn. Despite the same magnetic field strength, erosion there is approximately by 15% higher. Reason of this increase is a deformation of trajectory of a drifting electron in turn. Lateral dimension of the trajectory projected to the target is substantially larger in straight. To improve uniformity of erosion is therefore necessary to change shape of magnetic field by increasing the distance between pole pieces or decrease field strength so electrons would drift faster through turn which results in less ionization and therefore lower erosion.
a) Longitudal section
b) Transversal section
Fig. 5. Comparison of calculated and measured erosion profile in principal cross-sections. The corresponding experiment were performed with copper target sputtered for 12 hours, pressure of 0.3 Pa and power of 6 kW. Agreement between simulated and measured erosion profile is very good (Fig. 5 a, b). Small deviations may be results of redeposition which is not included in our model.
Fig. 7. Magnetic configuration of the straight remained unchanged, with Bp of 230 G. In the centre of turn is 225 G, but due to structure of used system there is an increase at ends of turn where field approaching 240 G
The last configuration is adjusted according to previous results in order to get system with uniform erosion rate over the whole target surface. The straight part is again unchanged and the field goes smoothly down to 190 G in turn (Fig. 9). As seen in Fig. 10 resulting erosion pattern is uniform.
Fig. 9. Contour lines of magnetic field in configuration with optimized erosion. To decrease erosion rate in turn, magnetic field smoothly decreases down to 190 G.
a) Model without recapturing
b) Model with recapturing of SE
Fig. 6. Erosion pattern calculated for ensemble of 20 000 electrons, applied voltage of 500 V, and argon pressure of 0.5 Pa. In order to examine influence of recapturing, model including recapturing was also calculated under same conditions. Simulated erosion profile is deeper at the input of strong turn (5% deeper than at the output), which may be sign of anomalous erosion. Results obtained from model with recapturing (b) of SE show less pronounced anomalous erosion.
Fig. 10. Simulated erosion of optimized system. The simulation were performed for pressure 0.3Pa and electrons.