How to simulate magnetron sputtering

By Nigel Atkinson

So, what is magnetron sputtering? It is a physical vapour deposition technique, in which a plasma in a chamber is used to generate ions that are accelerated towards a negative target, ejecting material, which is then allowed to deposit on a workpiece, or substrate as it is usually known.

Low pressure is important in providing a good quality coating, but in the standard system results in low deposition rates and high production costs. In magnetron sputter systems, the plasma is confined close to the target. As in the standard system, ions from the plasma, typically argon, are accelerated towards the target, and secondaries are produced. The secondary species are electrons, which enter the plasma, target ions, which might be recaptured by the target, and target neutrals. The last of these travel ballistically until they deposit on a surface inside the chamber – hopefully on the substrate.

The advantage of magnetron systems is that electrons are maintained in the plasma, giving a long interaction length. Compared with a standard plasma sputtering system operating at the same pressure, the magnetron system produces a higher Ar ion flux and hence higher target neutral flux. This results in the commercially important higher deposition rate, without prejudicing film quality.

The magnetron system is very widely used in a diverse range of applications, including:

  • Low emissivity coatings on glass
  • Deposition on circuits
  • Engineering coatings on tooling, etc.


Before looking at the details of magnetron simulation, a quick word on our simulation package, Opera. Opera is an electromagnetics led multi-physics simulation environment, available in both 2D and 3D versions. It includes a fully featured geometry module for creating and preparing models for analysis, a range of finite element solvers for electromagnetics, space-charge, thermal and stress thermal analyses, and a post-processing module for the extraction and display of the simulation results. All types of analysis are compatible with Opera’s built-in Optimizer facility.

While Opera also includes solvers for high frequency analysis, today we will look only at electro-and magneto-static applications. Opera has been developed over three decades and has a highly successful track record in many application areas; including x-ray tubes, electron lithography, ion sources and particle accelerators.

Our Opera-3d Space Charge module uses the finite element method to model the emission and transport of continuous particle beams. Using a nonlinear iterative solution method, Opera generates a self-consistent solution for the electrostatic fields, space-charge distribution and emission current. Particle trajectories are computed under the influence of both electric fields, and magnetic fields – these magnetic fields can be generated in a number of ways, from a simple applied uniform field, electromagnetic coils, to arbitrary field distributions imported from a magnetostatic analysis from, for example, the Opera magnetostatic solver. As well as coupling to the magnetostatic solver module, the Space Charge module can also be used to perform multiphysics analyses with other Opera physics modules such as the thermal solver.

Although we refer to the Opera “Space Charge solver” it should be noted that this solver is also capable of modelling neutral particles. Opera has for some time had the plasma free surface and volume emitters; the magnetron plasma emitter is something of a hybrid of the two, and allows the efficient simulation of low density magnetized plasmas. It has been developed with a principal application in mind – magnetron sputter simulation.

So, why do we want to simulate the magnetron? In general for similar reasons to many other devices – magnetron sputtering is a complex process, with performance dependent on a wide range of parameters. Simulation allows more rapid and less costly exploration of parameter space than does experiment – and can provide insight that is not available from practical testing.

Having performed the simulation, we can determine the full characteristics of the device, including: electrostatic and magnetostatic potentials and fields, charge density particle tracks, beam parameters and profiles, momenta, energy, current etc. These often-used metrics from Space Charge simulations may be produced using the standard features of the Opera Post-Processor.  We can also extract information more specific to this particular type of device, for example:

  • Target erosion profile
  • Target utilization
  • Deposition profile

The main features are:

  • Self-consistent magnetron plasma simulation
  • Handling of arbitrary geometry, electric and magnetic configurations

The software is fast– since Opera is not a PIC code, execution times are relatively short – something like this circular example will solve in around half an hour on a laptop. The space charge solver, like Opera’s other standard 3d solvers, can be run across several cores in a parallel solution. Among other things, speed enables us to run optimization routines, and, of course, the space charge solver is compatible with Opera’s standard Optimizer package. The Opera space charge solver is efficient in its use of memory – and this, combined with short run times gives the possibility of simulating an entire coater. A small selection of typical diagnostic results are shown here:

The voltage may displayed – values both without and with the effect of space-charge are available. This, of course, is a necessary diagnostic when assessing the potential for voltage breakdown in the device.

If we plot a voltage isosurface at the plasma meniscus potential (itself an output from the simulation), we can visualize the meniscus and so judge the extent of the plasma in the device. Even without performing any space-charge simulations, Opera has great utility in the magnetic design of the magnetron – itself critical to achieving a good product.

Line data can also be produced, as can parameter values on any of the structures in the model. Such results of course are of general application, not specific to magnetrons, and use standard Post-Processor features. The target erosion profile and utilization, and the deposition profile are critical performance features. Magnetron targets can be extremely expensive – a target used for architectural glass coating, for example, might be several metres long and cost several hundred thousand pounds. It is vital to maximize the utilization both to reduce target costs, and to reduce production down­time during replacement.

The maximum depth of the erosion groove will determine target end-of­life, and so the erosion profile needs to be optimized – the flatter the profile is across the groove, and the more uniform it is around the groove, the better will be the utilization. The erosion profile may be observed directly from the flux of sputtered species from the target. As you can see, the model shown here is of a simple circular design.

What about a more complex example? Here is one that we have bench-marked. The design is from Teer Coatings Ltd.
Both simulated and measured erosion profiles are shown here. Note that the groove is shown by the peaks in the line graph – which has a highly expanded vertical scale. As can be seen, agreement is excellent -and note the uniformity around the groove. Target end-of-life will be reached when the minimum target thickness is reached. Using this criterion, the simulations have shown agreement in the utilization of less than 0.5 percentage points – or just over 1%.

The erosion is at the same rate around the track – no one region will unduly determine the end-of-life – so this is a good design. This can also be seen qualitatively from the uniformity of the electron tracks. Tracks form all species in the simulation may be shown, either separately or in combination. Each may be colour coded to visualize various parameters, such as current, time-of-flight, velocity, etc. Here we use time-of-flight. Note that we are still only viewing results produced using the Post-Processor’s standard features.

Lastly, on the subject of magnetron simulation, as said before, the software is fast and efficient. This enables it to be used in the design of the entire coater, which might contain several magnetrons. Since each has its own magnet system, the interaction between them can give significant differences in performance compared with isolated devices.

On the right, for example, is a four magnetron coater; we can choose to have the same arrangement of magnets in each, or we can reverse their polarity in alternate units. This changes the field configuration in the coater, and in part determines the flux of electrons that reaches the chamber walls or the substrate. Speed also allows effective optimization of a magnetron design – to find out more about optimization visit our Optimizer page.

I must acknowledge and thank these organizations that have variously provided validation of the software, design specs, measured data and many of the images that have been used in this blog post. Thank you for reading, I hope that you have found this useful. More information can be found on our specialised webpages for charged particle devices, or contact us for further details.