If we consider a general ion device, in terms of simulation, what components might we encounter? Very often we have a source of particles – occasionally the particles that are eventually required, but more often, they are electrons or ions in a lower ionization state than needed. These enter a beam transport system, where the beam might be accelerated, focused and steered.
If the beam does not contain the required particle species, some interaction is required – either with a surface or volume. In this region exchange of charge and momentum takes place to give the required species. This often requires some sort of confinement system to increase the residence time of the particles in this region.
Once the required ions have been produced, they need to be extracted from the interaction region, usually electrostatically; unwanted particles that might also be extracted then need to be removed from the beam – using electric and/or magnetic fields – before the beam is transported for use. After transport, the beam is incident on its target, be it a further interaction volume or surface, and spent beams are incident on dumps, where the residual beam energy is absorbed.
So, what do we need a simulation tool to be able to do so that we can design and analyse an ion beam device?
We need to be able to generate primary particles; we need to be able to interact these particles with both electric and magnetic fields to accelerate, focus and steer the beam; and we need particle-particle, particle-surface and particle-volume interactions. In all of these we need to be able to simulate general scattering processes – where charge and momentum exchange can occur.
Having seen what we might need to simulate, I’d like to turn to how the features of Opera that help us to meet these needs. I’ll leave particle generation aside for the moment, and look at a couple of options for determining the interaction between charged particles, electric and magnetic fields.
We’ll start by considering the motion of charged particles in electric and magnetic fields. Since the particles are typically relativistic, it is convenient to cast Newton’s law of motion in terms of momentum, the rate of change of which is then given by the forces acting on the particle – the Lorentz force. Particle tracking using this simple formulation can be performed in the Opera Post-Processor. However, we have ignored the effect of the presence and motion of the charged particles on the fields. For a self consistent solution we need to include these, so we need some way to account for the interdependence.
In summary, the space charge solver in Opera incorporates an efficient technique that can track particles self-consistently in combined fields. The technique allows us to introduce primary particles, and enables interactions to produce secondary particles. The particle tracks carry current and have known momentum and power – so we can calculate power deposition. And we can do this fast enough to be able to simulate real-world devices.
I’ve mentioned tracking in combined fields several times, and the use of an applied magnetic field is common in ion beam devices. Opera provides several ways to add the applied magnetic field to the particle simulation. The simplest is the application of a uniform external field, specified by its components, Hx, Hy, Hz, in the Modeller.
A feature often used in Opera is to represent coils of various shapes as Biot-Savart conductors. These are extremely efficient, and may be included in a Opera’s space charge solver model; the resulting magnetic fields will be calculated, and used, during the space charge simulation. Alternatively you can import field data from measurements. The need to include the space charge from the particles is the norm, since its presence is often a performance determining factor. Conversely, very often, the magnetic field from the beam current is very small compared with the applied field, and is often ignored.
However, with an intense beam, the self-field can be significant, and must be calculated self-consistently in the simulation – Opera allows this as an option. Returning to what we need to calculate, we have described this so far – the interaction between particles and fields. We’ve mentioned the generation of particles, and their interactions, we’ll now look at this in a little more detail. In Opera, the generation of particles, and their interaction with other particles, surfaces and volumes, is enabled by a set of emission models. These models embody the physics of emission and interaction. Opera includes a wide range of such models that provide the ability to generate arbitrary species of particles, and to define their interactions. Among these are a number specifically for ion devices.
This is adequate for many applications and produces results quickly. This type of emitter is included in Opera, where it is known as the plasma free surface emitter. A quick mention for a post-processing feature -the two views in the centre show the ion beam trajectories coloured by their time of flight, and the potential distribution on device structure.
But what about extraction of results? Having simulated these processes, we need to extract useful metrics from the result. Opera as standard includes a very capable Post-Processor, with very flexible tools for generating many useful types of result.
A standard feature of the Post-Processor is the ability to display field quantities on the surfaces of the model, and on patches and lines placed anywhere within the model space. All such quantities may then be save in simple text format as required. While many of the field quantities are common across a range of Opera solvers, some apply specifically to particular applications, including space charge modelling. One of these is the voltage in the absence of space charge. We can see the significance of the space charge by comparing this with the actual voltage.
From these, simple additional computations can generate beam metrics, including the moments, emittance and phase space. This may be performed using Opera’s scripting language – and if required example scripts can be made available as a starting point for user-specific processing. When performing magnetron sputtering simulations the Post-processor can also display number density of the depositing species in the beam, and of surface material particles produced by secondary emission for erosion. This you can produce graphical output representing deposition and erosion rates.
The power deposited on surfaces of the model by the particle tracks can be captured on all surfaces on which a secondary emitter is defined. The deposited beam power density is then derived as the difference between incident power and the power in secondary emission species, and can be exported simply to Opera’s thermal simulator. Thermal analysis may then be performed – either steady state, or, by time-limiting the excitation, a transient thermal analysis may be run to simulate the effect of pulsed beams.
In summary the features of the Opera Space Charge solver provide a powerful and flexible tool for the design of ion beam devices. The techniques that it uses allow rapid and accurate analysis Opera provides all of the features required to perform a complete multiphysics analysis The Optimizer allows users to rapidly improve designs, even with competing requirements.