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Keeping a beady ion optics simulations

With the demise of the cathode ray tube (CRT, as used in old-style fat televisions), electrons and ions are not as apparent in a typical home as they once were. Electrons are tiny sub-atomic particles that carry a negative charge. Ions are still tiny, but much heavier than an electron and carrying either a positive or a negative charge. Carrying a charge means that these particles can be influenced and controlled by electrostatic and magnetic fields. In a CRT, electrons are accelerated through a vacuum and guided towards the inside face of the screen where they cause substances called phosphors to glow, creating the picture. Vacuum is needed as air molecules would impede the electrons and stop them lighting up the screen. A similar, less precise, process lights up old-style (pre-LED) fluorescent tubes. One device that most of us have, the microwave oven, generates microwave radiation from flying electrons.

In the workplace or laboratory there are many examples of devices that rely on flying charged particles. Much of what we do here at TSL involves flying electrons or ions. In sputter coating, ions are used like tiny cue balls to bash atoms from a solid material so that they coat onto a substrate. In an e-beam coater, a beam of electrons heats a material so that it evaporates and coats the sample. Our scanning electron microscope scans a beam of electrons across a sample to ping out secondary electrons from which to form an image. Sputter ion pumps and residual gas analysers use electrons and ions to create and monitor vacuum respectively. Many analytical instruments use electrons or ions. X-ray photoelectron spectroscopy (XPS) creates X-rays by accelerating a beam of electrons at an anode. The X-ray photons kick electrons out of the sample and the energy of these electrons is measured, providing information about the elements present at the sample surface.

To understand and predict the behaviour of ions and electrons in electrostatic and magnetic fields we need to apply various physical laws. This process can sometimes be greatly helped by using a computer to do the calculations and produce graphical and numerical outputs. SIMION 8.1 is an ion/electron simulation package that – with a little persuasion – can model some very sophisticated and complex situations. We will apply the capabilities of SIMION to help explain and illustrate the workings of an ion pump.

The ion pump (sometimes called a sputter ion pump) is a vacuum pump with no mechanical moving parts. It has moving parts, but these are all at the atomic or sub-atomic levels and include electrons, ions and individual atoms. I will attempt to explain in words how this works. The basic working unit of an ion pump is a Penning cell, a hollow cylindrical anode (an electron attractor) at a high positive potential and a pair of flat cathodes (sources of electrons) near the open ends of the anode (Figure 1). These are in vacuum. The cathodes are made of a reactive material such as titanium that can react with gas atoms to irreversably remove them from the vacuum as stable solid products.

The cathode material will rapidly develop a surface coating of these reaction products that will inhibit further reaction. The purpose of an ion pump is to remove individual atoms of titanium from the cathode to free them up for reacting with gases. Electrons (with a negative charge) from the cathodes are attracted into the anode space by the positive potential but experience a sideways force from a strong axial magnetic field and are prevented from hitting the anode. Instead they oscillate on serpentine trajectories and with long path lengths back and forth between the cathodes. If they strike a gas molecule they ionize it, giving it a positive charge and releasing another negative electron into the vacuum which can then oscillate and ionize other gas molecules. The positive gas ion is accelerated towards the negative cathode, which it strikes and cannons out a few titanium atoms (think of that cue ball striking the reds) that can stick to a surface somewhere and react with gas molecules that happen by.

Figure 1: The anode (green) of a Penning cell is at high positive potential relative to the cathodes (red)

There’s a lot going on there and it is not easy to get a sense of the bigger picture from this type of description. Let’s use SIMION to try to visualize what’s happening. We’ll leave out the magnetic field for now, but we’ll put the anode at +3000 V and the cathodes at 0 V. Let’s now release 10 electrons from the surface of each cathode (insider secret: SIMION doesn’t really do emission processes; like a benign creator, you have to bring electrons into being a fraction of a millimetre from the surface from which they emanate). Electrons have a negative charge, the anode is at positive potential, negative things are attracted to positive things so the electrons will fly straight at the anode, right? Not necessarily. Some do (Figure 2a) but some do not. How do we explain this variety of trajectories? Why are some electrons missing the anode entirely when we expect them to be attracted towards it?

Let’s change our mindset. Instead of thinking in terms of negative charges being attracted to an object at positive potential, let’s picture instead the space between them. With electrodes at differing potentials, the electric field between them must have a gradient. To an electron, the space between the cathodes feels like a BMXer’s half-pipe (Figure 3), with regions of high negative potential being like the top of a slope. Imagine sitting at the top of the potential gradient slope on one of the cathodes. If you roll electron marbles into the Penning cell, the overwhelming gradient is along the axis of the cell: they accelerate forwards along the cell. There is a slight arching curvature sideways towards the anode, so there will be some tendency to drift left or right, but the main gradient means that the marbles will tend to roll directly at the opposite cathode. If they get near the opposite cathode, the gradient there will send them back the way they came or divert them out of the cell (Figure 2a).

To give the electrons a fighting chance to meet and ionize gas molecules, we do not want them flying out of the cell or striking the anode; we need them to have long flight paths to increase the collision probabilty. Let’s take our simulation and introduce a strong magnetic field, say 2000 G, parallel to the axis of the cell. Now when the electrons fly they do not hit the anode (Figure 4a). Instead they oscillate back and forth between the two cathodes, rolling up and down the potential gradient. The sideways electrostatic gradient is still there, but if an electron exhibits any sideways movement and crosses the magnetic lines, it feels a force at right angles to the sideways movement. The result is that the electron paths are circular when viewed along the axis of the cell (Figure 4b).

Figure 2a: a cross-section showing electron trajectories. 1. Electron strikes anode directly 2. Electron misses anode and flies off into the distance 3. Electron flies directly at opposite cathode before u‑turning.

Figure 2b: a cutaway 3D view of the Figure 2a. The electrons that appear in 2a to stop in the middle of nowhere are actually striking the anode at points outside of the 2D cross‑section.

Figure 3: with the negative/positive potential field visualized within SIMION as physical slopes, it is easy to imagine electrons rolling down the steep gradients.

Figure 4a: with an axial 2000 G magnetic field applied, electrons are prevented from drifting towards the anode.

Figure 4b: Any lateral drift of the electrons causes a force at right angles to the drift, so the electron paths are circular (1) when viewed along the axis of the cell. The straighter trajectories (2) are positive ions accelerating towards the nearest cathode.

With longer flight paths because of the magnetic field, the probability of colliding with a gas molecule and ionizing it are increased. Several such events are seen in Figures 4a and 4b. To a positively charged the electric field gradients are reversed compared to those for an electron (Figure 5). Notice that the ions follow much straighter paths than the electrons. They feel a similar sideways force from the magnetic field but its effect on the ions is far less as they are so much heavier: a singly charged nitrogen ion, for example, has over 50 000x the mass of an electron. This brings us to some interesting phenomena: the trajectory of a charged particle depends on its mass in a magnetic field, but in an electrostatic field all particles with the same charge will follow the same trajectory with the speed dependent on the mass. The data from a large number of electron flights can be plotted to illustrate the distribution of the various events (Figure 6). The preferential sputtering from the centre of the cathode is what is observed in a real-world ion pump. It is a result of the slight curving of the potential gradient so that it is slightly lower along the centre of the cell than at the sides.

Figure 5: How the world feels to a positive ion.

Figure 6: Event positions gathered from a large number of electron flights plotted using Origin package.

A couple of confessions are in order at this point. There are no gas molecules wandering around in this model. The ionization events occur based entirely on a probabilistic calculation, the software running a piece of code at every little time step of every electron. The probability of a collision is calculated based on the electron’s velocity along with the ionization cross section, the temperature and the pressure of the gas. Introducing the magnetic field makes the paths of the electrons very long, so long, in fact, that the simulation is needlessly time‑consuming without giving any additional insight into the model. The ionization events of Figure 4 are based on the probabilistic calculation described earlier, but multiplied by a fudge factor of one million so that ionization occurs within a reasonable timespan and path length.

Ionization of the gas molecule is not the end of its journey. On striking the cathode the ion is likely to react with the titanium or become buried in the surface, but that surface is not a permanent one. The purpose of ionizing the gas molecule is to use it like a cue ball at the opening break in a frame of snooker: the ion strikes the cathode and ‘sputters’ titanium atoms into the vacuum where they can react and permanently remove gas molecules from the vacuum. The original ionized molecule is likely to emerge again from the cathode as material is sputtered away, so it will need to react again with some of the sputtered material, possibly on the inner surface of the anode. The sputtering of cathode material is not simulated in the current model and would probably be more usefully modelled with something like a molecular dynamics package.

We have learned that ‘rubber sheet’ visualizations of the electric field gradient can give better insights into a particle’s behaviour than simple consideration of its charge relative to electrodes, that a charged particle that crosses magnetic field lines will be deflected sideways to a degree that depends on its mass and that electron paths in a Penning cell can be so long before an ionization event that a fudge factor may be needed. I hope you have gained a small insight into how simulation and visualization can provide insight into charged particle behaviour.  At TSL we also use our charged particle simulation to model the electron beams of X‑ray sources for inspection systems and surface analysis instruments.