Setting up ray parameters for field-emission and Schottky cathodes


(For information on user-defined field-emission cathodes see note on Use-defined cathodes.)


Difficulties can occur for very small field-emission sources, and less often for very small extended schottky emission sources.


Choosing inital ray conditions.

Choosing sensible initial conditions for the rays is very important.

As described in text books (see for example Hawkes and Kasper) the electrons start inside the material with a negative energy -W, where W is the work function in eV, plus some thermal energy.  Outisde the cathode there is the external field E and also a less significant mirror-image potential.  Together these produce a potential barrier, through which the electron has to tunnel before emerging into free space with a positive kinetic energy.  In principle the classical trajectory integration used in the program should start from outside the barrier, preferably from near where the electron emerges from the barrier.  However this position cannot be  defined exactly because it depends on factors such as the initial enegy of the electron when it was inside the material of the cathode, so the program does not attempt to define it.  

Instead the user should set up the initial ray conditions using the following guidance:

(1) The height of the potential barrier is usually within about 1eV of the work function W, so a useful distance is d = W/E, where E is the external field (in V/m).  The distance s between the cathode surface and the starting position of the rays should obviously in general be d.  Left to its own devices, the CPO2DS program uses a distance that is half the length of the cathode segment, and CPO3DS uses the maximum distance from the centre to a corner.   If this distance set by the program is less than d defined above then electron is effective emitted while still inside the barrier, in which case the program might crash (usually with a 'negative kinetic energy' message).  To avoid this the advanced 'distance away' option should be used, with the value of this distance being adjusted by trial and error (this can be done by temporarily using a ray printing level to inspect the initial kinetic and potential energies, which should be comparable).  Or the starting positions can be observed by zooming (using the 'right-click' method) and clicking on contours/potentials/contours, to make sure that the starting positions are in a region of small positive potential.

(2) Another way of responding to the 'negative energy' message is to use the advanced 'add energy' option.

(3) Another, less satisfactory method is to use the advaced option to start all the rays with a constant empirical energy.

Setting up other ray parameters.

It is important to be careful about defining the step lengths for the rays after they have left the cathode.

The lengths of the first few steps usually need to be  comparable to the size of the emission tip.  Otherwise crashes can occur  because at the beginning of a step (before the accurate trajectory integration) the program uses the available information (the initial velocity, acceleration and step length) to estimate the final velocity, which might then be unphysical.

Of course, the required step length is very small compared with the distance between tha cathode and anode, so maintaining it would result in extremely long ray tracing times.  However the program has a very useful 'advanced' option for increasing the step length as the ray tracing progresses, which should usually be used.   The option is available at \databuilder\tracing and screen options\advanced options\option for changing step length\.  The obvious way to use this option for field emission sources is to use the energy of the particle to control the step length.  For example, if the radius of the emission tip is 10nm, then the maximum step length could be set at 10nm for an energy between 0 and 100eV, then at 1000nm from 100eV to 1000ev, then at something like 5% of the remaining distance for higher energies.  To determine the parameters requires some  experimentation, using a high printing level (temporarily) to inspect the step lengths and energies of the first few steps of the first ray.

Note that if a large change in the step length is requested then the program automatically makes the change more gradual.