Plasma and sputter sources
As well as cathode sources there are of course many other ways of specifying initial ray conditions. Here we deal with less usual sources.
Setting up particles from a plasma surface
In simulating plasmas it is usually assumed that to a good approximation the field inside a plasma is zero. It is also assumed that the field at the external surface (often called the meniscus) is also zero, as it is for a cathode that is governed by Childs Law. The local value of the current density Jext that is drawn from a given part of the meniscus is therefore determined by the local value of the external field Eext at a short distance d from this part. (This current density creates a space-charge cloud in front of the meniscus, so that the field at the meniscus itself then becomes zero.)
The current density Jint that flows inside the plasma at the inside surface of the meniscus is independent of the position and depends only on the temperature and composition of the plasma.
Equilibrium is achieved when Jext has the constant value Jint over the whole of the meniscus. This requires that Eext has the appropriate value and is constant over the whole of the meniscus. The meniscus therefore adjusts its shape so that this condition is satisfied. We assume here that the system is electrostatic, with no magnetic field.
The shape of the meniscus at the point where it meets the containing electrode (called the focus electrode) is particularly important. Here the meniscus should match the containing electrode smoothly, without a discontinuity in shape. This condition will be satisfied only for a particular value of Jint (see S Humphries Jr, Modeling ion extraction from a free-plasm surface with a flexible conformal mesh, J of Computational Physics, 204 (2005) 587-597).
In the CPO programs it is not possible to change the shape of a meniscus automatically or at run time. A manual iterative procedure must therefore be used. First, a meniscus that has approximately the expected shape is simulated as a Childs-Law cathode and is divided into segments. The external voltages are then adjusted to give approximately the required total current. The ray output file then contains information on the current from each segment and its area. The current density at each segment can therefore be deduced (a suitable external program will be needed to read and process the ray output file). In the ‘manual’ stage the shape of the meniscus is changed empirically to try to make Jext constant over its surface and equal to the value at the point nearest to the containing electrode (in order to try to match the meniscus shape to that electrode). This process is iterated until Jext is constant over the surface. Then the value of Jint is known (= Jext), which in turn defines the parameters of the plasma. Only three or four iteration should be needed to achieve constancy to better than 1%. The plasma has then been effectively simulated. An iterative process of this type has been described by Humphries (cited above).
Advice on the ‘manual’ stage:
The available information is the value of the emitted current density J for each segment of the plasma meniscus. The task is to change the positions of these segments so that (1) they all have the same J and (2) the outer border of the meniscus continues to touch the edge of the metal electrode that contains the plasma.
The current density J is proportional to Eext to the power of 3/2, according to Childs Law, where Eext is the field at a constant distance d from the surface. Making J constant over the surface of the meniscus is therefore equivalent to making E constant.
As an example, consider a meniscus that is expected to be approximately spherical in shape. It might be simulated in the first instance as a section of a sphere, the outer edge of which touches the edge of the containing electrode. If the radius is changed then the centre of curvature of the sphere must also be moved to satisfy the second condition. Initially its radius can be changed by a small amount to find how J changes across the meniscus. This information can then be used to estimate the radius that will give an approximately constant J. This procedure can then be applied iteratively. It would be possible to write a simple feed-back program that gives the new radius and the position of the centre automatically. At a later stage the meniscus might be simulated by two or more such spherical sections that join smoothly. When their radii are changed then all the positions of the centres must also be changed. An analogous iterative procedure could be used although the feed-back program would then be more complicated.
Sputter ion sources.