Recently, through mostly self-learning and vivid discussion with Dr. Ray Hill, I've made quite some progress in understanding the technique and work flow in designing an electrostatic-lens-based, ion optics column for charged particle apparatus.
First, I've managed to learn how to model an electrostatic lens, and to calculate its axial potential distribution with First Order Finite Element Method (FO-FEM). Knowing the potential, one can easily calculate the lens' paraxial optical properties, such as focal length, focus voltage, third-order spherical aberration and first order chromatic aberration.
A typical column design starts with designing the most critical elements in the column - the lenses. Two lenses are usually employed in an ion optics column. Lens design involves optimizing the geometry of the lens, such as bore sizes, electrode thickness and gap sizes between neighbouring electrodes to minimize spherical and chromatic aberration coefficients, within the physical boundaries set by practical limits, such as focus voltage, breakdown stability and etc. I've been able to model the objective lens and understand the effects of each geometrical factor on the optical properties of the lens.
After lenses are designed, they can be put together to form a column. In a column, one cares about one thing: for a given probe current, what is the minimum probe size that can be achieved. This calculation can be done using the so-called "d50" method, with which the probe size can be calculated from a series of parameters: beam energy, energy spread, spherical and chromatic aberration, probe current, source brightness and angular source intensity. I've developed several python-based programs to iteratively compute the Probe Size vs Probe Current curve of a given ion column.
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