Distortion is a classic problem in scanning-coil systems, and it is a different issue from resolution-limiting aberrations like coma or astigmatism. In SEM, STEM, and e-beam lithography, scan distortion is one of the main accuracy limits, even when resolution is excellent.
In a particle beam, the measure of the resistance of the beam to deflection by magnetic fields is expressed as the rigidity Bρ (units of Tesla.meter). If the beam is subject to a uniform perpendicular magnetic field B, the Lorentz force will create a circular motion. The bending radius becomes r = Bρ/B. After travelling a length s, the angular deflection is
$$ \theta \approx \tan\theta = \frac{L}{r} = \frac{BL}{B\rho} $$
This magnetic field is typically created by a saddle coil pair of length L along the beam direction.
A saddle coil consists of wires running along the beam tube, and then curved around the tube on both ends. The resulting geometry looks like a saddle. To create a perpendicular, almost uniform field another coil should be placed symmetrically on the other side of the beam, creating a saddle coil pair. Each pair can only scan in one direction, so two pairs are common for an xy-scanning application.
A single coil with the same angular wiring as two saddle coils, is possible by winding the wires around the beam. However, this is seldom used since a saddle coil pair can easily be produced and mounted onto the beam tube. Secondly, their symmetric angular wire leads to better cancellation of parasitic fields, leading to a cleaner uniform field.
Real scan coils do not create a perfect magnetic field, but with careful design and manufacturing distortion can be limited to acceptable limits. A quick overview of the design rules and manufacturability aspects are given here.
Non-uniform winding geometry, misaligned coil pairs, air gaps from inconsistent orthocyclic winding, uneven wire tension or relaxation, and asymmetric crossover placement produce parasitic fields and non-uniform B leading to distortion.
Tight, repeatable control can reduce distortion from noticeable to sub-resolution levels; the most critical tolerances are axial concentricity of the pair, angular position of windings (orthocyclic precision), crossover location repeatability, and consistent saddle-bend geometry—target micron-level positional repeatability and sub-degree angular repeatability where feasible.
Symmetric saddle coil pairs cancel opposing angular lead fields and isolate the central uniform perpendicular field; this symmetry reduces net parasitic multipoles and crosstalk compared with single wrapped geometries that have asymmetric return paths.
Perform magnetic field mapping (two-axis scans and multipole decomposition) to quantify distortion, verify concentric alignment with mechanical metrology, pot/epoxy the assembly for mechanical stability, and add magnetic/electrical shielding; re-test after potting and thermal cycling to confirm stability.
We partner with our customers to engineer and manufacture high-quality coils assemblies.
Through close collaboration, we tailor each solution to meet exact application requirements—ensuring reliability, performance, and seamless integration into advanced systems.
More information
