2D calculation of parasitic fields in misaligned multipole electron-optical systems.

The effects of geometrical imperfections in electron-optical components are usually evaluated in 3D simulations. These calculations inherently take a long time, require a large amount of memory, and do not directly produce the necessary axial field functions. We present a 2D perturbation method to calculate parasitic fields in misaligned multipole systems. Our method is based on finding an equivalent potential perturbation, similarly to Sturrock's method, but does not rely on the potential being differentiable. The method is directly applicable to both electrostatic and non-saturated magnetic problems. It does not require any 3D data and it is fully compatible with existing finite element method codes such as EOD. The proposed method produces axial field functions with an accuracy of units to a few tens of percents, depending on the number of unperturbed multipole field components used and the geometry. The results can then be used, for instance, to determine the parasitic imaging aberrations of the misaligned optical system using standard methods, in order to evaluate the effect of mechanical design tolerances.

Effect of sample tilt on PEEM resolution.

In electron microscopy design, the systems are usually assumed to be perfectly aligned or that possible small imperfections can be eliminated by simple multipole correctors (centering deflectors, stigmators) without loss of resolution. However, in some cases, like in the cathode lens between the sample and the objective lens in the photoemission electron microscope, even a small imperfection can impair the resolution significantly. Because of the strong field between the sample and the objective lens, even a small tilt of the sample generates a parasitic dipole field, which decreases resolution and causes image deformations. We present a simulation of the influence of a small sample tilt on the system resolution based on modern computational methods that enable simulation of the whole system including the parasitic fields, proper setting of centering deflectors and stigmators. The resolution is determined by simulating the point spread function and finding the size of its significant part. The procedure is shown on realistic data from the literature. We found out that the resolution becomes worse mainly in the direction of the parasitic dipole field.

Determination of analytical expansion from numerical field data.

We introduce a method of calculation of the analytical expansion of the field near the axis that is based on an application of Green's theorem. The approach is demonstrated on an example of a round electrostatic unipotential lens with field computed by the finite-element method and results are compared to methods of Hermite polynomials and wavelet transformation which are used in electron optics. The work is motivated by application to calculations of aberration coefficients where the high order axial field derivatives must be known.

A pitfall in the calculation of higher order aberrations.

When calculating aberration coefficients of secondary and higher order, there is a danger of misinterpreting the result. An example is given for a homogenous magnetic field and the source of the difficulty is described.

Coulomb interactions in Ga LMIS.

For low emission currents from around 1 microA Ga liquid-metal ion sources (LMIS) produce fine optically bright ion beams that are strongly limited by the Coulomb particle-particle interactions. We present computations of the energy spread, the beam virtual crossover size, and beam brightness based on direct numerical integration of the equation of motion in a numerically calculated field for a number of dimensions of the emission tip. The Coulomb particle-particle interactions are included into the calculation of ion beam evolution. A comparison with experimental data allows to estimate the tip size.

Accuracy of electrostatic lens computations with FOFEM.

The increased speed of personal computers enables fast computation of rotationally symmetric electrostatic lenses with the first-order finite element method in meshes with a large number of mesh points. In order to produce an estimate of accuracy of the computed potential, we propose a simple procedure based on doubling the number of mesh points in each coordinate. In this way, we can produce for the lower-density mesh at each point the information about error of the potential and visualize the sources of the computation errors.