Low-Energy Electron Inelastic Mean Free Path of Graphene Measured by a Time-of-Flight Spectrometer.

The detailed examination of electron scattering in solids is of crucial importance for the theory of solid-state physics, as well as for the development and diagnostics of novel materials, particularly those for micro- and nanoelectronics. Among others, an important parameter of electron scattering is the inelastic mean free path (IMFP) of electrons both in bulk materials and in thin films, including 2D crystals. The amount of IMFP data available is still not sufficient, especially for very slow electrons and for 2D crystals. This situation motivated the present study, which summarizes pilot experiments for graphene on a new device intended to acquire electron energy-loss spectra (EELS) for low landing energies. Thanks to its unique properties, such as electrical conductivity and transparency, graphene is an ideal candidate for study at very low energies in the transmission mode of an electron microscope. The EELS are acquired by means of the very low-energy electron microspectroscopy of 2D crystals, using a dedicated ultra-high vacuum scanning low-energy electron microscope equipped with a time-of-flight (ToF) velocity analyzer. In order to verify our pilot results, we also simulate the EELS by means of density functional theory (DFT) and the many-body perturbation theory. Additional DFT calculations, providing both the total density of states and the band structure, illustrate the graphene loss features. We utilize the experimental EELS data to derive IMFP values using the so-called log-ratio method.

Correction of parasitic aberrations of hexapole corrector using differential algebra method.

We demonstrate an application of the differential algebraic method in optimization of a hexapole corrector of spherical aberration for the transmission regime of the standard scanning electron microscope. We introduce the method by visualization of the effect of all correcting elements to illustrate the principle of the corrector. Special interest is given to parasitic aberrations and their correction using additional deflectors before and inside the corrector. They can alter the off-axial position and tilt of the beam in the hexapoles. The critical values of the parasitic aberration coefficients are calculated using a wave-optical method, which determines the stability of the deflection system, the lens doublet, and the hexapoles. The derived properties of the parasitic aberrations are used in an alignment procedure of the system with the corrector.

In lens BSE detector with energy filtering.

We present a new type of an in-lens detector designed for Thermo Fisher Scientific (FEI) electron microscopes with the Elstar column. A key feature of it is high-pass energy filtering to enable the detection of low-loss backscattered electrons with their energy close to the primary beam energy. We show an application of the detector in imaging of a biological sample where the signal from these electrons leads to a significant improvement in resolution.

Novel simulation method of space charge effects in electron optical systems including emission of electrons.

We present a comprehensive numerical method for iterative computation of electron optical systems influenced by space charge which can accurately describe all effects in an optical system, including areas near a cathode tip and all crossovers. We use two different algorithms of evaluating the space charge distribution in different parts of the system. The Monte-Carlo based particle-in-cell method is used in the vicinity of the cathode. The algorithm based on the calculation of the current density distribution from an aberration polynomial is used for the rest of the system. We introduce a re-meshing algorithm which adapts the finite element mesh used for the field calculation in each iteration to the actual space charge distribution to keep it sufficiently fine in all areas with non-zero space charge. The algorithm is finally tested on a design of an experimental electron-welding machine developed at the ISI of the CAS.

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.

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.