Parasitic Aberrations Research Articles

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.

Effect of magnetic quadrupole lens alignment on a nuclear microprobe resolution

The paper reports the research trends in developing probe-forming systems with high demagnification and analysis factors that limit a nuclear microprobe resolution. Parasitic aberrations caused by tilts and offsets of magnetic quadrupoles are studied in terms of their effect on probe parameters on a target. The most common arrangements of probe-forming systems such as a triplet and “Russian quadruplet” with separated geometry are considered. The accuracy prerequisites for the positioning of the quadrupoles are defined, and practical guidelines for alignment of probe-forming systems with high demagnification factors are suggested.

Cc, Cs, and parasitic correction in quadrupole probe-forming lenses

Approximate expressions are derived for the second and third order aberrations of a quadrupole doublet, allowing for aberrations intrinsic to fields of perfect symmetry, for parasitic aberrations of imperfect symmetry, and for compensating multipole lenses. Five third-order coefficients are found, and expressed in terms of four octopole strengths and the first-order parameters of the doublet as determined by its dimensions. For compensation of third-order aberrations of achromatic quadrupole/octopole lenses, either skew octopole lenses are required externally, or lenses with more than 8 poles are required coincident with the quadrupoles. If an octopole lens is added between the quadrupoles of the achromatic doublet, the spherical aberration of a condenser lens may be compensated. Such a Cs and Cc compensated quadrupole doublet is suitable for use as a probe-forming lens in focused ion beam systems and ion microscopes.

Development of Cs and Cc correctors for transmission electron microscopy

Novel spherical aberration (Cs) and chromatic aberration (Cc) correctors, which correct aberrations using a new principle, were developed. The asymmetric Cs correctors were designed for use in the probe- and image-forming systems at 300 kV to diminish undesired parasitic aberrations. The correctors composed of non-equivalent multipoles connecting with a demagnifying transfer doublet in the system. The axial aberrations were corrected well up to the fifth order except 6-fold astigmatism (A(6)) experimentally. Next, we developed superior Cs correctors for probe- and image-forming systems of low voltage microscope that uses triple dodecapoles to correct 6-fold astigmatism (A(6)). An important feature of this system is the rotation of the 3-fold astigmatism azimuth at the second dodecapole. The optimum rotation of the three hexapole fields for the compensation of A(6) was derived from theoretical calculations. The experimental results confirmed the compensation of A(6) and the third-order Cs. Finally, a unique Cc corrector, which utilized the concave lens effect formed by a long quadrupole field, was designed. The performance of the Cc corrector was investigated using a 30-kV transmission electron microscope. The results confirmed that Cc correction was achieved.

Design and performance of the HVE electrostatic nuclear microprobe

High Voltage Engineering (HVE) designed, built and tested its first electrostatic nuclear microprobe lens with micrometer lateral resolution, based on the “Russian” quadruplet configuration. Ray tracing and three dimensional finite element methods were applied to quantify the role of spherical and parasitic aberrations, to optimize the lens geometry (e.g. electrode to bore diameter ratio) and to determine allowable mechanical tolerances. The lateral resolution of the nuclear microprobe was measured using a 1.5MeV He+ ion beam. An image of 6.8 (±0.2) μm×6.1 (±0.2) μm (FWHM) was obtained for an object size of 100 (±1) μm×100 (±1) μm with 0.23mrad half-angle divergence (33% lens filling). This closely corresponds to the expected beam size based on the calculated theoretical demagnification of 16.08 (15.5 measured). Additionally, this indicates the little contribution of the spherical and parasitical aberrations and a good agreement between design and actual performance.

Nonlinear processes of probe formation of a beam with inhomogeneous phase density at nuclear microprobe

The work describes nonlinear processes of probe formation on the target with allowance for an inhomogeneous density of ion distribution in phase space in the object collimator plane taken from experimental data. The chromatic aberrations, intrinsic aberrations of the 3rd order and parasitic aberrations caused by sextupole and octupole components of the magnetic quadrupole lens field have been taken into account in the object-target phase coordinate transformation. The criterion of obtaining the optimal resolution was defined as the minimum spot size (FWHM) for a fixed ratio IFWHM/I0 of beam current in this spot to the total beam current. The conditions for which the initial density of ion distribution in phase space is matched with the ion-optical characteristics of the probe-forming system were considered. The influence of axial brightness and parasitic sextupole and octupole field components on the beam current distribution at the target has been determined.

Study of the aberrations of the IMP heavy ion microbeam irradiation system

A high energy heavy ion microbeam irradiation system is constructed at the Institute of Modern Physics (IMP) of the Chinese Academy of Sciences (CAS). A quadrupole focusing system, in combination with a series of slits, has been designed here. The IMP microbeam system is described in detail. The intrinsic and parasitic aberrations associated with the magnets are simulated. The ion beam optics of this microbeam system is investigated systematically. Then the optimized initial beam parameters are given for high spatial resolution and high hitting rates.

Control of parasitic aberrations in multipole optics

A method is described to find the optimal fourth order setup of a quadrupole-octupole third-order aberration corrector. Given accurate measurements of aberrations to fifth order, stimulus/response experiments can be used to synthesize pure controls for each measured aberration up to fourth order, including those which are caused by parasitic effects - symmetry violations, misalignments, construction mistakes, post-construction drift or other problems.

Control of Parasitic Aberrations in Multipole Corrector Optics

Extended abstract of a paper presented at Microscopy and Microanalysis 2008 in Albuquerque, New Mexico, USA, August 3 – August 7, 2008

Aberration-corrected STEM: current performance and future directions

Through the correction of spherical aberration in the scanning transmission electron microscope (STEM), the resolving of a 78 pm atomic column spacing has been demonstrated along with information transfer to 61 pm. The achievement of this resolution required careful control of microscope instabilities, parasitic aberrations and the compensation of uncorrected, higher order aberrations. Many of these issues are improved in a next generation STEM fitted with a new design of aberration corrector, and an initial result demonstrating aberration correction to a convergence semi-angle of 40 mrad is shown. The improved spatial resolution and beam convergence allowed for by such correction has implications for the way in which experiments are performed and how STEM data should be interpreted.

The Amsterdam quintuplet nuclear microprobe

A new nuclear microprobe comprising of a quintuplet lens system is being constructed at the Ion Beam Facility of the “Vrije Universiteit” Amsterdam in collaboration with the Microanalytical Research Centre of the University of Melbourne. An overview of the Amsterdam set-up will be presented. Detailed characterisation of the individual lenses was performed with the grid shadow method using a 2000 mesh Cu grid mounted at a relative angle of 0.5° to the vertical lens line focus. The lenses were found to have very low parasitic aberrations equal or below the minimum detectable limit for the method, which was approximately 0.1% for the sextupole component and 0.2% for the octupole component. We present experimental and theoretical grid shadow patterns, showing results for all five lenses.

Resolution limit of probe-forming systems with magnetic quadrupole lens triplets and quadruplets

Over the past decade, in MeV ion beam microanalysis efforts to achieve a spatial resolution better than 0.1 μm with a beam current of ∼100 pA have been connected with microprobes of new generation where the probe is formed by means of separated magnetic quadrupole lens structures [1]. However, as was pointed out in [2], no dramatic improvements in spatial resolution have been produced so far. For better understanding of the situation the authors carried out theoretical studies of multiparameter sets of probe-forming systems based on separated triplets and quadruplets of magnetic quadrupole lenses. Comparisons were made between the highest current values attained at different systems for a given beam spot size. The maximum parasitic sextupole and octupole field components were found whose contributions to spot broadening are tolerable. It is shown that the use of modern electrostatic accelerators [3] and precision magnetic quadrupole lenses [4,5] makes it possible to eliminate the effect of chromatic aberrations and second- and third-order parasitic aberrations resulting from distortions of the quadrupole lens symmetry. Therefore probe-forming systems with triplets and quadruplets of magnetic quadrupole lenses have a lower theoretical spatial resolution limit which is restricted mainly by intrinsic spherical third-order aberrations in state-of-the-art microprobes.

A two-regime probe-forming system for modern nuclear nanoprobes

This paper describes the long version of an optimized probe-forming system based on the divided Russian quadruplet of magnetic quadrupole lenses. The calculations include dominant intrinsic and parasitic lens aberrations. The feature of the system is a two-regime operation. This new versatile system is promising for modern nuclear nanoprobes. The system resolutions expected are presented.

The use of solenoid lenses in a two-stage nuclear microprobe probe-forming system

Nuclear microprobes typically achieve a demagnification between 20 and 100 by using a single-stage quadrupole multiplet as the probe-forming system. Whilst quadrupole lenses provide the strong field necessary for focusing MeV ions, they also have higher intrinsic spherical and chromatic aberrations, and also higher parasitic aberrations than found in solenoid lenses. Given the fundamentally superior spatial resolution which is attainable using solenoids, their use in a two-stage microprobe system comprising a magnetic quadruplet and a solenoid lens as the first and second demagnifying stages respectively is studied here. Calculated results are compared with a two-stage system comprising two quadruplets and also with an existing single-stage system.

Atomic Structure Determination Using the Focal-Series Reconstruction Technique

During the last five years the technique focal-series reconstruction has evolved to a powerful tool for investigating materials science problems in high-resolution transmission electron microscopy. Compared to the conventional interpretation of one single high-resolution image, the quantum mechanical electron wave function at the exit plane of the object (exit-plane wave function, EPW) is in many cases a better starting point for the materials analysis. The retrieval of the EPW is achieved on a routine basis by applying automated numerical procedures to a series of images taken from the same specimen area at different objective lens defocus values. The application of the reconstruction procedure allows one to remove numerically all the well known instrumental artifacts, such as nonlinear contrast formation or delocalisation effects due to spherical aberration and other parasitic aberrations. The reconstructed EPW gives thus direct insight into the atomic structure in the case of sufficiently thin objects and renders tedious image simulations of complicated defects unnecessary in many cases.

Tolerancing of electron beam lithography columns

A new software package has been developed for the tolerancing of complete electron and ion beam columns. The software computes the asymmetry aberrations caused by small mechanical imperfections in the construction and alignment of the lenses and deflectors. The imperfections considered include misalignments, tilts and ellipticities of individual polepieces, electrodes, coil windings and deflection plates. The asymmetry fields due to these mechanical errors are computed by perturbation methods, and the resulting parasitic aberrations are evaluated with asymmetry aberration integrals. The effects of aberration correction elements, such as alignment coils and stigmators, are also handled by the software. The overall effects of the aberrations can be displayed graphically. Illustrative results are presented for nanolithography and high-throughput lithography systems.

Nuclear microprobe design

Nuclear microprobes with a spatial resolution in the micron or smaller range require high-quality focusing systems. Important accelerator parameters for the design are the brightness and the beam energy spread. Ion-optical calculations are necessary to support the choice of focusing device that should be used. Parasitic aberrations, such as those associated with quadrupole misalignments have to be kept low to prevent beam spot enlargement. A scanning device is used when excessive heat damage should be prevented. A versatile vacuum chamber should be built to facilitate the necessary analytical detection techniques. In this paper some aspects of nuclear microprobe design are presented.

ISIOS: a program to calculate imperfect static charged particle optical systems

Recent achievements in analytical methods for the calculations of parasitic aberrations in particle optical systems lead to the development of the computer program ISIOS in which these methods are implemented in a general transfer matrix algorithm. The main features and capabilities of this program are described in this paper and examples of practical results concerning the estimation of tolerances for specific systems are given.

Correction of aberrations, a promising means for improving the spatial and energy resolution of energy-filtering electron microscopes

It is shown that the correction of aberrations is the most promising procedure for improving significantly the performance of electron microscopes. The basic parts of an analytical sub-ångström transmission electron microscope (SATEM) are discussed. The proposed analytical SATEM should yield a resolution limit of about 0.6 Å and allow isochromatic energy filtering with energy windows below 1 eV. For achieving these limits in practice, the incoherent parasitic aberrations must be sufficiently suppressed. In addition a monochromator for reducing the energy width of the incident electrons is mandatory. The correction of the aberrations is discussed for the objective lens, the energy filter and the projector system.

A superconducting solenoid as probe forming lens for microprobe applications

An improved nuclear microprobe system for applications in material science has been designed at the Dynamitron Tandem Laboratory of the University of Bochum. A superconducting solenoid as probe forming lens allows a wide range of projectile masses and energies. We describe the expected performance of the new system calculated by ray tracing and first experiments with the new lens system. The effects of chromatic, spherical and mechanical aberrations, including misalignment and beam scanning, were determined. The calculations show that a very high degree of axial symmetry of the focusing coil is of main importance to avoid parasitic aberrations. This demands extreme accuracy in the fabrication approaching the technical limits.