Gertrude F. Rempfer

A theoretical study of the hyperbolic electron mirror as a correcting element for spherical and chromatic aberration in electron optics

The spherical and chromatic aberrations of a converging electron mirror are of opposite sign from those of electron lenses. This important property makes it possible in principle to compensate the aberrations of electron lenses by means of an electron mirror and to design electron microscopes based on a corrected optics system incorporating an electron mirror. In this paper the properties of the hyperbolic electron mirror are calculated, and the conditions for simultaneous correction of spherical and chromatic aberrations are worked out for several types of electron microscopes. The hyperbolic mirror field is a rotationally symmetric potential field between two electrodes. The electrodes are shaped as equipotential surfaces of the hyperbolic field, except for an aperture on the axis of the positive electrode for entrance and exit of electrons. The effect of the aperture is to create a thin diverging aperture lens at the termination of the hyperbolic field. The properties of the mirror are calculated analy...

The resolution of photoelectron microscopes with UV, X-ray, and synchrotron excitation sources.

The resolution of emission electron microscopes is calculated by determining the intensity distribution in the image. The object is a small disc of uniform brightness centered on the axis. A finite object, as distinct form a point source, provides a non-zero current in the image without the requirement of infinite object brightness and the consequent infinities in the geometrical intensity distribution. The minimum object size, which in turn affects the resolution of the microscope, depends on the minimum current or contrast required in the image. In photoelectron microscopes with UV illumination just above the threshold for emission the predominant aberrations are the chromatic and spherical aberrations of the accelerating field and the spherical aberration of the objective lens. For higher energies, e.g. in the soft X-ray range, the chromatic aberration of the objective lens must also be taken into account, as the aberration coefficients of the accelerating field are greatly reduced. The intensity distributions in the image are calculated first for single energies. The intensity distribution for a beam with a range of energies is obtained by adding a series of single-energy distribution curves weighted according to the energy distribution function. In the presence of spherical aberration the position of the image formed by the electrons depends on the angle of emission. In image planes between the paraxial and marginal planes the combination of spherical aberration and defocus causes the the image spot to have a retrograde type of behavior as the angle of emission increases. The image spot initially moves away from the axis in the azimuth of emission and then returns to the axis and moves away in the opposite azimuth. As a result the intensity in the central portion of the image plane is enhanced. The single-energy intensity distribution curves calculated as a function of depth in the image reveal the existence of a compact, high-intensity image peak in an image plane located between the paraxial and marginal planes. This peak occurs in the plane in which the image spot has a maximum retrograde displacement equal to its radius. The present analysis shows that the resolution in the high-intensity plane is better than in the plane of least confusion, and the effects of aberrations in these two planes are quite different.(ABSTRACT TRUNCATED AT 400 WORDS)

Design and performance of a high-resolution photoelectron microscope

The design of a high-resolution photoelectron microscope (photoelectron emission microscope) is described. It is an oil-free ultrahigh-vacuum instrument utilizing electrostatic electron optics. New designs are presented for a specimen translator, cathode stage, aperture stop control, electrostatic hexapole stigmator, beam shutter, and camera system. These components could also be used in a low-energy electron microscope (LEEM). The theoretical resolution of this instrument is 5 nm for UV illumination near the photoemission threshold. The photoelectron microscope is now in operation at the University of Oregon, and it is achieving results within a factor of two of this design limit.

Unipotential electrostatic lenses: Paraxial properties and aberrations of focal length and focal point

An experimental study of electrostatic electron lenses as a function of geometrical and electrical parameters is described. The lenses are of the symmetrical three‐electrode unipotential type. The parameters are the thickness of the center electrode and the interelectrode spacing, both relative to the center electrode aperture diameter, and the ratio of lens voltage to cathode voltage. The lens properties are characterized in terms of the focal length and focal distance, and the spherical and chromatic aberrations of these quantities. In general, the principal surfaces of a lens are not plane, and the aberrations of focal length and focal distance are not the same. Expressions are derived relating the focal length and focal distance aberrations to the spherical and chromatic imaging aberration coefficients Cs and Cc, and the magnification aberrations. The advantages of formulating the lens properties in terms of focal length and focal distance and their aberrations, and the usefulness of the data presente...

Emission microscopy and related techniques : resolution in photoelectron microscopy, low energy electron microscopy and mirror electron microscopy

A unified treatment of the resolution of three closely related techniques is presented: emission electron microscopy (particularly photoelectron microscopy, PEM), low energy electron microscopy (LEEM), and mirror electron microscopy (MEM). The resolution calculation is based on the intensity distribution in the image plane for an object of finite size rather than for a point source. The calculations take into account the spherical and chromatic aberrations of the accelerating field and of the objective lens. Intensity distributions for a range of energies in the electron beam are obtained by adding the single-energy distributions weighted according to the energy distribution function. The diffraction error is taken into account separately. A working resolution is calculated that includes the practical requirement for a finite exposure time, and hence a finite non-zero current in the image. The expressions for the aberration coefficients are the same in PEM and LEEM. The calculated aberrations in MEM are somewhat smaller than for PEM and LEEM. The resolution of PEM is calculated to be about 50 A, assuming conventional UV excitation sources, which provide current densities at the specimen of 5 x 10(-5) A/cm2 and emission energies ranging up to 0.5 eV. A resolution of about 70 A has been demonstrated experimentally. The emission current density at the specimen is higher in LEEM and MEM because an electron gun is used in place of a UV source. For a current density of 5 x 10(-4) A/cm2 and the same electron optical parameters as for PEM, the resolution is calculated to be 27 A for LEEM and 21 A for MEM.

Simultaneous Correction of Spherical and Chromatic Aberrations with an Electron Mirror: An Electron Optical Achromat

Abstract: All lenses, whether for light or for electrons, have aberrations that limit their performance. In light optics the invention of the achromat over 200 years ago solved the problem of correcting spherical and chromatic aberrations; however, correcting aberrations of electron lenses remains a challenge. Spherical and chromatic aberrations constitute a fundamental barrier to improving resolution and reducing probe size in various types of electron-optical instruments. Recently, efforts have intensified to reduce probe size in microanalysis and lithography, and to improve resolution in the new emission microscopes being built for synchrotron light sources. The experiments described in this report show how an electron mirror can achieve simultaneous correction of spherical and chromatic aberrations.

Charging phenomena in PEEM imaging and spectroscopy.

Spectromicroscopy with the imaging technique of X-ray photoelectron emission microscopy (X-PEEM) is a microchemical analytical tool installed in many synchrotron radiation laboratories, and which is finding application in diverse fields of research. The method of sample analysis, X-ray absorption spectroscopy, does not encounter the same problems as X-ray photoemission spectroscopy when sample charging occurs, hence even good insulators may often be analyzed without any apparent artifacts in images or spectra. We show, however, that charging effects cannot be neglected. We model the effect of surface charge formation on the secondary electron yield from uniform samples to demonstrate that surface charge primarily reduces the yield of electrons which may contribute to the detected signal. We illustrate that on non-uniform insulating samples, localized centers of charge may substantially affect microscope imaging and resolution as the electrostatic field close to the surface is distorted. Finally, in certain circumstances non-uniform surface charge may lead to unexpected lineshapes in X-ray absorption spectra causing, in some extreme cases, negative spectra. These negative spectra are explained, and several strategies are reviewed to minimize the impact of sample charging when analyzing poorly conducting samples of any nature.

5.4 nm spatial resolution in biological photoemission electron microscopy.

We report a spatial resolution of 5.4 nm in images of sarcoplasmic reticulum from rabbit muscle. The images were obtained in an aberration-corrected photoemission electron microscope with a hyperbolic mirror as the correcting element for spherical and chromatic aberration. In-situ measurements and numerical simulations confirm the low residual aberration in the instrument and indicate the ultimate resolution in this type of microscopy to be below 2 nm.

A proposed modular imaging system for photoelectron and electron probe microscopy with aberration correction, and for mirror microscopy and low-energy electron microscopy

Abstract The design of an electron microscope is proposed which introduces a hyperbolic electron mirror to provide simultaneous correction of spherical and chromatic aberration. The beam-separating system is of novel design. The instrument is modular, and can be configured to be a photoelectron microscope (PEM, also called a photoelectron emission microscope, PEEM), an electron probe, or a transmission electron microscope (TEM), all with aberration correction. By substituting a high-voltage PEM-type specimen stage for the hyperbolic mirror, the instrument becomes a mirror electron microscope (MEM) or a low-energy electron microscope (LEEM).

Topographical effects in emission microscopy

An analysis of image formation and the origins of topographical effects in emission microscopy are presented. Simplified models of positive and negative surface relief are used in a quantitative treatment of several topographical effects. Negative surface relief is modeled by a trough having a hyperbolic field. The model for positive relief is a rounded ridge simulated by an equipotential surface of the electric field surrounding a half cylinder on a plane. The electron trajectories for the trough model are calculated in the principal azimuths, and analytical expressions are obtained for the time of flight and apparent distance from the anode of the virtual specimen surface formed in the acceleration process. Corresponding expressions for the ridge are derived for trajectories in the principal azimuth containing the cylinder axis. These expressions show that there is a very large depth magnification caused by relief. The effect is larger for negative than for positive topography of comparable geometries. The depth magnification for a trough or ridge is different for trajectories in different azimuths. The resulting astigmatic effect is greater for the trough than for the ridge. Topographical contrast is examined by calculating the trajectories of electrons emitted from the sloping walls of the trough. Tilting of the cone of electrons results in pronounced contrast, particularly when a limiting aperture stop is present. This treatment of topographical effects in emission microscopy differs from previous work in that the effects on the image are calculated analytically for simplified models of negative and positive topography. These results are generalized for the interpretation of photoelectron images of specimens with topography.