Aberration-corrected transmission electron microscopy

History

Early theoretical work

Scherzer's theorem is a theorem in the field of electron microscopy. It states that there is a limit of resolution for electronic lenses because of unavoidable aberrations.

German physicist Otto Scherzer found in 1936 that the electromagnetic lenses, which are used in electron microscopes to focus the electron beam, entail unavoidable imaging errors. These aberrations are of spherical and chromatic nature, that is, the spherical aberration coefficient C_s and the chromatic aberration coefficient C_c are always positive.

Scherzer solved the system of Laplace equations for electromagnetic potentials assuming the following conditions:

1. electromagnetic fields are rotationally symmetric,
2. electromagnetic fields are static,
3. there are no space charges.

He showed that under these conditions the aberrations that emerge degrade the resolution of an electron microscope up to one hundred times the wavelength of the electron. He concluded that the aberrations cannot be fixed with a combination of rotationally symmetrical lenses.

In his original paper, Scherzer summarized: "Chromatic and spherical aberration are unavoidable errors of the space charge-free electron lens. In principle, distortion (strain and twist) and (all types of) coma can be eliminated. Due to the inevitability of spherical aberration, there is a practical, but not a fundamental, limit to the resolving power of the electron microscope."

The resolution limit provided by Scherzer's theorem can be overcome by breaking one of the above-mentioned three conditions. Giving up rotational symmetry in electronic lenses helps in correcting spherical aberrations. A correction of the chromatic aberration can be achieved with time-dependent, i.e. non-static, electromagnetic fields (for example in particle accelerators).

Prototypes

The benefit of the scanning transmission electron microscope (STEM) and its potential for high-resolution imaging had been investigated by Albert Crewe. He investigated the need for a brighter electron source in the microscope, positing that cold field emission guns would be feasible. Through this and other iterations, Crewe was able to improve the resolution of the STEM from 30 Ångstroms (Å) down to 2.5 Å. Crewe's work made it possible to visualize individual atoms for the first time.

Crewe filed patents for electron aberration correctors, but could never get functioning prototypes.

In the early efforts to correct aberrations, low voltage electrostatic correctors were explored. These correctors used electrostatic lenses to manipulate the electron beam. The advantage of low voltage systems was their reduced chromatic aberration, as the energy spread of the electrons was lower at reduced voltages. Researchers found that by carefully designing these electrostatic elements, they could correct some of the spherical and chromatic aberrations that plagued early electron microscopes. These early correctors were crucial in understanding the behavior of electron optics and provided a stepping stone toward more sophisticated correction techniques.

Phase plate and similar ideas

The design parameters and functional requirements for phase plates were thoroughly examined in the context of their application as spherical aberration correctors. In particular, emphasis was placed on developing a programmable, electrostatic phase plate, highlighting its potential for precise control and adaptability in correcting aberrations.

First demonstrations

The first demonstration of aberration correction in TEM mode was demonstrated by Harald Rose and Maximilian Haider in 1998 using a hexapole corrector, and in STEM mode by Ondrej Krivanek and Niklas Dellby in 1999 using a quadrupole/octupole corrector. As the electron optic resolution improved, it became apparent that there also needed to be improvements to the mechanical stability of the microscopes to keep pace. Many aberration corrected microscopes heavily employ sound and temperature insulation, usually in an enclosure surrounding the microscope.