Aberration-corrected transmission electron microscopy

{{Main article|Scherzer's theorem}}

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{{cite journal |last1=Scherzer |first1=Otto |title=Über einige Fehler von Elektronenlinsen |journal=Zeitschrift für Physik |date=September 1936 |volume=101 |issue=9–10 |pages=593–603|doi=10.1007/BF01349606 |bibcode=1936ZPhy..101..593S |s2cid=120073021 }} 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.{{Cite journal|last=Schönhense|first=G.|date=2006|title=Time-Resolved Photoemission Electron Microscopy|journal=Advances in Imaging and Electron Physics|volume=142|pages=159–323|doi=10.1016/S1076-5670(05)42003-0|isbn=9780120147847}}

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.{{cite book |last1=Rose |first1=H. |title=Proceedings of the 2005 Particle Accelerator Conference |chapter=Aberration Correction in Electron Microscopy |chapter-url=https://accelconf.web.cern.ch/accelconf/p05/PAPERS/WOAC001.PDF |date=2005 |pages=44–48 |doi=10.1109/PAC.2005.1590354 |isbn=0-7803-8859-3 |s2cid=122693745 |accessdate=5 April 2020}}

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.{{cite web |title=Otto Scherzer. The father of aberration correction |url=https://www.microscopy.org/images/posters/Scherzer.pdf |website=Microscopy Society of America |accessdate=5 April 2020}} 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.{{cite journal |last1=Scherzer |first1=Otto |date=1947 |title=Sphärische und chromatische Korrektur von Elektronenlinsen |journal=Optik |volume=2 |pages=114–132}}{{Cite book |last=Orloff |first=Jon |url=https://books.google.com/books?id=_rYbAyf-iAkC |title=Handbook of Charged Particle Optics |date=1997 |publisher=CRC Press |isbn=978-0-8493-2513-7 |editor-last=Orloff |editor-first=Jon |location=Boca Raton, Fla. |page=234 |editor-last2=Chemical Rubber Company}}{{Cite book |last=Ernst |first=Frank |url=https://books.google.com/books?id=PJ91JeCvcGoC |title=High-Resolution Imaging and Spectrometry of Materials |date=2003 |publisher=Springer |isbn=978-3-540-41818-4 |editor-last=Rühle |editor-first=Manfred |series=Springer series in materials science |location=Berlin ; New York |page=237 |editor-last2=Ernst |editor-first2=F.}} A correction of the chromatic aberration can be achieved with time-dependent, i.e. non-static, electromagnetic fields (for example in particle accelerators).{{cite web |last1=Liao |first1=Yougui |title=Correction of Chromatic Aberration in Charged Particle Accelerators with Time-varying Fields |url=http://www.globalsino.com/EM/page3758.html |website=Practical Electron Microscopy and Database |accessdate=5 April 2020}}

The benefit of the scanning transmission electron microscope (STEM) and its potentional 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.{{Cite journal |last=Crewe |first=Albert V. |date=1966-11-11 |title=Scanning Electron Microscopes: Is High Resolution Possible?: Use of a field-emission electron source may make it possible to overcome existing limitations on resolution. |url=https://www.science.org/doi/10.1126/science.154.3750.729 |journal=Science |language=en |volume=154 |issue=3750 |pages=729–738 |doi=10.1126/science.154.3750.729 |pmid=17745977 |issn=0036-8075}} Through this and other iterations, Crewe was able to improve the resolution of the STEM from 30 Ångstroms (Å) down to 2.5 Å.{{Cite journal |last=Pennycook |first=S. J. |date=2012-12-01 |title=Seeing the atoms more clearly: STEM imaging from the Crewe era to today |url=https://www.sciencedirect.com/science/article/pii/S0304399112001076 |journal=Ultramicroscopy |series=Albert Victor Crewe Memorial Issue |volume=123 |pages=28–37 |doi=10.1016/j.ultramic.2012.05.005 |pmid=22727567 |issn=0304-3991}} Crewe's work made it possible to visualize individual atoms for the first time.{{Cite journal |last1=Crewe |first1=A. V. |last2=Wall |first2=J. |last3=Langmore |first3=J. |date=1970-06-12 |title=Visibility of Single Atoms |url=https://www.science.org/doi/10.1126/science.168.3937.1338 |journal=Science |language=en |volume=168 |issue=3937 |pages=1338–1340 |doi=10.1126/science.168.3937.1338 |pmid=17731040 |bibcode=1970Sci...168.1338C |issn=0036-8075}}

Crewe filed patents for electron aberration correctors,{{Cite patent|number=US4303864A|title=Sextupole system for the correction of spherical aberration|gdate=1981-12-01|invent1=Crewe|invent2=Kopf|inventor1-first=Albert V.|inventor2-first=David A.|url=https://patents.google.com/patent/US4303864A/en}}{{Cite patent|number=US4389571A|title=Multiple sextupole system for the correction of third and higher order aberration|gdate=1983-06-21|invent1=Crewe|inventor1-first=Albert V.|url=https://patents.google.com/patent/US4389571A/en}} 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.{{Cite journal |last=Rose |first=Harald |date=June 1990 |title=Outline of a spherically corrected semiaplanatic medium-voltage transmission electron microscope |journal=Optik |volume=85 |issue=1 |issn=0030-4026}} 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.{{Citation needed|date=August 2024}}

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.{{cite journal

| last1 = Verbeeck |first1 = Jo |last2 = Béché |first2 = Armand |last3 = Müller-Caspary |first3 = Knut |last4 = Guzzinati |first4 = Giulio |last5 = Luong |first5 = Minh Anh |last6 = Den Hertog |first6 = Martien |title = Demonstration of a 2 × 2 programmable phase plate for electrons |journal = Ultramicroscopy |volume = 190 |pages = 58–65 |year = 2018 |url = https://www.sciencedirect.com/science/article/pii/S0304399117305041 |doi = 10.1016/j.ultramic.2018.03.017|pmid = 29689445 }}{{cite journal |last1 = Vega Ibanez |first1 = Francisco |last2 = Beche |first2 = Armand |last3 = Verbeeck |first3 = Jo |title = Can a Programmable Phase Plate Serve as an Aberration Corrector in the Transmission Electron Microscope (TEM)?| journal =Microscopy and Microanalysis |volume = 29 |issue = 1 |pages = 341–351 |year = 2024 |url = https://academic.oup.com/mam/article/29/1/341/6987564 |doi = 10.1017/S1431927622012260|arxiv = 2205.07697 }}{{Cite journal |last1=Ribet |first1=Stephanie M |last2=Zeltmann |first2=Steven E |last3=Bustillo |first3=Karen C |last4=Dhall |first4=Rohan |last5=Denes |first5=Peter |last6=Minor |first6=Andrew M |last7=dos Reis |first7=Roberto |last8=Dravid |first8=Vinayak P |last9=Ophus |first9=Colin |date=2023-12-21 |title=Design of Electrostatic Aberration Correctors for Scanning Transmission Electron Microscopy |url=https://academic.oup.com/mam/article/29/6/1950/7321168 |journal=Microscopy and Microanalysis |language=en |volume=29 |issue=6 |pages=1950–1960 |doi=10.1093/micmic/ozad111 |pmid=37851063 |issn=1431-9276|arxiv=2303.09693 }}

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.

{{Main article|Nion (company)}}

Ondrej Krivanek and Niklas Dellby founded Nion in the late 1990s,{{Cite journal |last1=Batson |first1=P. E. |last2=Dellby |first2=N. |last3=Krivanek |first3=O. L. |date=2002-08-08 |title=Sub-ångstrom resolution using aberration corrected electron optics |url=https://www.nature.com/articles/nature00972 |journal=Nature |language=en |volume=418 |issue=6898 |pages=617–620 |doi=10.1038/nature00972 |pmid=12167855 |bibcode=2002Natur.418..617B |issn=0028-0836}} initially as a collaboration with IBM.{{Cite news |last=Pool |first=Rebecca |date=2022-11-21 |title=Nion: The company that transformed microscopy |url=https://analyticalscience.wiley.com/content/article-do/nion-company-transformed-microscopy |url-status=live |archive-url=https://web.archive.org/web/20240524233317/https://analyticalscience.wiley.com/content/article-do/nion-company-transformed-microscopy |archive-date=2024-05-24 |access-date=2024-05-24 |work=Wiley Analytical Science}} Their first products were correctors of spherical aberration correctors for existing STEMs. Later on, they designed an ACTEM from scratch, UltraSTEM 1.{{Cite web |last=Doughton |first=Sandi |date=2010-09-05 |title=Kirkland microscopes can examine matter one atom at a time |url=https://www.seattletimes.com/seattle-news/kirkland-microscopes-can-examine-matter-one-atom-at-a-time/ |url-status=live |archive-url=https://web.archive.org/web/20160325222836/https://www.seattletimes.com/seattle-news/kirkland-microscopes-can-examine-matter-one-atom-at-a-time/ |archive-date=2016-03-25 |access-date=2024-05-25 |website=The Seattle Times |language=en-US}}

The approach to aberration correction used by Rose and Haider formed the basis of the company CEOS. They produced modular correctors which could be incorporated into microscopes produced by other vendors, which led to commercial products from FEI, JEOL, Hitachi, and Zeiss.

{{Main article|Transmission Electron Aberration-corrected Microscope Project}}

The Transmission Electron Aberration-corrected Microscope (TEAM) project was a collaborative effort between Lawrence Berkeley National Laboratory (LBNL), Argonne National Laboratory (ANL), Brookhaven National Laboratory, Oak Ridge National Laboratory, and the University of Illinois, Urbana-Chamaign{{Cite web |title=The TEAM Project: When/Where |url=https://web.archive.org/web/20110211204321/ncem.lbl.gov/TEAM-project/files/when_where.html |access-date=2024-05-27 |website=web.archive.org}} with the technical goal of reaching spatial resolution 0.05 nanometers, smooth sample translation and tilt, while allowing for a variety of in-situ experiments.{{Cite web |date=2011-02-11 |title=The TEAM Project: What is the TEAM microscope? |url=http://ncem.lbl.gov/TEAM-project/files/what.html |access-date=2024-05-27 |archive-url=https://web.archive.org/web/20110211204252/http://ncem.lbl.gov/TEAM-project/files/what.html |archive-date=2011-02-11 }}

The TEAM project resulted in several microscopes, the first was the ACAT at Argonne National Laboratory in Illinois which had the first chromatic aberration corrector, then the TEAM 0.5 and TEAM I at the Molecular Foundry in California, and concluded in 2009.{{Cite journal |last1=Dahmen |first1=Ulrich |last2=Erni |first2=Rolf |last3=Radmilovic |first3=Velimir |last4=Ksielowski |first4=Christian |last5=Rossell |first5=Marta-Dacil |last6=Denes |first6=Peter |date=2009-09-28 |title=Background, status and future of the Transmission Electron Aberration-corrected Microscope project |url=https://royalsocietypublishing.org/doi/10.1098/rsta.2009.0094 |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |language=en |volume=367 |issue=1903 |pages=3795–3808 |doi=10.1098/rsta.2009.0094 |pmid=19687066 |bibcode=2009RSPTA.367.3795D |issn=1364-503X}} Both the TEAM microscopes are S/TEMs (they can be used in both TEM mode and STEM mode) that correct for both spherical aberration and chromatic aberration.{{Cite web |title=TEAM 0.5 |url=https://foundry.lbl.gov/instrumentation/team-0-5/ |url-status=live |archive-url=https://web.archive.org/web/20240512081250/https://foundry.lbl.gov/instrumentation/team-0-5/ |archive-date=2024-05-12 |access-date=2024-05-27 |website=Molecular Foundry |publisher=Lawrence Berkeley National Laboratory}}{{Cite web |title=TEAM I |url=https://foundry.lbl.gov/instrumentation/team-i/ |url-status=live |archive-url=https://web.archive.org/web/20240310192300/https://foundry.lbl.gov/instrumentation/team-i/ |archive-date=2024-03-10 |access-date=2024-05-27 |website=Molecular Foundry |publisher=Lawrence Berkeley National Laboratory}} The TEAM microscopes are managed by the National Center for Electron Microscopy, a facility of the Molecular Foundry at LBNL, and ACAT by the Center for Nanoscale Materials at ANL.

Several other aberration correctors have been designed and used in electron microscopes such as one by Takanayagi.{{Cite conference |last1=Sawada |first1=H. |last2=Hosokawa |first2=F. |last3=Kaneyama |first3=T. |last4=Tomita |first4=T. |last5=Kondo |first5=Y. |last6=Tanaka |first6=T. |last7=Oshima |first7=Y. |last8=Tanishiro |first8=Y. |last9=Yamamoto |first9=N. |date=2008 |editor-last=Luysberg |editor-first=Martina |editor2-last=Tillmann |editor2-first=Karsten |editor3-last=Weirich |editor3-first=Thomas |title=Performance of R005 Microscope and Aberration Correction System |conference=EMC 2008 14th European Microscopy Congress 1–5 September 2008, Aachen, Germany |publisher=Springer Berlin Heidelberg |publication-place=Berlin, Heidelberg |pages=47–48 |doi=10.1007/978-3-540-85156-1_24 |isbn=978-3-540-85154-7}} Similar correctors have also been used at much lower energies such as for LEEM instruments.{{Cite journal |last1=Tromp |first1=R.M. |last2=Hannon |first2=J.B. |last3=Ellis |first3=A.W. |last4=Wan |first4=W. |last5=Berghaus |first5=A. |last6=Schaff |first6=O. |date=June 2010 |title=A new aberration-corrected, energy-filtered LEEM/PEEM instrument. I. Principles and design |url=https://linkinghub.elsevier.com/retrieve/pii/S0304399110000835 |journal=Ultramicroscopy |language=en |volume=110 |issue=7 |pages=852–861 |doi=10.1016/j.ultramic.2010.03.005|pmid=20395048 }}

In their modern state, resolutions of about 0.1 nm are fairly routine in microscopes around the world. This is true for both standard higher-voltage electron microscopes as well as a few ones specially designed to operate at lower electron energies. An important offshoot of the improved optical resolution is a companion improvement in the mechanical stability. Exploiting these improvements, significantly better identification of chemical contents of materials has become possible, as well as their atomic structure. This has had a major impact on our understanding across multiple fields of study.

There is a significant difference in the usage of AC-TEM across various fields. Despite aberration correction for electron microscopes existing in the case of STEMs, the amount of electrons needed to form useful images is far greater than biological samples can handle before being destroyed by radiation damage. Life science studies still heavily rely on conventional TEMs, which form a full image with their electron beam (similar to a conventional light microscope).

AC-TEM has been used extensively in physical sciences, in part due to the imperviousness of samples to radiation damage. This has ranged across chemistry, materials science and physics.

Aberration correction have yet to be significantly used in the life sciences, due to generally low atomic weight contrast in biological systems and also the increased radiation damage. However, the side benefits such as improved mechanical stability and detectors have significantly improved data collection quality.

{{reflist}}{{Electron microscopy}}

Category:Crystallography

Category:Electron microscopy