# Introduction

Electron diffraction is a common tool for analyzing the surface structures of crystalline materials. The first diffraction patterns using electrons were aquired in 1927, only three years after de Broglie's discovery of the wave nature of matter.Electron diffraction is like X-ray diffraction in principle, but unlike X-rays, electrons have strong electrostatic interactions with matter. This strong interaction limits the electrons ability to penetrate further than a few atomic layers into the sample, resulting in good surface sensitivity.

Modern electron diffraction has split into a large variety of distinct techniques. They can be classified based on the energy or the application. Common uses of electron diffraction are low-energy electron diffraction (LEED), reflection high-energy electron diffraction (RHEED), electron diffraction in transmission electron microscopy (TEM, involving several different diffraction modes), and electron backscatter diffraction (EBSD, often used with Scanning Electron Microscopy).

Figure 1. Electron diffraction pattern obtained in a TEM using a parallel electron beam. Figure from Wikipedia. License: CC BY-SA 3.0.

# Principles of electron diffraction

Diffraction can occur when waves pass through an opening that is approximately the same size as the wavelength. In order to study materials with electron diffraction, we must have electron beams with wavelengths comparable to interatomic distances. The wavelength of electrons accelerated by an electric field can be calculated with:

$$\lambda = \frac{h}{sqrt{2m_{e}eU}}$$

Where                   λ is the wavelength

h is the Plank constant

me is the mass of the electron

e is the charge of one electron

U is the voltage

Voltages of 20 - 200 V are enough to obtain wavelengths suitable for electron diffraction (100 V = 1Å).

# Low-Energy Electron Diffraction (LEED)

LEED is typically done using accelerating voltages of 20 - 200 V. This low energy causes very limited electron penetration into the sample, allowing us to investigate the surface. LEED is therefore a method for studying the crystallography of surfaces or thin films using backscattered electrons.

In LEED, the position and intensity of diffraction peaks is monitored against electron energy. The electron source in LEED usually produces an electron beam of around 1 mm, which hits the sample perpendicularly. Between the electron source and the sample are grids and a phosphor screen. The purpose of the grids is to allow only elastically scattered electrons through. The phosphor screen is kept at a high positive potential to show clear fluorescence when it is struck by electrons. These spots form a periodic diffraction pattern, which can then be analyzed.

Figure 2. Instrumentation for LEED. Author: Reima Herrala.

# Reflection High-Energy Electron Diffraction (RHEED)

RHEED is used for determining the surface crystal structure, but it can also be used to monitor the growth mode and deposition rate of films. A key difference to LEED is that the electrons strike the sample at grazing angles (0.1 – 5 °). The energy of the electron beam in RHEED is typically 10 – 50 keV.

The high energy of the beam is enough to penetrate hundreds of nanometers into most materials, but the grazing angle of incidence limits the interaction to the topmost layer of atoms. The scattered electrons are collected on a phosphor screen and form a diffraction pattern.  When monitoring the growth of thin-films, the relative intensity of the diffracted beam can be plotted against time or angle.

The ability to monitor the growth of films is based on the low angle of the electron beam. Films that grow layer by layer with a smooth surface will result in a RHEED pattern of lines and streaks . Structured surfaces with 3D topography will instead create diffraction spots. This difference can be used to evaluate the growth of a film in situ. RHEED is suited to both low and high pressures.

Figure 3. Instrumentation for RHEED. Author: Reima Herrala.

# Modern applications and developments

Electron diffraction is still a routine tool for monitoring the growth of thin films. In metallurgy, automated EBSD is used for analyzing orientation correlations between phases, grains and domains, phase identification, and size distribution of different constituents. Figure 4 shows the EBSD diffraction patterns of ferrite and austenite.

Figure 4. EBSD diffraction patterns of ferrite (left) and austenite (right).  (License: CC BY 4.0)

Recent advances in a technique called MicroED (micro-electron diffraction) has allowed the imaging of several protein structures. This method uses a transmission electron microscope, where the protein sample is held at cryogenic temperatures to protect it from radiation damage. Data is acquired by rotating the sample unidirectionally, which results is a diffraction movie. The accumulated dose can be lower than 9 electrons per Å2. The resolution of MicroED imaged protein structures is typically above 2,5 Å.

# References

 1 1 2 3 Mittemeijer E.J., Welzel U. Modern Diffraction Methods. John Wiley & Sons, 2012. 2 1 2 3 4 Brundle C., Evans R., Charles A.Jr., Wilson, Shaun. Encyclopedia of Materials Characterization - Surfaces, Interfaces, Thin Films. Elsevier, 1992. 3 1 Girolami, Gregory S., X-Ray Crystallography. University Science Books, 2016. 4 1 2 3 4 5 Martin, Peter M. Handbook of Deposition Technologies for Films and Coatings - Science, Applications and Technology (3rd Edition). William Andrew Publishing, 2010. 5 1 2 3 Koster G., Huijben M., Rijnders G. Epitaxial Growth of Complex Metal Oxides. Elsevier, 2015. 6 1 2 Borrajo-Pelaez R., Hedström P. Recent developments of crystallographic analysis methods in the scanning electron microscope for applications in metallurgy. Critical Reviews in Solid State and Materials Sciences, 2018, 43, pp. 455 – 474. Doi: https://doi.org/10.1080/10408436.2017.1370576 7 1 Rodriguez J. A., Eisenberg D. S., Gonen T. Taking the measure of MicroED. Current Opinion in Structural Biology, 2017, 46, pp. 79 – 86. Doi: https://doi.org/10.1016/j.sbi.2017.06.004

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