# Ultrafast electron diffraction

Ultrafast electron diffraction, also known as femtosecond electron diffraction, is a pump-probe experimental method based on the combination of optical pump-probe spectroscopy and electron diffraction. Ultrafast electron diffraction provides information on the dynamical changes of the structure of materials. It is very similar to time resolved crystallography, but instead of using X-rays as the probe, it uses electrons. In the ultrafast electron diffraction technique, a femtosecond (10$^{–15}$ second) laser optical pulse excites (pumps) a sample into an excited, usually non-equilibrium, state. The pump pulse may induce chemical, electronic or structural transitions. After a finite time interval, a femtosecond electron pulse is incident upon the sample. The electron pulse undergoes diffraction as a result of interacting with the sample. The diffraction signal is, subsequently, detected by an electron counting instrument such as a charge-coupled device camera. Specifically, after the electron pulse diffracts from the sample, the scattered electrons will form a diffraction pattern (image) on a charge-coupled device camera. This pattern contains structural information about the sample. By adjusting the time difference between the arrival (at the sample) of the pump and probe beams, one can obtain a series of diffraction patterns as a function of the various time differences. The diffraction data series can be concatenated in order to produce a motion picture of the changes that occurred in the data. Ultrafast electron diffraction can provide a wealth of dynamics on charge carriers, atoms, and molecules.

## History

The design of early ultrafast electron diffraction instruments was based on X-ray streak cameras, the first reported ultrafast electron diffraction experiment demonstrating an electron pulse length of 100 picoseconds (10$^{–10}$ seconds). The temporal resolution of ultrafast electron diffraction has been reduced to the attosecond (10$^{–18}$ second) time scale to perform attosecond electron diffraction measurements which reveal electron motion dynamics.

## Electron Pulse Production

The electron pulses are typically produced by the process of photoemission in which a femtosecond optical pulse is directed toward a photocathode. If the incident laser pulse has an appropriate energy, electrons will be ejected from the photocathode through a process known as photoemission. The electrons are subsequently accelerated to high energies, ranging from tens of kiloelectron-volts to several megaelectron-volts, using an electron gun.

## Electron Pulse Compression

Generally, two methods are used in order to compress electron pulses in order to overcome pulsewidth expansion due to Coulomb repulsion. Generating high-flux ultrashort electron beams has been relatively straightforward, but pulse duration below a picosecond proved extremely difficult due to space-charge effects. Space-charge interactions increase in severity with bunch charge and rapidly act to broaden the pulse duration, which has resulted in an apparently unavoidable trade-off between signal (bunch charge) and time-resolution in ultrafast electron diffraction experiments. Radio-frequency (RF) compression has emerged has an leading method of reducing the pulse expansion in ultrafast electron diffraction experiments, achieving temporal resolution well below 50 femtoseconds. Shorter electron beams below 10 femtoseconds are ultimately required to probe the fastest dynamics in solid state materials and observe gas phase molecular reactions.

## Single shot

For studying irreversible process, a diffraction signal is obtained from a single electron bunch containing $10^{5}$ or more particles.

## Stroboscopic

When studying reversible process, especially weak signals caused by, e.g., thermal diffuse scattering, a diffraction pattern is accumulated from many electron bunches, as many as $10^{8}$.

## Resolution

The resolution of an ultrafast electron diffraction apparatus can be characterized both in space and in time. Spatial resolution comes in two distinct parts: real space and reciprocal space. Real space resolution is determined by the physical size of the electron probe on the sample. A smaller physical probe size can allow experiments on crystals that cannot feasibly be grown in large sizes.
High reciprocal space resolution allows for the detection of Bragg diffraction spots that correspond to long periodicity phenomena. It can be calculated with the following equation:
    $\Delta s={\frac {2\pi }{\lambda _{e}}}{\frac {\varepsilon _{n}}{\sigma _{x}}}$,
where Δs is the reciprocal space resolution, λ$_e$ is the Compton wavelength of the electrons, ϵ$_n$ is the normalized emittance of the electrons, and σ$_x$ is the size of the probe on the sample.
Temporal resolution is primarily a function of the bunch length of the electrons and the relative timing jitters between the pump and probe.