Ultrashort electron pulses for diffraction, crystallography and microscopy: theoretical and experimental resolutions

Abstract

Pulsed electron beams allow for the direct atomic-scale observation of structures with femtosecond to picosecond temporal resolution in a variety of fields ranging from materials science to chemistry and biology, and from the condensed phase to the gas phase. Motivated by recent developments in ultrafast electron diffraction and imaging techniques, we present here a comprehensive account of the fundamental processes involved in electron pulse propagation, and make comparisons with experimental results. The electron pulse, as an ensemble of charged particles, travels under the influence of the space-charge effect and the spread of the momenta among its electrons. The shape and size, as well as the trajectories of the individual electrons, may be altered. The resulting implications on the spatiotemporal resolution capabilities are discussed both for the N-electron pulse and for single-electron coherent packets introduced for microscopy without space-charge.

Single-electron pulses for ultrafast diffraction

“…This marks a significant improvement over conventional sources of electron pulses, where temporal broadening was reported in the 150-to 300-fs regime (14,18,29,33). In spite of the lower quantum efficiency at 286 nm, single or a few electrons per pulse can still be generated with our optical UV source.…”

“…Ultrafast diffraction is an interference process, and electrons are scattered individually from the sample's atoms as quantum wave packets (17,18). On the detector, each electron interferes with itself and generates an event with highest probability at the positions of diffraction features and unlikely in-between.…”

“…Only such scatterers that lie within the coherence volume of the electron packets can contribute to the contrast of a diffraction pattern. The minimum transversal and longitudinal coherence lengths L t and L l of an electron beam are given by L t ≈ ℏ∕ðm e Δv t Þ and L l ≈ ℏv 0 ∕ð2ΔEÞ (18,41,42); v 0 is the mean longitudinal velocity of the accelerated packet. Assuming that our beams are described by these limits, the reported improvements of velocity spread and energy bandwidth at photon energies close to the work function should, besides improving temporal resolution, also enhance the coherence and interference contrast of single-electron diffraction patterns.…”

“…Such packets can be generated by photoelectric emission from metal films illuminated with femtosecond lasers, followed by acceleration in static or radio-frequency electric fields. In multielectron packets, space-charge effects dominate the temporal structure and energy distribution; hence electron density has to be traded off against resolution (18,19). In contrast, space charge is absent in packets containing only one single electron at a time (12).…”

Development of an Ultrafast Low-Energy Electron Diffraction Setup

“…To achieve precise temporal control over the emission process, pulsed electron sources are commonly driven by intense laser pulses [150,[163][164][165]. Most state of the art femtosecond photocathodes are based on the classical photoelectric effect, i.e., for moderate light intensities, electron emission occurs upon absorption of a photon with an energy ω above the work function Φ of the material (Fig.…”