Sculpturing the electron wave function using nanoscale phase masks

Abstract

Electron beams are extensively used in lithography, microscopy, material studies and electronic chip inspection. Today, beams are mainly shaped using magnetic or electric forces, enabling only simple shaping tasks such as focusing or scanning. Recently, binary amplitude gratings achieved complex shapes. These, however, generate multiple diffraction orders, hence the desired shape, appearing only in one order, retains little of the beam energy. Here we demonstrate a method in electron-optics for arbitrarily shaping electron beams into a single desired shape, by precise patterning of a thin-membrane. It is conceptually similar to shaping light beams using refractive or diffractive glass elements such as lenses or holograms - rather than applying electromagnetic forces, the beam is controlled by spatially modulating its wavefront. Our method allows for nearly-maximal energy transference to the designed shape, and may avoid physical damage and charging effects that are the scorn of commonly-used (e.g. Zernike and Hilbert) phase-plates. The experimental demonstrations presented here - on-axis Hermite-Gauss and Laguerre-Gauss (vortex) beams, and computer-generated holograms - are a first example of nearly-arbitrary manipulation of electron beams. Our results herald exciting prospects for microscopic material studies, enables electron lithography with fixed sample and beam and high resolution electronic chip inspection by structured electron illumination.

Theoretical study of precision and accuracy of strain analysis by nano-beam electron diffraction

“…For this purpose, Grillo et al [35,36] propose a controllable phase shift of the electron wave which shifts more intensity to diffracted beams of higher order. The maybe most promising idea for our purpose is shown by Shiloh et al [37]. They demonstrate a method for forming an electron beam into a single desired shape by thin patterned SiN membranes.…”

Structured quantum waves

“…In 2014, however, a new class of holographic mask, already widely used in photon optics and known as the phase hologram, was reported to achieve electron beam shaping by directly imprinting controllable phases onto electron wavefunctions, resulting in unprecedented high efficiencies and low absorption losses 49,50 . This technique was shown to produce high-quality electron Bessel 36 and LG beams, with various azimuthal parameters .…”

Normal modes and mode transformation of pure electron vortex beams

“…The main technique for the realization of electron vortex beams includes computer-generated holographic masks applied in similar ways to those routinely adopted in the creation of optical vortex beams [24,25]. Other techniques include spiral phase plates [21,26], proposed spin-orbit angular momentum converters [27] and a method which relies on the Aharonov-Bohm effect [28,29]. More recently, such beams have also been generated using electron sieves [30].…”