Sculpturing the Electron Wave Function

Abstract

Coherent electrons such as those in electron microscopes, exhibit wave phenomena and may be described by the paraxial wave equation. In analogy to light-waves, governed by the same equation, these electrons share many of the fundamental traits and dynamics of photons. Today, spatial manipulation of electron beams is achieved mainly using electrostatic and magnetic fields. Other demonstrations include simple phase-plates and holographic masks based on binary diffraction gratings. Altering the spatial profile of the beam may be proven useful in many fields incorporating phase microscopy, electron holography, and electron-matter interactions. These methods, however, are fundamentally limited due to energy distribution to undesired diffraction orders as well as by their binary construction. Here we present a new method in electron-optics for arbitrarily shaping of electron beams, by precisely controlling an engineered pattern of thicknesses on a thin-membrane, thereby molding the spatial phase of the electron wavefront. Aided by the past decade's monumental leap in nano-fabrication technology and armed with light-optic's vast experience and knowledge, one may now spatially manipulate an electron beam's phase in much the same way light waves are shaped simply by passing them through glass elements such as refractive and diffractive lenses. We show examples of binary and continuous phase-plates and demonstrate the ability to generate arbitrary shapes of the electron wave function using a holographic phase-mask. This opens exciting new possibilities for microscopic studies of materials using shaped electron beams and enables electron beam lithography without the need to move the electron beam or the sample, as well as high resolution inspection of electronic chips by structured electron illumination.