Using dynamically scattered electrons for 3-dimensional potential reconstruction

Three-dimensional charge density maps computed by first-principles methods provide information about atom positions and the bonds between them, data which is particularly valuable when trying to understand the properties of point defects, dislocations, and interfaces. This letter presents a method by which 3-dimensional maps of the electrostatic potential, related to the charge density map by the Poisson equation, can be obtained experimentally at 0.1 nm resolution or better. This method requires data acquired by holographic transmission electron microscopy (TEM) methods such as off-axis electron holography or focal series reconstruction for different directions of the incident electron beam. The reconstruction of the 3-dimensional electrostatic (and absorptive) potential is achieved by making use of changes in the dynamical scattering within the sample as the direction of the incident beam varies.