Using dynamically scattered electrons for three-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 are particularly valuable when trying to understand the properties of point defects, dislocations and interfaces. This paper presents a method by which three-dimensional maps of the electrostatic potential, related to the charge-density map by the Poisson equation, can be obtained experimentally at 1 A resolution or better, especially at low accelerating voltages. The method requires data acquired by holographic transmission electron microscopy methods such as off-axis electron holography or focal series reconstruction for slightly (e.g. +/-2 degrees) different directions of the incident electron beam. The reconstruction of the three-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.