Position averaged convergent beam electron diffraction: theory and applications

A finely focused angstrom-sized coherent electron probe produces a convergent beam electron diffraction pattern composed of overlapping orders of diffracted disks that sensitively depends on the probe position within the unit cell. By incoherently averaging these convergent beam electron diffraction patterns over many probe positions, a pattern develops that ceases to depend on lens aberrations and effective source size, but remains highly sensitive to specimen thickness, tilt, and polarity. Through a combination of experiment and simulation for a wide variety of materials, we demonstrate that these position averaged convergent beam electron diffraction patterns can be used to determine sample thicknesses (to better than 10%), specimen tilts (to better than 1mrad) and sample polarity for the same electron optical conditions and sample thicknesses as used in atomic resolution scanning transmission electron microscopy imaging. These measurements can be carried out by visual comparison without the need to apply pattern-matching algorithms. The influence of thermal diffuse scattering on patterns is investigated by comparing the frozen phonon and absorptive model calculations. We demonstrate that the absorptive model is appropriate for measuring thickness and other specimen parameters even for relatively thick samples (>50nm).