Reconstruction of the projected crystal potential in transmission electron microscopy by means of a maximum-likelihood refinement algorithm

The projected crystal potential is reconstructed from a nonperiodic high-resolution transmission electron microscopy exit wave function using a maximum-likelihood refinement algorithm. The convergence and the accuracy of the algorithm are investigated using simulated exit wave functions of SiGe, a Shockley partial dislocation in Ge and an area containing randomly distributed Ge columns at different specimen thicknesses. The performance of two different start models for the projected crystal potential is investigated: the weak-phase-object model and a model based on the electron-channelling approximation. The reconstruction is successful even under the strongly nonlinear dynamical diffraction conditions at larger specimen thicknesses, relevant for high-resolution work, and on specimen areas large enough to cover defects in crystalline materials.