A study in the computation time required for the inclusion of strain field effects in Bloch-wave simulations of TEM diffraction contrast images

As transmission electron microscopy (TEM) imaging techniques continue to become more quantitative, interpretation of the experimental images demands that accurate image simulations be computed incorporating all important aspects of the image including: compositional, crystallographic and microscope effects, as well as contrast due to strain fields arising from stresses created by lattice misfit or defects. Incorporation of the effects of strain fields in the simulation of diffraction-contrast TEM images in the Bloch-wave formalism requires the integration of a system of first-order differential equations in order to modify the excitation amplitudes and produce contrast in the image. This integration is computationally demanding with the time for integration scaling as the cube of the number of beams included in the calculation. In order to investigate the computational requirements of the integration, a variety of numerical integration packages were evaluated with respect to timing and accuracy in the simulation of quantum dot, spherical inclusion and screw dislocation images. It was determined that a class of Adams-multistep methods can provide a decrease in computation time ranging from 2 to 4 as compared to the standard Runge-Kutta 4(5) approach depending on the simulation conditions.