RESUMO
We present a gradient-descent-based approach to determining the projected electrostatic potential from four-dimensional scanning transmission electron microscopy measurements of a periodic, crystalline material even when dynamical scattering occurs. The method solves for the scattering matrix as an intermediate step, but overcomes the so-called truncation problem that limited previous scattering-matrix-based projected structure determination methods. Gradient descent is made efficient by using analytic expressions for the gradients. Through simulated case studies, we show that iteratively improving the scattering matrix determination can significantly improve the accuracy of the projected structure determination.
RESUMO
High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) is a valuable method for composition determination of nanomaterials. However, light elements do not scatter efficiently into the scattering angles employed for HAADF-STEM which hinders the composition determination of material systems containing light elements by HAADF-STEM. This makes the usage of lower scattering angles favourable. Moreover, static atomic displacements (SADs) caused by the small covalent radius of the substituting light elements in semiconductor alloys increase the scattering intensity at low angles. Nevertheless, at low angles, a quantitative match between complementary image simulations and experiments is not straight forward, since e.g. inelastic scattering and correlated phonon movement is often neglected in simulations. In this study, we establish a method to quantify material systems containing light elements at low angles by resolving the remaining sources of discrepancy. An outstanding agreement between simulations and experiments is achieved by using a combination of an in-column energy filter and a fast pixelated detector. By applying this method to GaNxAs1-x quantum wells, a good agreement of the TEM results with results from high-resolution x-ray diffraction is obtained. The method developed enables the nanoscale analysis of functional materials containing light elements, especially in the presence of SADs.
RESUMO
Quantitative scanning transmission electron microscopy (STEM) allows composition determination for nanomaterials at an atomic scale. To improve the accuracy of the results obtained, optimized imaging parameters should be chosen for annular dark field imaging. In a simulation study, we investigate the influence of imaging parameters on the accuracy of the composition determination with the example of ternary III-V semiconductors. It is shown that inner and outer detector angles and semi-convergence angle can be optimized, also in dependence on specimen thickness. Both, a minimum sampling of the image and a minimum electron dose are required. These findings are applied experimentally by using a fast pixelated detector to allow free choice of detector angles.