3‐D Strain Fields in Low‐Dimensional III–V Semiconductors: A Combined Finite Elements and HRTEM Approach

A versatile route toward the study of strain fields of low-dimensional III-V semiconductor nanostructures is presented, by combining quantitative high-resolution transmission electron microscopy (HRTEM) observations with the finite elements method (FEM). FEM facilitates a fast and straightforward three-dimensional (3-D) analysis of elastic properties for various growth orientations and compositional profiles down to the nanoscale. FEM calculations are employed to simulate elastic stress-strain fields of III-V cubic heterostructures comprising InAs surface and buried quantum dots (QDs) grown on GaAs(211)B substrates, and (111)-oriented GaAs/AlxGa(1-x)As core-shell nanowires (NWs) on Si. The results are compared with experimental strain maps obtained from HRTEM images by geometric phase analysis (GPA), as well as with molecular dynamics (MD) atomistic simulations. In the former, the compositional grading along the growth axis was considered, and, in the latter, elastic fields were calculated as a function of the shell's chemical composition and shell-to-NW diameter ratios. The agreement between FEM calculations with experimental and theoretical results implies that the plane-stress state can adequately describe the encountered elastic fields. Most importantly, through the determined stress-strain state, strain fields can be translated into 3-D maps of chemical composition in the nanostructures, extracted from 2-D experimental projections.