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

摘要

A versatile route toward the study of strain fields of low-dimensional III–Vrnsemiconductor nanostructures is presented, by combining quantitative highresolutionrntransmission electron microscopy (HRTEM) observations with thernfinite elements method (FEM). FEM facilitates a fast and straightforward threedimensionalrn(3-D) analysis of elastic properties for various growth orientationsrnand compositional profiles down to the nanoscale. FEM calculations arernemployed to simulate elastic stress–strain fields of III–V cubic heterostructuresrncomprising InAs surface and buried quantum dots (QDs) grown on GaAs(211)Brnsubstrates, and (111)-oriented GaAs/AlxGa(1u0001x)As core–shell nanowires (NWs)rnon Si. The results are compared with experimental strain maps obtained fromrnHRTEM images by geometric phase analysis (GPA), as well as with molecularrndynamics (MD) atomistic simulations. In the former, the compositional gradingrnalong the growth axis was considered, and, in the latter, elastic fields wererncalculated as a function of the shell’s chemical composition and shell-to-NWrndiameter ratios. The agreement between FEM calculations with experimentalrnand theoretical results implies that the plane-stress state can adequatelyrndescribe the encountered elastic fields. Most importantly, through the determinedrnstress–strain state, strain fields can be translated into 3-D maps ofrnchemical composition in the nanostructures, extracted from 2-D experimentalrnprojections.