title: Dynamical effects in strain measurements by dark-field electron holography.
abstract: Here, we study the effect of dynamic scattering on the projected geometric phase and strain maps reconstructed using dark-field electron holography (DFEH) for non-uniformly strained crystals. The investigated structure consists of a {SiGe/Si} superlattice grown on a (001)-Si substrate. The three-dimensional strain field within the thin TEM lamella is modelled by the finite element method. The observed projected strain is simulated in two ways by multiplying the strain at each depth in the crystal by a weighting function determined from a recently developed analytical two-beam dynamical theory, and by simply taking the average value. We demonstrate that the experimental results need to be understood in terms of the dynamical theory and good agreement is found between the experimental and simulated results. Discrepancies do remain for certain cases and are likely to be from an imprecision in the actual two-beam diffraction conditions, notably the deviation parameter, and points to limitations in the 2-beam approximation. Finally, a route towards a 3D reconstruction of strain fields is proposed.
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France; EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium.
authors: E
authors: E
authors: Javon
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France; EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium; Institute of Structure Physics, Technische Universität Dresden, 01062 Dresden, Germany.
authors: A
authors: A
authors: Lubk
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France.
authors: R
authors: R
authors: Cours
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France; CEA, LETI, Minatec Campus, 17 rue de Martyrs, 38054 Grenoble, France.
authors: S
authors: S
authors: Reboh
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France.
authors: N
authors: N
authors: Cherkashin
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France.
authors: F
authors: F
authors: Houdellier
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France.
authors: C
authors: C
authors: Gatel
authors: CEMES-CNRS and Université de Toulouse, 29 rue Jeanne Marvig, F-31055 Toulouse, France.
authors: M J
authors: MJ
authors: Hÿtch
keywords: Dark-field; Dynamical scattering; Electron holography; Strain measurement