Strain relaxation in TEM lamellae probed by 4D-STEM: from projected strain to dynamical-diffraction-based reconstruction of composition

Scanning Transmission Electron Microscopy (STEM) provides the spatial resolution necessary to determine material composition from strain measurements on the nanoscale, but it relies on thin, electron-transparent lamellae. In such lamellae, the tetragonal distortion established during epitaxial growth partially relaxes at the free surfaces created during specimen preparation. The resulting three-dimensional strain field breaks the direct link between measured strain and composition, and intensity distribution within diffraction discs associated with dynamic diffraction varies, hindering precise evaluation of the strain state from locally recorded diffraction patterns. Rather than mereley suppressing these effects, this thesis explicitly investigates how surface strain-relaxation in thin TEM lamellae causes deviations from bulk assumptions in 4D-STEM measurements across strained interfaces, and how these deviations can be exploited to recover, among other quantities, information about the bulk strain state. First, electron scattering from strain fields that vary along the beam direction due to surface relaxation is discussed within both the kinematical approximation and a dynamical description. A continuum-mechanical model is derived that predicts the strain state of a thin lamella based on growth assumptions. The model captures the evolution of the strain state with decreasing specimen thickness from the biaxially strained bulk limit toward the uniaxially strained infinitely thin lamella limit. Using narrow (Al,Ga)N layers embedded in GaN as a model system, the impact of relaxation on STEM-based strain measurements is investigated experimentally. A patterned illumination aperture is employed to enable precise measurements robust to variations in dynamic diffraction conditions, and implications for the interpretability of the resulting strain maps using these apertures are discussed. Relaxation-induced intensity redistributions within diffraction discs are examined systematically by comparing simulations based on the relaxed strain field with simulations enforcing a bulk-like strain distribution. The analysis reveals distinct impacts of the three parameters: lamella thickness, layer width, and layer composition on dynamic diffraction. Additionally, a general thickness-dependent sensitivity to relaxation is observed. Finally, a method is presented to determine these three parameters from the observed dynamical-diffraction variations. Experimental datasets are matched to simulations, and the parameters are extracted by minimizing the discrepancy between the two under systematic parameter variation. The reconstructed values agree well with reference methods (X-ray diffraction and STEM-EDS), despite remaining challenges, particularly when assumptions of the employed strain models (e.g., sharp material interfaces) are violated. The proposed method remains applicable over a broad range of lamella thicknesses, reducing the need for precise thickness control during specimen preparation, and it requires no additional instrumentation beyond a state-of-the-art STEM.

Author dc:creator

• Otto, Frederik

Advisor dc:contributor.advisor

• Lehmann, Michael

Licence dc:rights.uri

• https://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Identifier URI

https://doi.org/10.14279/depositonce-25952

OAI identifier oai:identifier

oai:depositonce.tu-berlin.de:11303/27118