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HOLZ lines splitting on SiGe/Si relaxed samples: analytical solutions for the kinematical equation
C Alfonso1, L Alexandre, Ch Leroux
1CNRS, IM2NP (UMR 6242), Faculté des Sciences et Techniques, Campus de Saint-Jérôme, Avenue Escadrille Normandie Niemen-Case 262, F-13397 Marseille Cedex, France. claude.alfonso@univ-cezanne.fr
Ultramicroscopy
|January 23, 2010
Summary
Sample thinning for TEM causes strain relaxation, leading to HOLZ line splitting in CBED patterns. This study introduces analytical solutions to model this phenomenon, enabling accurate measurement of sample displacement.
Area of Science:
- Materials Science
- Solid State Physics
- Electron Microscopy
Background:
- Sample preparation for Transmission Electron Microscopy (TEM) significantly alters the bulk sample's strain state.
- Surface relaxation in thinned samples is a primary cause of Higher Order Laue Zone (HOLZ) line splitting in Convergent Beam Electron Diffraction (CBED) patterns.
- Previous simulations relied on complex finite element modeling and dynamical or kinematical electron diffraction frameworks.
Purpose of the Study:
- To develop new analytical solutions for the kinematical theory of electron diffraction.
- To approximate deformation profiles using simple mathematical functions.
- To provide a method for analytically calculating rocking curve profiles and separating deformation contributions.
Main Methods:
- Development of simplified analytical expressions for the kinematical electron diffraction equation.
- Approximation of sample deformation profiles using basic mathematical functions.
- Application of these analytical solutions to model HOLZ line splitting and extract displacement information.
Main Results:
- HOLZ line splitting in CBED patterns due to surface relaxation was accurately reproduced.
- A method was established to analytically calculate rocking curve profiles.
- Maximum displacement amplitude was extracted with approximately 10% accuracy, improvable to 1% with adjustments.
- The influence of displacement profile shape on rocking curves was demonstrated.
Conclusions:
- The proposed analytical solutions offer a simplified yet accurate approach to understanding strain relaxation effects in TEM samples.
- This method facilitates the quantitative analysis of displacement profiles from CBED rocking curves.
- The findings provide insights into separating different contributions to rocking curves and improving accuracy in displacement measurements.
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