Lattice strain and tilt mapping in stressed Ge microstructures using X-ray Laue micro-diffraction and rainbow filtering

Tardif, Samuel; Gassenq, A.; Guilloy, Kévin; Pauc, N.; Dias, Guilherme Osvaldo; Hartmann, Jean‐Michel; Widiez, J.; Zabel, T.; Marin, Esteban; Sigg, H.; Faist, Jérôme; Chelnokov, A.; Reboud, V.; Calvo, V.; Micha, Jean‐Sébastien; Robach, Odile; Rieutord, F.

doi:10.1107/s1600576716010347

Cited by 20 publications

(16 citation statements)

References 60 publications

(69 reference statements)

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“…A robust, although time-consuming, technique for the local measurement of intra-granular strains in the bulk at micrometre spatial and 10 −4 strain accuracy is Differential Aperture X-ray Microscopy (DAXM) (Larson et al, 2002;Levine et al, 2006;Robach et al, 2013;Tardif et al, 2016) [32,33,34,35], a variant of polychromatic X-ray Laue micro-diffraction. More recently, using monochromatic micro-beam scanning, a far-field detector and an established 3DXRD indexing procedure (ImageD11) (Wright, 2017) [36], Hektor et al has shown local sensitivity of the method to hydrostatic strain (Hektor et al, 2019) [37], and Hayashi et al has demonstrated mapping the full strain tensor over a region containing 37 3 voxels at 1.2 µm spacing deep inside a steel specimen (Hayashi et al, 2019) [38].…”

Section: Intragranular Strain (Type III Stresses)mentioning

confidence: 99%

Three-dimensional reconstruction of intragranular strain and orientation in polycrystals by near-field X-ray diffraction

Reischig

Ludwig

2020

Current Opinion in Solid State and Materials Science

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A theoretical framework is proposed for simultaneous reconstruction of the three-dimensional grain shapes, intragranular strain and orientation fields inside polycrystals from near-field X-ray diffraction images, using box beam illumination. The approach, named Iterative Tensor Field (ITF) reconstruction, uses a tensor field representation and a kinematical forward simulation model to reproduce the measured diffraction signal from individual grains. The framework establishes a link between the local deformation components inside the grains and the intensities of the diffraction signal in the measured images by forming a local linear problem. This is solved using a large scale linear optimisation method in every main iteration of the underlying non-linear problem. The optimisation enforces smooth gradients and the objective function may include regularisation constraints of static equilibrium or input from a Crystal Plasticity FEM simulation. The method has modest computational requirements and enables efficient scanning of millimetre or sub-millimetre sized specimens. Results on experimental data measured on a Gum metal specimen are presented, which demonstrate convergence and the feasibility of the approach. The mathematical formulation, data representation and challenges in the reconstruction and validation are discussed. The physical aspects of the contrast phenomenon, the deformation sensitivity of the technique, and potential means of error assessment are described. A number of alternative concepts for a polycrystalline deformation model and potential solvers are also presented.

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Section: Intragranular Strain (Type III Stresses)mentioning

confidence: 99%

Three-dimensional reconstruction of intragranular strain and orientation in polycrystals by near-field X-ray diffraction

Reischig

Ludwig

2020

Current Opinion in Solid State and Materials Science

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“…10 The bridge geometry was chosen so as to obtain an homogeneous, pure tetragonal strain in the central region. 41 The process used brought the whole released structure into contact with the silicon substrate, allowing further lithographic steps on the sample (figure 1.c).…”

Section: Strained Micro-bridges Fabricationmentioning

confidence: 99%

Germanium under High Tensile Stress: Nonlinear Dependence of Direct Band Gap vs Strain

Guilloy¹,

Pauc²,

Gassenq³

et al. 2016

ACS Photonics

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Germanium is a strong candidate as a laser source for silicon photonics. It is widely accepted that the band structure of germanium can be altered by tensile strain so as to reduce the energy difference between its direct and indirect band gaps. However, the conventional gap deformation potential model most widely adopted to describe this transition happens to have been investigated only up to 1 % uniaxially loaded strains. In this work, we use a micro-bridge geometry to uniaxially stress germanium along [100] up to ε 100 = 3.3 % longitudinal strain and then perform electro-absorption spectroscopy. We accurately measure the energy gap between the conduction band at the Γ point and the light-and heavy-hole valence bands. While the experimental results agree with the conventional linear deformation potential theory up to 2 % strain, a significantly nonlinear behavior is observed at higher strains. We measure the hydrostatic and tetragonal shear deformation potential of germanium to be a = −9.1 ± 0.3 eV and b = −2.32 ± 0.06 eV and introduce a second order deformation potential. The experimental results are found to be well described by tight-binding simulations. These new high strain coefficients will be suitable for the design of future CMOS-compatible lasers and opto-electronic devices based on highly strained germanium.2

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“…With the tunable-energy mode, the focusing of the beam on the sample surface may change during the measurements. Accuracies close to 10 À4 were obtained on Áa=a in Ge single-and UO 2 polycrystals (Robach et al, 2013) and a full strain analysis was performed in stressed Ge microstructures (Tardif et al, 2016). Measurements with a two-dimensional energy dispersive X-ray CCD detector in a strained copper single crystal have demonstrated the advantages of single-shot acquisitions for determining the components of the full strain tensor (Abboud et al, 2017).…”

Section: Introductionmentioning

confidence: 87%

Full elastic strain tensor determination at the phase scale in a powder metallurgy nickel-based superalloy using X-ray Laue microdiffraction

et al. 2017

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao. Laue microdiffraction is used to determine the full elastic strain tensor of the and 0 phases in grains of a nickel-based superalloy with a coarse-grained microstructure. A 'rainbow' filter and an energy dispersive point detector are employed to measure the energy of Bragg reflections. For the two techniques, an uncertainty of AE2.5 Â 10 À3 Å is obtained for the undetermined crystal lattice parameter. Our measurements show that the filter method provides better confidence, energy resolution, accuracy and acquisition time. The sensitivity of each method with respect to the -0 lattice mismatch is demonstrated with measurements in samples with average precipitate sizes of 200 and 2000 nm. For the 200 nm precipitate size, the lattice mismatch is less than 2 Â 10 À3 Å and the dilatational strains are close to AE1.5 Â 10 À3 depending on the considered phase. For the 2000 nm precipitate size, the lattice mismatch is close to 8 Â 10 À3 Å and almost no elastic strain occurs in the microstructure.

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Lattice strain and tilt mapping in stressed Ge microstructures using X-ray Laue micro-diffraction and rainbow filtering

Cited by 20 publications

References 60 publications

Three-dimensional reconstruction of intragranular strain and orientation in polycrystals by near-field X-ray diffraction

Three-dimensional reconstruction of intragranular strain and orientation in polycrystals by near-field X-ray diffraction

Germanium under High Tensile Stress: Nonlinear Dependence of Direct Band Gap vs Strain

Full elastic strain tensor determination at the phase scale in a powder metallurgy nickel-based superalloy using X-ray Laue microdiffraction

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