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Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias.

Levine LE, Okoro C, Xu R - IUCrJ (2015)

Bottom Line: Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges.For these measurements, three widely separated reflections were examined from selected, individual grains along the via.The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles.

View Article: PubMed Central - HTML - PubMed

Affiliation: Materials Science and Engineering Division, National Institute of Standards and Technology , 100 Bureau Drive, STOP 8553, Gaithersburg, Maryland 20899-8553, USA.

ABSTRACT
Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.

No MeSH data available.


Related in: MedlinePlus

Energy-integrated distribution of diffracted X-ray intensity on the area detectors from a single grain in the Cu-TSV: (a)  on orange, (b) 046 on purple and (c)  on yellow.
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fig3: Energy-integrated distribution of diffracted X-ray intensity on the area detectors from a single grain in the Cu-TSV: (a) on orange, (b) 046 on purple and (c) on yellow.

Mentions: Fig. 3 ▸ shows the energy-integrated diffracted intensity on all three area detectors from a single grain located approximately 7.5 µm deep in the Cu-TSV. Each detector exhibits sharp diffraction spots from low dislocation density volumes and diffuse scattering associated with high dislocation density. The separation of the peaks indicates that the low dislocation regions have slightly different crystallographic orientations, suggesting that the high dislocation density regions form walls that separate low dislocation density cell interiors. To set the angular scale, the subtended angle between spots A and B on the orange detector (Fig. 3 ▸a) is about 0.45°. This pattern of grain breakup into distinct dislocation cells was observed in nearly all of the grains we examined, independent of their position along the via. We also note that as we are illuminating the microstructure with a microbeam, the relative intensity of the diffraction spots in Fig. 3 ▸ reflects the relative intersected volumes, and not the actual dislocation cell volumes.


Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias.

Levine LE, Okoro C, Xu R - IUCrJ (2015)

Energy-integrated distribution of diffracted X-ray intensity on the area detectors from a single grain in the Cu-TSV: (a)  on orange, (b) 046 on purple and (c)  on yellow.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4645108&req=5

fig3: Energy-integrated distribution of diffracted X-ray intensity on the area detectors from a single grain in the Cu-TSV: (a) on orange, (b) 046 on purple and (c) on yellow.
Mentions: Fig. 3 ▸ shows the energy-integrated diffracted intensity on all three area detectors from a single grain located approximately 7.5 µm deep in the Cu-TSV. Each detector exhibits sharp diffraction spots from low dislocation density volumes and diffuse scattering associated with high dislocation density. The separation of the peaks indicates that the low dislocation regions have slightly different crystallographic orientations, suggesting that the high dislocation density regions form walls that separate low dislocation density cell interiors. To set the angular scale, the subtended angle between spots A and B on the orange detector (Fig. 3 ▸a) is about 0.45°. This pattern of grain breakup into distinct dislocation cells was observed in nearly all of the grains we examined, independent of their position along the via. We also note that as we are illuminating the microstructure with a microbeam, the relative intensity of the diffraction spots in Fig. 3 ▸ reflects the relative intersected volumes, and not the actual dislocation cell volumes.

Bottom Line: Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges.For these measurements, three widely separated reflections were examined from selected, individual grains along the via.The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles.

View Article: PubMed Central - HTML - PubMed

Affiliation: Materials Science and Engineering Division, National Institute of Standards and Technology , 100 Bureau Drive, STOP 8553, Gaithersburg, Maryland 20899-8553, USA.

ABSTRACT
Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.

No MeSH data available.


Related in: MedlinePlus