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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

All six stress tensor components plotted as a function of depth along the Cu-TSV axis. The uncertainties are one standard deviation.
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fig5: All six stress tensor components plotted as a function of depth along the Cu-TSV axis. The uncertainties are one standard deviation.

Mentions: Fig. 5 ▸ shows all six stress tensor components plotted as a function of depth along the axis of the Cu-TSV. For all depths, the off-diagonal components are much smaller than the diagonal components, and the diagonal terms are approximately equal at each depth, consistent with a primarily hydrostatic stress state. The uncertainties for the diagonal components are also consistent with a hydrostatic stress state, although the overlaps suggest a slight overestimation of the uncertainties. It is also worth noting that calculating unit-cell parameters and stress tensors from individual dislocation cells within a single grain gives consistent results. For example, the lattice parameters measured in all of the cells evident in Fig. 3 ▸ vary by, at most, a strain of just 2.0 × 10−4 and the resulting stress state is, again, mostly hydrostatic.


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

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

All six stress tensor components plotted as a function of depth along the Cu-TSV axis. The uncertainties are one standard deviation.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig5: All six stress tensor components plotted as a function of depth along the Cu-TSV axis. The uncertainties are one standard deviation.
Mentions: Fig. 5 ▸ shows all six stress tensor components plotted as a function of depth along the axis of the Cu-TSV. For all depths, the off-diagonal components are much smaller than the diagonal components, and the diagonal terms are approximately equal at each depth, consistent with a primarily hydrostatic stress state. The uncertainties for the diagonal components are also consistent with a hydrostatic stress state, although the overlaps suggest a slight overestimation of the uncertainties. It is also worth noting that calculating unit-cell parameters and stress tensors from individual dislocation cells within a single grain gives consistent results. For example, the lattice parameters measured in all of the cells evident in Fig. 3 ▸ vary by, at most, a strain of just 2.0 × 10−4 and the resulting stress state is, again, mostly hydrostatic.

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