Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias
Abstract
We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-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.
- Authors:
-
- National Institute of Standards and Technology, Gaithersburg, MD (United States)
- National Institute of Standard and Technology, Gaithersburg, MD (United States)
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1248965
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- IUCrJ
- Additional Journal Information:
- Journal Volume: 2; Journal Issue: 6; Journal ID: ISSN 2052-2525
- Publisher:
- International Union of Crystallography
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; microelectronics; copper through-Si vias; full elastic strain; stress tensor measurement
Citation Formats
Levine, Lyle E., Okoro, Chukwudi A., and Xu, Ruqing. Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias. United States: N. p., 2015.
Web. doi:10.1107/S2052252515015031.
Levine, Lyle E., Okoro, Chukwudi A., & Xu, Ruqing. Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias. United States. https://doi.org/10.1107/S2052252515015031
Levine, Lyle E., Okoro, Chukwudi A., and Xu, Ruqing. Wed .
"Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias". United States. https://doi.org/10.1107/S2052252515015031. https://www.osti.gov/servlets/purl/1248965.
@article{osti_1248965,
title = {Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias},
author = {Levine, Lyle E. and Okoro, Chukwudi A. and Xu, Ruqing},
abstractNote = {We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-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.},
doi = {10.1107/S2052252515015031},
journal = {IUCrJ},
number = 6,
volume = 2,
place = {United States},
year = {Wed Sep 30 00:00:00 EDT 2015},
month = {Wed Sep 30 00:00:00 EDT 2015}
}
Web of Science
Works referenced in this record:
The Race to X-ray Microbeam and Nanobeam Science
journal, December 2011
- Ice, G. E.; Budai, J. D.; Pang, J. W. L.
- Science, Vol. 334, Issue 6060
Polychromatic X-ray microdiffraction studies of mesoscale structure and dynamics
journal, February 2005
- Ice, G. E.; Larson, B. C.; Yang, W.
- Journal of Synchrotron Radiation, Vol. 12, Issue 2
Formation and Subdivision of Deformation Structures During Plastic Deformation
journal, May 2006
- Jakobsen, B.
- Science, Vol. 312, Issue 5775
Direct determination of elastic strains and dislocation densities in individual subgrains in deformation structures
journal, June 2007
- Jakobsen, Bo; Poulsen, Henning F.; Lienert, Ulrich
- Acta Materialia, Vol. 55, Issue 10
Submicrometre-resolution polychromatic three-dimensional X-ray microscopy
journal, December 2012
- Larson, B. C.; Levine, L. E.
- Journal of Applied Crystallography, Vol. 46, Issue 1
Three-dimensional X-ray structural microscopy with submicrometre resolution
journal, February 2002
- Larson, B. C.; Yang, Wenge; Ice, G. E.
- Nature, Vol. 415, p. 887-890
Elastic Properties of Metals and Alloys. II. Copper
journal, October 1974
- Ledbetter, H. M.; Naimon, E. R.
- Journal of Physical and Chemical Reference Data, Vol. 3, Issue 4
Using X-ray microbeam diffraction to study the long-range internal stresses in aluminum processed by ECAP
journal, December 2013
- Lee, I-Fang; Phan, Thien Q.; Levine, Lyle E.
- Acta Materialia, Vol. 61, Issue 20
Validating classical line profile analyses using microbeam diffraction from individual dislocation cell walls and cell interiors
journal, March 2012
- Levine, Lyle E.; Geantil, Peter; Larson, Bennett C.
- Journal of Applied Crystallography, Vol. 45, Issue 2
Disordered long-range internal stresses in deformed copper and the mechanisms underlying plastic deformation
journal, August 2011
- Levine, Lyle E.; Geantil, Peter; Larson, Bennett C.
- Acta Materialia, Vol. 59, Issue 14
X-ray microbeam measurements of individual dislocation cell elastic strains in deformed single-crystal copper
journal, July 2006
- Levine, Lyle E.; Larson, Bennett C.; Yang, Wenge
- Nature Materials, Vol. 5, Issue 8
Synchrotron-based measurement of the impact of thermal cycling on the evolution of stresses in Cu through-silicon vias
journal, June 2014
- Okoro, Chukwudi; Levine, Lyle E.; Xu, Ruqing
- Journal of Applied Physics, Vol. 115, Issue 24
A Detailed Failure Analysis Examination of the Effect of Thermal Cycling on Cu TSV Reliability
journal, January 2014
- Okoro, Chukwudi; Lau, June W.; Golshany, Fardad
- IEEE Transactions on Electron Devices, Vol. 61, Issue 1
X-ray microbeam measurements of long-range internal stresses in commercial-purity aluminum processed by multiple passes of equal-channel angular pressing
journal, December 2014
- Phan, Thien Q.; Lee, I-Fang; Levine, Lyle E.
- Scripta Materialia, Vol. 93
Strain-tensor components expressed in terms of lattice parameters
journal, January 1978
- Schlenker, J. L.; Gibbs, G. V.; Boisen, M. B.
- Acta Crystallographica Section A, Vol. 34, Issue 1
Spatially resolved Poisson strain and anticlastic curvature measurements in Si under large deflection bending
journal, June 2003
- Yang, Wenge; Larson, B. C.; Ice, G. E.
- Applied Physics Letters, Vol. 82, Issue 22
Works referencing / citing this record:
Unexpected δ-Phase Formation in Additive-Manufactured Ni-Based Superalloy
journal, January 2016
- Idell, Y.; Levine, L. E.; Allen, A. J.
- JOM, Vol. 68, Issue 3
Evaluation of intragranular strain and average dislocation density in single grains of a polycrystal using K-map scanning
journal, September 2016
- Filippelli, Ernesto; Chahine, Gilbert; Borbély, András
- Journal of Applied Crystallography, Vol. 49, Issue 5
Stress, strain and Raman shifts
journal, February 2019
- Angel, Ross J.; Murri, Mara; Mihailova, Boriana
- Zeitschrift für Kristallographie - Crystalline Materials, Vol. 234, Issue 2
High Resolution Mapping of Orientation and Strain Gradients in Metals by Synchrotron 3D X-ray Laue Microdiffraction
journal, March 2019
- Zhang, Yubin; Barabash, Rozaliya
- Quantum Beam Science, Vol. 3, Issue 1