Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias
Lyle E. Levine, Chukwudi A. Okoro, Ruqing Xu
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 m long polycrystalline copper via in Si. Determining all of the components of these tensors from sub-micrometer regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume, and accurate determination 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.