Micro-scale measurement and modeling of stress in silicon surrounding a tungsten-filled through-silicon via

Abstract

The stress in silicon surrounding a tungsten-filled through-silicon via (TSV) is measured using confocal Raman microscopy line scans across the TSV both before and after etch removal of an oxide stack used as a mask to define the TSV during fabrication. Stress in the silicon arose in response to both athermal deposition and thermal expansion mismatch effects. The complex three-dimensional stress and strain field in silicon surrounding the TSV is modeled using finite element analysis, taking into account both athermal and thermal effects and the elastic anisotropy of silicon. Comparison of the measurements and model results shows that no one component of the stress tensor correlates with the Raman peak shift generated by the deformed silicon. An analysis is developed to predict the Raman shift in deformed silicon that takes into account all the components of the stress or strain tensor; the results of the model are then used as inputs to the analysis for direct comparison with measured peak shifts as a function of distance from the TSV. Good agreement between the measured and predicted peak shifts is obtained for the case of the intact oxide stack. A discrepancy between the measured and predicted shifts was observed adjacent to the TSV with the oxide stack removed; further modeling suggests the discrepancy is explained by the formation of a small void at the TSV-silicon interface during etching. The combined measurement-modeling approach serves to both validate the model, in this case for TSV design, and to extend the measurement capability of confocal Raman microscopy to complex stress fields.