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A Compact Analytic Model of the Strain Field Induced by Through Silicon Vias.
- Source :
-
IEEE Transactions on Electron Devices . Mar2012, Vol. 59 Issue 3, p777-782. 6p. - Publication Year :
- 2012
-
Abstract
- The thermoelastic strains are induced by through silicon vias due to the difference of thermal expansion coefficients between the copper (\sim\!\!\18\ \ppm/^\circ \C) and silicon (\sim\!\!\2.8\ \ppm/^\circ \C) when the structures are exposed to a thermal ramp in the process flow. A compact analytic model (Bessel function) of the strain field is obtained using Kane–Mindlin theory, and has a good agreement with the finite-element simulations. The elastic strains in the silicon in the radial direction and angular direction are tensile and compressive, respectively. The linear superposition of the analytic model of a single via can be used in the multi-via configuration. Due to the interaction of vias, the slightly larger errors of strain occur between the two close vias when the linear superposition is used. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189383
- Volume :
- 59
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Electron Devices
- Publication Type :
- Academic Journal
- Accession number :
- 73612263
- Full Text :
- https://doi.org/10.1109/TED.2011.2180534