A Compact Analytic Model of the Strain Field Induced by Through Silicon Vias

作者：Jan Sun Rong^*; Chou Tien Pei; Yeh Che Yu; Liu Chee Wee; Goldstein Robert V; Gorodtsov Valentin A; Shushpannikov Pavel S

来源：IEEE Transactions on Electron Devices, 2012, 59(3): 777-782.

DOI：10.1109/TED.2011.2180534

• Compact modeling
• strain field
• through silicon via (TSV)

The thermoelastic strains are induced by through silicon vias due to the difference of thermal expansion coefficients between the copper (similar to 18 ppm/degrees C) and silicon (similar to 2.8 ppm/degrees 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.

• 出版日期2012-3
• 单位中国科学院电工研究所