Analytical solution on interfacial reliability of 3-D through-silicon-via (TSV) containing dielectric liner

• An analytical solution, considering the effects of the liner, is derived.
• It is utilized for interfacial reliability analysis for 3-D TSV.
• The validity of analytical solution is verified by FEA approach.
• The dimensions of TSV are investigated with steady-state ERR.
• The analysis results will give guidelines in the TSV architecture design.

Interfacial reliability is a challenging issue in through-silicon-via (TSV) technique. To accurately investigate the interfacial reliability of TSV, this paper developed an analytical solution approach, in which the effects of the liner are considered. The validity of the analytical solution is executed by comparison with finite element simulation results. Results show that two approaches have good agreement, with a deviation within 10%, illustrating the validity of the analytical solution developed in this study. Then, using the developed analytical solution, the effects of via diameter, the liner thickness, and the liner materials of TSV on interfacial reliability are investigated with the steady-state energy release rate (ERR). Analytical results show that the steady-state ERR is not only determined by the coefficient of thermal expansion (CTE) mismatch between adjacent materials, but also affected by the products (E × CTE2) of Young’s modulus (E) and CTE2 of the liner. Liner materials with lower E × CTE2 values will lead to lower steady-state ERR. Additionally, the combined effects of copper via diameter and liner thickness on ERR declare that the ERR highly depends on copper via diameter.