Nonlinear Electrothermal Model for Investigating Transient Temperature Responses of a Through-Silicon Via Array Applied With Gaussian Pulses in 3-D IC

In this paper, a through-silicon via (TSV) array under Gaussian pulse is studied comprehensively with a rigorous consideration of its electrothermal characteristics. To enhance the computational efficiency and reduce the memory cost, we develop a unified radial point interpolation method (RPIM) to handle these TSV electrothermal coupling problems. The comparison between the results of the proposed formulas and fine-grid finite-element method (FEM) shows that the RPIM has a very high accuracy and reduces computational time by up to 88% in comparison with the fine-grid FEM. The transient temperature responses are studied in detail for three layouts of single-layered TSV arrays with different silicon dioxide layer thicknesses and areas enclosed by TSVs. Furthermore, the two-layered TSV array structure including microbumps and RDLs is simulated electrothermally to verify the scalability of this method. Our work demonstrated the capability of addressing a large number of TSV arrays and the proposed method enables faster and more accurate electrothermal design of TSV-based 3-D ICs.