Abstract
An accurate equivalent thermal model is proposed to calculate the equivalent thermal conductivity (ETC) of shield differential through-silicon via (SDTSV). The mathematical expressions of ETC in both horizontal and vertical directions are deduced by considering the anisotropy of SDTSV. The accuracy of the proposed model is verified by the finite element method (FEM), and the average errors of temperature along the X-axis, Y-axis, diagonal line, and vertical directions are 1.37%, 3.42%, 1.76%, and 0.40%, respectively. Compared with COMSOL, the proposed model greatly improves the computational efficiency. Moreover, the effects of different parameters on the thermal distribution of SDTSV are also investigated. The thermal conductivity is decreased with the increase in thickness of SiO2. With the increase in pitch, the maximum temperature of SDTSV increases very slowly when β = 0 , and decreases very slowly when β = 90. The proposed model can be used to accurately and quickly describe the thermal distribution of SDTSV, which has a great prospect in the design of 3D IC.
Highlights
Model for Shield DifferentialThrough-silicon via (TSV) is a key structure of 3D integrated circuits (IC) [1,2,3,4,5]
An accurate equivalent thermal model is proposed to describe the thermal distribution of shielded differential throughsilicon vias (SDTSV), and the main conclusions can be summarized as follows: (1)
An accurate equivalent thermal model is established for SDTSV, which can describe the thermal distribution of SDTSV along an arbitrary angle
Summary
Through-silicon via (TSV) is a key structure of 3D integrated circuits (IC) [1,2,3,4,5]. Established a fast and accurate equivalent thermal model for TSV. ICs, and the proposed model worked well with the full-wave extraction method when the work frequency was up to 100 GHz. Fu et al [30] investigated the equivalent circuit model of shielded differential annular through-silicon via, and analyzed its thermomechanical stress. With the increase in oxide layers, finer grids are needed in the FEM, which can greatly increase the calculation burden and run-time; it is important to establish an accurate ETC model for SDTSV in order to quickly describe its heat distribution in both horizontal and vertical directions. The accuracy of the proposed ETC model is verified by FEM, and the effects of different parameters on the thermal distribution of SDTSV are investigated and analyzed.
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