Modeling Through-silicon Via Interconnection In Three-dimensional Integration

In recent years, with the rapid development of integrated circuits, Moore’s Law has been approaching the physical and manufacturing limits. As a promising candidate of More-Than-Moore technology, the three-dimensional(3-D) integration stacks up multiple Moore’s Law wafers or chips in the third spatial dimension. In 3-D integration, one of the key issues is the vertical interconnection. Compared with the conventional wire bonding vertical interconnection structure, the Through-Silicon Via(TSV) interconnects go directly through the silicon wafers or chips, providing the shortest interconnect length and thus better the signal and power integrity.According to different applications and fabrication technologies, TSV interconnection structures may have different profiles, such as the circular TSV, the rectangular TSV, the tapered TSV, the annular TSV, the coaxial TSV etc. Among them, the annular TSV has good thermal stress properties, alleviating the mismatch effect of the coefficients of thermal expansion between the metal conductor and silicon substrate. The shield differential TSV combines the advantages of the coaxial TSV and the differential signal TSV, providing good crosstalk noise suppression property and effectively eliminating the common mode noise, and thus possessing good electromagnetic property.The main work of this thesis is to extract the resistance-inductance-conductancecapacitance(RLGC) parameters of the annular TSV and the shield differential TSV. The RL parameter is referred to as the impedance parameter, while the GC parameter is referred to as the admittance parameter. To accomplish this thesis, the electromagnetic theory and concepts involved are introduced with the author’s own understanding. The innovative contributions of this thesis are as follows:1. The equivalent circuit of the annular TSV pair is constructed according to the structural features. The impedance parameters in the equivalent circuit are derived by analytically calculating the eddy current fields based on the linear decomposition and superposition principle. The admittance parameters are derived based on the approximate analytic formulas. At last, the scattering parameters are obtained according to the RLGC parameters. The results are validated by comparing with those from the finite element method based full wave solver ANSYS HFSS.2. The eddy-current fields of the shield differential TSV pair are calculated in cylindrical coordinate systems considering the structural features. The electromagnetic quantities are expressed with Fourier- Bessel series in the corresponding cylindrical coordinates, and coordinate transformations are implemented by using Graf’s addition theorem to construct equations with the boundary conditions. Although the field expressions involve infinite series, convergent result can be obtained with only a few orders, providing high computational efficiency. The impedance parameters are derived with two methods, i.e. the energy method and the mode analysis method, both of which provide consistent results, although the mode analysis method is more concise. The results are validated by comparing with those from the finite element method based eddy current solver ANSYS Maxwell.