| Three-dimensional integrated circuits (3D ICs) are stacking a large number of chips or circuit modules in vertical direction and using through-silicon vias (TSVs) to realize electrical connections between devices in different layers, and to achieve one or more functions. They have the advantages of reducing interconnects length and chip area, increasing interconnects density, and achieving heterogeneous integration, etc. TSVs are the key component to realize 3D ICs and their electromagnetic characteristics play a decisive role to the overall performance of 3D ICs. In this paper, the electromagnetic characteristics of novel TSVs are deep studied and the main results obtained as follows:1. The accurate formulas for the oxide capacitance and the silicon substrate capacitance in tapered-through-silicon vias (T-TSVs) are proposed. The electric field is non-uniform distribution in T-TSVs due to its non-uniform three-dimensional structure. In order to get accurate formulas for the capacitance of T-TSVs, the conformal mapping and infinitesimal calculus methods were used properly based on the analytical results of the local electric field structure in T-TSVs. The comparison between the results of the proposed formulas and the three-dimensional quasi-static electromagnetic field parasitic parameters extraction software Q3D shows that the maximum errors of the oxide capacitance and the silicon substrate capacitance are 1% and 3%, respectively. When the slope angle of T-TSVs equals to zero, the proposed formulas can be reduced to the formulas for the capacitance in cylindrical TSVs.2. The equivalent-circuit model of T-TSVs is established. In view of the gradual change property of T-TSVs’dimensions in their length direction, a T-TSV is divided in two equal parts in its length direction, and the obtained two parts can be viewed as proximate cylindrical TSVs to handle. Then, the equivalent-circuit models of the two parts are established, according to the equivalent-circuit structure of cylindrical TSVs and combined with the resistance-inductance-capacitance-conductance (RLCG) parameters model of T-TSVs. Finally, the complete equivalent-circuit model of a T-TSV is obtained by connecting the two equivalent-circuit models of the two parts in series. The equivalent-circuit model is verified using three-dimensional full-wave electromagnetic field simulation software HFSS, showing that it is highly accurate up to 10 GHz. Furthermore, the effects of the lower radius, the thickness of the silicon oxide layer, the distance between the signal and the ground T-TSVs, and the conductivity of silicon substrate on the S-parameters of T-TSVs are analyzed using the established equivalent-circuit model.3. The structure of shield differential through-silicon vias (SDTSVs) and their equivalent-circuit model are proposed. The structure of SDTSVs is similar to that of coaxial TSVs, but they use two TSVs to transmit differential signals in their internal. The outer shells of SDTSVs both as the return path of the inner differential signal wires and as the shielding layer to suppress neighboring electromagnetic noise. Compared with single-ended coaxial TSVs, SDTSVs do not need any extra processing steps and combine the advantages of coaxial TSVs and differential TSVs. Since the original equivalent-circuit model of SDTSVs is complex, and is not convenient to use, so it is further simplified using the"△-Y-△" transforming method and the simplified equivalent-circuit model of SDTSVs is obtained. The results of the S-parameters of SDTSVs obtained from the HFSS simulation agree well with that from the simplified equivalent-circuit model up to 100GHz.4. A full-wave extraction method for the RLCG parameters of SDTSVs is proposed. First, the S-parameters matrix of SDTSVs obtained from full-wave simulation is converted into ABCD matrix. Then, the characteristic impedances and the propagation constants in even mode and odd mode are obtained from the theoretical ABCD matrix of SDTSVs. Finally, the full-wave extraction expressions of RLCG parameters of SDTSVs are derived based on the obtained characteristic impedances and the propagation constants theoretical expressions in even mode and odd mode of SDTSVs. The results of the RLCG parameters of SDTSVs obtained from the HFSS full-wave extraction agree well with that from the theoretical model calculation up to 100GHz. In addition, the proposed full-wave extraction method for the RLCG parameters of SDTSVs can be applied to all of differential transmission lines.5. The electromagnetic characteristics of SDTSVs are deeply analyzed using their simplified equivalent-circuit model. In the actual application, we are most interested in the magnitude of the differential-mode insertion loss and the real part of the differential characteristic impedance of SDTSVs. In this paper, the effects of the radius of the signal wire, the thickness of the silicon oxide layer, the distance between the two signal wires, the radius of the shielding layer, and the conductivity of silicon substrate on these two parameters are analyzed to provide helpful design guidelines for SDTSVs in future 3D ICs.6. The concept of distortionless TSVs and their design requirements and design method are proposed. The design requirements, which is the relationship of RLCG parameters of distortionless TSVs should be satisfied, are derived according to the theory of transmission lines. The effective resistance and inductance of multi-walled carbon nanotube (MWCNT) bundles are calculated using the partial element equivalent circuit (PEEC) method and compare with that of metallic copper (Cu), showing that only MWCNT bundles suitable as the conductor of distortionless TSVs. So, the proposed design method is for MWCNT bundles. The linearity of the propagation constant with the frequency of the designed distortionless TSV using the proposed design method is obviously higher than that of Cu-TSV with the identical structural parameters. Therefore, the designed distortionless TSV can effectively reduce the distortion degree of transmitted signals.
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