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By using integrated lumped elements based on through-silicon via (TSV) technology, a 3-D low-pass filter (LPF) with ultracompact size and ultrawide stopband is proposed. The 3-D magnetic coupling is enhanced between microsize spiral inductors to increase the mutual inductance and improve the high-frequency performance. A coaxial TSV with enhanced capacitance in high resistivity silicon (HRS) is utilized both as capacitor and as a vertical interconnection without any overhead in area and routing. The 3-D nature of the proposed filter yields a miniaturized size of 0.2 x 0.10 mm². The LPF is analyzed with equivalent circuit model and validated with the well-matched S-parameters obtained by finite element method simulation and measurement. With -3-dB cutoff frequency at 2.6 GHz, the LPF exhibits an insertion loss below 1 dB, a reflection loss over 17 dB in the passband, and a suppression level over 20 dB from 5.28 up to 40 GHz in the stopband.

A balanced substrate-integrated waveguide (SIW) bandpass filter (BPF) is designed and fabricated based on through-quartz-via (TQV) technologies in this article. Sixth-order filtering response centered at 41.4 GHz with equal source and load termination is achieved by the transformation of the Chebyshev polynomial. By exploiting cross-coupled resonators, the 3-dB fractional bandwidth (FBW) achieves 12.1%, and the out-of-band rejection is better than 30 dB with frequencies up to $2f_{0}$ . High CM suppression can be achieved up to $2.2f_{0}$ with the help of two slots on the bottom metal layer. Based on the theory of the proposed SIW BPF, asymmetric diplexer with different resonance orders for two channels is studied with high isolation and wide stopband. The mixed dual-mode (TE101 and TE301) and single-mode (TE101) junction resonators provide a transition between the input port and two channels. Diplexer with lower and upper channels centered at 20.2 and 37.5 GHz, respectively, is fabricated and measured to verify the proposed structure, which exhibits high isolation better than 40 dB over the whole band and a wide stopband up to $3f_{0}$ of the lower channel. Measured results are in good agreement with the simulations.

SCHOTT D263T glass substrate is investigated for millimeter-wave (mm-wave) antenna-in-package applications using integrated passive device (IPD) technology. For comparison, the ring-resonator method and transmission-line method are used to extract the dielectric constant ($\varepsilon \text{r}$ ) of the glass substrate up to 67 GHz. The extracted results show good correlation between the two methods. Compared with the ring-resonator method, the transmission-line method requires higher measurement and simulation accuracies as the frequency decreases. Based on the extracted substrate data, a miniaturized Yagi-Uda dipole antenna operating at 60 GHz is designed, fabricated and measured. The measured results show that the antenna achieves a fractional impedance bandwidth (|S11| 2. The simulated radiation efficiency is >90% from 45 to 67 GHz, and the measured results agree well with the simulations.

A bandwidth optimization model for a novel equivalent 90° transmission-line section is proposed in this paper. Furthermore, the structure of 3-D compact 3-dB branch-line directional coupler and its equivalent-circuit model are presented. They can achieve both excellent isolations between each branch and high-density integration by using equivalent 90° transmission-line sections and coaxial through-silicon via technology in 3-D integrated circuits. Finally, a 3-D coupler is designed with the center frequency of 100 GHz, as well as the bandwidth and size reach 20 GHz and $174\times 236.9\times 208.7\,\,\mu \text{m}^{3}$ , respectively. The results of the 3-D full-wave field solver High-Frequency Structure Simulator and the proposed model are well matched, showing that the proposed model can be used to quickly evaluate the electrical performance of the 3-D coupler before manufacture, thus effectively promoting the design efficiency and quality.

This paper presents a novel 3-D capacitive interconnection technology for a 3-D microsystem, which is called through-silicon capacitor (TSC). Two vias similar to through-silicon via (TSV) are bonded vertically by one oxide bonding layer to form the capacitive coupling. Without the adoption of the backside via revealing process, the complicated back-thinning process for TSC will be reduced further, resulting in the lower cost and lower yield loss for 3-D microsystem. Finite-element analysis indicates that under the same dimensions, TSC has much stronger capacitive coupling effect than conventional capacitive coupling interconnect does. Then, SPICE simulation is carried out and demonstrates that a TSC channel with the radius of $2.5~\mu \text{m}$ , the height of 30- $\mu \text{m}$ via, and the thickness of 1- $\mu \text{m}$ bonding layer can achieve 4-Gb/s data rate and consumes only 0.08 mW/(Gb/s). Moreover, the high-frequency analysis shows that the far-end crosstalk induced by TSC is superior to that induced by TSV. Finally, the potential applications, features, advantages, and disadvantages of TSC, TSV, and capacitive coupling interconnection (CCI) technologies are compared.

The shielded-pair through-silicon vias (SPTSVs) proposed in this paper feature superior transmission properties and high jamming immunity suitable for differential-mode and common-mode transmissions. Based on the recursive approximation algorithm, a novel and efficient method for characterizing the electromagnetic-temperature distribution in dielectrics is proposed for SPTSVs. In addition, considering the proximity effects and eddy current effect in substrate, the ultrabroadband parasitic admittance and electrical coupling models are derived based on 2-D time-varying field and transient polarization mechanism. The collaborative finite-element analysis shows that the proposed model highly agrees with the 3-D full-wave simulation (HFSS 14.0 and Maxwell v16) and the analytical calculation. Then, the dielectric relaxation properties for substrate and oxide are deeply characterized with different design parameters. Finally, the impacts of the substrate effect on electrical characteristics of SPTSVs are revealed.

This paper proposes a substrate integrated waveguide bandpass filter (SIW BPF), exploiting the through-dielectric via (TDV)-based 3-D integrated circuit (3-D IC) technology. The SIW BPF is designed on the dielectric cavity that is etched on the traditional low-resistivity silicon (LRSi) in a 3-D IC system, acting as the insulating material between through-silicon via plugs and LRSi. This construction can reduce prominent eddy current losses in LRSi and coupling losses among TDV plugs for the millimeter-wave application. Benzocyclobutene and glass are chosen as the dielectric cavity due to the low dielectric constant and loss tangent. The detailed design procedure beginning from the normalized Chebyshev low-pass filter to the final optimized SIW BPF is presented. The filter having a 12.5% fractional bandwidth is centered at 159.67 GHz. The return losses and insertion loss across the passband are about −10 and −1.5 dB, respectively. Numerical analysis of the advanced design system and full-wave simulation results of Ansoft’s HFSS show a good agreement.

In this paper, an ultra-compact low-pass filter (LPF) with wide stopband is proposed based on lumped L-C structure in through-silicon via-based 3-D stacked configuration. The spiral inductor (L), interdigital capacitor (C), and the proposed LPF are theoretically analyzed based on parasitic parameters and equivalent circuit models. To evaluate the characteristics, the proposed LPF is simulated by HFSS, fabricated with CMOS-process-compatible technology, and measured with de-embedding method. Simulation and measured results are in good agreement. Compared with the other literature, the proposed LPF has the most compact size of $0.028\lambda _{g }\times 0.017 \lambda _{g}$ . ( $\lambda _{g}$ is the guide wavelength at $f_{c}$ .) With the cutoff frequency at 10.05 GHz, the filter has an insertion loss of 0.14 dB and reflection loss over 13 dB from dc to 9 GHz in the passband. The suppression levels are better than 20 dB from 20.4 up to 40 GHz in the stopband.

A wideband equivalent-circuit model of coaxial-annular through-silicon vias (TSVs) for three-dimensional (3-D) integrated circuits is proposed in this paper. Rigorous closed-form formulas for the resistance and inductance of coaxial-annular TSVs are derived by computing the longitudinal electrical field in Cu and the longitudinal magnetic vector potentials in ${\rm{SiO}}_{2}$ and Si substrate with Bessel functions. The equivalent-circuit model can appropriately capture the skin effect in Cu as well as eddy-current effect in Si substrate. The proposed model is verified using 3-D full-wave field solver high frequency simulator structure, showing that it can yields highly accurate results up to 100 GHz.

The 3-D multistrata integration puts forward high requirements for signal integrity. The shielded-pair through-silicon vias (SPTSVs) proposed in this paper feature superior transmission properties and high jamming immunity suitable for differential-mode and common-mode transmission. Based on the quasi-static field theory, a wideband impedance model of SPTSVs considering the proximity effect, the line-to-line crosstalk, and the eddy current effect is derived. The parasitic parameters calculated by the impedance model are further given. The finite-element analysis shows that the proposed model highly agrees with the 3-D full-wave simulation and the analytical calculation. In addition, the characteristics of the impedance and the transmission coefficient are deeply analyzed with different design parameters. Finally, the impacts of the substrate effect and the metal–oxide–semiconductor effect on electrical characteristics of SPTSVs are revealed.

A novel $\pi $ -type equivalent-circuit model of through-silicon vias (TSVs) for 3-D integrated circuits (3-D ICs) considering eddy current and proximity effects is proposed in this paper. The numerical models for the serial resistance and inductance of TSVs are derived by computing the longitudinal electrical field in Cu and the longitudinal magnetic vector potentials in SiO2 and Si substrate with Fourier-Bessel series. Furthermore, the closed-form formulas for the parallel capacitance and conductance of TSVs are derived by using the conformal mapping method. The proposed $\pi $ -type equivalent-circuit model is verified using 3-D full-wave field solver High-Frequency Structural Simulator, showing that it is highly accurate up to 100 GHz. Using the proposed model, the electrical performance of TSVs with high density can be evaluated accurately and quickly in a wideband frequency range.

An equivalent-circuit model of Cu-carbon nanotube heterogeneous coaxial through-silicon vias (HCTSVs) in 3-D integrated circuits (3-D ICs) is proposed in this paper. Based on the complex effective conductivity method, the resistances and inductances of Cu-single walled carbon nanotube (SWCNT) HCTSVs and Cu-multi walled carbon nanotube (MWCNT) HCTSVs are compared with that of Cu coaxial through-silicon vias (CTSVs). Furthermore, using the proposed model, the magnitudes of their insertion losses are compared. It is shown that the transmission performance of Cu-SWCNT HCTSVs with higher metallic fraction and Cu-MWCNT HCTSVs is better than that of Cu CTSVs, and the improvement of Cu-MWCNT HCTSVs is more obvious at high frequencies. Finally, the transmission characteristics of Cu-MWCNT HCTSVs are analyzed deeply to provide helpful design guidelines for them in future high-speed 3-D ICs.

This letter presents an approach to design the fourth-harmonic mixer based on a pair of antiparallel Schottky diodes. To implement the proposed fourth-harmonic mixer, a two-level local oscillator (LO) low-pass filter is used to suppress the second, third, and fourth harmonics of the LO frequency, further to improve the isolation between RF and LO ports. Also, two shorted grounds are adopted to ensure the wideband performance of the proposed mixer. Furthermore, a wideband fourth-harmonic operating at 325–500 GHz is fabricated and measured. The results show that it has very low conversion loss from 15 to 22 dB in the whole operational band.

In this paper, a new model of the parasitic inductance using a glass core substrate is proposed. Based on the magnetic flux equation, the expressions are derived considering the different profiles of Through Glass Vias(TGVs). According to the skin effect, the magnetic flux density is solved as a frequency-varying parameter. The formulas can be used to calculate the self-partial inductance and mutual-partial inductance. The inductance model is verified by comparing with the results of 3-D full-wave electromagnetic solver High Frequency Simulator Structure (HFSS). The proposed model and HFSS results show accordance with each other up to 100 GHz.

Based on the TSV technology, a compact passive resonator utilizing spiral inductor and coaxial TSV capacitor is proposed. And the compact stack configuration integrates the whole resonator in a microsize as small as 75μm×75μm. Furthermore, the adopted spiral inductor, coaxial TSV capacitor and resonator are characterized with equivalent circuit model. The transmission parameters from equivalent circuit models and HFSS simulation are matched very well. The proposed resonator exhibits an insertion loss below 1.0dB and a return loss over −20 dB at the center frequency of 2.7GHz in the passband. And the −3dB bandwidth of resonant peak in the resonant frequency span are within the range from 1.4GHz to 5.2GHz, which demonstrates the superior characteristic of the resonator.

An equivalent-circuit model of shield differential through-silicon vias (SDTSVs) in 3-D integrated circuits (3-D ICs) is proposed in this paper. The proposed model is verified using the 3-D full-wave field solver High Frequency Simulator Structure, showing that it is highly accurate up to 100 GHz. Furthermore, a full-wave extraction method for the resistance–inductance–capacitance–conductance (RLCG) parameters of SDTSVs is also proposed in this paper, which can be applied to all of differential transmission lines. It is shown that the results of the RLCG parameters obtained from the full-wave extraction method agree well with that from the analytical calculation up to 100 GHz, further validating the accuracy of the proposed model. Finally, using the proposed model, a deep analysis of electrical characteristics of SDTSVs is carried out to provide helpful design guidelines for them in future 3-D ICs.

The three-dimensional integrated circuits (3D ICs) based on through silicon via (TSV) technology offer a solution to meet the continuously increasing demand on high-speed electronic products. In order to comprehensively evaluate the signal transmission of TSV in increasing signal frequency, accuracy equivalent circuit model is necessary. In this paper, a method of double-T type equivalent circuit modelling for TSVs is proposed and applied to coaxial TSV and ground-signal (GS)-type TSVs. Furthermore, the transmission parameters (S21) of the double-T models are evaluated by SPICE and compared with the results of 3-D full-wave electromagnetic field simulation (HFSS). The good accordance of the results up to 50GHz verifies the accuracy of the proposed method.

The polymer-cavity through-silicon vias (TSVs) on low resistivity silicon (LRSi) are proposed in this letter to reduce the conductive substrate losses for microwave applications, due to that the coupling loss of conventional LRSi is considerable in high speed three-dimensional integrated circuits (3-D ICs). The accurate wideband equivalent circuit model and simplified π-model are derived based on the physical design parameters, which are established by the ADS software. Well agreements between the proposed models and 3D full-wave EM field simulation of Ansoft's HFSS are shown with the operating frequencies up to 20 GHz.

A simple formula for the internal impedance of mixed carbon nanotube (CNT) bundles is proposed in this paper. It can appropriately capture the skin effect as well as temperature effect of mixed CNT bundles. The computing time and results of the simple formula and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed simple formula can improve the efficiency dramatically, and has very high accuracy in the whole frequency range considered, with maximum errors of 1.2% and 2.5% for the resistance and the internal inductance, respectively.

This letter first proposes novel formulas for the calculation of the oxide capacitance and the silicon substrate capacitance in Tapered-Through Silicon vias (T-TSVs). 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 method was used properly based on the analytical results of the local electric field structure in T-TSVs. When the slope angle equals to zero, the obtained formulas can be reduced to the formulas of cylindrical TSVs. The comparison between the results of the proposed formulas and the three-dimensional quasi-static field solver shows that the proposed formulas have very high accuracy, with maximum errors of 1% and 3% for the oxide capacitance and the silicon substrate capacitance, respectively.

The concept of a distortionless through silicon via (TSV), which uses a multiwalled carbon nanotube (MWCNT) as conductor material, is proposed. The design requirements and the design method for the distortionless TSV are presented. In the high-frequency band, the propagation constant of the traditional Cu-TSV will deviate from the linear function of the frequency because of the skin effect, inducing the transmission signal distortion. MWCNT bundles have properties where the resistance and the inductance are almost constant with the frequency, which can meet the design requirements for a distortionless TSV. Compared with the identical dimensions Cu-TSV, the TSV designed by using the proposed method with MWCNT bundles as the conductor material has the preferable linearity of the propagation constant with the frequency in the high-frequency band, so that it can reduce the distortion of the transmission signal.

Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube (CNT) bundles, in which the number of CNTs for a given diameter follows a Gaussian distribution, is proposed in this paper. It can appropriately capture the skin effect as well as the temperature effect of mixed CNT bundles. The results of the closed-form expression and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed model has very high accuracy in the whole frequency range considered, with maximum errors of 1% and 2.3% for the resistance and the internal inductance, respectively. Moreover, by using the proposed model, the high-frequency electrical characteristics of mixed CNT bundles are deeply analyzed to provide helpful design guidelines for their application in future high-performance three-dimensional integrated circuits.

We propose a new conductivity model of multi-walled carbon nanotube (MWCNT) interconnects considering the influence of temperature. For each shell of MWCNT interconnects, it may present the property of ballistic transport or may suffer from acoustic photo and optical phonon (OP) scattering depending on their mean free paths (MFPs) and the wire length. Furthermore, since the MFPs are proportional to the shell diameter, five regions exist in the wire length in which the factors influencing the conductivity are determined. Thus the conductivity is modeled in five cases according to their lengths, and the final obtained model is a 5-piecewise function. By using this model, the influence of temperature on the conductivity is examined and analyzed. It is shown that the conductivity demonstrates different, changing behaviors with the increase of temperature in the five cases. Additionally, the influence of OP scattering on the conductivity does not need to be taken into account at room temperatures, whereas this influence will produce a decline region in the conductivity at high temperatures.