Wen-Sheng Zhao

Signal Transmission Analysis of Multilayer Graphene Nano-Ribbon (MLGNR) Interconnects

Signal transmission characteristics of some multilayer graphene nano-ribbon (MLGNR) interconnects are studied in this paper, with an equivalent single-conductor (ESC) model implemented for the analysis of their transient responses. In this model, both capacitive and inductive couplings between adjacent GNR layers are treated appropriately. According to the derived transfer function using the fourth-order approximation, the output voltage waveforms are predicted for both 14- and 22-nm technology nodes. In particular, the effects of Fermi level of MLGNR on the time delay of the transmitted rectangular pulse are examined and compared. Based on the decoupled partially differential equations (PDEs) for the common and differential modes of voltage wave propagation in the edge-coupled MLGNR interconnects, their output voltage responses are also predicted for different technology nodes, which are useful for the evaluation of on-chip signal integrity or EMC and EMI issues of MLGNR-built transmission lines for the future ICs.

Electromagnetic Compatibility-Oriented Study on Through Silicon Single-Walled Carbon Nanotube Bundle Via (TS-SWCNTBV) Arrays

Electromagnetic compatibility-oriented study is performed for accurately characterizing through silicon single-walled carbon nanotube bundle via (TS-SWCNTBV) array in this paper. Based on the modified equivalent lumped-element circuit model of a pair of TS-SWCNTBVs, its forward transmission coefficient, in comparison with copper- and tungsten-based TSVs, is investigated for different metallic fractions of the SWCNTs, with quantum effects treated appropriately. The 3-D transmission-line method (TLM) is further employed for studying mutual couplings in three, four, and nine TS-SWCNTBV arrays, respectively, where the effects of their geometrical and physical parameters on the effective capacitance and conductance are examined in detail. Also, transient coupling noises in different arrays excited by a clock signal, respectively, are predicted and compared, which are useful for the design of high density TS-SWCNTBV arrays with better signal transmission performance.

Comparative Study on Multilayer Graphene Nanoribbon (MLGNR) Interconnects

Based on an equivalent single-conductor (ESC) model of multilayer graphene nanoribbon (MLGNR) interconnects with side contacts, comparative study on their distributed parameters and transmission characteristics is performed in this paper. It is found that the number of conducting channels of a metallic MLGNR interconnect is the linear function of its width and Fermi energy, which can be described by an analytical equation. Its equivalent inductance and capacitance in the ESC model can also be characterized by a set of closed-form equations. Furthermore, according to the ITRS projection, transmission performance of the MLGNR interconnects with different contacts are predicted and compared with their Cu and carbon nanotube counterparts at different technology nodes. Also, some numerical results prove that MLGNR interconnects can provide better performance than Cu wires in particular at intermediate level. Even with the maximum crosstalk impacts considered, the advantage of MLGNR interconnects over Cu wires can still be kept.

Reconfigurable Terahertz Leaky-Wave Antenna Using Graphene-Based High-Impedance Surface

The concept of graphene-based two-dimensional leaky-wave antenna (LWA), allowing both frequency tuning and beam steering in the terahertz band, is proposed in this paper. In its design, a graphene sheet is used as a tuning part of the high-impedance surface (HIS) that acts as the ground plane of such 2-D LWA. It is shown that, by adjusting the graphene conductivity, the reflection phase of the HIS can be altered effectively, thus controlling the resonant frequency of the 2-D LWA over a broad band. In addition, a flexible adjustment of its pointing direction can be achieved over a wide range, while keeping the operating frequency fixed. Transmission-line methods are used to accurately predict the antenna reconfigurable characteristics, which are further verified by means of commercial full-wave analysis tools.

Frequency- and Temperature-Dependent Modeling of Coaxial Through-Silicon Vias for 3-D ICs

Temperature-dependent investigations of circular and square coaxial through-silicon vias (C-TSVs) are carried out in this paper, which can provide an effective solution to suppressing various couplings, such as intra- and intersubstrate, and crosstalk among multi-TSVs. An equivalent lumped-element circuit model is proposed for both C-TSVs, and their parasitic capacitance values, per-unit-height distributed parameters, characteristic impedance values, and S-parameters are characterized and compared numerically for different frequencies and temperatures. Furthermore, self-heating effects in both C-TSVs are investigated with a set of closed-form equations derived for determining their thermal resistances. Their average power handling capabilities are addressed, which are verified using the static finite-element method.

ELECTROTHERMAL EFFECTS IN HIGH DENSITY THROUGH SILICON VIA (TSV) ARRAYS

Electrothermal effects in various through silicon via (TSV) arrays are investigated in this paper. An equivalent lumped-element circuit model of a TSV pair is derived. The temperature-dependent TSV capacitance, silicon substrate capacitance and conductance are examined for low-, medium-, and high-resistivity silicon substrates, respectively. The partial-element equivalent-circuit (PEEC) method is employed for calculating per-unit-length (p.u.l.) resistance, inductance, insertion loss and characteristic impedances of copper and polycrystalline silicon (poly-Si) TSV arrays, and their frequencyand temperature-dependent characteristics are treated rigorously. The modified time-domain finite-element method (TD-FEM), in the presence of a set of periodic differential-mode voltage pulses, is also employed for studying transient electrothermal responses of 4and 5-TSV arrays made of different materials, with their maximum temperatures and thermal crosstalk characterized thoroughly.

Carbon-Based Interconnects for RF Nanoelectronics

In this article, circuit-oriented modeling techniques for both carbon nanotube (CNT) and graphene nanoribbon (GNR) interconnects will be introduced. Based on their circuit models, the transmission characteristics of single-walled CNT (SWCNT), multiwalled CNT (MWCNT), and multilayered GNR (MLGNR) interconnects will be further shown theoretically. By taking the self-heating effect (SHE) into account, temperature distribution along an SWCNT array and its transient thermal response will be demonstrated by solving a one-dimensional heat conduction equation, together with its impact on the signal transmission characteristics examined. Then, theoretical analyses of both CNT- and graphene-built very large-scale integration interconnects will be presented. In particular, the concept of “almost-carbon integration” will be proposed, where both CNT and graphene advantages are integrated effectively into future three-dimensional integrated circuits. Keywords: carbon nanomaterials; interconnect

Electrical Modeling of Three-Dimensional Carbon-Based Heterogeneous Interconnects

One three-dimensional (3-D) carbon-based heterogeneous interconnect scheme, consisting of a couple of horizontal multilayer graphene transmission lines (MLG-TL) and vertical through silicon carbon nanotube bundle vias (TS-CNTBV), is proposed and investigated theoretically. For its realization, some metallic bumps are used to integrate MLG-TLs with TS-CNTBVs, and contact resistance among them are characterized and compared. The lumped-element circuit model of a couple of MLG-TLs is also combined with that of TS-CNTBVs, with anomalous skin effect treated in an appropriate way. Numerical studies are performed for capturing distributed parameters as well as transmission characteristics of MLG-TLs, TS-CNTBVs, and whole 3-D interconnects at different operating frequencies. It is believed that this study can provide some useful information about carbon-based heterogeneous interconnects, where both graphene and carbon nanotube advantages can be exploited for the future 3-D ICs.

Wideband Modeling of Graphene-Based Structures at Different Temperatures Using Hybrid FDTD Method

An efficient finite-difference time-domain (FDTD) algorithm is proposed for studying frequency- and temperature-dependent characteristics of some graphene-based structures, with auxiliary differential equation-FDTD method and its conformal modification technique integrated together for handling such atomically thin and electrically dispersive periodic geometries. Numerical results are presented to show their tunable transmittances, surface plasmon polarization-mode characteristics and Fano resonances, where the effects of chemical potential of graphene, biasing electric field strength, as well as operating temperature are captured and investigated in detail.

Wideband Modeling and Characterization of Differential Through-Silicon Vias for 3-D ICs

This paper presents the wideband modeling and analysis of differential through-silicon vias (D-TSVs) in 3-D ICs. An equivalent-circuit model of the ground-signal-signal-ground-type D-TSVs is given and validated against a commercial full-wave electromagnetic simulation tool. The common- and differential-mode impedances are extracted using the partial-element equivalent-circuit method, while the admittances are calculated analytically, with the MOS effects considered and treated appropriately. The circuit model can also be used for studying the differential annular TSVs (ATSVs). It is shown that the ATSVs are more suitable for transmitting differential signals in comparison with the cylindrical TSVs. Based on the equivalent-circuit model, the characteristic impedances and the forward transmission coefficients of the D-TSVs made of Cu and carbon nanotubes are characterized and compared under different settings of frequencies and temperatures.