A survey of carbon nanotube interconnects for energy efficient integrated circuits

This article is a review of the state-of-art carbon nanotube interconnects for Silicon application with respect to the recent literature. Amongst all the research on carbon nanotube interconnects, those discussed here cover 1) challenges with current copper interconnects, 2) process & growth of carbon nanotube interconnects compatible with back-end-of-line integration, and 3) modeling and simulation for circuit-level benchmarking and performance prediction. The focus is on the evolution of carbon nanotube interconnects from the process, theoretical modeling, and experimental characterization to on-chip interconnect applications. We provide an overview of the current advancements on carbon nanotube interconnects and also regarding the prospects for designing energy efficient integrated circuits. Each selected category is presented in an accessible manner aiming to serve as a survey and informative cornerstone on carbon nanotube interconnects relevant to students and scientists belonging to a range of fields from physics, processing to circuit design

Modeling Solder Ball Array Interconnects for Power Module Optimization

PowerSynth is a software platform that can co-optimize power modules utilizing a 2D topology and wire bond interconnects. The novel 3D architectures being proposed at the University of Arkansas utilize solder ball interconnects instead of wire bonds. Therefore, they currently cannot be optimized using PowerSynth. This paper examines methods to accurately model the parasitic inductance of solder balls and ball grid arrays so they may be implemented into software for optimization. Proposed mathematical models are validated against ANSYS Electromagnetics Suite simulations. A comparison of the simulated data shows that mathematical models are well suited for implementation into optimization software platforms. Experimental measurements proved to be inconclusive and necessitate future work

Entire domain basis function expansion of the differential surface admittance for efficient broadband characterization of lossy interconnects

This article presents a full-wave method to characterize lossy conductors in an interconnect setting. To this end, a novel and accurate differential surface admittance operator for cuboids based on entire domain basis functions is formulated. By combining this new operator with the augmented electric field integral equation, a comprehensive broadband characterization is obtained. Compared with the state of the art in differential surface admittance operator modeling, we prove the accuracy and improved speed of the novel formulation. Additional examples support these conclusions by comparing the results with commerical software tools and with measurements

Near-field scanning microwave microscope for interline capacitance characterization of nanoelectronics interconnect

We have developed a noncontact method for measurement of the interline capacitance in Cu/low-k interconnect. It is based on a miniature test vehicle with net capacitance of a few femto-Farads formed by two 20-\mu m-long parallel wires (lines) with widths and spacings the same as those of the interconnect wires of interest. Each line is connected to a small test pad. The vehicle impedance is measured at 4 GHz by a near-field microwave probe with 10 \mu m probe size via capacitive coupling of the probe to the vehicle's test pads. Full 3D finite element modeling at 4 GHz confirms that the microwave radiation is concentrated between the two wires forming the vehicle. An analytical lumped element model and a short/open calibration approach have been proposed to extract the interline capacitance value from the measured data. We have validated the technique on several test vehicles made with copper and low-k dielectric on a 300 mm wafer. The vehicles interline spacing ranges from 0.09 to 1 \mu m and a copper line width is 0.15 \mu m. This is the first time a near-field scanning microwave microscope has been applied to measure the lumped element impedance of a test vehicle

Guaranteed passive parameterized model order reduction of the partial element equivalent circuit (PEEC) method

The decrease of IC feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the system under study as a function of design parameters, such as geometrical and substrate features, in addition to frequency (or time). Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters. We propose an innovative PMOR technique applicable to PEEC analysis, which combines traditional passivity-preserving model order reduction methods and positive interpolation schemes. It is able to provide parametric reduced-order models, stable, and passive by construction over a user-defined range of design parameter values. Numerical examples validate the proposed approach

Construction and applications of the Dirichlet-to-Neumann operator in transmission line modeling

The Dirichlet-to-Neumann (DIN) operator is a useful tool in the characterization of interconnect structures. in. combination with the Method of Moments; it con. be used for the calculation, of the per-unit length transmission line parameters of multi-conductor Or to directly determine the interval impedance of conductors. This paper presents a new and fast calculation method for the DIN boundary operator in the important case of rectangular structures, based on the superposition of parallel-plate waveguide modes. Especially for its non-differential form, some numerical issues need to be addressed. It is further explained how the DtN operator can be determined for composite geometries. The theory is illustrated with some numerical examples

Compact and accurate models of large single-wall carbon-nanotube interconnects

Single-wall carbon nanotubes (SWCNTs) have been proposed for very large scale integration interconnect applications and their modeling is carried out using the multiconductor transmission line (MTL) formulation. Their time-domain analysis has some simulation issues related to the high number of SWCNTs within each bundle, which results in a highly complex model and loss of accuracy in the case of long interconnects. In recent years, several techniques have been proposed to reduce the complexity of the model whose accuracy decreases as the interconnection length increases. This paper presents a rigorous new technique to generate accurate reduced-order models of large SWCNT interconnects. The frequency response of the MTL is computed by using the spectral form of the dyadic Green's function of the 1-D propagation problem and the model complexity is reduced using rational-model identification techniques. The proposed approach is validated by numerical results involving hundreds of SWCNTs, which confirm its capability of reducing the complexity of the model, while preserving accuracy over a wide frequency range