Andrea G. Chiariello

Circuit Models of Carbon-Based Interconnects for Nanopackaging

This paper proposes an equivalent circuital model to describe the electrical propagation along nanoscale interconnects, made either by carbon nanotubes or graphene nanoribbons. The circuital models are derived from an electrodynamical model for the transport of conduction electrons, and are expressed in the frame of the classical transmission line theory. The per-unit-length parameters, despite their simple expressions, retain the main phenomena occurring at nanoscale, such as the kinetic and quantum effects. In addition, the circuit parameters are expressed as functions of the temperature and the transverse size of the interconnect, thus allowing a qualitative and quantitative analysis of their impact in the electrical performance of the interconnects. The models are used to study some challenging problems in nanopackaging, such as the degradation of electrical performance due to self-heating and the high-frequency current crowding problem because of the skin-effect. Interconnects and vias are analyzed, referring to the 14-nm technology node.

Electrical Modeling of Carbon Nanotube Vias

This paper investigates the electrical behavior of vias made by bundles of either single-walled or multiwalled carbon nanotubes (CNTs). The electronic transport in the CNTs is modeled through the kinetic inductance, the quantum capacitance, and the electrical resistance, which depend on the equivalent number of the CNT conducting channels. The dependence of such a number on the CNT radius, chirality, and temperature is described by using the quasi-classical transport theory. Since for the common mode the effects of the intershell tunneling are negligible, the interaction between different shells is described by using the classical electromagnetic theory. A simple but accurate equivalent lumped model for vias made by CNT bundles is proposed. Vias of interest in nanoelectronic applications are here analyzed, with particular focus on the behavior of electrical parameters versus temperature and frequency.

Size and temperature effects on the resistance of copper and carbon nanotubes nano-interconnects

The electrical performances of nano-interconnects are affected by temperature and size, which may seriously limit the current density and the reliability. This paper introduces such effects in the modelling of the electrical resistance of nano-interconnects, either made by copper and carbon-nanotubes. A simple and accurate semi-analytical model is proposed to describe the impact of size and temperature changes on the resistance of carbon nanotube interconnects. Case-studies are carried out with reference to 22nm technology node applications.

A Transmission-Line Model for Full-Wave Analysis of Mixed-Mode Propagation

The paper presents a generalized transmission line model able to describe the high-frequency mixed-mode propagation along electrical interconnects. The model is derived from a full-wave formulation and extends the validity of the standard transmission line (TL) model to frequency ranges where the propagation is no longer of transmission electron microscopy (TEM)-type. This generalized TL model describes the high-frequency differential and common mode propagation and the mode conversion. Within its validity limits, the proposed model provides solutions in good agreement with those obtained through full-wave models. Case studies are carried out to evaluate the high-frequency mode conversion in asymmetric interconnects.

Metallic Carbon Nanotube Interconnects, Part I: a Fluid Model and a 3D Integral Formulation

This paper illustrates the inclusion, in a 3D integral formulation of Maxwell equations, of a fluid model for the study of the electrodynamics of metallic carbon nanotubes in the frequency domain. The effective conduction electrons are modeled as an infinitesimally thin cylindrical layer of compressible fluid, whose dynamics are described by means of the linearized Eulers equation. The resulting integral equations are solved numerically by the finite element method, using the facet elements and the null-pinv decomposition. The proposed formulation is applied to study carbon nanotubes interconnects

Effectiveness in 3-D Magnetic Field Evaluation of Complex Magnets

Numerical high-accuracy evaluation of 3-D magnetic field generated by complex magnetic structures can be a quite demanding task. In order to save the computational effort, while preserving the accuracy level, a number of simple magnetic elements able to model complex 3-D structures are available. In this paper, a critical comparison of different modeling has been carried out in the perspective of a graphical processing unit implementation.

GPU-accelerated analysis of vertical instabilities in ITER including three-dimensional volumetric conducting structures

In this paper, we study the axisymmetric vertical instability of elongated configurations, including the effect of volumetric three-dimensional conducting structures surrounding the plasma. In order to deal with the huge computational models arising from the realistic geometrical description, a GPU-based (graphics processing units) acceleration is pursued. The method is applied to some ITER configurations, for which the open-loop growth rates, the input–output transfer functions and the gain and phase margins are computed.

Electrical behaviour of carbon nanotube Through-Silicon Vias

The paper investigates the high-frequency distribution of the current density in Through-Silicon Vias made by bundles of carbon nanotubes (CNTs). These bundles are described by means of a recently proposed circuit model which, in spite of its simplicity, accounts for the kinetic and quantum phenomena involved in the electrical propagation along CNTs and includes the effects of size, temperature and chirality. The particular electrical properties of such a new material make the CNT-based TSVs quite insensitive to skin-effect and proximity effect. This is shown with reference to a case-study of a TSV pair for the technology node of 22 nm, for which the effects of frequency and temperature variation are analyzed.

Metallic Carbon Nanotube Interconnects, Part II: a Transmission Line Model

In this paper a transmission line model is derived to describe the propagation along single-wall carbon nanotubes, candidate to be used as interconnects in nanoelectronics applications. The model is obtained in a consistent way from a fluid model of the electron conduction along such a nanostructure. The per-unit-length parameters are strongly dependent on the effects related to the electron inertia and the quantum fluid pressure. The values of the signal propagation velocity, characteristic impedance and characteristic damping of the obtained transmission line are very different from that obtainable, in principle, by ideally scaling the conventional technology. A successful benchmark test with a full-wave model is presented and some case-studies are carried out to investigate the possibility to use such structures as the future interconnects

Signal integrity analysis of carbon nanotube on-chip interconnects

The paper deals with the signal integrity performances of a nanoscale on-chip interconnect made by using the carbon nanotube technology. As conventional copper does, this material can be used for fabricating both horizontal traces and vertical vias. Carbon nanotubes interconnects outperform copper ones in terms of electrical, thermal and mechanical properties. However their inductance is much higher compared to that of conventional material, due to inertial effects. Usually this inductance is neglected in the circuit equivalent representation of carbon nanotube interconnects. Here we use a recently proposed circuit model to study the effects of the inductance on the signal integrity. The analysis is carried out by referring to a realistic configuration foreseen for the future 22 nm technology.