-
[show abstract]
[hide abstract]
ABSTRACT: The electromagnetic behavior of multiwall carbon nanotubes (MWCNTs), in the frequency range where only intraband transitions are allowed, depends on the combinations of different aspects: the number of effective conducting channels of each shell, the electron tunneling between adjacent shells, and the electromagnetic interaction between shells and the environment. This paper proposes a general transmission-line (TL) model for describing the propagation of electric signals along MWCNTs at microwave through terahertz frequencies that takes into account all these aspects. The dependence of the number of conducting channels of the single shell on the shell chirality and radius is described in the framework of the quasi-classical transport theory. The description of the intershell tunneling effects on the longitudinal transport of the π-electrons is carried on the basis of the density matrix formalism and Liouville's equation. The electromagnetic coupling between the shells and ground plane is described in the frame of the classical TL theory. The intershell tunneling qualitatively changes the form of the TL equations through the tunneling inductance and capacitance operators, which have to be added, respectively, in series to the (kinetic and magnetic) inductance matrix and in parallel to the (quantum and electrical) capacitance matrix. For carbon nanotube (CNT) lengths greater than 500 nm, the norm of the tunneling inductance operator is greater than 60% of the norm of the total inductance in the frequency range from gigahertz to terahertz. The tunneling inductance is responsible for a considerable coupling between the shells and gives rise to strong spatial dispersion. The model has been used to analyze the eigenmodes of a double-wall CNT above a ground plane. The intershell tunneling gives arise to strong anomalous dispersion in antisymmetrical modes.
IEEE Transactions on Nanotechnology 05/2012; 11(3):554 - 564. · 2.29 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: This paper proposes a model for the electrical propagation along carbon nanotubes, based on a quasi-classical Boltzmann transport model. The model is accurate enough to include quantistic and kinetic effects involved at nanoscale, and simple enough to provide equivalent circuits with the physically meaningful parameters. These parameters are expressed in terms of the equivalent number of conducting channels, which takes into account CNT chiralities, temperature and diameter. This allows simulating realistic CNT bundles proposed as nano-interconnects for future VLSI applications.
Journal of Nanoelectronics and Optoelectronics 12/2011; 7(1):12-16. · 0.56 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
Signal Propagation on Interconnects (SPI), 2011 15th IEEE Workshop on; 06/2011
-
[show abstract]
[hide abstract]
ABSTRACT: In carbon nanotubes (CNTs) with large radii, either metallic or semiconducting, several subbands contribute to the electrical conduction, while in metallic nonarmchair nanotubes with small radii the wall curvature induces a large energy gap. In this paper, we propose a model for the signal propagation along single wall CNTs (SWCNTs) of arbitrary chirality, at microwave through terahertz frequencies, which takes into account both these characteristics in a self-consistent way. We first study an SWCNT, disregarding the wall curvature, in the frame of a semiclassical treatment based on the Boltzmann equation in the momentum-independent relaxation time approximation. It allows expressing the longitudinal dynamic conductivity in terms of the number of effective conducting channels. Next, we study the behavior of this number as the nanotube radius varies and its relation with the kinetic inductance and quantum capacitance. Furthermore, we show that the effects of the spatial dispersion are negligible in the collision dominated regimes, whereas they may be important in the collisionless regimes, giving rise to sound waves propagating with the Fermi velocity. Then, we study the effects on the electron transport of the terahertz quantum transition induced by the wall curvature by using a quantum kinetic approach. The nanotube curvature modifies the kinetic inductance and gives arise to an additional RLC branch in the equivalent circuit, related to the terahertz quantum transition. The proposed model can be used effectively for analyzing the signal propagation in complex structures composed of SWCNTs with different chirality, such as bundles of SWCNTs and multiwall CNTs, providing that the tunneling between adjacent shells may be disregarded.
IEEE Transactions on Nanotechnology 02/2011; · 2.29 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
Electrical Performance of Electronic Packaging and Systems (EPEPS), 2010 IEEE 19th Conference on; 11/2010
-
[show abstract]
[hide abstract]
ABSTRACT: The paper deals with the problem of the efficient extraction of the impedance matrix for a complex full-package structure. This result applies to ranges from DC to frequencies for which the skin effect is pronounced but the radiation and other full-wave effects are still negligible. The model identifies the impedance matrix by enforcing a physically consistent behavior to the resistance and reactance of the package in the low and high frequency limits. The identification is made by using only 5 frequency samples of the impedance matrix, which could be either given by measurements or numerical simulations. In this paper we have used a commercial 3D electromagnetic code (FastHenry) to provide the 5 starting points and the reference values to validate the procedure. Benchmark tests and case-studies are carried out, confirming the accuracy of the model.
Signal Propagation on Interconnects (SPI), 2010 IEEE 14th Workshop on; 06/2010
-
[show abstract]
[hide abstract]
ABSTRACT: This Chapter has analyzed the use of carbon nanotubes as possible innovative material to fabricate high-speed interconnects at various hierarchical levels of the future nanoelectronics technology. The electromagnetic model presented here to describe the electrical propagation along CNT interconnects is derived from a semi-classical solution of the transport equation. All the quantistic and kinetic effects affecting the electrodynamics of charge carriers are taken into account through global parameters (kinetic inductance and quantum capacitance) which have been simply related to the number of effective conducting channel per CNT shell. Both the rigorous approach and a simple approximation have been provided to evaluate this number for CNT shells of arbitrary chirality, hence allowing the modelling of either single-wall and multi-wall CNTs. The electrodynamical model provides a constitutive equation for the CNT interconnect, which is coupled to the Maxwell equation: the problem is then solved in the frame of the classical transmission line theory, so obtaining simple equivalent RLC circuits for single CNTs and bundles of CNTs. These models are consistent with those used in literature for metallic CNTs, but introduce the possibility to deal with arbitrary chiralities and CNT diameters. The analysis of CNT transmission lines highlights unusual behaviours with respect to the Cu lines, mainly due to the strong influence of the kinetic and quantistic terms over the classical electromagnetic inductance and capacitance parameters. Some case-studies have been carried out referring to a realistic use of CNTs to build interconnects for wiring and for packaging nanotechnology ICs. In the considered examples typical values of the future 22nm technology nodes have been assumed. A signal integrity analysis is performed with reference to an on-chip interconnect arrangement, where the conventional Cu material is replaced by a bundle of CNTs. Next, the EMC behaviour of two adjacent traces in a stripline is analyzed, checking the high-frequency effects and the crosstalk noise. Finally the use of CNTs as pillars for nanopackaging is studied and the introduced parasitics are compared to conventional material realization. Carbon nanotube interconnects are shown to have better behaviour with respect to conventional Cu ones in terms of SI and EMC performances, introduced parasitics and response to temperature variations. From a practical point of view, these simulated performances may be achieved provided that good quality bundles are realized, i.e. bundles of high density, good direction control and good terminal contacts.
03/2010; , ISBN: 978-953-307-054-4
-
[show abstract]
[hide abstract]
ABSTRACT: The paper deals with the evaluation of the far-field radiated emissions from high-speed interconnects when the frequencies are such that the distribution of the currents along the traces is no longer of TEM-type. Instead of a computationally expensive numerical full-wave model, here a generalized transmission line model is used to obtain the current distributions. This full-wave transmission line model is derived from an integral formulation and is here extended to include in efficient way the layered media Green's Functions. The proposed tool is successfully benchmarked to references given in literature and case-studies of practical interest are carried out, referring to a coupled microstrip, driven either by differential and common mode currents. This analysis highlights the existence of a transition range where the error made by evaluating the emission using the classical transmission line current distribution is still negligible. Here a rule of thumb is derived which provides a simple criterion to estimate this extension of the range of validity of the classical transmission line.
Progress In Electromagnetics Research. 01/2010; 101:125-138.
-
[show abstract]
[hide abstract]
ABSTRACT: The paper presents recent advances in carbon nanotube interconnect modeling, with focus on their application to nanoscale chip packaging. An enhanced electrical model of carbon nanotube bundles is used, able to take into account the effects of different nanotube sizes covered by this application. The use of carbon nanotubes as chip to package interconnects at nanoscale dimensions is analyzed and the electrical parasitics introduced by these interconnects are compared to those predicted by other packaging technologies.
Nanotechnology, 2009. IEEE-NANO 2009. 9th IEEE Conference on; 08/2009
-
[show abstract]
[hide abstract]
ABSTRACT: The paper presents a self-consistent semi-classical model describing the electrical behavior of carbon nanotube interconnects. The model deals with the general case of arbitrary chirality and takes rigorously into account the effects of nanotube size and chirality on its electrical parameters. The general model includes as particular cases the models currently used in literature to describe metallic carbon nanotubes with small radius. The analysis of bundles of single-walled and multi-walled carbon nanotubes is carried-out. The model is also used to derive a semi-analytical approximation for the number of equivalent conduction channels in a multi-walled carbon nanotube shell.
Nanotechnology, 2009. IEEE-NANO 2009. 9th IEEE Conference on; 08/2009
-
[show abstract]
[hide abstract]
ABSTRACT: The paper investigates the EMC behavior of carbon nanotube interconnects, which are candidate to replace copper in future nanoscale technology. In particular, two problems are addressed: the influence of the kinetic inductance on the high-frequency behavior and the crosstalk performances of such interconnects. A recently proposed model is used to describe these interconnects within the frame of the classical transmission line theory, while retaining the necessary accuracy in describing the typical quantistic and inertial effects involved at such a scale.
Electromagnetic Compatibility - EMC Europe, 2009 International Symposium on; 07/2009
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
Signal Propagation on Interconnects, 2009. SPI '09. IEEE Workshop on; 06/2009
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, a new circuit model for the propagation of electric signals along carbon nanotube interconnects is derived from a fluid model description of the nanotube electrodynamics. The conduction electrons are regarded as a 2-D charged fluid, interacting with the electromagnetic field produced by the ion lattice, the conduction electron themselves, and the external sources. This interaction may be assumed to be governed by a linearized Euler's equation, which provides the nanotube constitutive equation to be coupled to Maxwell equations. A derivation of a circuit model is then possible within the frame of the classical multiconductor transmission-line (TL) theory. The elementary cell of this TL model differs from those proposed in literature, due to the definition of the circuit variable corresponding to the voltage. When considering small nanotube radius, we obtain values for the kinetic inductance and quantum capacitance that are consistent with literature. These values are corrected here to take into account the influence of larger values of radius properly. Conversely, the value of the per unit length resistance is roughly half of the value usually adopted in literature. The multiconductor TL model is used to study the scaling law of the parameters with the number of carbon nanotubes in a bundle.
IEEE Transactions on Nanotechnology 06/2009; · 2.29 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: This paper addresses the problem of scaling interconnects to nanometric dimensions in future very-large-scale integration applications. Traditional copper interconnects are compared to innovative interconnects made by bundles of metallic carbon nanotubes. A new model is presented to describe the propagation of electric signals along carbon nanotube (CNT) bundles, in the framework of the classical transmission line theory. A possible implementation of a future scaled microstrip based on CNT bundle is analyzed and compared to a conventional microstrip.
IEEE Transactions on Advanced Packaging 12/2008; · 1.12 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: This paper presents an electromagnetic and a circuit model to describe the propagation of electric signals along interconnects made by carbon nanotubes. The models are both derived from an enhanced fluid description of the carbon nanotube electrodynamics, which takes into account size effects disregarded in the literature. The electromagnetic model is obtained in a surface integral formulation by coupling the fluid equation to the full-wave Maxwell equations and is numerically solved using a null-pinv decomposition technique. The circuit model is derived within the frame of the classical multiconductor transmission line theory. Both the models are used to analyze case-studies of interest where the carbon nanotube technology is used to build electrical nano-interconnects.
Electronics System-Integration Technology Conference, 2008. ESTC 2008. 2nd; 10/2008
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, we use a fluid model to describe the dynamics of the conduction electrons of multiwall carbon nanotubes. A 3-D integral formulation of Maxwell's equations is used and numerically solved with a finite-elements approach based on div-conforming basis functions. The null-pinv decomposition is used to avoid the low-frequency breakdown.
IEEE Transactions on Magnetics 07/2008; · 1.36 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: The scaling of the integrated circuits foreseen by the technology roadmap imposes tight requirements to the interconnects, in terms of latency, energy density and bandwidth. Innovative solutions are proposed to replace the traditional copper technology at nanometric scale. In this paper we investigate the behavior of some of these innovative interconnects, namely carbon nanotube interconnects, arrays of plasmonic nanoparticles and surface plasmon-polariton waveguides. Starting from the electrodynamic models describing such structures, the performances in terms of latency and decay lengths are compared.
Signal Propagation on Interconnects, 2008. SPI 2008. 12th IEEE Workshop on; 06/2008
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
IEEE Transactions on Advanced Packaging 06/2008; · 1.12 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: A transmission line (TL) model describing the propagation of electric signals along metallic single wall carbon nanotube (CNT) interconnects is derived in a simple and self-consistent way within the framework of the classical electrodynamics. The conduction electrons of metallic CNTs are modelled as an infinitesimally thin cylindrical layer of a compressible charged fluid with friction, moving in a uniform neutralizing background. The dynamic of the electron fluid is studied by means of the linearized hydrodynamic equations with the pressure assumed to be that of a degenerate spin-½ ideal Fermi gas. Transport effects due to the electron inertia, quantum fluid pressure and electron scattering with the ion lattice significantly influence the propagation features of the TL. The simplicity and robustness of the fluid model make the derivation of the TL equations more straightforward than other derivations recently proposed in the literature and provide simple and clear definitions of the per unit length (p.u.l.) TL parameters. In particular, this approach has provided a new circuit model that can be used effectively in the analysis of networks composed of CNT transmission lines and lumped elements. The differences and similarities between the proposed model and those given in the literature are highlighted. Copyright © 2006 John Wiley & Sons, Ltd.
International Journal of Circuit Theory and Applications 12/2007; 36(1):31 - 51. · 1.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: In order to investigate the possible application of carbon nanotubes as interconnects, an electromagnetic macroscopic model is presented. The conduction electrons of the nanotube are considered as a two-dimensional fluid moving on the surface representing the positive ion lattice. The linearized Euler's equation describing the fluid motion is used as a macroscopic constitutive relationship to be coupled to Maxwell's equations. A surface integral formulation of the coupled problem is solved numerically using a finite element method based on a null-pinv basis functions.
Electromagnetics in Advanced Applications, 2007. ICEAA 2007. International Conference on; 10/2007
