A Common Electromagnetic Framework for Carbon Nanotubes and Solid Nanowires—Spatially Dispersive Conductivity, Generalized Ohm's Law, Distributed Impedance, and Transmission Line Model

General equations are presented for the spatially dispersive conductivity, distributed impedance, Ohm's law relation, and transmission line model of both carbon nanotubes (CNTs) and solid material nanowires. It is shown that spatial dispersion results in an intrinsic (material-dependent) transmission-line capacitance. Spatial dispersion is numerically unimportant in metal nanowires, but leads to a shift in propagation constant of a few percent for CNTs and semiconducting nanowires. Theoretically, spatial dispersion is important for both nanowires and nanotubes, and is necessary to preserve the inductance-capacitance-velocity relation , where is kinetic inductance, is intrinsic capacitance, and is electron Fermi velocity. It is shown that in order to obtain the correct intrinsic capacitance, it is necessary to use a charge-conserving form of the relaxation-time approximation to Boltzmann's equation. Numerical results for the propagation constant of various nanowires and CNTs are presented. The general formulation developed here allows one to compute, and directly compare and contrast, properties of CNTs and solid nanowires.

[1]  N. D. Mermin,et al.  Lindhard Dielectric Function in the Relaxation-Time Approximation , 1970 .

[2]  G. Hanson.  Radiation Ef ciency of Nanoradius Dipole Antennas in the Microwave and Far-Infrared Regime , 2008 .

[3]  G. Miano,et al.  An Integral Formulation for the Electrodynamics of Metallic Carbon Nanotubes Based on a Fluid Model , 2006, IEEE Transactions on Antennas and Propagation.

[4]  P. Burke,et al.  Microwave transport in metallic single-walled carbon nanotubes. , 2005, Nano letters.

[5]  P. J. Burke.  An RF circuit model for carbon nanotubes , 2003 .

[6]  W. Steinhögl,et al.  Comprehensive study of the resistivity of copper wires with lateral dimensions of 100 nm and smaller , 2005 .

[7]  G. Miano,et al.  Signal Propagation in Carbon Nanotubes of Arbitrary Chirality , 2011, IEEE Transactions on Nanotechnology.

[8]  K. Kano.  Semiconductor Devices , 1997 .

[9]  T. Sarkar,et al.  Analysis of Multiconductor Transmission Lines , 1988, 31st ARFTG Conference Digest.

[10]  A. Ishimaru.  Electromagnetic Wave Propagation, Radiation, and Scattering , 1990 .

[11]  H J Li,et al.  Multichannel ballistic transport in multiwall carbon nanotubes. , 2005, Physical review letters.

[12]  J. Wesstrom.  Signal propagation in electron waveguides: Transmission-line analogies , 1996 .

[13]  J. Meindl,et al.  Performance comparison between carbon nanotube and copper interconnects for gigascale integration (GSI) , 2005, IEEE Electron Device Letters.

[14]  A. R. Melnyk,et al.  Theory of Optical Excitation of Plasmons in Metals , 1970 .

[15]  Tullio Rozzi,et al.  Optical absorption of carbon nanotube diodes: Strength of the electronic transitions and sensitivity to the electric field polarization , 2008 .

[16]  Halevi.  Hydrodynamic model for the degenerate free-electron gas: Generalization to arbitrary frequencies. , 1995, Physical review. B, Condensed matter.

[17]  A. V. Gusakov,et al.  Electrodynamics of carbon nanotubes: Dynamic conductivity, impedance boundary conditions, and surface wave propagation , 1999 .

[18]  Paul L. McEuen,et al.  Measurement of the quantum capacitance of interacting electrons in carbon nanotubes , 2006 .

[19]  A. Holmes-Siedle,et al.  Semiconductor Devices , 1976, 2018 International Semiconductor Conference (CAS).

[20]  J. Meindl,et al.  Compact physical models for multiwall carbon-nanotube interconnects , 2006, IEEE Electron Device Letters.

[21]  Arthur Nieuwoudt,et al.  Modeling and design challenges and solutions for carbon nanotube-based interconnect in future high performance integrated circuits , 2006, JETC.

[22]  Y. Massoud,et al.  Evaluating the impact of resistance in carbon nanotube bundles for VLSI interconnect using diameter-dependent modeling techniques , 2006, IEEE Transactions on Electron Devices.

[23]  H. Thomas,et al.  Dielectric function in the relaxation-time approximation generalized to electronic multiple-band systems , 1980 .

[24]  D. Mencarelli,et al.  Boundary Immittance Operators for the SchrÖdinger–Maxwell Problem of Carrier Dynamics in Nanodevices , 2009, IEEE Transactions on Microwave Theory and Techniques.

[25]  Zhen Yu,et al.  Electrical Properties of 0.4 cm Long Single-Walled Carbon Nanotubes , 2004, cond-mat/0408332.

[26]  A. Naeemi,et al.  Impact of electron-phonon scattering on the performance of carbon nanotube interconnects for GSI , 2005, IEEE Electron Device Letters.

[27]  S. Datta,et al.  Transport effects on signal propagation in quantum wires , 2005, IEEE Transactions on Electron Devices.

[28]  G. V. Chester,et al.  Solid State Physics , 2000 .

[29]  Metallic Carbon Nanotube Interconnects, Part II: a Transmission Line Model , 2006, 2006 IEEE Workship on Signal Propagation on Interconnects.

[30]  G. Hanson,et al.  Radiation Efficiency of Nano-Radius Dipole Antennas in the Microwave and Far-infrared Regimes , 2008, IEEE Antennas and Propagation Magazine.

[31]  Martin Dressel,et al.  Electrodynamics of solids , 2002 .

[32]  G. Hanson.  Drift-Diffusion: A Model for Teaching Spatial-Dispersion Concepts and the Importance of Screening in Nanoscale Structures , 2010, IEEE Antennas and Propagation Magazine.

[33]  R. Kaul,et al.  Microwave engineering , 1989, IEEE Potentials.

[34]  A. Carlo,et al.  Negative quantum capacitance of gated carbon nanotubes , 2005 .

[35]  A. Maffucci,et al.  A transmission line model for metallic carbon nanotube interconnects , 2008, Int. J. Circuit Theory Appl..