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 LkCdos = v(F)(2), where L-k is kinetic inductance, C-dos is intrinsic capacitance, and v(F) 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.