Analytical Model of Carbon Nanotube Electrostatics: Density of States, Effective Mass, Carrier Density, and Quantum Capacitance

Fundamental electrostatic properties of achiral carbon nanotubes (CNTs) are derived analytically. These include an exact derivation of the density of states within the nearest neighbor tight-binding formalism, the group velocity, and the effective mass. In addition, the non-degenerate equilibrium carrier density, and quantum capacitance are presented analytically. The quantum capacitance is used to provide a low energy C-V theory for a top-gated CNT device with good correlation to experimental data.