Carrier density and quantum capacitance for semiconducting carbon nanotubes

A full-band analytical model of the equilibrium carrier density for single-wall semiconducting carbon nanotubes (sCNTs) is presented. The carrier density, which is a fundamental property of all semiconductors, is obtained using a semiempirical method for degenerate positions of the Fermi level and shows good agreement with numerical tight-binding results. The quantum capacitance is subsequently derived from the carrier density and used to develop a C-V model with good agreement with experimental quantum capacitance measurements. An analytical model of the gate coupling function of sCNTs is also reported which relates the internal surface potential with the external applied gate voltage. The diameter temperature and Fermi level dependency, and the essential properties of carbon nanotubes device physics are captured in these analytical equations.