Electronic structure calculations for a carbon nanotube capacitor with a dielectric medium

Abstract

We report first-principles electronic structure calculations based on the density-functional theory (DFT) that reveal characteristic features of nanometer-scale capacitors consisting of triple-walled (TW) carbon nanotubes (CNTs). Calculated electron densities under bias voltages provide atom-scale clarifications of the dielectric responses of the intercalated CNT as well as quantum spill of the stored charge densities from the electrode CNTs. Our DFT-based analysis shows that redistribution of the electron density in the TWCNT under the bias voltage is essentially a superposition of the stored-charge distribution near the electrode CNTs and the dielectric-polarization-charge distribution due to the intercalated CNT. The dielectric polarization due to the intercalated CNT screens the electric field due to the stored charges and hereby enhances the electrostatic capacitance of the TWCNT capacitor. From the calculated capacitance, we estimate an effective dielectric constant of the intercalated CNT to be ${ϵ}_{\ensuremath{\infty}}^{\text{eff}}\ensuremath{\sim}1.88$, a comparable value to ${\text{SiO}}_{2}$ which is widely used in the modern semiconductor devices. It is also clarified that the amount of the stored charge in the nanometer-scale capacitor is not obtained by spatial integration of the corresponding electron density owing to substantial overlap of the quantum spill and the polarization charge but should be defined through the amount of charges injected into particular electron states of each electrode. We also discuss a modification of the band gap of the TWCNT under the bias voltage in terms of the local variation in the electrostatic potential.