Quantum size dependence of electron distribution on carbon nanotubes and its influence on field emission

Abstract

A two-dimensional model of quasi-free-electrons is used to compute the electron axial distribution on a carbon nanotube and the energy distribution of the field emitted electrons. The nature of the substrate-nanotube contact is taken into account by varying the boundary condition for the electronic wave function. In qualitative agreement with the experimental results to date, regular patterns of the axial electron density and electron accumulation on the nanotube cap are obtained. The energy distribution of the field emitted electrons shows a multiple peak structure superimposed over a very fine distribution of maxima. Such a multiple peak structure is also qualitatively confirmed in experiments. The behavior of the distribution of the emitted electrons with the extraction voltage and with the operation temperature is investigated.

Possibility of constructing microwave antenna with carbon nanotubes

“…5 Now, consider applying a small external axial timedependent harmonic excitation on a CNT, which can be expressed as…”

“…Here, based on the work of Filip et al 5 first we discuss the wave functions of a single electron in a nanotube excited by a microwave source. Numerical results reveal that electrons in CNTs under external time-harmonic excitation oscillate at the same frequency as the excitation, which indicates that CNTs are indeed radiating under the external excitation.…”

Modelling of electron transfer from a carbon nanotube cap into the vacuum under high extraction fields

“…The discovery of carbon nanotubes (CNTs) and other high aspect ratio structures introduced important supplementary difficulties when implementing the FN formalism. One such problem is the influence of the electronic structure on the FE process [1][2][3][4]. Other unique situations arise when the anode is moved very close to the emitter's tip, at distances comparable to its radius [5,6] when structural changes to the potential energy barrier to the vacuum are likely to appear.…”

“…The non-electrostatic energy jump, χ, at r=r 0 is taken into account as a separate parameter. Using this potential energy scheme, the solutions of the Schrödinger equation on the 2D CNT manifold [3,4] are connected to the 3D ones in vacuum, which obey the radiating boundary condition. Having found the electronic wave function, the radial component of the probability current density in vacuum can be computed and from there the emission current follows allowing for a comparison to experimental current-voltage (I-V) diagrams.…”

“…The anode is placed at some distance away from the emitter's tip. The CNT is modelled as a two-dimensional (2D) manifold where electrons behave as quasifree and independent particles [3,4]. The electrons are bound on the CNT surface by a onedimensional (1D) potential well, due to the restriction imposed by the cylindrical symmetry.…”