J. P. Xanthakis

Local electric field at the emitting surface of a carbon nanotube

We present a method for the calculation of the local electric field at the surface of a nanoscopic emitting structure. The method is here applied to carbon nanotubes (NT) where symmetry makes the application of the method easier. The NT is simulated as a cylindrical array of touching spheres, each sphere representing an atom of the tube. The electrostatic potential is written as a linear combination of the potentials produced by each of the spheres. We calculate the local electric field and the corresponding enhancement factor γ for both open and closed nanotubes. For a closed NT we find for γ a simple polynomial expression in terms of the ratio of the height h of the tube to its radius R, which for h/R<40 reduces to a frequently quoted formula of γ. For an open single-wall NT we find that γ is three times greater than that of a single-wall NT of the same h/R. As the thickness of the wall increases this difference diminishes. From these results one may deduce a possible explanation as to why in some experiments a closed NT emits more current than a corresponding open one while in other experiments the opposite holds true.

Electron emission from amorphous carbon nitride films

We propose a model of field electron emission from amorphous carbon nitride films. According to this model, emission occurs at protrusions of the film surface. Most of the emitted electrons come from states with energy within a rather narrow region about the Fermi level, which shifts with nitrogen concentration but remains within the mobility gap of the film. The model reproduces reasonably well the observed variation of the emitted current with the externally applied electric field and with the nitrogen concentration.

Enhancement factor of open thick-wall carbon nanotubes

We have calculated the electric field around and on the surface of an open thick-wall carbon nanotube (CNT) of height h, external radius R, and wall thickness w. To accomplish that we simulate the CNT as a vertical array of touching toroids, each of external radius R and cross section radius w/2, and then we express the problem in toroidal coordinates. From our calculations we obtain the enhancement factor γ as a function of h, R, and w. By fitting to our numerical results we obtain an empirical but simple formula for γ, which extrapolates to that of a closed CNT in the limiting case of w=R.

Self focusing of field emitted electrons at an ellipsoidal tip

In models of field emission the needle is usually terminated by a hemispherical cap. Here we choose to terminate it with a hemiellipsoidal cap and use a three-dimensional Wentzel–Kramers–Brillouin method for the computations. This has two important consequences: as the ellipsoid becomes more elongated, (a) the effective emission area is decreased and (b) the quantum mechanically computed electron paths converge toward the needle axis. Both mechanisms produce a self-focusing of the field emitted electrons.

Fundamental Aspects of Near-Field Emission Scanning Electron Microscopy

Abstract In a previous publication (Kirk, 2010) the experimental technique of imaging near-field emission scanning electron microscopy (NFESEM) imaging was introduced. In NFESEM, a sharp tip in positioned at distances of a few 10nm from a metallic surface. Above a threshold voltage, electrons are field emitted from the tip. The field-emitted current is used, while scanning the tip across the surface at a well-defined, constant distance, to generate a topographic image of the surface with subnanometer vertical spatial resolution and a few-nanometer lateral spatial resolution. In this review, we discuss the fundamental physical processes that occur in NFESEM and provide some quantitative results. It is our goal to provide sufficient background information to allow NFESEM-based instruments to be developed in other laboratories.

Field emission from open multiwall carbon nanotubes: A case of non-Fowler–Nordheim behavior.

Open multiwall carbon nanotubes (MWCNTs) have a non-Fowler–Nordheim (non-FN) emission characteristic, even after the cleaning process, in contrast to closed carbon nanotubes (CNTs), which become FN-like after the cleaning process. We have calculated the emitted current from open MWCNTs using our previously calculated transmission coefficients, which were derived by the use of a multidimensional WKB method. Our results reveal that the non-FN behavior of open CNTs should be attributed to the following two features of the two-dimensional (angle and distance dependent) tunneling potential V(r,θ). (a) V(r,θ) deviates from the approximately linear (with distance) potentials associated with planar surfaces with this nonlinearity having nothing to do with the image potential. (b) The individual walls of the MWCNTs essentially see different tunneling potentials due to the angle dependence of V(r,θ). From our calculations we also find that only a few layers of the open MWCNTs contribute to the current at low fields...

Scaling properties of a non-Fowler–Nordheim tunnelling junction

Recent experimental work [1] has shown that there is a simple scaling function for the current I in a sharp tunneling junction as a function of the tip anode distance d. When the emitter has a large radius of curvature R the tunneling potential depends linearly on the field and scaling the latter with d obviously leads to the scaling of the current. But when the emitter is sharp and the barrier is of a non-Fowler-Nordheim type, scaling the field does not necessarily lead to scaling of the current with d. Here we show that for d>>R it does.

Derivation of a Fowler-Nordheim type equation for highly curved field-emitters

The traditional Fowler-Nordheim (FN) equation has been repeatedly shown to fail for highly curved surfaces. In the past there have been modifications to it mostly for spherical surfaces. In this paper we derive a generalized FN-type equation which is valid for all potentials and surfaces. Both the current density at the emitter apex J(θ=0) and the effective emission area are derived rigorously. From our method the radius of curvature of the emitter can be extracted with sufficient accuracy. An application of our theory to the results of the ETH group verifies this.

Lateral distribution of field-emitted electrons from a carbon nanofiber array: A theoretical calculation

The authors have calculated the lateral distribution of field emitted electrons from a carbon nanofiber (CNF) array—a quantity of importance in designing field emission displays—by calculating the electron distribution from an individual CNF and subsequently summing the contribution from all individual CNFs. The authors have not obtained the absolute value of the current but only its relative distribution in space. The full width at half maximum of the lateral distribution has been examined with respect to the following parameters: 1) the CNF tip radius, 2) the anode to cathode distance, and 3) the cathode to anode potential difference. Reasonable agreement with experimental results is obtained.

Comment on “Model calculation for enhancement factor of a gated field emission nanotube” [J. Appl. Phys. 102, 114503 (2007)]

In a recent publication Lei et al.1 calculated the enhancement factor of a gated open nanotube (NT) simulated as a cylindrically folded, zero-thickness sheet of metal. In this comment we argue that (a) the form of the tube (zero thickness) leads to unphysical results and (b) the method of calculation of the enhancement factor is wrong both physically and mathematically, leading to totally irrelevant information about the strength of the tunneling barrier of an electron emitted from the NT.