Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Abstract

Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields $F_{\text{M}}$. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF-values that vary with $F_{\text{M}}$. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use density functional theory (DFT) to derive real-charge distributions, and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analysed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field, and behave in the same qualitative manner as the classical FEF-values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via DFT approaches. Although many issues of detail remain to be explored, this appears to be a significant step forwards in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.

arXiv commentA slightly revised version has been published - citation below - under a title different from that originally used. The new title is: "Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure"

References in corpus (7)

• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• Density functional method for nonequilibrium electron transport
• An Atomic-resolution nanomechanical mass sensor
• Development of simple quantitative test for lack of field emission orthodoxy
• Nanostructures mechanically stable with desirable characteristic field enhancement factor: a response from scale invariance in electrostatics
• Origin of the literature discrepancies in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters

Cited by in corpus (5)

• Modeling the Field Emission Enhancement Factor for Capped Carbon Nanotubes using the Induced Electron Density
• On the quantum mechanics of how an ideal carbon nanotube field emitter can exhibit a constant field enhancement factor
• Field emitter electrostatics: efficient improved simulation technique for highly precise calculation of field enhancement factors
• Universal scaling of electrostatic effects of a curved counter-electrode on the emitter field enhancement
• Analytical Advances about the apex Field Enhancement Factor of a Hemisphere on a Post Model