Restoring Observed Classical Behavior of the Carbon Nanotube Field Emission Enhancement Factor from the Electronic Structure

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 FM. 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 FM. 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 first-principles electronic structure calculations to derive real-charge distributions and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analyzed 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 first-principles 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 first-principles approaches. This is a significant step forward 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