Modeling of Carbon Nanotube Emission Using Airy Functions

Modeling of electron field emission has not advanced significantly since Fowler and Nordheim described the phenomenon eighty years ago. While their approach provides remarkable agreement with experiments for a large number of cases, the theory is strictly valid for planar geometries and low temperatures. Carbon nanotubes have been considered for field emission energy conversion devices. Under high-temperature conditions and significant field enhancement, the approximations used in the Fowler-Nordheim formalism become invalid. The present work predicts electron current densities emitted from carbon nanotubes using Airy functions to predict transmission and temperature dependent supply functions. Results indicate that Fowler-Nordheim compares favorably with the Airy function model for materials with large work function (φ ≈ 5eV, in the present study) at room temperatures. However, for materials with smaller work functions, the difference between the Airy function model and Fowler-Nordheim can be significant.