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.

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