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Summary form only given. The potential barrier of a single carbon nanotube is not exactly known up to now. We propose a simple model for the potential barrier of a single open carbon nanotube, in which the carbon nanotube is described by a δ-function potential valley through which the electrons are transfered from the Fermi sea to the vacuum by the strong applied field. We compute the potential barrier curve self-consistently by numerically solving the schrodinger equation with Numerov algorithm, and then discuss the effects of such kind of the potential barrier on the field emission.